two tailed hypothesis test questions

Upper-tailed, Lower-tailed, Two-tailed Tests

The research or alternative hypothesis can take one of three forms. An investigator might believe that the parameter has increased, decreased or changed. For example, an investigator might hypothesize:  

The exact form of the research hypothesis depends on the investigator's belief about the parameter of interest and whether it has possibly increased, decreased or is different from the null value. The research hypothesis is set up by the investigator before any data are collected.

Rejection Region for Upper-Tailed Z Test (H : μ > μ ) with α=0.05

The decision rule is: Reject H if Z 1.645.

Rejection Region for Lower-Tailed Z Test (H 1 : μ < μ 0 ) with α =0.05

The decision rule is: Reject H 0 if Z < 1.645.

Rejection Region for Two-Tailed Z Test (H 1 : μ ≠ μ 0 ) with α =0.05

The decision rule is: Reject H 0 if Z < -1.960 or if Z > 1.960.

The complete table of critical values of Z for upper, lower and two-tailed tests can be found in the table of Z values to the right in "Other Resources."

Critical values of t for upper, lower and two-tailed tests can be found in the table of t values in "Other Resources."

• Step 4. Compute the test statistic.  

Here we compute the test statistic by substituting the observed sample data into the test statistic identified in Step 2.

• Step 5. Conclusion.  

The final conclusion is made by comparing the test statistic (which is a summary of the information observed in the sample) to the decision rule. The final conclusion will be either to reject the null hypothesis (because the sample data are very unlikely if the null hypothesis is true) or not to reject the null hypothesis (because the sample data are not very unlikely).  

If the null hypothesis is rejected, then an exact significance level is computed to describe the likelihood of observing the sample data assuming that the null hypothesis is true. The exact level of significance is called the p-value and it will be less than the chosen level of significance if we reject H 0 .

Statistical computing packages provide exact p-values as part of their standard output for hypothesis tests. In fact, when using a statistical computing package, the steps outlined about can be abbreviated. The hypotheses (step 1) should always be set up in advance of any analysis and the significance criterion should also be determined (e.g., α =0.05). Statistical computing packages will produce the test statistic (usually reporting the test statistic as t) and a p-value. The investigator can then determine statistical significance using the following: If p < α then reject H 0 .  

• Step 1. Set up hypotheses and determine level of significance

H 0 : μ = 191 H 1 : μ > 191                 α =0.05

The research hypothesis is that weights have increased, and therefore an upper tailed test is used.

• Step 2. Select the appropriate test statistic.

Because the sample size is large (n > 30) the appropriate test statistic is

• Step 3. Set up decision rule.  

In this example, we are performing an upper tailed test (H 1 : μ> 191), with a Z test statistic and selected α =0.05.   Reject H 0 if Z > 1.645.

We now substitute the sample data into the formula for the test statistic identified in Step 2.  

We reject H 0 because 2.38 > 1.645. We have statistically significant evidence at a =0.05, to show that the mean weight in men in 2006 is more than 191 pounds. Because we rejected the null hypothesis, we now approximate the p-value which is the likelihood of observing the sample data if the null hypothesis is true. An alternative definition of the p-value is the smallest level of significance where we can still reject H 0 . In this example, we observed Z=2.38 and for α=0.05, the critical value was 1.645. Because 2.38 exceeded 1.645 we rejected H 0 . In our conclusion we reported a statistically significant increase in mean weight at a 5% level of significance. Using the table of critical values for upper tailed tests, we can approximate the p-value. If we select α=0.025, the critical value is 1.96, and we still reject H 0 because 2.38 > 1.960. If we select α=0.010 the critical value is 2.326, and we still reject H 0 because 2.38 > 2.326. However, if we select α=0.005, the critical value is 2.576, and we cannot reject H 0 because 2.38 < 2.576. Therefore, the smallest α where we still reject H 0 is 0.010. This is the p-value. A statistical computing package would produce a more precise p-value which would be in between 0.005 and 0.010. Here we are approximating the p-value and would report p < 0.010.                  

In all tests of hypothesis, there are two types of errors that can be committed. The first is called a Type I error and refers to the situation where we incorrectly reject H 0 when in fact it is true. This is also called a false positive result (as we incorrectly conclude that the research hypothesis is true when in fact it is not). When we run a test of hypothesis and decide to reject H 0 (e.g., because the test statistic exceeds the critical value in an upper tailed test) then either we make a correct decision because the research hypothesis is true or we commit a Type I error. The different conclusions are summarized in the table below. Note that we will never know whether the null hypothesis is really true or false (i.e., we will never know which row of the following table reflects reality).

Table - Conclusions in Test of Hypothesis

In the first step of the hypothesis test, we select a level of significance, α, and α= P(Type I error). Because we purposely select a small value for α, we control the probability of committing a Type I error. For example, if we select α=0.05, and our test tells us to reject H 0 , then there is a 5% probability that we commit a Type I error. Most investigators are very comfortable with this and are confident when rejecting H 0 that the research hypothesis is true (as it is the more likely scenario when we reject H 0 ).

When we run a test of hypothesis and decide not to reject H 0 (e.g., because the test statistic is below the critical value in an upper tailed test) then either we make a correct decision because the null hypothesis is true or we commit a Type II error. Beta (β) represents the probability of a Type II error and is defined as follows: β=P(Type II error) = P(Do not Reject H 0 | H 0 is false). Unfortunately, we cannot choose β to be small (e.g., 0.05) to control the probability of committing a Type II error because β depends on several factors including the sample size, α, and the research hypothesis. When we do not reject H 0 , it may be very likely that we are committing a Type II error (i.e., failing to reject H 0 when in fact it is false). Therefore, when tests are run and the null hypothesis is not rejected we often make a weak concluding statement allowing for the possibility that we might be committing a Type II error. If we do not reject H 0 , we conclude that we do not have significant evidence to show that H 1 is true. We do not conclude that H 0 is true.

 The most common reason for a Type II error is a small sample size.

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Content ©2017. All Rights Reserved. Date last modified: November 6, 2017. Wayne W. LaMorte, MD, PhD, MPH

Two Tailed Test: Definition, Examples

Hypothesis Testing > Two Tailed Test

What is a Two Tailed Test?

A two tailed test tells you that you’re finding the area in the middle of a distribution. In other words, your rejection region (the place where you would reject the null hypothesis ) is in both tails.

For example, let’s say you were running a z test with an alpha level of 5% (0.05). In a one tailed test, the entire 5% would be in a single tail. But with a two tailed test, that 5% is split between the two tails, giving you 2.5% (0.