| | Chapter 3
Experimental Errors and
Error Analysis This chapter is largely a tutorial on handling experimental errors of measurement. Much of the material has been extensively tested with science undergraduates at a variety of levels at the University of Toronto. Whole books can and have been written on this topic but here we distill the topic down to the essentials. Nonetheless, our experience is that for beginners an iterative approach to this material works best. This means that the users first scan the material in this chapter; then try to use the material on their own experiment; then go over the material again; then ... provides functions to ease the calculations required by propagation of errors, and those functions are introduced in Section 3.3. These error propagation functions are summarized in Section 3.5. 3.1 Introduction 3.1.1 The Purpose of Error Analysis For students who only attend lectures and read textbooks in the sciences, it is easy to get the incorrect impression that the physical sciences are concerned with manipulating precise and perfect numbers. Lectures and textbooks often contain phrases like: For an experimental scientist this specification is incomplete. Does it mean that the acceleration is closer to 9.8 than to 9.9 or 9.7? Does it mean that the acceleration is closer to 9.80000 than to 9.80001 or 9.79999? Often the answer depends on the context. If a carpenter says a length is "just 8 inches" that probably means the length is closer to 8 0/16 in. than to 8 1/16 in. or 7 15/16 in. If a machinist says a length is "just 200 millimeters" that probably means it is closer to 200.00 mm than to 200.05 mm or 199.95 mm. We all know that the acceleration due to gravity varies from place to place on the earth's surface. It also varies with the height above the surface, and gravity meters capable of measuring the variation from the floor to a tabletop are readily available. Further, any physical measure such as can only be determined by means of an experiment, and since a perfect experimental apparatus does not exist, it is impossible even in principle to ever know perfectly. Thus, the specification of given above is useful only as a possible exercise for a student. In order to give it some meaning it must be changed to something like: Two questions arise about the measurement. First, is it "accurate," in other words, did the experiment work properly and were all the necessary factors taken into account? The answer to this depends on the skill of the experimenter in identifying and eliminating all systematic errors. These are discussed in Section 3.4. The second question regards the "precision" of the experiment. In this case the precision of the result is given: the experimenter claims the precision of the result is within 0.03 m/s 1. The person who did the measurement probably had some "gut feeling" for the precision and "hung" an error on the result primarily to communicate this feeling to other people. Common sense should always take precedence over mathematical manipulations. 2. In complicated experiments, error analysis can identify dominant errors and hence provide a guide as to where more effort is needed to improve an experiment. 3. There is virtually no case in the experimental physical sciences where the correct error analysis is to compare the result with a number in some book. A correct experiment is one that is performed correctly, not one that gives a result in agreement with other measurements. 4. The best precision possible for a given experiment is always limited by the apparatus. Polarization measurements in high-energy physics require tens of thousands of person-hours and cost hundreds of thousand of dollars to perform, and a good measurement is within a factor of two. Electrodynamics experiments are considerably cheaper, and often give results to 8 or more significant figures. In both cases, the experimenter must struggle with the equipment to get the most precise and accurate measurement possible. 3.1.2 Different Types of Errors As mentioned above, there are two types of errors associated with an experimental result: the "precision" and the "accuracy". One well-known text explains the difference this way: " " E.M. Pugh and G.H. Winslow, p. 6. The object of a good experiment is to minimize both the errors of precision and the errors of accuracy. Usually, a given experiment has one or the other type of error dominant, and the experimenter devotes the most effort toward reducing that one. For example, in measuring the height of a sample of geraniums to determine an average value, the random variations within the sample of plants are probably going to be much larger than any possible inaccuracy in the ruler being used. Similarly for many experiments in the biological and life sciences, the experimenter worries most about increasing the precision of his/her measurements. Of course, some experiments in the biological and life sciences are dominated by errors of accuracy. On the other hand, in titrating a sample of HCl acid with NaOH base using a phenolphthalein indicator, the major error in the determination of the original concentration of the acid is likely to be one of the following: (1) the accuracy of the markings on the side of the burette; (2) the transition range of the phenolphthalein indicator; or (3) the skill of the experimenter in splitting the last drop of NaOH. Thus, the accuracy of the determination is likely to be much worse than the precision. This is often the case for experiments in chemistry, but certainly not all. Question: Most experiments use theoretical formulas, and usually those formulas are approximations. Is the error of approximation one of precision or of accuracy? 3.1.3 References There is extensive literature on the topics in this chapter. The following lists some well-known introductions. D.C. Baird, (Prentice-Hall, 1962) E.M. Pugh and G.H. Winslow, (Addison-Wesley, 1966) J.R. Taylor, (University Science Books, 1982) In addition, there is a web document written by the author of that is used to teach this topic to first year Physics undergraduates at the University of Toronto. The following Hyperlink points to that document. 3.2 Determining the Precision 3.2.1 The Standard Deviation In the nineteenth century, Gauss' assistants were doing astronomical measurements. However, they were never able to exactly repeat their results. Finally, Gauss got angry and stormed into the lab, claiming he would show these people how to do the measurements once and for all. The only problem was that Gauss wasn't able to repeat his measurements exactly either! After he recovered his composure, Gauss made a histogram of the results of a particular measurement and discovered the famous Gaussian or bell-shaped curve. Many people's first introduction to this shape is the grade distribution for a course. Here is a sample of such a distribution, using the function . We use a standard package to generate a Probability Distribution Function ( ) of such a "Gaussian" or "normal" distribution. The mean is chosen to be 78 and the standard deviation is chosen to be 10; both the mean and standard deviation are defined below. We then normalize the distribution so the maximum value is close to the maximum number in the histogram and plot the result. In this graph, Finally, we look at the histogram and plot together. We can see the functional form of the Gaussian distribution by giving symbolic values. In this formula, the quantity , and . The is sometimes called the . The definition of is as follows. Here is the total number of measurements and is the result of measurement number . The standard deviation is a measure of the width of the peak, meaning that a larger value gives a wider peak. If we look at the area under the curve from graph, we find that this area is 68 percent of the total area. Thus, any result chosen at random has a 68% change of being within one standard deviation of the mean. We can show this by evaluating the integral. For convenience, we choose the mean to be zero. Now, we numericalize this and multiply by 100 to find the percent. The only problem with the above is that the measurement must be repeated an infinite number of times before the standard deviation can be determined. If is less than infinity, one can only estimate measurements, this is the best estimate. The major difference between this estimate and the definition is the . This is reasonable since if = 1 we know we can't determine Here is an example. Suppose we are to determine the diameter of a small cylinder using a micrometer. We repeat the measurement 10 times along various points on the cylinder and get the following results, in centimeters. The number of measurements is the length of the list. The average or mean is now calculated. Then the standard deviation is to be 0.00185173. We repeat the calculation in a functional style. Note that the package, which is standard with , includes functions to calculate all of these quantities and a great deal more. We close with two points: 1. The standard deviation has been associated with the error in each individual measurement. Section 3.3.2 discusses how to find the error in the estimate of the average. 2. This calculation of the standard deviation is only an estimate. In fact, we can find the expected error in the estimate, As discussed in more detail in Section 3.3, this means that the true standard deviation probably lies in the range of values. Viewed in this way, it is clear that the last few digits in the numbers above for function adjusts these significant figures based on the error. is discussed further in Section 3.3.1. 3.2.2 The Reading Error There is another type of error associated with a directly measured quantity, called the "reading error". Referring again to the example of Section 3.2.1, the measurements of the diameter were performed with a micrometer. The particular micrometer used had scale divisions every 0.001 cm. However, it was possible to estimate the reading of the micrometer between the divisions, and this was done in this example. But, there is a reading error associated with this estimation. For example, the first data point is 1.6515 cm. Could it have been 1.6516 cm instead? How about 1.6519 cm? There is no fixed rule to answer the question: the person doing the measurement must guess how well he or she can read the instrument. A reasonable guess of the reading error of this micrometer might be 0.0002 cm on a good day. If the experimenter were up late the night before, the reading error might be 0.0005 cm. An important and sometimes difficult question is whether the reading error of an instrument is "distributed randomly". Random reading errors are caused by the finite precision of the experiment. If an experimenter consistently reads the micrometer 1 cm lower than the actual value, then the reading error is not random. For a digital instrument, the reading error is ± one-half of the last digit. Note that this assumes that the instrument has been properly engineered to round a reading correctly on the display. 3.2.3 "THE" Error So far, we have found two different errors associated with a directly measured quantity: the standard deviation and the reading error. So, which one is the actual real error of precision in the quantity? The answer is both! However, fortunately it almost always turns out that one will be larger than the other, so the smaller of the two can be ignored. In the diameter example being used in this section, the estimate of the standard deviation was found to be 0.00185 cm, while the reading error was only 0.0002 cm. Thus, we can use the standard deviation estimate to characterize the error in each measurement. Another way of saying the same thing is that the observed spread of values in this example is not accounted for by the reading error. If the observed spread were more or less accounted for by the reading error, it would not be necessary to estimate the standard deviation, since the reading error would be the error in each measurement. Of course, everything in this section is related to the precision of the experiment. Discussion of the accuracy of the experiment is in Section 3.4. 3.2.4 Rejection of Measurements Often when repeating measurements one value appears to be spurious and we would like to throw it out. Also, when taking a series of measurements, sometimes one value appears "out of line". Here we discuss some guidelines on rejection of measurements; further information appears in Chapter 7. It is important to emphasize that the whole topic of rejection of measurements is awkward. Some scientists feel that the rejection of data is justified unless there is evidence that the data in question is incorrect. Other scientists attempt to deal with this topic by using quasi-objective rules such as 's . Still others, often incorrectly, throw out any data that appear to be incorrect. In this section, some principles and guidelines are presented; further information may be found in many references. First, we note that it is incorrect to expect each and every measurement to overlap within errors. For example, if the error in a particular quantity is characterized by the standard deviation, we only expect 68% of the measurements from a normally distributed population to be within one standard deviation of the mean. Ninety-five percent of the measurements will be within two standard deviations, 99% within three standard deviations, etc., but we never expect 100% of the measurements to overlap within any finite-sized error for a truly Gaussian distribution. Of course, for most experiments the assumption of a Gaussian distribution is only an approximation. If the error in each measurement is taken to be the reading error, again we only expect most, not all, of the measurements to overlap within errors. In this case the meaning of "most", however, is vague and depends on the optimism/conservatism of the experimenter who assigned the error. Thus, it is always dangerous to throw out a measurement. Maybe we are unlucky enough to make a valid measurement that lies ten standard deviations from the population mean. A valid measurement from the tails of the underlying distribution should not be thrown out. It is even more dangerous to throw out a suspect point indicative of an underlying physical process. Very little science would be known today if the experimenter always threw out measurements that didn't match preconceived expectations! In general, there are two different types of experimental data taken in a laboratory and the question of rejecting measurements is handled in slightly different ways for each. The two types of data are the following: 1. A series of measurements taken with one or more variables changed for each data point. An example is the calibration of a thermocouple, in which the output voltage is measured when the thermocouple is at a number of different temperatures. 2. Repeated measurements of the same physical quantity, with all variables held as constant as experimentally possible. An example is the measurement of the height of a sample of geraniums grown under identical conditions from the same batch of seed stock. For a series of measurements (case 1), when one of the data points is out of line the natural tendency is to throw it out. But, as already mentioned, this means you are assuming the result you are attempting to measure. As a rule of thumb, unless there is a physical explanation of why the suspect value is spurious and it is no more than three standard deviations away from the expected value, it should probably be kept. Chapter 7 deals further with this case. For repeated measurements (case 2), the situation is a little different. Say you are measuring the time for a pendulum to undergo 20 oscillations and you repeat the measurement five times. Assume that four of these trials are within 0.1 seconds of each other, but the fifth trial differs from these by 1.4 seconds ( , more than three standard deviations away from the mean of the "good" values). There is no known reason why that one measurement differs from all the others. Nonetheless, you may be justified in throwing it out. Say that, unknown to you, just as that measurement was being taken, a gravity wave swept through your region of spacetime. However, if you are trying to measure the period of the pendulum when there are no gravity waves affecting the measurement, then throwing out that one result is reasonable. (Although trying to repeat the measurement to find the existence of gravity waves will certainly be more fun!) So whatever the reason for a suspect value, the rule of thumb is that it may be thrown out provided that fact is well documented and that the measurement is repeated a number of times more to convince the experimenter that he/she is not throwing out an important piece of data indicating a new physical process. 3.3 Propagation of Errors of Precision 3.3.1 Discussion and Examples Usually, errors of precision are probabilistic. This means that the experimenter is saying that the actual value of some parameter is within a specified range. For example, if the half-width of the range equals one standard deviation, then the probability is about 68% that over repeated experimentation the true mean will fall within the range; if the half-width of the range is twice the standard deviation, the probability is 95%, etc. If we have two variables, say and , and want to combine them to form a new variable, we want the error in the combination to preserve this probability. The correct procedure to do this is to combine errors in quadrature, which is the square root of the sum of the squares. supplies a function. For simple combinations of data with random errors, the correct procedure can be summarized in three rules. will stand for the errors of precision in , , and , respectively. We assume that and are independent of each other. Note that all three rules assume that the error, say , is small compared to the value of . If z = x * y or then In words, the fractional error in is the quadrature of the fractional errors in and . If z = x + y or z = x - y then In words, the error in is the quadrature of the errors in and . If then or equivalently includes functions to combine data using the above rules. They are named , , , , and . Imagine we have pressure data, measured in centimeters of Hg, and volume data measured in arbitrary units. Each data point consists of { , } pairs. We calculate the pressure times the volume. In the above, the values of and have been multiplied and the errors have ben combined using Rule 1. There is an equivalent form for this calculation. Consider the first of the volume data: {11.28156820762763, 0.031}. The error means that the true value is claimed by the experimenter to probably lie between 11.25 and 11.31. Thus, all the significant figures presented to the right of 11.28 for that data point really aren't significant. The function will adjust the volume data. Notice that by default, uses the two most significant digits in the error for adjusting the values. This can be controlled with the option. For most cases, the default of two digits is reasonable. As discussed in Section 3.2.1, if we assume a normal distribution for the data, then the fractional error in the determination of the standard deviation , and can be written as follows. Thus, using this as a general rule of thumb for all errors of precision, the estimate of the error is only good to 10%, ( one significant figure, unless is greater than 51) . Nonetheless, keeping two significant figures handles cases such as 0.035 vs. 0.030, where some significance may be attached to the final digit. You should be aware that when a datum is massaged by , the extra digits are dropped. By default, and the other functions use the function. The use of is controlled using the option. The number of digits can be adjusted. To form a power, say, we might be tempted to just do function. Finally, imagine that for some reason we wish to form a combination. We might be tempted to solve this with the following. then the error is Here is an example solving . We shall use and below to avoid overwriting the symbols and . First we calculate the total derivative. Next we form the error. Now we can evaluate using the pressure and volume data to get a list of errors. Next we form the list of pairs. The function combines these steps with default significant figure adjustment. The function can be used in place of the other functions discussed above. In this example, the function will be somewhat faster. There is a caveat in using . The expression must contain only symbols, numerical constants, and arithmetic operations. Otherwise, the function will be unable to take the derivatives of the expression necessary to calculate the form of the error. The other functions have no such limitation. 3.3.1.1 Another Approach to Error Propagation: The and Datum value error Data[{{789.7, 2.2}, {790.8, 2.3}, {791.2, 2.3}, {792.6, 2.4}, {791.8, 2.5},
{792.2, 2.5}, {794.7, 2.6}, {794., 2.6}, {794.4, 2.7}, {795.3, 2.8},
{796.4, 2.8}}]Data[{{789.7, 2.2}, {790.8, 2.3}, {791.2, 2.3}, {792.6, 2.4}, {791.8, 2.5},
{792.2, 2.5}, {794.7, 2.6}, {794., 2.6}, {794.4, 2.7}, {795.3, 2.8},
{796.4, 2.8}}] The wrapper can be removed. {{789.7, 2.2}, {790.8, 2.3}, {791.2, 2.3}, {792.6, 2.4}, {791.8, 2.5},
{792.2, 2.5}, {794.7, 2.6}, {794., 2.6}, {794.4, 2.7}, {795.3, 2.8}, {796.4, 2.8}}{{789.7, 2.2}, {790.8, 2.3}, {791.2, 2.3}, {792.6, 2.4}, {791.8, 2.5},
{792.2, 2.5}, {794.7, 2.6}, {794., 2.6}, {794.4, 2.7}, {795.3, 2.8}, {796.4, 2.8}} The reason why the output of the previous two commands has been formatted as is that typesets the pairs using ± for output. A similar construct can be used with individual data points. Datum[{70, 0.04}]Datum[{70, 0.04}] Just as for , the typesetting of uses The and constructs provide "automatic" error propagation for multiplication, division, addition, subtraction, and raising to a power. Another advantage of these constructs is that the rules built into know how to combine data with constants. The rules also know how to propagate errors for many transcendental functions. This rule assumes that the error is small relative to the value, so we can approximate. or arguments, are given by . We have seen that typesets the and constructs using ±. The function can be used directly, and provided its arguments are numeric, errors will be propagated. One may typeset the ± into the input expression, and errors will again be propagated. The ± input mechanism can combine terms by addition, subtraction, multiplication, division, raising to a power, addition and multiplication by a constant number, and use of the . The rules used by for ± are only for numeric arguments. This makes different than 3.3.1.2 Why Quadrature? Here we justify combining errors in quadrature. Although they are not proofs in the usual pristine mathematical sense, they are correct and can be made rigorous if desired. First, you may already know about the "Random Walk" problem in which a player starts at the point = 0 and at each move steps either forward (toward + ) or backward (toward - ). The choice of direction is made randomly for each move by, say, flipping a coin. If each step covers a distance , then after steps the expected most probable distance of the player from the origin can be shown to be Thus, the distance goes up as the square root of the number of steps. Now consider a situation where measurements of a quantity are performed, each with an identical random error . We find the sum of the measurements. , it is equally likely to be + as - , and which is essentially random. Thus, the expected most probable error in the sum goes up as the square root of the number of measurements. This is exactly the result obtained by combining the errors in quadrature. Another similar way of thinking about the errors is that in an abstract linear error space, the errors span the space. If the errors are probabilistic and uncorrelated, the errors in fact are linearly independent (orthogonal) and thus form a basis for the space. Thus, we would expect that to add these independent random errors, we would have to use Pythagoras' theorem, which is just combining them in quadrature. 3.3.2 Finding the Error in an Average The rules for propagation of errors, discussed in Section 3.3.1, allow one to find the error in an average or mean of a number of repeated measurements. Recall that to compute the average, first the sum of all the measurements is found, and the rule for addition of quantities allows the computation of the error in the sum. Next, the sum is divided by the number of measurements, and the rule for division of quantities allows the calculation of the error in the result ( the error of the mean). In the case that the error in each measurement has the same value, the result of applying these rules for propagation of errors can be summarized as a theorem. Theorem: If the measurement of a random variable is repeated times, and the random variable has standard deviation , then the standard deviation in the mean is Proof: One makes measurements, each with error . {x1, errx}, {x2, errx}, ... , {xn, errx} We calculate the sum. sumx = x1 + x2 + ... + xn We calculate the error in the sum. This last line is the key: by repeating the measurements times, the error in the sum only goes up as [ ]. The mean Applying the rule for division we get the following. This completes the proof. The quantity called Here is an example. In Section 3.2.1, 10 measurements of the diameter of a small cylinder were discussed. The mean of the measurements was 1.6514 cm and the standard deviation was 0.00185 cm. Now we can calculate the mean and its error, adjusted for significant figures. Note that presenting this result without significant figure adjustment makes no sense. The above number implies that there is meaning in the one-hundred-millionth part of a centimeter. Here is another example. Imagine you are weighing an object on a "dial balance" in which you turn a dial until the pointer balances, and then read the mass from the marking on the dial. You find = 26.10 ± 0.01 g. The 0.01 g is the reading error of the balance, and is about as good as you can read that particular piece of equipment. You remove the mass from the balance, put it back on, weigh it again, and get = 26.10 ± 0.01 g. You get a friend to try it and she gets the same result. You get another friend to weigh the mass and he also gets = 26.10 ± 0.01 g. So you have four measurements of the mass of the body, each with an identical result. Do you think the theorem applies in this case? If yes, you would quote = 26.100 ± 0.01/ [4] = 26.100 ± 0.005 g. How about if you went out on the street and started bringing strangers in to repeat the measurement, each and every one of whom got = 26.10 ± 0.01 g. So after a few weeks, you have 10,000 identical measurements. Would the error in the mass, as measured on that $50 balance, really be the following? The point is that these rules of statistics are only a rough guide and in a situation like this example where they probably don't apply, don't be afraid to ignore them and use your "uncommon sense". In this example, presenting your result as = 26.10 ± 0.01 g is probably the reasonable thing to do. 3.4 Calibration, Accuracy, and Systematic Errors In Section 3.1.2, we made the distinction between errors of precision and accuracy by imagining that we had performed a timing measurement with a very precise pendulum clock, but had set its length wrong, leading to an inaccurate result. Here we discuss these types of errors of accuracy. To get some insight into how such a wrong length can arise, you may wish to try comparing the scales of two rulers made by different companies — discrepancies of 3 mm across 30 cm are common! If we have access to a ruler we trust ( a "calibration standard"), we can use it to calibrate another ruler. One reasonable way to use the calibration is that if our instrument measures and the standard records , then we can multiply all readings of our instrument by / . Since the correction is usually very small, it will practically never affect the error of precision, which is also small. Calibration standards are, almost by definition, too delicate and/or expensive to use for direct measurement. Here is an example. We are measuring a voltage using an analog Philips multimeter, model PM2400/02. The result is 6.50 V, measured on the 10 V scale, and the reading error is decided on as 0.03 V, which is 0.5%. Repeating the measurement gives identical results. It is calculated by the experimenter that the effect of the voltmeter on the circuit being measured is less than 0.003% and hence negligible. However, the manufacturer of the instrument only claims an accuracy of 3% of full scale (10 V), which here corresponds to 0.3 V. Now, what this claimed accuracy means is that the manufacturer of the instrument claims to control the tolerances of the components inside the box to the point where the value read on the meter will be within 3% times the scale of the actual value. Furthermore, this is not a random error; a given meter will supposedly always read too high or too low when measurements are repeated on the same scale. Thus, repeating measurements will not reduce this error. A further problem with this accuracy is that while most good manufacturers (including Philips) tend to be quite conservative and give trustworthy specifications, there are some manufacturers who have the specifications written by the sales department instead of the engineering department. And even Philips cannot take into account that maybe the last person to use the meter dropped it. Nonetheless, in this case it is probably reasonable to accept the manufacturer's claimed accuracy and take the measured voltage to be 6.5 ± 0.3 V. If you want or need to know the voltage better than that, there are two alternatives: use a better, more expensive voltmeter to take the measurement or calibrate the existing meter. Using a better voltmeter, of course, gives a better result. Say you used a Fluke 8000A digital multimeter and measured the voltage to be 6.63 V. However, you're still in the same position of having to accept the manufacturer's claimed accuracy, in this case (0.1% of reading + 1 digit) = 0.02 V. To do better than this, you must use an even better voltmeter, which again requires accepting the accuracy of this even better instrument and so on, ad infinitum, until you run out of time, patience, or money. Say we decide instead to calibrate the Philips meter using the Fluke meter as the calibration standard. Such a procedure is usually justified only if a large number of measurements were performed with the Philips meter. Why spend half an hour calibrating the Philips meter for just one measurement when you could use the Fluke meter directly? We measure four voltages using both the Philips and the Fluke meter. For the Philips instrument we are not interested in its accuracy, which is why we are calibrating the instrument. So we will use the reading error of the Philips instrument as the error in its measurements and the accuracy of the Fluke instrument as the error in its measurements. We form lists of the results of the measurements. We can examine the differences between the readings either by dividing the Fluke results by the Philips or by subtracting the two values. The second set of numbers is closer to the same value than the first set, so in this case adding a correction to the Philips measurement is perhaps more appropriate than multiplying by a correction. We form a new data set of format { }. We can guess, then, that for a Philips measurement of 6.50 V the appropriate correction factor is 0.11 ± 0.04 V, where the estimated error is a guess based partly on a fear that the meter's inaccuracy may not be as smooth as the four data points indicate. Thus, the corrected Philips reading can be calculated. (You may wish to know that all the numbers in this example are real data and that when the Philips meter read 6.50 V, the Fluke meter measured the voltage to be 6.63 ± 0.02 V.) Finally, a further subtlety: Ohm's law states that the resistance is related to the voltage and the current across the resistor according to the following equation. V = IR Imagine that we are trying to determine an unknown resistance using this law and are using the Philips meter to measure the voltage. Essentially the resistance is the slope of a graph of voltage versus current. If the Philips meter is systematically measuring all voltages too big by, say, 2%, that systematic error of accuracy will have no effect on the slope and therefore will have no effect on the determination of the resistance . So in this case and for this measurement, we may be quite justified in ignoring the inaccuracy of the voltmeter entirely and using the reading error to determine the uncertainty in the determination of . 3.5 Summary of the Error Propagation Routines | - Wolfram|Alpha Notebook Edition
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Percent error or percentage error expresses the difference between an approximate or measured value and an exact or known value as a percentage. It is a well-known type of error calculation, along with absolute and relative error. Percent error plays a crucial role in validating hypotheses and assessing the accuracy of measurements in scientific research, and it also plays a fundamental role in quality control processes, where deviations from expected values could signify potential flaws in manufacturing or experimental procedures. Here is the formula used to calculate percent error, along with an example calculation. Key Points: Percent Error- The purpose of a percent error calculation is to gauge how close a measured value is to a true value.
- Percent error is equal to the difference between an experimental and theoretical value, divided by the theoretical value, and then multiplied by 100 to give a percent.
- In some fields, percent error is always expressed as a positive number. In others, it is correct to have either a positive or negative value. The sign helps determine whether recorded values consistently fall above or below expected values.
Percent Error FormulaPercent error is the difference between a measured or experiment value and an accepted or known value, divided by the known value, multiplied by 100%. For many applications, percent error is always expressed as a positive value. The absolute value of the error is divided by an accepted value and given as a percent. Percent Error = | Accepted Value - Experimental Value | / Accepted Value x 100% For chemistry and other sciences, it is customary to keep a negative value, should one occur. Whether error is positive or negative is important. For example, you would not expect to have a positive percent error comparing actual to theoretical yield in a chemical reaction . If a positive value was calculated, this would give clues as to potential problems with the procedure or unaccounted reactions. When keeping the sign for error, the calculation is the experimental or measured value minus the known or theoretical value, divided by the theoretical value and multiplied by 100%. Percent Error = [Experimental Value - Theoretical Value] / Theoretical Value x 100% Percent Error Calculation Steps- Subtract one value from another. The order does not matter if you are dropping the sign (taking the absolute value. Subtract the theoretical value from the experimental value if you are keeping negative signs. This value is your "error."
- Divide the error by the exact or ideal value (not your experimental or measured value). This will yield a decimal number.
- Convert the decimal number into a percentage by multiplying it by 100.
- Add a percent or % symbol to report your percent error value.
Percent Error Example CalculationIn a lab, you are given a block of aluminum . You measure the dimensions of the block and its displacement in a container of a known volume of water. You calculate the density of the block of aluminum to be 2.68 g/cm 3 . You look up the density of a block of aluminum at room temperature and find it to be 2.70 g/cm 3 . Calculate the percent error of your measurement. - Subtract one value from the other: 2.68 - 2.70 = -0.02
- Depending on what you need, you may discard any negative sign (take the absolute value): 0.02 This is the error.
- Divide the error by the true value: 0.02/2.70 = 0.0074074
- Multiply this value by 100% to obtain the percent error: 0.0074074 x 100% = 0.74% (expressed using two significant figures ). Significant figures are important in science. If you report an answer using too many or too few, it may be considered incorrect, even if you set up the problem properly.
Percent Error vs. Absolute and Relative ErrorPercent error is related to absolute error and relative error . The difference between an experimental and known value is the absolute error. When you divide that number by the known value you get relative error . Percent error is relative error multiplied by 100%. In all cases, report values using the appropriate number of significant digits. Why Is Percent Error Important?Percent error is used extensively across various fields such as physics, chemistry, engineering, and statistics. Because it measures deviations from a true value or accepted value, percent error can be utilized to validate hypotheses during experiments or ensure quality control in manufacturing processes. - Popular Math Terms and Definitions
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Statistics By Jim Making statistics intuitive Percent Error: Definition, Formula & ExamplesBy Jim Frost Leave a Comment Percent error compares an estimate to a correct value and expresses the difference between them as a percentage. This statistic allows analysts to understand the size of the error relative to the true value. It is also known as percentage error and % error. It is a concept that relates to measurement error. In this context, the estimate and correct values can be the following: - Estimate : A measurement, approximation, experimentally derived value, or a guess.
- Correct Value : A quantity that has been proven or generally accepted as being valid. It can be a standard measurement for an item used in testing measurement systems. Or, a known value that is correct on a theoretical basis, such as the circumference of a circle.
Why Assess Percent Error? The measurement instrument, estimation process, personnel, or a combination of factors can cause these errors. When the error becomes large enough, it can invalidate your estimates. At that point, you’ll need to take corrective measures. However, there is no standard cutoff point because it varies by subject area. The purpose for calculating the percentage error depends on the context. In scientific studies and quality management projects, analysts use it to compare measured values to known values to assess the validity of their measurements. Alternatively, researchers use it to compare a value from an experiment to a theoretical or true value to understand the validity of their experimental calculations. To calculate this type of measurement error, you must know the correct value. When you don’t know it, you’ll need to use another method, such as evaluating measurement variability. After covering the formula, I’ll go over several examples of using it in different contexts. Learn more about percentages in my posts, Percent Change and Relative Frequencies and Their Distributions . Percent Error FormulaFinding the percent error involves three steps: - Calculate the error, which is the Estimate – Correct Value.
- Divide by the Correct Value.
- Multiply by 100 to produce a percentage.
When calculating this statistic, some fields of study retain the plus or minus values to indicate whether the Estimate is above or below the Correct value. However, other areas use the absolute value of the error, which always produces positive values. In the percent error equations below, the bars (|) indicate using the absolute value. When you don’t use the absolute value of the error, you’ll obtain positive percentages when the Estimate is greater than the Correct value and negative values when the Estimate is lower. However, the absolute value form always produces positive values. Check to see which version is the norm for your field! Below are the percent error formulas:  Examples of Percent ErrorFor these percent error examples, I use the percent error formula that retains the positive and negative signs because it provides more information. Remove the negative signs to produce the absolute value form. Guesses / Rough EstimationsImagine you’re planning a party and estimate that 15 people will attend. In reality, 18 people attend.  Your guess was in error by -16.67%, meaning that it was too low. Assessing MeasurementsMeasurements are inexact. They are approximations of the actual characteristic. Human error and device limitations can contribute to measurement error. For example, quality control analysts are assessing the measurement system for their inspection process. They need to obtain valid measurements of part lengths. A standard part they use for testing has an agreed upon length of 5.0mm. An inspector measures this part and records 5.2mm.  The inspector’s measurement contains 4% error and it was too high. When you’re using percent error to compare measurements to a known standard item, smaller errors represent measurements that are close to the correct value. If your measurements have more significant errors, you might need to make adjustments to your measurement system. Related posts : Accuracy vs. Precision and Random vs. Systematic Error . Comparing Experimental Values to Known ValuesIn the third century BCE, Eratosthenes, a Greek librarian in Egypt, used the Sun’s positions at two locations at the same time to estimate the Earth’s circumference as being 43,075km. Currently, the Earth’s circumference has a known value of 40,096km.  Eratosthenes’ experiment had an error of 7.4%. That’s on the high side, but it’s not too shabby for someone living in ancient Egypt! Share this: Reader InteractionsComments and questions cancel reply. Learn The Types Learn About Different Types of Things and Unleash Your Curiosity Understanding Experimental Errors: Types, Causes, and SolutionsTypes of experimental errors. In scientific experiments, errors can occur that affect the accuracy and reliability of the results. These errors are often classified into three main categories: systematic errors, random errors, and human errors. Here are some common types of experimental errors: 1. Systematic ErrorsSystematic errors are consistent and predictable errors that occur throughout an experiment. They can arise from flaws in equipment, calibration issues, or flawed experimental design. Some examples of systematic errors include: – Instrumental Errors: These errors occur due to inaccuracies or limitations of the measuring instruments used in the experiment. For example, a thermometer may consistently read temperatures slightly higher or lower than the actual value. – Environmental Errors: Changes in environmental conditions, such as temperature or humidity, can introduce systematic errors. For instance, if an experiment requires precise temperature control, fluctuations in the room temperature can impact the results. – Procedural Errors: Errors in following the experimental procedure can lead to systematic errors. This can include improper mixing of reagents, incorrect timing, or using the wrong formula or equation. 2. Random ErrorsRandom errors are unpredictable variations that occur during an experiment. They can arise from factors such as inherent limitations of measurement tools, natural fluctuations in data, or human variability. Random errors can occur independently in each measurement and can cause data points to scatter around the true value. Some examples of random errors include: – Instrument Noise: Instruments may introduce random noise into the measurements, resulting in small variations in the recorded data. – Biological Variability: In experiments involving living organisms, natural biological variability can contribute to random errors. For example, in studies involving human subjects, individual differences in response to a treatment can introduce variability. – Reading Errors: When taking measurements, human observers can introduce random errors due to imprecise readings or misinterpretation of data. 3. Human ErrorsHuman errors are mistakes or inaccuracies that occur due to human factors, such as lack of attention, improper technique, or inadequate training. These errors can significantly impact the experimental results. Some examples of human errors include: – Data Entry Errors: Mistakes made when recording data or entering data into a computer can introduce errors. These errors can occur due to typographical mistakes, transposition errors, or misinterpretation of results. – Calculation Errors: Errors in mathematical calculations can occur during data analysis or when performing calculations required for the experiment. These errors can result from mathematical mistakes, incorrect formulas, or rounding errors. – Experimental Bias: Personal biases or preconceived notions held by the experimenter can introduce bias into the experiment, leading to inaccurate results. It is crucial for scientists to be aware of these types of errors and take measures to minimize their impact on experimental outcomes. This includes careful experimental design, proper calibration of instruments, multiple repetitions of measurements, and thorough documentation of procedures and observations. You Might Also Like:Patio perfection: choosing the best types of pavers for your outdoor space, a guide to types of pupusas: delicious treats from central america, exploring modern period music: from classical to jazz and beyond. Last updated 20/06/24: Online ordering is currently unavailable due to technical issues. We apologise for any delays responding to customers while we resolve this. 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- > Experimental errors
 Book contents- Frontmatter
- Glossary and Conventions
- 1 Experimental errors
- 2 Least squares fitting
- Appendix 1 Useful formulae
- Appendix 2 Partial differentiation
- Appendix 3 The binomial distribution
- Appendix 4 The Poisson distribution
- Appendix 5 Student's t distribution
- Appendix 6 Statistical tables
- Appendix 7 Random numbers
1 - Experimental errorsPublished online by Cambridge University Press: 05 June 2012 Why estimate errors? When performing experiments at school, we usually considered that the job was over once we obtained a numerical value for the quantity we were trying to measure. At university, and even more so in everyday situations in the laboratory, we are concerned not only with the answer but also with its accuracy. This accuracy is expressed by quoting an experimental error on the quantity of interest. Thus a determination of the acceleration due to gravity in our laboratory might yield an answer g = (9.70 ± 0.15) m/s 2 . In Section 1.4, we will say more specifically what we mean by the error of ±0.15. At this stage it is sufficient to state that the more accurate the experiment the smaller the error; and that the numerical value of the error gives an indication of how far from the true answer this particular experiment may be. The reason we are so insistent on every measurement including an error estimate is as follows. Scientists are rarely interested in measurement for its own sake, but more often will use it to test a theory, to compare with other experiments measuring the same quantity, to use this parameter to help predict the result of a different experiment, and so on. Then the numerical value of the error becomes crucial in the interpretation of the result. Access optionsSave book to kindle. To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle . Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service . - Experimental errors
- Louis Lyons
- Book: A Practical Guide to Data Analysis for Physical Science Students
- Online publication: 05 June 2012
- Chapter DOI: https://doi.org/10.1017/CBO9781139170321.003
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Workload installation failed: Workload manifest dependency 'Microsoft.NET.Workload.Emscripten.Current' version '9.0.0-preview.6.24319.1' is lower than version '9.0.0-preview.7.24319.4' required by manifest 'microsoft.net.workload.mono.toolchain.current' [C:\Program Files\dotnet\sdk-manifests\9.0.100-preview.6\microsoft.net.workload.mono.toolchain.current\9.0.0-preview.6.24324.3\WorkloadManifest.json] | | The text was updated successfully, but these errors were encountered: |  No branches or pull requests  Humans may soon live to be 1000 years old, says renowned scientist UNDATED (WKRC) - A renowned scientist claims humans may soon live to be around 1,000 years old. According to BGR, futurist Raymon Kurzweil believes he has found a way to extend the life of a human for thousands of years. Per the outlet, citing Kurzweil's new book, nanorobots may be the key to slowing the aging process and extending human life. Experts have raised concerns about extending the life of humans for thousands of years. It has not deterred acclaimed scientists from researching new anti-aging therapies, however, which continues to be a common focus of their research, per BGR. Unlike many scientists who seek only to slow the deterioration of the body, Kurzweil wishes to use nanotechnology to "cure aging itself," according to the outlet. In his new book, entitled The Singularity is Nearer , and in an essay published in Wired , Kurzweil explores the idea of blending biotechnology and artificial intelligence (AI) to help overcome the aging process. According to BGR, as cells reproduce over the years, they accumulate errors, which result in aging. Anti-aging therapies aim to reduce the number of errors, which allows the body to repair itself more quickly. Per BGR, Kurzweil understands that his projections may sound absurd in our current day, but said he believes advancements in medical nanorobots will soon cure aging across the board. According to the outlet, a single human body might require several hundred-billion nanobots to repair and augment degrading organs to assure their function remains in peak condition.  Help | Advanced Search  Mathematics > Geometric TopologyTitle: genus non-increasing totally positive unknotting number. Abstract: The genus non-increasing totally positive unknotting number is the minimum number of crossing changes that transform a knot into the unknot, such that all the crossing changes are positive-to-negative crossing changes that do not increase the genus. We show that the genus non-increasing totally positive unknotting number can be arbitrary large for genus one knots. | Comments: | 10 pages, 3 Figures | | Subjects: | Geometric Topology (math.GT) | | Cite as: | [math.GT] | | | (or [math.GT] for this version) | | | Focus to learn more arXiv-issued DOI via DataCite | Submission historyAccess paper:. - HTML (experimental)
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- Simpson, Matthew J
In vitro cell biology experiments are routinely used to characterize cell migration properties under various experimental conditions. These experiments can be interpreted using lattice-based random walk models to provide insight into underlying biological mechanisms, and continuum limit partial differential equation (PDE) descriptions of the stochastic models can be used to efficiently explore model properties instead of relying on repeated stochastic simulations. Working with efficient PDE models is of high interest for parameter estimation algorithms that typically require a large number of forward model simulations. Quantitative data from cell biology experiments usually involves non-negative cell counts in different regions of the experimental images, and it is not obvious how to relate finite, noisy count data to the solutions of continuous PDE models that correspond to noise-free density profiles. In this work we illustrate how to develop and implement likelihood-based methods for parameter estimation, parameter identifiability and model prediction for lattice-based models describing collective migration with an arbitrary number of interacting subpopulations. We implement a standard additive Gaussian measurement error model as well as a new physically-motivated multinomial measurement error model that relates noisy count data with the solution of continuous PDE models. Both measurement error models lead to similar outcomes for parameter estimation and parameter identifiability, whereas the standard additive Gaussian measurement error model leads to non-physical prediction outcomes. In contrast, the new multinomial measurement error model involves a lower computational overhead for parameter estimation and identifiability analysis, as well as leading to physically meaningful model predictions. - Physics - Applied Physics;
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 Article ContentsIntroduction, materials and methods, supplementary data, acknowledgements, author contributions, conflict of interest, data availability. Disrupting cell wall integrity impacts endomembrane trafficking to promote secretion over endocytic trafficking - Article contents
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Natalie Hoffmann, Eskandar Mohammad, Heather E McFarlane, Disrupting cell wall integrity impacts endomembrane trafficking to promote secretion over endocytic trafficking, Journal of Experimental Botany , Volume 75, Issue 12, 24 June 2024, Pages 3731–3747, https://doi.org/10.1093/jxb/erae195 - Permissions Icon Permissions
The plant cell wall provides a strong yet flexible barrier to protect cells from the external environment. Modifications of the cell wall, either during development or under stress conditions, can induce cell wall integrity responses and ultimately lead to alterations in gene expression, hormone production, and cell wall composition. These changes in cell wall composition presumably require remodelling of the secretory pathway to facilitate synthesis and secretion of cell wall components and cell wall synthesis/remodelling enzymes from the Golgi apparatus. Here, we used a combination of live-cell confocal imaging and transmission electron microscopy to examine the short-term and constitutive impact of isoxaben, which reduces cellulose biosynthesis, and Driselase, a cocktail of cell-wall-degrading fungal enzymes, on cellular processes during cell wall integrity responses in Arabidopsis. We show that both treatments altered organelle morphology and triggered rebalancing of the secretory pathway to promote secretion while reducing endocytic trafficking. The actin cytoskeleton was less dynamic following cell wall modification, and organelle movement was reduced. These results demonstrate active remodelling of the endomembrane system and actin cytoskeleton following changes to the cell wall. Plant cells are surrounded by a polysaccharide-rich cell wall that provides mechanical support, enables cell expansion, and acts as a physical barrier against biotic and abiotic stresses ( Anderson and Kieber, 2020 ). Cell wall biosynthesis is mediated by the endomembrane system, which consists of the endoplasmic reticulum, Golgi bodies, the trans -Golgi network (TGN)/early endosomes, multi-vesicular bodies/pre-vacuolar compartments/late endosomes (LEs), the vacuole, and transport vesicles ( Hoffmann et al. , 2021 ). The major structural component of the cell wall, cellulose, is produced by CELLULOSE SYNTHASE (CESA) enzymes that are trafficked through the Golgi and TGN before localizing to the plasma membrane where they are active ( Pedersen et al. , 2023 ). The cell wall matrix polysaccharides, hemicelluloses and pectins, are synthesized by Golgi-resident proteins and then trafficked through the TGN prior to secretion to the cell wall ( Hoffmann et al. , 2021 ). Vesicle trafficking and organelle movement are primarily dependent on a dynamic actin cytoskeleton, associated myosin motors, and actin–myosin-driven cytoplasmic streaming ( Nebenführ et al. , 1999 ; Sampathkumar et al. , 2013 ). The structure and composition of the cell wall is not static and responds both to developmental cues and to external stress. Recent research has uncovered the existence of a complex cell wall integrity mechanism in which changes to cell wall structure activate intracellular signalling that can act to correct or alleviate cell wall modifications ( Vaahtera et al. , 2019 ). This sensing system is intricately linked with the mechanical strength of the cell wall and turgor pressure, as these forces work against each other to prevent cell bursting ( Bacete and Hamann, 2020 ). Other known stimulators of cell wall integrity signalling include low molecular mass cell wall fragments, such as pectin-derived oligogalacturonides ( Voxeur et al. , 2019 ) or cellulose-derived compounds ( Tseng et al. , 2022 ; Martín-Dacal et al. , 2023 ). Recent work has identified several receptors that are involved in perceiving cell wall modification and the immediate downstream processes following activation. These include post-translational modifications ( Wang et al. , 2020 ; Tseng et al. , 2022 ), alterations to gene expression, increased salicylic acid and jasmonic acid phytohormones, and production of reactive oxygen species ( Hamann et al. , 2009 ; Wormit et al. , 2012 ; Engelsdorf et al. , 2018 ; Gigli-Bisceglia et al . 2018 ; Chaudhary et al. , 2020 ; Bacete et al. , 2022 ). Cell wall composition also changes in response to cell wall integrity signalling. For example, cell wall changes have been documented following pathogen infection ( Chowdhury et al. , 2014 ) or reduced cellulose biosynthesis ( Hamann et al. , 2009 ), including deposition of callose or the phenolic polymer lignin ( Denness et al. , 2011 ; Chaudhary et al. , 2020 ). Furthermore, inhibition of cellulose biosynthesis led to up-regulation of genes involved in cell wall remodelling ( Duval and Beaudoin, 2009 ; Hamann et al. , 2009 ). Although CESA secretion to the plasma membrane is altered during cell wall integrity responses ( McFarlane et al. , 2021 ), it is unclear whether matrix polysaccharide and cell wall protein secretion are also altered by activation of cell wall integrity signalling. Therefore, the specifics of how endomembrane system organization and function change in response to cell wall disruption, as well as the underlying mechanisms for these changes, are still unknown. Increasing evidence supports the role of the TGN/early endosomes in mediating responses during developmental and stress conditions ( Uemura et al ., 2019 ; Oda et al. , 2020 ). High resolution imaging has shown that within a single TGN there are distinct subdomains mediating secretory, endocytic, and vacuolar trafficking pathways ( Heinze et al. , 2020 ; Shimizu et al. , 2021 ). Imaging techniques have also identified two populations of TGN: Golgi-associated TGN (GA-TGN) and Golgi-independent TGN (GI-TGN) ( Viotti et al. , 2010 ; Kang et al. , 2011 ; Uemura et al ., 2014 , 2019 ). GA-TGN and GI-TGN are thought to represent functionally distinct compartments, with GA-TGN being involved in both endocytic and secretory pathways and GI-TGN being primarily involved in secretion ( Kang et al. , 2011 ; Uemura et al ., 2019 ). The proportion of GI-TGNs increased during root development ( Uemura et al ., 2014 ) and following powdery mildew infection ( Uemura et al ., 2019 ), suggesting that increasing the number of GI-TGNs could promote secretory trafficking under specific conditions. In this study, we characterized how endomembrane system structure and function respond to cell wall modifications induced by isoxaben (ISX) treatment, which inhibits cellulose biosynthesis ( Scheible et al. , 2001 ), or following damage to the cell wall using Driselase (Dri), which contains a combination of fungal cell wall-degrading enzymes, including cellulase, xylanase, mannanase, and pectinase ( Kubicek et al. , 2014 ; Engelsdorf et al. , 2018 ). Using live-cell confocal imaging and high-resolution electron microscopy, we show that ISX or Dri treatment imparts distinctive effects on the endomembrane system under short-term and constitutive treatments. Both conditions reduced the dynamics of the actin cytoskeleton and adjusted the balance between endocytic trafficking and secretion to favour increased secretion, presumably to accommodate increased trafficking from the Golgi apparatus to fortify the cell wall. Plant materialsThe Arabidopsis Columbia-0 (Col-0) accession was used in this study. Fluorescent lines used for this study are listed in Supplementary Table S1 . Growth conditionsSeeds were surface-sterilized for 10 min using 3% sodium hypochlorite (Javel) and 0.1% Triton X-100 (Thermo Fisher Scientific) and rinsed five times in sterile water, then sown on half strength Murashige and Skoog (½ MS) medium with vitamins (Phyto Technology Laboratories) with 2.5 mM MES (Thermo Fisher Scientific) and 0.7% agar (Thermo Fisher Scientific) at pH 5.8, supplemented with 1% w/v sucrose (Thermo Fisher Scientific). Seeds were then stratified for 2–4 d at 4 °C. For root analyses, seedlings were grown vertically for 5 d under ~100 µmol m −2 s −1 light at 21 °C for 18 h and in the dark at 18 °C for 6 h. For etiolated hypocotyl analyses, seeds were light-treated for 5 h and then grown in the dark for 5 d under the same temperature cycle. Stress and inhibitor treatmentsEither 20 mM or 20 µM stock solutions of isoxaben (ISX; Sigma-Aldrich, cat. no. 36138) were prepared in 100% ethanol and stored at −20 °C. ISX was added to slightly cooled molten ½ MS + sucrose + agar before being poured into plates with a final concentration of no more than 0.001% v/v ethanol in the medium. A 2% w/v solution of Driselase (Dri; Sigma-Aldrich, cat. no. D9515) was prepared in deionized H 2 O and filter-sterilized, then added to slightly cooled molten ½ MS + sucrose + agar before being poured into plates. To ensure Dri enzyme activity, plates were made fresh for each experiment and used for no longer than 1 week. For constitutive treatment, seeds were directly germinated on stress medium (½ MS + sucrose + 2 nM ISX or 0.03% Dri) and grown for 5 d. For short-term treatments, seeds were germinated on sterile filter-paper strips on ½ MS + 1% sucrose plates and grown for 5 d. The filter-paper strips were gently transferred to stress medium plates (+200 nM ISX or +0.05% Dri) and left to grow vertically in the growth chamber for the designated times. As a control, seeds were mock-treated for 4 h with an equal volume of ethanol for a final concentration of 0.001% v/v. For boiled Dri control experiments, 0.03% or 0.05% Dri solution was heat-inactivated at 100 °C for 10 min, prior to being added to ½ MS + 1% sucrose medium. Boiled Dri plates were then used for root growth assays and for root morphology imaging, and were compared with no treatment (NT) plates (½ MS + sucrose). A 10 mM stock of LatrunculinB (LatB) from Latruncula magnifica (Sigma-Aldrich, cat. no. L5288) was prepared in dimethyl sulfoxide (DMSO) and stored at −20 °C. For short-term treatments, a 25 µM working solution was prepared in liquid ½ MS + 1% sucrose. For fABD2–green fluorescent protein (GFP) imaging and NAG–GFP speed quantification, 5-day-old seedlings were treated with LatB for 1 h prior to imaging. For co-treatment of LatB with either ISX or Dri, 5-day-old seedlings were incubated in liquid ½ MS + 1% sucrose with 0.25% DMSO (Mock), 25 µM LatB, 200 nM ISX, or 0.05% Dri for 4 h or 24 h prior to measuring root length. Quantification of seedling phenotypesFor seedling growth assays, plates of 5-day-old seedlings were scanned using an Epson V550 photo scanner. Quantification of root or etiolated hypocotyl lengths was performed manually in FIJI ( Schindelin et al. , 2012 ). For calculation of the change in length following short-term stress treatments, the length of each stress-treated seedling was divided by the mean length of mock-treated seedlings at a given time point. Data were consistent for at least three independent experiments. Fluorescent dyesA 0.5 mg ml −1 stock solution of propidium iodide (PI; Thermo Fisher Scientific, cat. no. AC440300250) was prepared in deionized H 2 O and stored at 4 °C in the dark. Five-day-old seedlings were incubated in a 15 µM working solution in deionized H 2 O for 15 min in the dark prior to being imaged. Molecular Probes FM1-43 (Thermo Fisher Scientific, cat. no. T35356) was suspended in DMSO to 15 µM and stored at −20 °C in the dark. For FM1-43 uptake quantification, 5-day-old roots were incubated in a 1.5 µM solution in liquid ½ MS + 1% sucrose for 5 min on ice, rinsed in ½ MS twice on ice, then mounted on a slide (denoting start of endocytosis). Epidermal cells in the elongation zone were monitored for 30 min, taking an image every 1 min. In a separate experiment, roots were stained with FM1-43 and rinsed as above, then cells in the elongation zone were imaged following 60 min of FM1-43 uptake. Confocal microscopySeedlings were mounted on a custom-built slide ( Verbančič et al. , 2021 ) in water under a pad of 0.8% agarose. For root analyses, all imaging was performed on the early elongation zone of roots. Seedlings were imaged using a Nikon Eclipse Ti2-E inverted microscope equipped with a CSU-W1 spinning disk with dual Photometrics Prime95b sCMOS cameras. Fluorophores were excited using a 488 nm laser for GFP (90 mW, 0.5% power for NAG–GFP co-localization analyses and 19% power for all other imaging) and a 561 nm laser for red fluorescent protein (RFP; 70 mW, 60% power for VHAa1–RFP co-localization analyses and 24% for all other imaging). Fluorescence emission was collected using a band emission filter of 525/36 nm for GFP and 605/52 nm for RFP. For analysis of dual fluorescent lines, the 488 nm and 561 nm lasers were excited simultaneously and emission was separated with a 561 nm long-pass dichroic mirror. For FM1-43 or PI staining, the dye was excited using the 488 nm or 514 nm (30 mW, ~25% power) laser, respectively, and collected using the 605/52 nm emission filter. All images were collected using either a ×40 oil-immersion objective lens (CFI Plan Fluor, NA 1.3, WD 0.24) or a ×100 oil-immersion objective lens (Apochromat TIRF, MRD01991, NA 1.49, WD 0.12). Pixel size for the ×100 objective lens is 110 nm (9.0909 pixels μm −1 ). Laser settings and exposure times were kept identical between treatments and biological replicates of the same experiment. Quantification of cell perimeter, volume, and cell deathImages of the elongation zone of PI-stained roots taken with the ×40 objective were used to calculate the size and volume of cells following ISX and Dri treatment. z -Stacks of depth 4–21 µm were isolated for individual cells that had started elongating but prior to formation of root hairs (i.e. the maturation zone). Due to differences in root growth between treatments, the length of this zone differed between treatments, but the zone was evident due to the presence of swollen cells for ISX treatment. Cell perimeter (for a rectangular cell, or circumference for swollen ISX cells) was calculated manually from maximum projection images in FIJI. n >16 cells from four to eight biological replicates per treatment. Due to difficulties in approximating the volume of bulging cells and swollen cells for ISX-treated roots using standard mathematical equations for cuboids or perfect spheres, cell volume was calculated manually from these images by measuring the surface area and known z -step height for each image within a z -stack; n >16 cells from four to eight biological replicates per treatment. The number of dead cells per root was counted manually by identification of PI-stained nuclei in ×40 images. Cells only within the elongation zone of roots were assessed, starting after the root apical meristem where cells are starting to elongate (and start to swell for ISX/Dri treatment) and ending prior to formation of root hairs. PI is normally excluded from internal staining of intact living cells, but if the cell is non-viable PI will enter the cell and bind to DNA. n >4 roots per treatment. Fluorescence recovery after photobleachingFluorescence recovery after photobleaching (FRAP) of PIP2A–GFP or LTI6B–GFP was performed on 5-day-old roots using the ×100 objective. A circular region of interest (12 µm diameter) at the plasma membrane was completely bleached using the 405 nm laser (50 mW) at 100% intensity with a 100 µs dwell. For PIP2A–GFP, fluorescence recovery was monitored for 30 min, with an image taken every 2 min. For LTI6B–GFP, fluorescence recovery was monitored for 5 min, with an image taken every 2.5 s. Quantification was performed as per McKenna (2022) , using data normalized to pre-bleach values. Quantification of endocytosis and endocytic trafficking using FM1-43The plasma membrane signal for any given time point was calculated by manually outlining single cells, and subtracting the fluorescence intensity of the cytoplasm from the fluorescence intensity of the whole cell (denoting plasma membrane signal) using measurements from FIJI ( Schindelin et al. , 2012 ). Data are representative of n =17–24 cells from each time point from six biological replicates. Quantification of organelle sizeFive-day-old roots were imaged using the ×100 objective. Regions of interest from NAG–GFP/VHAa1–mRFP or WAVE7–RFP were selected from z -stacks (100 pixels×100 pixels with 0.2 µm z -spacing, for a total of 4 µm stack). Regions of interest were manually thresholded in FIJI, with a minimum object size of 50 pixels and a maximum object size of 1000 pixels for NAG–GFP and WAVE7–RFP, and a minimum object size of 10 pixels and a maximum object size of 1000 pixels for VHAa1–mRFP. The size of organelles was calculated using the ‘AnalyzeParticles’ plugin. n =34 regions of interest for Golgi/TGN and n =24 for late endosomes from 12–15 biological replicates. Quantification of organelle number and co-localization using DiAnaRegions of interest from NAG–GFP/VHAa1–mRFP or WAVE7–RFP were selected from z -stacks (100 pixels×100 pixels with 0.2 µm z -spacing, for a total of 4 µm stack) and segmented using the DiAna plugin on FIJI ( Gilles et al. , 2017 ). Regions of interest were manually thresholded, with a minimum object size of 50 pixels and a maximum object size of 1000 pixels for NAG–GFP, and a minimum object size of 10 pixels and a maximum object size of 1000 pixels for VHAa1–mRFP. Segmented objects were used to calculate organelle number, distance between organelles, and co-localization using default settings. n =34 regions of interest from 12 biological replicates. The number of GA- and GI-TGNs was calculated using NAG–GFP/VHAa1–mRFP regions of interest. GA-TGNs were identified as TGNs significantly co-localizing with a Golgi body whereas GI-TGNs were identified as TGNs not significantly co-localizing with a Golgi body, using a segmented 3D image in DiAna. GI-TGNs were manually confirmed on the image, with GI-TGNs being VHAa1–mRFP TGN that are physically separate from a NAG–GFP Golgi body and move independently ( Uemura et al ., 2014 ). Quantification of organelle speedFive-day-old NAG–GFP or WAVE7–RFP roots were used to monitor organelle speed using the ×100 objective. A 1.2 µm (0.2 µm z -spacing) z -stack was imaged every 2 s for a total time of 30 s. A 100 × 100 pixel region of interest for each time point was generated in FIJI ( Schindelin et al. , 2012 ), and individual organelle speeds were calculated manually using the ‘ManualTracking’ plugin using default parameters. n >78 Golgi per treatment from six biological replicates for NAG–GFP, and n >126 late endosomes for WAVE7-RFP from six biological replicates. For washout experiments, 5-day-old roots were treated with 200 nM ISX or 0.05% Dri for 24 h, then transferred to ½MS + 1% sucrose medium (without ISX or Dri) for 2 h prior to imaging. Quantification of actin occupancy and dynamicsActin occupancy (measure of local abundance) was measured based on Higaki (2017) . Briefly, z -stacks of fABD2–GFP roots (depth 5–6 µm, spacing 0.5 µm) were taken with a ×100 objective. In FIJI, z -stacks were converted into maximum projections and cropped into 100 × 100 pixel regions of interest, with each region representing one cell or region of a cell. Maximum projections were manually thresholded to remove background, smoothed, and skeletonized using the Skeleton 2D/3D plugin. The density of the skeletonized actin cytoskeleton was measured and compared with the area of the region to obtain actin density. n >25 regions of interest per treatment from eight biological replicates. For actin dynamics, 5-day-old fABD2–GFP roots were imaged using the ×100 objective lens. A 5–6 µm z -stack (0.5 µm per step) was imaged every 2 s for a total time of 2 min. A 100 × 100 pixel region of interest for each time point was generated in FIJI ( Schindelin et al. , 2012 ), and the maximum projection images were used for analysis. The FIJI macro JaCoP ( Bolte and Cordelières, 2006 ) was used to calculate Pearson’s correlation coefficient between sequential time points (time point 1 versus time point 2, time point 2 versus time point 3, etc.). Three regions of interest per image were averaged for one replicate. A high Pearson’s correlation coefficient indicates low dynamics (actin does not change frame-to-frame) whereas a low correlation coefficient indicates high dynamics (actin organization does not stay the same frame-to-frame). n >25 regions of interest per treatment from eight biological replicates. Ratiometric sec–GFP quantificationFive-day-old ratiometric sec–GFP roots were used to monitor secretion using the ×100 objective. A 2 µm z -stack (0.2 µm spacing) of GFP and RFP was imaged. A 50 × 50 pixel region of interest was generated in FIJI ( Schindelin et al. , 2012 ). Using the maximum projection image, the fluorescence intensities of GFP and RFP channels were measured and compared. n =36 regions of interest from six biological replicates per treatment. Transmission electron microscopy cryofixation and embeddingFive-day-old root tips were dissected and submerged in 1-hexadecene (Sigma-Aldrich, cat. no. H2131) as a cryoprotectant prior to loading into B-type high-pressure freezing planchets (Electron Microscopy Sciences, cat. no. 71167). Samples were frozen with a high-pressure freezer (Leica EM ICE) and transferred to freeze-substitution vials under liquid nitrogen. Samples were freeze-substituted in 8% (v/v) 2,2-dimethoxypropane (Sigma-Aldrich, cat. no. D136808) and 2% (w/v) osmium tetroxide (Electron Microscopy Sciences, cat. no. 19100) in anhydrous acetone over 5 d at −85 °C, slowly brought to room temperature over 3–4 h, separated from their sample carrier, and rinsed with anhydrous acetone five times. Spurr’s resin (Electron Microscopy Sciences, cat. no. 14300) was gradually infiltrated in an ascending series of 10, 20, 30, 40, 50, 60, 80, and 100% resin for 2–3 h each or overnight. Two additional 100% resin exchanges were performed for 3 h each, and then samples were polymerized in BEEM embedding capsules (Electron Microscopy Sciences) for 24 h at 65 °C. Transmission electron microscopy sectioning and imagingSections of ∼70 nm were cut with a DiATOME knife on a Leica Ultracut E ultramicrotome, suspended on copper grids (ProSci Tech) coated with 1% formvar (Electron Microscopy Sciences). Samples were poststained with UranyLess (Electron Microscopy Sciences, cat. no. 22409) for 1 min and Reynolds’ lead citrate ( Reynolds, 1963 ; all chemicals from Thermo Fisher Scientific) for 10 min. Grids were imaged using a Hitachi HT7700 transmission electron microscope at 80 kV accelerating voltage with a tungsten filament coupled to an AMT XR-111 digital camera. Images were captured with AMT Capture Engine software. Transmission electron microscopy quantificationQuantification of Golgi ultrastructure was performed manually using FIJI; see Supplementary Fig. S8 for a description of parameters. Data visualizationMost data ( n >24) are presented in a violin plot, which is a kernel density plot that ranges from the minimum to the maximum value. Within each violin plot there is a box plot. The box represents the 25–75% quartiles, and the median is represented by a horizontal line within the box. The whiskers of the box represent the minimal and maximal values of the sample. Changes in cell wall integrity induced by isoxaben or Driselase impact plant growth and cell morphologyTo test the impact of cell wall integrity responses on cellular processes, we utilized two commonly used treatments, isoxaben (ISX), which inhibits cellulose biosynthesis ( Scheible et al. , 2001 ), and Driselase (Dri), a cocktail of fungal enzymes including cellulases, xylanases, mannanases, and pectinases ( Engelsdorf et al. , 2018 ). Cellular and molecular responses to ISX have been extensively documented in a time-dependent manner ( Supplementary Fig. S1A ). However, many of these studies used a high concentration of ISX (600 nM), which under our conditions induced substantial cell death in the root elongation zone after 4 h as indicated by PI staining of the nucleus ( Supplementary Fig. S1B ). We therefore tested a range of concentrations and durations for both ISX and Dri to assess the impact on seedling growth and cell morphology. Wild-type Col-0 seedlings germinated and grown on ½ MS medium including 1% sucrose and a range of concentrations of ISX (0.5–5 nM) for 5 d showed a reduction in root and etiolated hypocotyl length and substantial cell swelling at higher concentrations ( Supplementary Fig. S2 ). Short-term treatment with 200 nM ISX, which had lower amounts of cell death relative to 600 nM ISX ( Supplementary Fig. S1C ), caused initial cell swelling as early as 4 h, and reduced root length was apparent after 24 h ( Supplementary Fig. S3 ). Consistent with previous work ( Gutierrez et al. , 2009 ), imaging of fluorescently tagged CELLULOSE SYNTHASE3 (GFP–CESA3) ( Desprez et al. , 2007 ; Crowell et al. , 2009 ) in root cells showed decreased GFP–CESA3 abundance at the plasma membrane after 1 h of 200 nM ISX ( Supplementary Fig. S3E ), confirming ISX is active and sufficient to trigger CESA internalization and reduce cellulose synthesis. From these results, we selected a short-term treatment of 200 nM ISX for 4 h and 24 h and a constitutive 5 d treatment on 2 nM ISX, which represent initial cell swelling, the onset of root growth inhibition/severe cell morphological changes, and a constitutive treatment, respectively, to assess the impact of ISX on cellular processes. The effect of Dri on wild-type Col-0 showed differing effects relative to Mock, compared with ISX treatment. Constitutive growth on ½ MS medium with 1% sucrose and a range of concentrations of Dri showed reduced root length and degradation of the root apical meristem, but comparably minor changes in etiolated hypocotyl length or morphology ( Supplementary Fig. S4 ). Short-term treatments with 0.05% Dri decreased root length after 4 h, with initial cell swelling observed at this time ( Supplementary Fig. S5 ). We therefore selected a short-term treatment of 0.05% Dri for 4 h and 24 h and a constitutive 5 d treatment on 0.03% Dri. Due to the comparably minor effect of Dri on etiolated hypocotyls, we focused subsequent work on the elongation zone of light-grown roots, which is highly sensitive to stress treatments ( Hamann et al. , 2009 ). Treatment with boiled Dri eliminated the degradation of the root apical meristem at all time points and did not cause root growth inhibition at 4 h, but still caused some cell swelling and root growth inhibition after 24 h and 5 d treatment ( Supplementary Fig. S6A , B ), suggesting that non-enzymatic components of Dri also somewhat impact root growth and morphology. Following selection of the ISX and Dri concentrations and time points, we performed further morphological analysis using the PI-stained roots of both ISX and Dri treatments. Cell size and volume increased significantly following 24 h ISX treatment due to cell swelling ( Supplementary Fig. S6C , D ). We also used internal staining of nuclei with PI as a proxy for cell death, and found that 4 h and 24 h ISX had significantly more cell death relative to Mock-treated controls, consistent with previous work ( Hamann et al. , 2009 ), and there was also increased cell death following 5 d Dri treatment ( Supplementary Fig. S6E ). Despite the increased cell death, the vast majority of cells at the lower (200 nM) ISX concentration were still viable, as were the cells in the Dri-treated roots under our growth conditions. Together, the combination of short-term and constitutive treatments allowed us to specifically dissect early, middle-term, and long-term responses to cell wall modification induced by ISX or Dri ( Fig. 1 ).  Summary of the treatments used in this work. Arabidopsis Col-0 was treated with either isoxaben (ISX), which reduces cellulose biosynthesis, or Driselase (Dri), a combination of fungal enzymes that degrades cellulose, hemicelluloses, and pectins. For short-term treatments, 5-day-old roots were transferred to medium containing either 200 nM ISX or 0.05% Dri and left to grow for 4 h or 24 h. For constitutive treatment, Col-0 seeds were germinated and grown on medium containing 2 nM ISX or 0.03% Dri for 5 d prior to analysis. Mock-treated Col-0 seedlings were treated with an equal volume ethanol for 4 h. Images are maximum-projection images of PI-stained root tissue and are representative of six biological replicates. Scale bars are 50 µm. Disrupting cell wall integrity increases secretion to the cell wallCell wall fortification under cell wall integrity stress requires secretion from the Golgi apparatus and TGN: matrix polysaccharides are synthesized at the Golgi apparatus and secreted to the cell wall ( Hoffmann et al. , 2021 ) and CESAs are trafficked through the Golgi apparatus to synthesize cellulose at the plasma membrane ( Zhu and McFarlane, 2022 ). Therefore, we assessed the impact of ISX and Dri treatment on Golgi and TGN morphology using the dual fluorescent marker line NAG–GFP/VHAa1–mRFP ( Fig. 2A ; Supplementary Fig. S7A , B ), which labels cis -Golgi cisterna via an N -acetylglucosaminyltransferase, which is part of the N -glycosylation pathway (NAG–GFP), and the TGN with VHAa1, a component of the V-type H + -ATPase that maintains the pH of the TGN ( Grebe et al. , 2003 ; Dettmer et al. , 2006 ), in root elongation zone epidermal cells. Golgi body size significantly increased following 24 h ISX and both 4 h and 24 h Dri treatments ( Fig. 2B ), but there were no changes to Golgi body number ( Fig. 2C ). There were also no significant differences for VHAa1–mRFP-labelled TGN size ( Fig. 2D ) or number ( Supplementary Fig. S7C ). Use of the dual Golgi and TGN marker allowed us to dissect whether a TGN was Golgi-associated (GA-TGN) or Golgi-independent (GI-TGN), based on co-localization with a Golgi body and movement together with, or independently of, a Golgi stack ( Uemura et al ., 2014 ). Association between Golgi and TGN was higher in 24 h ISX treatment, as there was a significantly lower distance between the two organelles ( Supplementary Fig. S7D ). The proportion of GI-TGNs in Mock-treated roots was similar to those observed by Uemura et al . (2019) . ISX or Dri treatment did not significantly alter the number of GA-TGNs or GI-TGNs ( Supplementary Fig. S7E , F ), resulting in a similar GI-TGN:GA-TGN proportion between treatments ( Fig. 2E ). These results suggest that Golgi body size increases following short-term ISX or Dri, but there are no changes to the size or number of TGNs.  Treatment with isoxaben (ISX) or Driselase (Dri) impacts Golgi and trans -Golgi network (TGN) morphology. (A) Representative maximum-projection images of 5-day-old Col-0 root elongation zone epidermal cells with the dual Golgi (green) and TGN (magenta) marker NAG–GFP/VHAa1–RFP. White dashed circles indicate Golgi-independent trans -Golgi network (GI-TGN). Scale bar is 2 µm. (B) Quantification of Golgi size. (C) Quantification of the number of Golgi bodies. (D) Quantification of TGN size. (E) Proportion of GI-TGN to Golgi-associated trans -Golgi network (GA-TGN). (F) Representative TEM images of Mock-, 4 h-ISX-, or 4 h-Dri-treated 5-day-old high-pressure frozen root elongation zone epidermal cells. Scale bars are 200 nm. g denotes Golgi bodies, cis-/trans- denotes the face of the Golgi. (G) Quantification of GA-TGN vesicle diameter. See Supplementary Fig. S8 for more information about TEM parameters. For fluorescence imaging, n =34 regions of interest from each treatment from 12 biological replicates. For TEM, n =83, 123, and 182 TGN from Mock, 4 h ISX, and 4 h Dri, respectively, from three biological replicates. Letters indicate significantly different means using a one-way ANOVA with a Dunn’s post-hoc test with Bonferroni correction, P <0.05; n.s., not significant. To examine further whether ISX or Dri treatment impacts the size or morphology of GA-TGN and GI-TGNs, we assessed Golgi body and TGN ultrastructure at high resolution using transmission electron microscopy (TEM) of high-pressure frozen, freeze-substituted roots. Due to the fragile state of 24 h-treated roots, we instead looked at early ultrastructural changes following 4 h of ISX or Dri treatment ( Fig. 2F ; Supplementary Fig. S8 ). Overall cell and cell wall morphology was similar between Mock and ISX treatments, while there was cell wall degradation and cell detachment observed during Dri treatment ( Supplementary Fig. S8A – C ). We next examined four parameters of Golgi and TGN ultrastructure, including the length of Golgi cisterna, the diameter of the margins of trans -Golgi cisternae (a measure of vesicle formation), and the diameter of TGN vesicles at both the GA-TGN and the GI-TGN ( Supplementary Fig. S8G ). There were no differences in Golgi ultrastructure between treatments ( Supplementary Fig. S8H , I ), but for Dri treatment, there was a significant increase in GA-TGN vesicle diameter ( Fig. 2G ). Together, these results suggest that Golgi and TGN number are unchanged following ISX or Dri treatment, but short-term treatment increases the size of Golgi bodies following either ISX or Dri, and increases the size of the GA-TGN following Dri treatment. We next asked whether anterograde secretion to the plasma membrane and cell wall was impacted by ISX or Dri treatment. Since there are currently no methods to track polysaccharide secretion from the Golgi apparatus directly using live-cell imaging, we used a ratiometric secreted GFP (ratiosec–GFP) marker, in which a vacuolar-targeted RFP is produced in equimolar amounts to a secreted form of GFP ( Samalova et al. , 2006 ), to quantify protein secretion of GFP to the apoplast ( Supplementary Fig. S9 ). Short-term 4 h and 24 h treatments of ISX or Dri showed increased secretion of GFP, while constitutive treatments had only a minor effect. Since the accumulation of GFP in the apoplast is pH-sensitive, and cell wall integrity signalling can increase the pH of the apoplast ( Kesten et al. , 2019 ), we decided to confirm these results by assessing the real-time secretion of the plasma membrane protein PIP2A–GFP, a putative aquaporin ( Cutler et al. , 2000 ), using FRAP experiments ( Fig. 3A ; Supplementary Fig. S10 ). PIP2A–GFP was previously shown to be a good marker for de novo secretion, as it shows very limited diffusion in the plasma membrane ( Luu et al. , 2012 ). Interestingly, both 4 h and 24 h ISX treatments showed a significant increase in fluorescence recovery 30 min after photobleaching, relative to Mock treatment, with 4 h Dri treatment also showing a significant increase in recovery ( Fig. 3B , C ).  PIP2A–GFP fluorescence recovery at the plasma membrane is increased with isoxaben (ISX) or Driselase (Dri). (A) Representative images of pre-bleach, bleach, and 15–30 min recovery of PIP2A–GFP fluorescence (white) in 5-day-old root elongation zone epidermal cells. The bleached region is outlined by a dashed white circle. Scale bars are 5 µm. (B) Mean fluorescence recovery curves of PIP2A–GFP following bleaching. (C) Plateau value, the fluorescence intensity at which the fluorescence recovery after photobleaching (FRAP) curve levels off, normalized to the pre-bleach value, following bleaching. n >5 regions of interest from five biological replicates. Letters indicate significantly different means using a one-way ANOVA with Dunn’s post-hoc test with Bonferroni correction, P <0.05. While PIP2A–GFP exhibits low diffusion in the plasma membrane under standard conditions ( Luu et al. , 2012 ), previous work showed that the lateral mobility of plasma membrane-localized proteins increased following separation of the plasma membrane from the cell wall via plasmolysis or cell wall degradation ( Feraru et al. , 2011 ; Martinière et al. , 2012 ), and ISX treatment decreased the total range of movement of proteins ( Martinière et al. , 2012 ). We therefore performed FRAP experiments using LTI6B–GFP ( Cutler et al. , 2000 ), a single-pass transmembrane protein that shows fast lateral diffusion in the plasma membrane ( McKenna et al. , 2019 ), to evaluate whether changes to cell wall integrity following ISX or Dri treatment might affect plasma membrane protein diffusion and complicate our interpretation of the PIP2A–GFP data. Short-term ISX treatment, as well as 5 d Dri treatment, reduced the recovery of LTI6B–GFP in the bleached region after 2 min ( Supplementary Fig. S11 ), providing evidence that short-term ISX and constitutive Dri treatment reduces the mobility of LTI6B–GFP in the plasma membrane. Therefore, changes to lateral diffusion of plasma membrane-localized proteins are unlikely to have contributed to the increased recovery of PIP2A–GFP at the plasma membrane. Together, these results provide evidence that bulk secretion of proteins, and presumably cell wall material, is stimulated following short-term ISX or Dri treatment. Cell wall integrity responses decrease endocytic traffickingGiven our results that cell wall modification by ISX or Dri increased anterograde trafficking, we next assessed the retrograde trafficking pathway by imaging the late endosome (LE) marker WAVE7–RFP, which labels RabF2a ( Geldner et al. , 2009 ) ( Fig. 4A ; Supplementary Fig. S12A ). Twenty-four hours of ISX treatment increased LE size ( Fig. 4B ) but decreased the number of organelles ( Fig. 4C ), while there were no consistent trends for Dri treatment. No apparent changes were observed to LE ultrastructure using TEM images ( Supplementary Fig. S8K – M ), but this may be due to the earlier time point of high-pressure frozen seedlings for TEM (4 h) versus the later changes observed using fluorescence imaging (24 h). To monitor initial endocytosis from the plasma membrane, we quantified the uptake of the lipophilic dye FM1-43 ( Emans et al. , 2002 ) following ISX or Dri treatment ( Fig. 4D ; Supplementary Fig. S12B ). There were no significant differences for FM1-43 uptake within the first 5 min for any treatment, indicating that the initial steps of endocytosis are unaffected by these treatments ( Supplementary Fig. S12C ), but from 15–30 min there was a significant decrease in internal FM1-43 signal for 24 h and 5 d treatments of ISX or Dri ( Supplementary Fig. S12D ). After 60 min, FM1-43 uptake was significantly reduced in short-term ISX and 5 d Dri treatments ( Fig. 4E ). These results suggest that while the initial steps of endocytosis from the plasma membrane are unaffected following ISX or Dri treatment, the rate of endocytic trafficking from the early endosome to the late endosome and/or from the late endosome to the vacuole is reduced for short-term ISX and constitutive Dri treatments.  Late endosome (LE) size is increased with isoxaben (ISX) treatment, and endocytic trafficking is reduced following ISX or Driselase (Dri) treatment. (A) Representative maximum-projection images of WAVE7–RFP LEs from 5-day-old, light-grown root elongation zone epidermal cells. (B) LE size. (C) LE number. n >45 regions of interest from 14 biological replicates. (D) Representative images of FM1-43 endocytosis in 5-day-old, light-grown root elongation zone epidermal cells after 5, 15, 30, or 60 min. Images from 5–30 min represent the same cell over a time progression, while images at 60 min represent different roots. (E) Quantification of plasma membrane (PM):internal ratio of FM1-43 after 60 min of endocytosis. n =17–24 cells from six biological replicates. Letters represent significantly different means using a one-way ANOVA and Dunn’s post-hoc test with Bonferroni correction, P <0.05. Scale bars are 2 µm for (A) and 5 µm for (D). Disrupting cell wall integrity decreases organelle movement and dynamics of the actin cytoskeletonDuring the live-cell imaging of the Golgi apparatus, TGN, and LE, we observed that organelle movement was reduced by ISX or Dri treatment. These results are similar to the reduced Golgi body movement following ISX treatment observed by Gutierrez et al. (2009) . We quantified these using the Golgi marker NAG–GFP ( Fig. 5 ; Supplementary Fig. S13A ) and the LE marker WAVE7–RFP ( Supplementary Fig. S13B , C ). Both organelles showed significantly decreased speed following short-term ISX or 24 h Dri treatments. This effect was reversible, as 24 h ISX or Dri treatment followed by a 2 h wash-out in ½ MS medium significantly increased the movement of Golgi relative to 24 h-treated roots ( Fig. 5B ; Supplementary Fig. S13A ).  Treatment with isoxaben (ISX) or Driselase (Dri) reduces Golgi speed. (A) Representative maximum-projection images from time lapses of Golgi (NAG–GFP; green) in 5-day-old Col-0 root elongation zone epidermal cells. Three representative Golgi bodies are tracked for 30 s and are indicated by white, magenta, or blue boxes. The final images show a line trace of the movement of the Golgi over 30 s. (B) Quantification of Golgi body speed. Wash-out experiments were performed by treating 5-day-old roots with 200 nM ISX or 0.05% Dri for 24 h, then moving them to normal ½ MS medium for 2 h prior to imaging. Scale bars are 2 µm. Letters represent significantly different values using a one-way ANOVA with Tukey’s test, P <0.01. n >78 Golgi/treatment, from six biological replicates. Due to the association between organelle movement and the actin cytoskeleton ( Nebenführ et al. , 1999 ), we hypothesized that the changes in organelle movement might be due to changes to actin. We therefore imaged actin via fABD2–GFP, the fluorescently tagged f-actin binding domain of FIMBRIN1 ( Sheahan et al. , 2004 ), following ISX or Dri treatment ( Fig. 6A ; Supplementary Fig. S14A ). Actin occupancy (density, or a measure of local abundance) was significantly reduced in 24 h and 5 d treatments of ISX or Dri ( Fig. 6B ). Using a Pearson’s correlation coefficient-based method to determine bulk actin remodelling and dynamics ( Vidali et al. , 2010 ), we found that actin remodelling was significantly reduced by short-term treatment of ISX or Dri ( Fig. 6C , D ; Supplementary Fig. S14B ). These results suggest that cell wall modification from ISX or Dri treatment impacts the organization and dynamics of the actin cytoskeleton, which may underlie the reduced organelle speeds that we observed.  Cortical actin occupancy and dynamics are decreased following isoxaben (ISX) or Driselase (Dri) treatment. (A) Representative maximum-projection images of 5-day-old fABD2–GFP root elongation zone epidermal cells. (B) Quantification of cortical actin occupancy (density). n >25 regions of interest for eight biological replicates. Letters represent significantly different means using a one-way ANOVA and Dunn’s post-hoc test with Bonferroni correction, P <0.05. (C) Representative maximum-projection images of fABD2–GFP actin filaments at 0 s (green), 30 s (magenta), and 60 s (cyan), with overlaid image. The amount of overlap of the three colours indicates degree of actin dynamics over 60 s. (D) Pearson’s correlation coefficient to quantify dynamics of actin over 60 s. A high Pearson’s correlation coefficient indicates low dynamics (actin filaments do not change over time), whereas a low Pearson’s correlation coefficient indicates increased dynamics. n =42 regions of interest from 14 biological replicates. Asterisks indicate significantly different means from Mock-treated seedlings at 5, 30, and 55 s using a one-way ANOVA and Dunn’s post-hoc test with Bonferroni correction, P <0.05. Scale bars are 5 µm for (A) and 2 µm for (C). To further connect the reduced actin dynamics with slower organelle movement, we treated seedlings with the actin depolymerizing drug LatrunculinB (LatB; Baluška et al. , 2001 ). LatB treatment depolymerized the actin cytoskeleton as visualized by fABD2–GFP ( Supplementary Fig. S15A ) and significantly reduced Golgi body speed ( Supplementary Fig. S15B , C ). To test whether actin remodelling is important for the response to ISX or Dri, we co-treated seedlings with LatB and either ISX or Dri and measured root length after 4 h or 24 h treatment ( Supplementary Fig. S15D ). Co-treatment of ISX+LatB or Dri+LatB did not significantly impact root length at any time point relative to ISX or Dri treatment alone, indicating that actin remodelling is not strictly required following cell wall integrity disruption via ISX or Dri treatment. Changes to cell wall integrity triggered by isoxaben or Driselase treatment impact overlapping intracellular processes to increase secretionIn this work we provide evidence that cell wall modification broadly impacts cell morphology, endomembrane system structure and function, and organization and dynamics of the actin cytoskeleton ( Fig. 7 ). We propose a model for how root cells respond to short-term cell wall modification following ISX or Dri treatment ( Fig. 8 ). ISX treatment inhibits cellulose biosynthesis and activates cell wall signalling, perhaps through a mechanosensitive mechanism ( Hamann et al. , 2009 ; Engelsdorf et al. , 2018 ). The weakening of the cell wall observed following ISX treatment ( Bacete et al. , 2022 ) is caused by rapid internalization of CESAs from the plasma membrane ( Paredez et al ., 2006 ) and consequently reduced cellulose production ( Hamann et al. , 2009 ). The impact of ISX has been shown to be tissue-dependent and conditional on nutrient and sucrose concentration in the medium ( Engelsdorf et al. , 2018 ; Ogden et al. , 2023 ). Dri weakens the cell wall via digestion of structural polysaccharides ( Zhang et al. , 2019 ), presumably triggering mechanosensitive mechanisms and also causing release of small cell wall oligosaccharides from cellulose ( Tseng et al. , 2022 ; Martín-Dacal et al. , 2023 ) or pectin ( Voxeur et al. , 2019 ) that may bind to cognate receptors at the plasma membrane. Both treatments reduced actin dynamics, decreased organelle movement, and increased secretion while decreasing endocytic trafficking. Consistent with the altered trafficking pathways, organelle number and morphology were impacted, including increased LE size after ISX treatment, larger GA-TGN vesicles following Dri treatment, and larger Golgi bodies after both treatments. Interestingly, most of the changes observed under short-term modification were not seen in the constitutive treatments ( Fig. 7 ), indicating that plant cells can habituate to low levels of cell wall signalling and/or cell wall stress over longer periods.  Summary of spinning disk confocal and TEM imaging results from short-term and constitutive ISX and Dri treatment. The percentage change from Mock-treated seedlings is indicated, and the relative intensity of the change is visualized by a heatmap, where red indicates increased values relative to Mock-treated, white indicates no change from Mock-treated, and blue indicates decreased values relative to Mock-treated. Significant differences ( P <0.05) from Mock-treated are denoted by asterisks. GA-TGN, Golgi-associated trans -Golgi network; GI-TGN, Golgi-independent trans -Golgi network; LE, late endosome; n.d., not determined; TEM, transmission electron microscopy.  Proposed model for how short-term cell wall integrity signalling triggered by isoxaben (ISX) or Driselase (Dri) impacts endomembrane system structure and function. Under ISX treatment, reduced cellulose synthesis presumably activates cell wall integrity signalling via receptors, which transduce intracellular signals. Golgi body and late endosome size is increased, while organelle movement significantly slows due to, in part, reduced actin dynamics. The rate of secretion increases, while the rate of endocytic trafficking decreases. Under Dri treatment, breakdown of cellulose and matrix polysaccharides activates cell wall integrity signalling. Golgi and GA-TGN size increases. Organelle movement and actin dynamics are decreased, and the rate of secretion is increased while rate of endocytic trafficking is decreased. GA-TGN, Golgi-associated trans -Golgi network; GI-TGN, Golgi-independent trans -Golgi network; PM, plasma membrane. Cell wall integrity responses impact organelle morphology and movementWe hypothesized that remodelling of intracellular processes, including production and secretion of new cell wall components, would occur between 4 and 24 h of cell wall modification. This was based on previous time course experiments in roots that indicated a transcriptional response after 3–4 h of ISX treatment ( Hamann et al. , 2009 ), production of phytohormones by 7 h ( Engelsdorf et al. , 2018 ), and altered cell wall composition by 12 h ( Denness et al. , 2011 ). The precise time course following Dri treatment is less established, but severe root tip degradation and increased phytohormone levels were seen by 7 h and altered cell wall composition by 24 h ( Engelsdorf et al. , 2018 ). Golgi and TGN number, size, and ultrastructure have been shown to change in response to increased polysaccharide production ( Young et al. , 2008 ; Wang et al. , 2017 ; Meents et al. , 2019 ) and stress conditions ( Uemura et al ., 2019 ), so we first evaluated the ultrastructure of the Golgi apparatus and TGN. We hypothesized that GI-TGN number might be affected, specifically under Dri treatment, as cell wall damage and infection by powdery mildew increased the number of GI-TGNs ( Uemura et al ., 2019 ). Unexpectedly, cell wall modification induced by ISX or Dri did not impact Golgi body or TGN number. Short-term ISX and Dri treatment increased Golgi body size, and Dri treatment specifically increased the size of GA-TGNs ( Fig. 2 ), which is similar to the increased Golgi body and TGN size observed in cells undergoing higher rates of cell wall biosynthesis and secretion ( Young et al. , 2008 ; Meents et al. , 2019 ). Despite observing no changes to TGN structure here, the TGN is important for ISX response, as mutants with defective TGN function were hypersensitive to ISX ( Brüx et al. , 2008 ). Besides the changes to the Golgi apparatus and TGN, 24 h ISX treatment increased the size of LEs while decreasing the number of LEs. Both biotic and abiotic stress can impact the rate of endocytosis or secretion. For example, increased secretion of cell wall components and defence compounds was observed following pathogen infection ( Chowdhury et al. , 2014 ; Uemura et al ., 2019 ), and multiple studies have shown that osmotic ( Zwiewka et al. , 2015 ) or salt ( Luu et al. , 2012 ; Baral et al. , 2015 ) stresses can impact the rate of secretion or endocytosis. Furthermore, increased CESA enzyme secretion from the Golgi apparatus to the plasma membrane is required as part of cell wall fortification in response to cell wall integrity stresses, such as ISX treatment, and mutants with defects in this response are hypersensitive to ISX ( McFarlane et al. , 2021 ; Vellosillo et al. , 2021 ). Altering the flux between anterograde or retrograde trafficking could modulate cell size and water content by adjusting the amount of membrane at the plasma membrane or changing the concentration of ion transporters or aquaporins ( Zwiewka et al. , 2015 ). Following short-term treatment of ISX or Dri, we observed a significant increase in secretion of PIP2A–GFP to the plasma membrane ( Fig. 3 ) and secreted GFP to the apoplast ( Supplementary Fig. S9 ), suggesting that bulk secretion pathways were stimulated. Although we cannot exclude that increased PIP2A–GFP recovery could be due to changes to protein biosynthesis, the large increase in fluorescence recovery at the earliest time point following ISX or Dri treatment suggests it is not due to alterations in transcription or protein biosynthesis. There was also a significant decrease in the rate of FM1-43 endocytic trafficking ( Fig. 4E ) after 15–60 min. Increased secretory rates and decreased endocytic trafficking rates were also observed after 10 min in root cells during hypoosmotic stress ( Zwiewka et al. , 2015 ), which causes cell swelling similar to ISX or Dri treatment, and there is a complex relationship between responses to changes to cell wall integrity and osmotic stress ( Hamann et al. , 2009 ; Engelsdorf et al. , 2018 ). Therefore, it would be interesting to investigate the role of osmotic changes in cell wall responses in the future. Together, our results indicate that the balance between secretion and endocytic trafficking is adjusted when cell wall integrity is perturbed, presumably to allow cell wall fortification. Disrupting cell wall integrity may indirectly modify the actin cytoskeleton to compound impacts on intracellular trafficking and secretionPrevious studies have examined the effects of ISX on microtubule organization. Although ISX had no effect on in vitro microtubule polymerization ( Fisher and Cyr, 1998 ), short-term ISX treatments, similar to our 4 h treatment, resulted in minor microtubule reorientation, from longitudinal to oblique orientation in root elongation zone cells ( Paredez et al ., 2008 ). This reorientation may be the result of the mechanical equilibrium between cellulose synthesis and microtubule organization ( Schneider et al ., 2022 ). Genetic disruption of cellulose synthesis did not affect microtubule orientation in the short term, but microtubule reorganization was observed after the onset of cell swelling, after 24 h ( Sugimoto et al ., 2001 ). The effect of Dri treatment on microtubules has not been examined, but microtubules are sensitive to physical signals from the cell wall ( Hardham et al. , 2008 ), which may be impacted by cell wall digestion through Dri. During the live-cell imaging, we observed that organelle movement and actin dynamics were significantly reduced following short-term treatments of ISX or Dri, with organelles being almost immobile following 24 h ISX treatment, but that this movement significantly recovered after 2 h wash-out ( Fig. 5 ). This is similar to the decreased actin dynamics seen in mature rosette cells following ISX treatment ( Tolmie et al. , 2017 ). An altered actin cytoskeleton has also been shown to decrease the rate of endocytosis of the dye FM4-64 ( Sampathkumar et al. , 2013 ), which could also explain the reduced endocytic trafficking observed in this study following short-term ISX or Dri treatment. However, actin remodelling was not strictly required for plant growth responses under ISX or Dri treatment ( Supplementary Fig. S14 ). While this study has informed on the various intracellular changes that occur at different time points following cell wall modification, the underlying mechanisms for how these processes happen are still unknown. Changes to the morphology and function of the endomembrane system following cell wall modification could be mediated through direct and indirect mechanisms. For example, the small GTPases ROP1 and ROP6 are implicated in actin cytoskeleton regulation and trafficking of endomembrane vesicles ( Chen et al. , 2012 ; Venus and Oelmüller, 2013 ). Recent work has shown that the cell wall integrity sensor FERONIA (FER) is upstream of ROP6 activity following mechanosensing ( Tang et al. , 2022 ), changes to pectin methylesterification status ( Lin et al. , 2022 ), or osmotic stress ( Smokvarska et al. , 2023 ). Therefore, future work could examine whether the reduced dynamics of the actin cytoskeleton following ISX or Dri treatment is FER- and/or ROP6-dependent. Together, the results from this work indicate that activation of cell wall integrity responses impacts cell morphology, plasma membrane dynamics, structure and function of the endomembrane system, and organization and movement of the actin cytoskeleton. These internal changes could provide mechanisms to produce new cell wall components to fortify the cell wall and protect the cell from bursting when cell wall integrity is compromised. The following supplementary data are available at JXB online. Fig. S1. Summary of previous research examining short-term impact of ISX on Arabidopsis seedlings. Fig. S2. Constitutive growth on ISX reduces root and hypocotyl growth and impacts tissue morphology. Fig. S3. Short-term treatment of 200 nM ISX impacts growth and cell morphology. Fig. S4. Constitutive growth on Dri reduces growth and alters tissue morphology in light-grown roots. Fig. S5. Short-term treatment of 0.05% Dri impacts plant growth and cell morphology. Fig. S6. ISX and Dri cause cell swelling, but heat-inactivated Dri has only minor effects. Fig. S7. Other time points and parameters examining impact of ISX or Dri on the Golgi and TGN. Fig. S8. Additional TEM images and quantification. Fig. S9. ISX and Dri treatment impact secretion to the apoplast. Fig. S10. Additional data for PIP2A–GFP FRAP. Fig. S11. LTI6B–GFP FRAP following ISX or Dri treatment. Fig. S12. Additional time points for LE size and number, and endocytic trafficking of FM1-43. Fig. S13. Additional time points for movement of Golgi and measurements of LE speed following ISX or Dri treatment. Fig. S14. Additional images for cortical actin organization and dynamics following ISX or Dri treatment. Fig. S15. LatB depolymerizes actin filaments, reduces Golgi speed, and impacts plant growth, but does not exacerbate cell wall integrity signalling-induced phenotypes. Table S1. Fluorescent lines used for imaging. AbbreviationsCELLULOSE SYNTHASE fluorescence recovery after photobleaching Golgi-associated trans -Golgi network Golgi-independent trans -Golgi network late endosome LatrunculinB propidium iodide transmission electron microscopy trans -Golgi network We would like to thank the CSB Imaging Facility and the SickKids Nanoscale Biomedical Imaging Facility for their technical support and advice. NH and HEM were involved in project conceptualization. NH, EM, and HEM performed the formal analyses. NH generated the methodology and performed the data visualization. NH wrote the original draft of the manuscript, and NH, EM, and HEM contributed to reviewing and editing. HEM was involved in funding acquisition and supervision. The authors declare they have no conflict of interest. HEM is the Canada Research Chair in Plant Cell Biology. This work was supported by the Natural Sciences and Engineering Research Council of Canada NSERC Discovery Grant (2020-05959), Canada Foundation for Innovation and the Ontario Research Fund grants (38721), and an Ontario Early Researcher Award (ER21-16-256) to HEM, an NSERC Canada Doctoral Scholarship and an Ontario Graduate Scholarship to NH. The data underlying this article will be shared upon request to the corresponding author. Anderson CT , Kieber JJ. 2020 . Dynamic construction, perception, and remodeling of plant cell walls . Annual Review of Plant Biology 71 , 39 – 69 . Google Scholar Bacete L , Hamann T. 2020 . The role of mechanoperception in plant cell wall integrity maintenance . Plants 9 , 574 . Bacete L , Schulz J , Engelsdorf T , et al. . 2022 . THESEUS1 modulates cell wall stiffness and abscisic acid production in Arabidopsis thaliana . Proceedings of the National Academy of Sciences, USA 119 , e2119258119 . 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Low-cost and reliable substrate-based phenotyping platform for screening salt tolerance of cutting propagation-dependent grass, paspalum vaginatum- Zhiwei Liu 1 , 2 , 3 , 4 na1 ,
- Wentao Xue 1 , 2 , 3 , 5 na1 ,
- Qijuan Jiang 2 , 6 ,
- Ademola Olufolahan Olaniran 4 &
- Xiaoxian Zhong 1 , 2 , 3 , 5
Plant Methods volume 20 , Article number: 94 ( 2024 ) Cite this article 111 Accesses 1 Altmetric Metrics details Salt tolerance in plants is defined as their ability to grow and complete their life cycle under saline conditions. Staple crops have limited salt tolerance, but forage grass can survive in large unexploited saline areas of costal or desert land. However, due to the restriction of self-incompatible fertilization in many grass species, vegetative propagation via stem cuttings is the dominant practice; this is incompatible with current methodologies of salt-tolerance phenotyping, which have been developed for germination-based seedling growth. Therefore, the performance of seedlings from cuttings under salt stress is still fuzzy. Moreover, the morphological traits involved in salt tolerance are still mostly unknown, especially under experimental conditions with varying levels of stress. To estimate the salt tolerance of cutting propagation-dependent grasses, a reliable and low-cost workflow was established with multiple saline treatments, using Paspalum vaginatum as the material and substrate as medium, where cold stratification and selection of stem segments were the two variables used to control for experimental errors. Average leaf number (ALN) was designated as the best criterion for evaluating ion-accumulated salt tolerance. The reliability of ALN was revealed by the consistent results among four P. vaginatum genotypes, and three warm-season (pearl millet, sweet sorghum, and wild maize) and four cold-season (barley, oat, rye, and ryegrass) forage cultivars. Dynamic curves simulated by sigmoidal mathematical models were well-depicted for the calculation of the key parameter, Salt 50 . The reliability of the integrated platform was further validated by screening 48 additional recombinants, which were previously generated from a self-fertile mutant of P. vaginatum . The genotypes displaying extreme ALN-based Salt 50 also exhibited variations in biomass and ion content, which not only confirmed the reliability of our phenotyping platform but also the representativeness of the aerial ALN trait for salt tolerance. ConclusionsOur phenotyping platform is proved to be compatible with estimations in both germination-based and cutting propagation-dependent seedling tolerance under salt stresses. ALN and its derived parameters are prone to overcome the species barriers when comparing salt tolerance of different species together. The accuracy and reliability of the developed phenotyping platform is expected to benefit breeding programs in saline agriculture. Key messageA novel phenotyping system was developed to screen for salt tolerance of erect stems of Paspalum vaginatum. IntroductionSalinity is a major abiotic stress in agricultural regions, aggravated by large quantities of industrial pollution, excessive use of chemical fertilizers, inappropriate irrigation [ 1 ], and more recently, climate change induced by global warming [ 2 , 3 ]. Therefore, the mechanisms of salt tolerance in plants, involving myriad pathways and genes, remain a top issue for researchers dealing with crop failure under salinization [ 4 ]. Crop yields are still limited by high soil salinity [ 5 ], despite advances in genomic editing technology [ 6 , 7 , 8 , 9 ]. A complementary plan for land utilization in coastal or desert saline regions might involve the planting of salt-tolerant grass species for forage production [ 10 ]. In the major sexually propagated forage cultivars, such as silo corn [ 11 ], sweet sorghum, millet [ 12 ], barley, oat, rye, and ryegrass [ 13 ], seed germination and seedling growth uniformity can be finely controlled artificially by, for example, seed priming [ 14 ] or warm/cold stratification at the initial growth stage [ 15 , 16 ]. However, forage grasses such as Paspalum vaginatum , Pennisetum purpureum , and Miscanthus sacchariflorus are only weakly self-fertile and their cultivation depends on vegetative propagation, which lacks growth-stage uniformity and subsequently, confounds experimental repeatability. Seedling tolerance to stresses has been widely investigated in hydroponic systems, which are operationally convenient for controlling salinity, but are disadvantageous for root development since growth in most grass cultivars is aerobic. Moreover, evaporation results in fluctuations in ion concentration, leading to inconsistent stress levels and the need for frequent solution replacements, subsequently raising costs. Alternatively, soil-based potting suits root growth, but lack the ability to control salt concentration, thereby weakening data reliability [ 17 ]. These disadvantages have been further revealed by comparing salt tolerance in salt-containing hydroponics and saline soil, where expression of tolerance in the former was not a reliable criterion for the latter [ 18 ]. Substrate-based incubation has been successfully applied to phenotype root architecture [ 19 ] and frost tolerance [ 20 ], and more recently, seedlings under salt stress [ 21 , 22 ], indicating its potential as a better medium than field soil or sand. Stress-induced morphological responses (SIMR) at the anatomical level include inhibition of cell elongation, localized stimulation of cell division, and alterations in cell-differentiation status [ 23 ]. At the morphological level, responses to salt stress are reflected in plant height and biomass, although the reliability of these indicators is still under debate [ 18 ]. Additional scores and scales for growth stages under salt stress have been well-developed for monocotyledons [ 24 ], the model plant Arabidopsis [ 25 ], and barley [ 26 ], mainly based on the appearance and number of leaves in the vegetative stage. Phenotyping of seedlings under salt stress is still subject to methodological limitations [ 27 ], where seedling tolerance involves calculating their indices or scores relative to control conditions [ 18 ] to minimize the confounding effect of variations among non-stressed seedlings. However, single stress treatments might not be sufficient to extract the comprehensive characteristics of tolerance dynamics under increasing salt concentrations [ 28 ], hence affecting both genetic analyses and breeding efforts toward enhanced salt tolerance [ 27 ]. On the other hand, sigmoidal mathematical models have been previously applied to describe seed dormancy and germination, as well as germination under salt stress, and key parameters of the simulated curves have been extracted for further genetic analyses [ 28 , 29 ]. However, the growth dynamics of seedlings derived from cutting propagation are less described by mathematical models, which also have not been adopted for cutting propagation-dependent seedling growth under saline conditions, thus confounding the dissection of major variables controlling their growth behaviors. Materials and methodsTo develop a low-cost and reliable phenotyping screening platform for not only seed germination-based but also cutting propagation-dependent seedling tolerance under salt stress, in the present study, we compared genotypes of the cutting propagation-dependent grass, Paspalum vaginatum , along with seed germination-based warm-season and cold-season grass cultivars for salt stress in a novel system which uses substrate as the medium, selected stem segments as the material, and mathematical simulation curves under multiple stresses as the basis for salt-tolerance estimations. The different comparisons revealed two dominant factors in controlling experimental errors for cutting propagation-dependent grass and a reliable criterion for salt tolerance. Genotypes of P. vaginatum and warm/cold-season grass cultivarsWe used P. vaginatum cultivar Adalayd and its related mutagenic offspring SP2, SP3 and SPD1 for salt-tolerance screening, in parallel with warm-season grasses: pearl millet ( Pennisetum glaucum cv. Wanshu), wild maize ( Purus frumentum cv. Huafeng3), sweet sorghum ( Sorghum bicolor cv. Big Kahuna), and cold-season grasses: barley ( Hordeum vulgare cv. Morex), oat ( Avena sativa cv. Baiyan2), rye ( Secale cereale cv. Dongmu70) and ryegrass ( Lolium perenne cv. Petrel). The phylogeny of P. vaginatum is schematized in Additional file 1, where genotypes of SP2 and SP3 are the self-compatible M 1 generation, and SPD1 is a dwarfed M 2 individual separated from SP3 seeds. Forty-eight M 2 recombinants harvested from SP3 were also screened for salt tolerance. All of this material was conserved and provided by the Grass Germplasm Bank of Jiangsu Province, China. Workflow of substrate-based phenotyping system for salt-tolerance screening of erect stems of P. vaginatumA seedling tray was used to propagate cuttings of P. vaginatum (Fig. 1 ). Each tray was composed of a base to hold the solution, a 12-hole seedling plate and a transparent cover. Dry soil substrate from Pindstrup Plus Orange (100% blonde peat; 100 g) blended with 100 ml fertilizer solution (Kyle Soluble N-P-K Fertilizer/water = 1/1000) was used to fill each hole in the seedling plate; the plate was then immersed in 400 ml of the same fertilizer solution (Fig. 1 A). Once the substrate was saturated, a maximum of 9 erect stems were embedded in each seedling hole dispersively (Fig. 1 B, Step 1). The cover was closed and the tray was placed in the dark at 7 ℃ for 8 days of cold stratification (Fig. 1 , Step 2), then incubated in a chamber with day/night conditions of 26/18 ℃ and a 14/10 h photoperiod (Fig. 1 , Step 3).  Visualized workflow of substrate-based phenotyping platform for cutting propagation-dependent grasses under salt stress. A 12-hole seedling tray is used to carry the substrate (medium) to maintain the salinity levels ( A ). Erect stems of P. vaginatum are prepared in 6-cm segments for cutting propagation ( B ), with Seg2 considered optimal (Step 1). After 8-day stratification at 7 ℃ in the dark (Step 2), the setup (tray, base, and cover) is incubated under day/night conditions of 26/18 ℃ and 14/10 h photoperiod (Step 3). NaCl is applied to the solution in the base at different concentrations when the seedlings reach the first unfolded leaf stage (Step 4). The solution in the base is renewed every 4 days (Step 5 & C ). Seedlings are harvested at 20 days after treatment for trait measurements (Step 6 & D ). Data are mathematically modeled by a 3-parameter sigmoid function (Step 7 & E ), and then parameter-Salt 50 is calculated according to each simulation curve (Step 8 & F ) Once stem growth reached the first unfolded leaf stage, salt stress was applied (Fig. 1 , Step 4). Considering the strong tolerance of P. vaginatum to salt stress, we chose 100 mM, 200 mM, 300 mM, 400 mM, and 500 mM NaCl solutions for treatments, in parallel with control conditions (no NaCl added). The solution in the tray base was renewed every 4 days to maintain constant salinities (Fig. 1 , Step 5). Specifically, we refilled the base solution to the original weight with water to make up for the water lost by evaporation, then drained the base after 3 h imbibition, and refilled it with the respective solutions to the original weight (Fig. 1 C). After 20 days of incubation, seedlings were first measured for morphological traits and then harvested from plates (Fig. 1 , Step 6), and rinsed with fresh water for further analysis (Fig. 1 D). Seeds of both warm- and cold-season grass cultivars were similarly added to the surface of the imbibed substrate in the tray as described for P. vaginatum , after 30 min surface sterilization (3% hydrogen peroxide). The same cold stratification was also applied to minimize variation among treatments. The cold- and warm-season grasses reached the first unfolded leaf stage after 2 and 4 days, respectively. All grass cultivars germinated fully (> 90%) under our experimental conditions. Salt stress was applied at the one unfolded leaf stage. In the two-way experimental design, the cold stratification treatment was considered a variable, in parallel with the no-stratification condition. Considering the differences among stem internodes, different intervals of cv. Adalayd’s erect stem were taken as another variable: Segment 1 (Seg1) started upon the primordium apex, Seg2 was clipped upon the first node, and Seg3 was cut upon the second node (Fig. 1 B). All three segment types were chopped to 6 cm length, downward from their origins. In the formal workflow, we chose Seg2 as the standard for all experiments, including the validation with the 48 recombinants, and constructed four independent replicates for each P. vaginatum genotype. Morphological trait and ion content measurementsPlant height was measured as the distance from the incision to the growth apex. Leaf developmental stage was also digitalized as average leaf number (ALN) by our established scales which are illustrated in Fig. 2 and described in Table 1 . Accordingly, first leaf emergence was divided into four major scales: when the pericladium emerged from the tip of the erect stem, assigned as 0.2; when the first leaf just emerged from the pericladium – 0.5; when the first leaf extended through the pericladium – 0.8; and the first unfolded leaf was assigned the value of 1.0 (Fig. 2 A). Using a similar reasoning, the second to fifth leaves were also digitalized (Fig. 2 B). In an initial trial with cv. Adalayd, plant height and ALN were measured on selected days after the stress (DAS) was applied: DAS04, DAS08, DAS12, DAS16, DAS20, and DAS24. We selected DAS20 for the formal workflow as the day on which the experiment was terminated.  Schematics of digital scale of leaf developmental stage for average leaf number (ALN) estimate. Development of the first-leaf stage is divided into 4 scales (0.2, 0.5, 0.8, 1.0) in (A): pericladium emergence, leaf emergence, leaf extension and leaf unfolding, respectively. Values of 1.5 and 2.0 are used to mark the one-and-a-half leaf and two-leaf stages in ( A ). Accordingly, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5 and 5.0 are photographed in ( B ) The seedlings were harvested and root, stem, and leaf organs were separated manually and oven-dried for biomass measurements. Dry samples were further digested with 5 ml nitrate on a block digestion system (PerkinElmer SPB50-48) for 10 min at 70 ℃, 40 min at 130 ℃, and nitrate dry-out at 160 ℃, and 25 ml volumetric solution was filtered through a syringe (pore size = 0.45 μm). Na + , K + and Ca 2+ concentrations were measured by ICP-OES (PerkinElmer Avio200) and the corresponding ion contents were calculated by standard curves with ICP Standard Solution (Agilent, ICM-462). To measure the ion stability in the solution contained in the base, 2 ml was sampled into a digestion tube from each box after replenishing the solution with water, then dehydrated at 90 ℃. Following the above digestion procedures, 5 ml nitrate was added to the tube. Final ICP-OES intensities of Na + were calibrated by the values measured from standard solutions of 0, 100, 200, 300, 400, and 500 mM NaCl, and calculated into equivalent concentrations. The K + content was only measured by ICP intensities. Mathematical model simulations for curve dynamics and salt-tolerance calculationsMathematical modeling of seedling growth under multiple salt concentrations was conducted as previously described [ 29 ] and as illustrated in Fig. 1 E, with curves simulated by the 3-parameter sigmoid function, which best fit the six experimental observations compared to the other functions: where variables a , b and x 0 were estimated by Sigmaplot 14.0 and defined as follows: a is a limit value for Y max , b controls the shape and steepness of the simulated curve, and x 0 is the half-maximal activation level of the curve. Y max was calculated for each genotype by Eq. ( 1 ) as follows: Salt 50 represents the NaCl concentration ( x axis) at which the seedling Y max is reduced by half (Fig. 1 F), and was calculated by solving Eq. (2) as follows: The data for each treatment were averaged for further curve simulation for all of the experimental material. Two-way ANOVA was conducted using STATISTICA 7, taking stratification and segments as factors. A principal component analysis (PCA) was run with all of the collected phenotypic data using the software PAST, and graphed with GraphPad Prism 10. Pearson correlation matrix was calculated by R package “corrplot” at a significance level of p < 0.005. Two major experimental variables determining seedling performance of cutting propagation-dependent grass under salt stressFour P. vaginatum genotypes, and three warm-season and four cold-season grass cultivars were compared for salt tolerance using our substrate-based salt-stress phenotyping protocol, illustrated in Fig. 3 A. At the first unfolded leaf stage, different amounts of NaCl were added to the solution in the container base to simulate different levels of salt stress. The solution was renewed every 4 days. To verify constant solution salinities during the entire experimental stress period, solutions of each NaCl concentration were sampled at each analyzed time point for Na + and K + contents (Fig. 3 B). Both Na + and K + presented stable concentrations at all time points, confirming a reliable stress strength and adequate nutritional conditions, respectively.  Stepwise validation of major factors determining experimental errors in seedling performance of cutting propagation-dependent grass under salt stress. ( A ) The overall procedure. ( B ) Na + and K + concentrations at each solution renewal step. Squares in Na + heatmap represent concentrations, and in K + heatmap, ICP intensities. ( C ) Comparison of CVs of plant height (PH) and average leaf number (ALN) for stratification (S = stratification, NS = no stratification), and segment factor (Seg1 = segment1, Seg2 = segment2, Seg3 = segment3); ns, not significant; ** p < 0.01 (t-test); different letters indicate significant difference at p < 0.05 (Tukey HSD); uppercase and lowercase letters represent two independent comparisons. ( D ) Final seedling stems of cv. Adalayd after different treatments (S0 = no salt; S100, S200, S300, S400, S500 = 100, 200, 300, 400 and 500 mM NaCl, respectively) are shown; bar = 10 cm. ( E ) PH and ALN values of each replicate are plotted against the salinities and fitted with the 3-parameter sigmoid function for dynamic curves Preliminary trials revealed that in contrast to seed germination, growth uniformity of the cuttings propagated from the erect stem stage was not significantly related to growth conditions (data not shown). Here we considered stratification (S)/no stratification (NS), and segments (Seg1, 2, 3; Fig. 1 B) as the two major variables determining the experimental errors for stem growth after cutting propagation. The coefficients of variation (CVs) for both plant height and ALN were further tested. Plant height following S or NS showed a non-significant difference ( p = 0.5707), but the CVs of ALN after stratification vs. no stratification were significantly lower ( p = 0.0085, Fig. 3 C). In the crossed experimental design, stratification combined with Seg2 gave the lowest CVs for both plant height and ALN (Fig. 3 C). Two-way ANOVA (Additional file 2) displayed sum of squares (SS) of 86.4% and 64.5% for the stratification and segment parameters corresponding to ALN and plant height, respectively, exhibiting the dominance of stratification for the ALN trait but that of segment for plant height. The statistics suggested divided responses of the morphological traits to the different experimental variables when estimating the uniformity of seedling performance under multiple salinities. Moreover, the duration of seedling incubation was also examined by comparing six time points: DAS04, DAS08, DAS12, DAS16, DAS20, and DAS24. Plant height and ALN were respectively investigated at each time point, and further simulated by the sigmoidal function. The R 2 coefficients of the curve simulations were compared (Additional file 3). At DAS20, coefficients of the simulated curves for both morphological traits were well saturated at R 2 > 0.98, meaning that 20 days of incubation was sufficient. We validated full procedures on P. vaginatum cv. Adalayd, setting up the conditions of cold stratification, Seg2 stem, and 20 days incubation after salt stress as the formal parameters, and the final seedling propagation from erect stems is shown in Fig. 3 D. Values of plant height and ALN vs. salt concentration were plotted (Fig. 3 E) and gave dynamic sigmoid and parabola-shaped curves, respectively, suggesting their different responses to salinity. Profiling morphological dynamics under multiple salinities reveals the reliable criterion of salt toleranceThe morphological traits plant height, ALN, biomass, and Na + , K + and Ca 2+ contents of each seedling organ were plotted against salinity: 0, 100, 200, 300, 400 and 500 mM NaCl (Fig. 4 A and Additional file 4). Datasets for most of the traits were well-simulated by sigmoidal curves, except stem biomass in P. vaginatum genotypes and Ca 2+ content in all material (shown in Additional file 4). In general, all of the traits decreased with increasing salinity (Fig. 4 A), as a consequence of the Na + accumulation.  Trait dynamics vs. salinities and trait correlations among P. vaginatum genotypes, and warm-season and cold-season grass cultivars. ( A ) Plant height, average leaf number (ALN), and leaf biomass and Na + and K + contents are plotted against salinity level using the 3-parameter sigmoid function for the curve simulations. S0 = no salt; S100, S200, S300, S400, S500 = 100, 200, 300, 400 and 500 mM NaCl, respectively. ( B ) Correlation matrix of 11 traits constructed by the Pearson method; significant correlation coefficients at p < 0.005. Purple and red color refer to positive and negative correlations, respectively. PH = plant height, Bm = biomass, R = root, S = stem, L = leaf. ( C ) Linear regression analysis of the relationship between leaf Na + content and traits of PH/ALN is performed with the listed regression equations Overall, morphological traits (plant height, ALN, and leaf biomass) of the warm-season and cold-season grass cultivars exhibited steep curves in response to increasing salt strength, in contrast to the flatter trend of the P. vaginatum genotypes. Notably, the average leaf Na + content in P. vaginatum genotypes increased sharply to a maximum of 15 mg/g, compared to the drastic accumulation to 40–90 mg/g in grass cultivars except sweet sorghum and ryegrass. In contrast, leaf K + contents decreased to an average level of 20 mg/g in all grass cultivars, compared to the abundant K + resource (40 mg/g) in P. vaginatum genotypes. Looking at the individual plant types, cv. Adalayd gave the highest values of plant height and biomass but the lowest level for leaf Na + content, in contrast to the pattern of the SPD1 genotype. ALN of SPD1 was significantly higher than in other genotypes among the salt-stress treatments. In the category of warm-season grasses, sweet sorghum stood out mainly due to the distinct sigmoid curves for both morphological and ion traits. Similarly, ryegrass showed unique trends in all traits compared to the other cold-season grasses. To discover the best criterion for tolerance to accumulated ions, a Pearson correlation matrix with significance at p < 0.005 was conducted for the P. vaginatum genotypes, and the warm-season and cold-season grass cultivars (Fig. 4 B). Aside from the strong correlations displayed within groups for biomass and ion contents, plant height and ALN were both strongly negatively correlated with Na + contents of all organs. In total, 21 and 22 correlations beyond the significance threshold were achieved for plant height and ALN in all three matrixes. To further confirm the relationships between leaf Na + contents and plant height/ALN, linear regression analysis was performed with the regression equations in Fig. 4 C, resulting in robust negative dependencies, and indicating accurate representations of plant height and ALN for leaf Na + contents under salt stress. Therefore, we regarded both plant height and ALN as the “aerial” traits correlated to ion accumulation and salt tolerance. Key parameter of simulated curve can screen for P. vaginatum genotypes inheriting extreme tolerance to salinityWe used Salt 50 as the key parameter of the simulated curves to estimate the salt tolerance of the different genotypes and cultivars. The two aerial traits, plant height and ALN, were assigned for their Salt 50 calculations, and the results are compared in Fig. 5 A. For P. vaginatum genotypes, no significant differences were detected between plant height-Salt 50 and ALN-Salt 50 . However, the Salt 50 values of warm- and cold-season grasses calculated from plant height were clearly lower than those calculated from ALN. More specifically, the Salt 50 parameters varied significantly between warm- and cold-season grasses when calculated from plant height, but insignificantly when calculated from ALN. It seems that the plant height-derived Salt 50 values are divided around the general threshold of 300 mM for most of the grass cultivars, but ALN-based parameters narrowed the variation among different species.  Salt tolerance estimation for different categories of grass cultivars and recombinants of P. vaginatum offspring. ( A ) The key parameter of Salt 50 , representing salt tolerance, is calculated according to simulated curves of plant height (PH) and average leaf number (ALN), and compared among P. vaginatum genotypes (PV), and warm-season (WS) and cold-season (CS) grass cultivars; statistical significance is shown. ( B ) 48 recombinants of SP3 offspring combined with P. vaginatum genotypes and grass cultivars (warm- and cold-season cultivars). ( C ) Salt 50 values for each P. vaginatum genotype and 48 recombinants (52 in total); 4 P. vaginatum genotypes, and the extreme lines PV17 and PV74, are indicated with arrows. (D) PCA performed on 48 recombinants, using data of biomass and ion content Taking the lower CVs in the seedling replicates (Fig. 3 C) and equivalent data range on y axis among various species (Fig. 4 A) as priors, we applied ALN-dependent Salt 50 for further salt tolerance estimations. Using the aforedescribed workflow, 48 recombinants were randomly selected from a seed population of SP3 offspring to screen for salt tolerance. The Salt 50 calculated from their ALN curves are grouped in Fig. 5 B, and further arranged in ascending order by individuals (Fig. 5 C). An average Salt 50 value of 500 mM was observed for the group of SP3 offspring, which is much higher than the average of 350 mM in the grass cultivars. Three genotypes of P. vaginatum were ordered in a middle position of the SP3 seed population, leaving the SPD1 ranked in the extreme high level of salt tolerance (Fig. 5 C). Moreover, as indicated by the line extremities in Fig. 5 C, recombinants of PV74 and PV17 were also highlighted in the PCA plot (Fig. 5 D), which was constructed from plant height/ALN-independent datasets of organ biomass and Na + and K + contents. This confirmed that the key parameter Salt 50 calculated from ALN-simulation curves is valid for salt tolerance screening of populations with big sample sizes. Substrate-based platform for salt stress application as an intermediate between hydroponic cultivation and pottingTo maintain a stable pH environment, hydroponic solutions have to be renewed every 2 days in salt-stress studies, as found with rice [ 30 ], barley [ 31 ], wheat [ 32 ], and cucumber [ 33 ], and equipped with an air pump for sufficient oxygen supplementation. Strong correlation matrices can be achieved between root and shoot traits under these elaborate conditions [ 33 ]. To simplify the operational conditions, soil-like substrate has recently become popular in potting experiments for short salt-stress incubation, e.g., with maize seedlings, but abundant gene functions still have to be verified [ 21 , 22 , 34 ], even though the actual salt concentration in the substrate is irrelevant after the one-time watering to saturation. This might limit long-term screening results, especially at low salinity levels, because most of the salt is gradually taken up by the plants. In the present study, this same substrate was used as the medium in a 12-hole seedling tray with a base holding the corresponding solution (Fig. 1 A). The substrate in the plate easily absorbs the salt and other nutrients present in the solution in the base, and the tray can be separated from the base as well—a great convenience for solution renewal (Fig. 1 C). Indeed, measurements of the solution in the base confirmed stable concentrations of both Na + and K + with renewal every 4 days (Fig. 3 B). The small granular structure of the organic substrate prevents leaching from the plate and subsequently maintains strong buffering power in terms of salinities; it also creates more space between the granules, benefiting root development in comparison to pure hydroponics. In fact, substrate–solution mixtures tend to provide an intermediate status between pure hydroponics and substrate-based potting; they not only maintain a stable level of stress but are also suitable for root growth. Therefore, our use of the seedling tray and base with substrate provided stable stress levels and sufficient interspacing for root development, with no need for sophisticated procedures, thus improving experimental operability. Salt stress in cutting propagation is distinct from that in seed germinationCold stratification is frequently used to obtain uniform seedling performance in vernalization-requiring plants, such as Arabidopsis [ 35 ], most of the winter-type Triticeae [ 36 , 37 ], and some grass species [ 38 ]. However, due to its weak ability to produce seeds (except cv. Sea Spray), the flowering time of P. vaginatum is of less concern [ 39 ]. From our observations, vernalization could promote P. vaginatum growth and early flowering. Hence, it is not surprising that the seedling emergence from P. vaginatum erect stems was significantly unified by the 8-day cold treatment, as reflected in the comparison of ALN-NS and ALN-S groups (Fig. 3 C); moreover, stratification tended to be the dominant factor in controlling CVs of ALN (two-way ANOVA, Additional file 2), a novel result. Surprisingly, Seg2 was the best stem fragment for cutting propagation under salt stress, regardless of the application of stratification (Fig. 3 C). This implies that the seedling performance of erect stems is not gradually improved by lower intervals, as evidenced by fact that the CVs of ALN-S-Seg3 were not significantly reduced compared to those of Seg2. The variations caused by stem segments also could not be narrowed by improving growing conditions (data not shown). This phenomenon is probably due to the different physiological functions of stem internodes in grass, as determined genetically for sorghum [ 40 ]. The internode between the primordium and first node is believed to be the growth apex for leaf formation; its growth rate mainly up to the primordium status at sampling time is therefore dramatically altered, as is that of the internode between the second and third node, which might be responsible for stem elongation. All of these situations complicate stem cutting propagation more than do effects of seed germination. Moreover, the dynamics of leaf Na + content in stem propagation could be distinguished (Fig. 4 A), characterized by the steep increase in Na + content in the 100 mM NaCl treatment among all 4 P. vaginatum genotypes, in contrast to initial Na + increases in other grass cultivars corresponding to low salinity. It seems that leaf Na + accumulation occurs without any retention at low salinities in P. vaginatum genotypes, but somehow stagnates at a stable level (15 mg/g) responding to the salinity increases (Fig. 4 A). Here we hypothesized that the stem might take up Na + through the incisions at the early stage of cutting propagation due to the delayed root emergence, which also might limit Na + transport under high salinities. Unlikely, Na + uptake in cold/warm-season grass must be managed by the root, which is initiated first during seed germination then restricts Na + transport. These points require further confirmation. ALN and it derived parameter is more suitable for profiling stress-induced morphological responsesPlant height and biomass are easily disturbed by many subtle factors. For instance, as we discussed above, the stem fragments carrying the primordium or elongation internodes can hardly be unified for repeatability, and this certainly hinders the phenotyping of salt tolerance. This issue is reflected not only in a previous study on soybean tolerance to salt stress [ 41 ], but also in the two-way ANOVA results showing segment as a dominant factor for CVs in plant height (Additional file 2). Biomass is also frequently affected by leaf shape and size, as reported in cucumber [ 33 ] and other crops [ 42 ]. Moreover, these morphological traits do not contain the core feature of stress-induced morphological responses, especially the aspect of alterations in cell differentiation, but are more inclined to be useful for selection through breeding. In contrast, leaf number tends to reflect the actual developmental stage under both non-stress [ 43 ] and salt-stress [ 44 ] conditions, which might not be significantly disturbed by variations in meristem potential and organ shape. Based on this advantage, the dynamics of salt tolerance depicted by ALN is reflected in the most uniform curves in the comparisons of Fig. 4 A and Additional file 4, considering that both axes are calibrated on the same scale. It is prone to overcome the barriers when comparing salt tolerance of different species together. However, the ALN-based parameter displayed a higher Salt 50 than the plant height-derived Salt 50 , challenging the average threshold of salt tolerance at around 300 mM [ 45 ]. Nevertheless, significance testing for plant height-Salt 50 between warm- and cold-season grass cultivars indicated significantly lower salt tolerance in the former; this was not fully supported by our results since only the root Na + content of cold-season grasses was higher (Additional file 4), nor has it been sufficiently reported in the literature. This discrepancy might arise from the faster growth rate of warm-season grasses, resulting in higher plant height for the no-salt treatment under our incubation conditions; this does not occur with the ALN-based parameter. Moreover, ALN-based salt tolerance was validated by 48 recombinants of SP3 offspring; the extreme lines (PV17 and PV74) for ALN-Salt 50 were consistently divergent in the PCA plot (Fig. 5 C, D) using completely different datasets. Overall, ALN-derived Salt 50 might more realistically reflect salt tolerance. Halophyte or glycophyte? P. vaginatum , a potential model plant for salt-tolerance studiesDesignated as a halophyte, the strong tolerance of P. vaginatum to high salinities has been well-established [ 46 , 47 , 48 ]. Based on the average of Salt 50 calculated from the 48 recombinants, almost 500 mM NaCl solution is required to halve its leaf numbers, nearly on par with a number of halophytes if considering only the tolerated concentrations, including Thellungiella halophila (500 mM) [ 49 ], Plantago crassifolia (400 mM) [ 50 ], Puccinellia tenuiflora (400 mM) [ 51 ], and Suaeda maritima (400 mM) [ 52 ], as recently summarized [ 3 ]. However, distinct from the preference for high Na + accumulation in halophytes (higher than 45 mg/g) [ 53 ], low Na + concentrations were detected not only within our P. vaginatum genotypes (below 15 mg/g) but also in others (below 9 mg/g) [ 46 ], raising the question of whether P. vaginatum should be regarded as a type of halophyte. Definitions of halophytes are still manifold [ 54 ] in the context of salt-tolerant plants defined as ‘obligatory’ or ‘facultative’ halophytes [ 3 ]. Halophytes are believed to have begun as wild plants adapted to saline environments that were able to survive and complete their life cycle in habitats with a soil salinity equivalent to at least seawater (from our understanding). Advances in our knowledge are key to really understanding halophyte biology. Even so, typical halophytes have several similarities, one being active salt uptake under low-salt conditions, implying the existence of inherent mechanisms of constitutive stress defense and homeostasis [ 55 ]. Our results displayed active uptake of Na + , but mainly due to stem transport in the process of cutting propagation (as discussed above). It seems that P. vaginatum is able to avoid salt stress by preventing Na + import, which better fits the halotropism model of glycophytes [ 56 , 57 ]. We therefore prefer to regard P. vaginatum as a strongly salt-tolerant glycophyte turfgrass. Compared to the distant wild halophytes, the mechanism in P. vaginatum for shutting Na + out of its organs might be more constructive for salt-tolerance improvement in staple crops. To conclude, a low-cost and reliable phenotyping platform is introduced for screening not only seed germination-based but also cutting propagation-dependent seedlings’ tolerance to various levels of salt stress. P. vaginatum genotypes, and warm-season and cold-season grass cultivars were compared using this platform, taking substrate as the medium and mathematical simulation curves as the basis for salt-tolerance estimations. The procedure of cold stratification and selection of stem segments were considered two principals in controlling experimental errors. Among morphological traits, ALN and its derived parameter Salt 50 were designated as the best criteria for evaluating salt tolerance. The integrated platform was also further tested by screening 48 recombinants, where the genotypes displaying extreme ALN-based salt tolerance were also highlighted in the datasets of biomass and ion content, confirming the reliability of our phenotyping platform, as well as the reproducibility of ALN as an indicator of salt-tolerance. The accuracy and reliability of this phenotyping platform is expected to benefit breeding programs in saline agriculture. Data availabilityThe datasets used and/or analyzed during the current study are available from the corresponding authors on reasonable request. Munns R, Tester M. Mechanisms of salinity tolerance. Annu Rev Plant Biol. 2008;59(1):651–81. Article CAS PubMed Google Scholar Daneshmand H, Alaghmand S, Camporese M, Talei A, Yeh PJF, Daly E. Long-term impacts of partial afforestation on water and salt dynamics of an intermittent catchment under climate change. Water. 2020;12(4):1067. Article Google Scholar Grigore MN, Vicente O. 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This work was supported by Innovation and Popularization of Forestry Science and Technology program grants from the Jiangsu Forestry Bureau in China (No. LYKJ [2021]23), by Central Financial Fund for Forestry Science and Technology Demonstration (No. SU [2023]TG12) and by the foundation of Grass Germplasm Bank from the Jiangsu Forestry Bureau in China. Author informationZhiwei Liu and Wentao Xue these authors contributed equally to this work. Authors and AffiliationsNational Forage Breeding Innovation Base (JAAS), Nanjing, P. R. China Zhiwei Liu, Wentao Xue & Xiaoxian Zhong Institute of Animal Science, Jiangsu Academy of Agricultural Sciences, Nanjing, P. R. China Zhiwei Liu, Wentao Xue, Qijuan Jiang & Xiaoxian Zhong Key Laboratory for Crop and Animal Integrated Farming of Ministry of Agriculture and Rural Affairs, Nanjing, P. R. China College of Agriculture, Engineering and Science, University of KwaZulu-Natal, Durban, South Africa Zhiwei Liu & Ademola Olufolahan Olaniran Key Laboratory of Saline-Alkali Soil Improvement and Utilization (Coastal Saline-Alkali Lands), Ministry of Agriculture and Rural Affairs, Nanjing, P.R. China Wentao Xue & Xiaoxian Zhong College of Agro-Grassland Science, Nanjing Agricultural University, Nanjing, P. R. China Qijuan Jiang You can also search for this author in PubMed Google Scholar ContributionsX.Z. and W.X. provided the material, Z.L., W.X., and Q.J. designed and performed the experiments, W.X. analyzed the data and wrote the manuscript, X.Z. and A.O.O. edited the manuscript. All authors read and approved the final manuscript. Corresponding authorsCorrespondence to Ademola Olufolahan Olaniran or Xiaoxian Zhong . Ethics declarationsEthics approval and consent to participate. The authors declare that the experiments comply with the current laws of P. R. of China and Republic of South Africa. Consent for publicationCompeting interests. The authors declare that they have no competing interests. Additional informationPublisher’s note. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Electronic supplementary materialBelow is the link to the electronic supplementary material. Supplementary Material 1Supplementary material 2, supplementary material 3, supplementary material 4, rights and permissions. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . The Creative Commons Public Domain Dedication waiver ( http://creativecommons.org/publicdomain/zero/1.0/ ) applies to the data made available in this article, unless otherwise stated in a credit line to the data. Reprints and permissions About this articleCite this article. Liu, Z., Xue, W., Jiang, Q. et al. Low-cost and reliable substrate-based phenotyping platform for screening salt tolerance of cutting propagation-dependent grass, paspalum vaginatum . Plant Methods 20 , 94 (2024). https://doi.org/10.1186/s13007-024-01225-z Download citation Received : 30 December 2023 Accepted : 11 June 2024 Published : 19 June 2024 DOI : https://doi.org/10.1186/s13007-024-01225-z Share this articleAnyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative - Salt tolerance
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There are two concepts we need to understand in experimental error, ... the percent of the total number of measurements within one to three standard deviations from the mean. Note from the right side of the above Figure, 68.2% of data is within one standard deviation, 95.4% is within two standard deviations and 99.7% is within three standard ...
or as a percent relative error, % e. %e = X¯¯¯¯ − μ μ × 100 (9.9.9.2) (9.9.9.2) % e = X ¯ − μ μ × 100. Although Equation 9.9.9.1 9.9.9.1 and Equation 9.9.9.2 9.9.9.2 use the mean as the measure of central tendency, we also can use the median. The convention for representing a statistical parameter is to use a Roman letter for a ...
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Multiplication/Division: The number of significant figures in the result is the same as the number in the least precise measurement used in the calculation. It is common to carry one additional significant figure through extended calculations and to round off the final ... Experimental Error
Statistical Treatment of Random Errors. Let's consider as an example the volume of water delivered by a set of 25 mL pipets. A manufacturer produces these to deliver 25.00 mL at 20°C with a stated tolerance of ±0.03 mL. A sample of 100 pipets is tested for accuracy by measuring the delivered volumes.
Tutorial - Experimental errors 1 Tutorial - Experimental errors Content ... number preceding the 5 is even we round down; if the number preceding the 5 is odd we round up (or vice versa). When dealing with a small number of measurements as in the case of first year labs the latter rule is irrelevant. For
from experimental data. In this lab course, we will be using Microsoft Excel to record ... Systematic errors are usually due to imperfections in the equipment, improper or biased observation, or the presence of additional physical e ects not taken into account. (An example might be an experiment on forces and acceleration in which
1Adapted from "Introduction to Experimental Error," Susan Cartwright, University of Sheffield, UK (2003). 2This is referred to as the mode. 1. ... For example, the spread in the number of heads nin our coin-flipping experiment, or the resolution uncertainties of an instrument, are statistical errors. ...
When two numbers are added, the smallest number of digits beyond the decimal point is retained in the sum. Thus, 37.57 + 3.932 = 41.50 not 41.502. Confusion arises when one wishes to add numbers like ... The three principal kinds of errors in experimental measurements are sys ...
or. dy − dx. - These errors are much smaller. • In general if different errors are not correlated, are independent, the way to combine them is. dz =. dx2 + dy2. • This is true for random and bias errors. THE CASE OF Z = X - Y. • Suppose Z = X - Y is a number much smaller than X or Y.
Random and systematic errors are types of measurement error, a difference between the observed and true values of something.
Random errors are due to fluctuations in the experimental or measurement conditions. Usually these errors are small. Taking more data tends to reduce the effect of random errors. Examples of Random Errors
This is a function of 2 variables ( N and Δ t) so you need to calculate the corresponding partial derivatives according to equation (1.3) as follows: d f d N = 1 2 N Δ t and d f d Δ t = − 1 N 2 Δ t 3. Combining the derivatives and uncertainties you get: σ f = ( 1 2 N Δ t) 2 N + ( − 1 N 2 Δ t 3) 2 σ t 2.
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As mentioned above, there are two types of errors associated with an experimental result: the "precision" and the "accuracy". One well-known text explains the difference this way: The word "precision" will
Preface. This book is written as a guide for the presentation of experimental including a consistent treatment of experimental errors and inaccuracies. is meant for experimentalists in physics, astronomy, chemistry, life and engineering. However, it can be equally useful for theoreticians produce simulation data: they are often confronted with ...
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The Excel function LINEST ("line statistics") is able to calculate the errors in the slope and y-intercept of a linear function of the form = + . To do so, follow the directions below: Organize your data into a column of x-values and y-values. Create a scatter plot of your data and fit a linear trendline.
Calculate percent error given estimated or experimental values and theoretical actual values. Calculator shows work and calculates absolute error and relative error.
After covering the formula, I'll go over several examples of using it in different contexts.
These errors are often classified into three main categories: systematic errors, random errors, and human errors. Here are some common types of experimental errors: 1. Systematic Errors. Systematic errors are consistent and predictable errors that occur throughout an experiment. They can arise from flaws in equipment, calibration issues, or ...
The substances are navy beans, Styrofoam and ice. 1) Navy Beans: Each group will take a clean and dry 250 ml beaker, weigh it on a top-loading balance and record its mass. Remove the beaker from the balance and then weigh it again. Weigh the beaker a total of 5 times. Ask yourself if you always get the same results.
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The text was updated successfully, but these errors were encountered: All reactions dotnet-issue-labeler bot added Area-Workloads untriaged Request triage from a team member labels Jun 25, 2024
The report indicates the lead yearbook advisor was working to complete the yearbook on April 11 including completing the entry for the Jewish Student Union in the Groups section.
Anti-aging therapies aim to reduce the number of errors, which allows the body to repair itself more quickly. Tue, 25 Jun 2024 11:27:48 GMT (1719314868202) Story Infinite Scroll - News3 v1.0.0 ...
View PDF HTML (experimental) Abstract: The genus non-increasing totally positive unknotting number is the minimum number of crossing changes that transform a knot into the unknot, such that all the crossing changes are positive-to-negative crossing changes that do not increase the genus. We show that the genus non-increasing totally positive unknotting number can be arbitrary large for genus ...
In vitro cell biology experiments are routinely used to characterize cell migration properties under various experimental conditions. These experiments can be interpreted using lattice-based random walk models to provide insight into underlying biological mechanisms, and continuum limit partial differential equation (PDE) descriptions of the stochastic models can be used to efficiently explore ...
Introduction. Plant cells are surrounded by a polysaccharide-rich cell wall that provides mechanical support, enables cell expansion, and acts as a physical barrier against biotic and abiotic stresses (Anderson and Kieber, 2020).Cell wall biosynthesis is mediated by the endomembrane system, which consists of the endoplasmic reticulum, Golgi bodies, the trans-Golgi network (TGN)/early endosomes ...
Visualized workflow of substrate-based phenotyping platform for cutting propagation-dependent grasses under salt stress. A 12-hole seedling tray is used to carry the substrate (medium) to maintain the salinity levels (A).Erect stems of P. vaginatum are prepared in 6-cm segments for cutting propagation (B), with Seg2 considered optimal (Step 1).After 8-day stratification at 7 ℃ in the dark ...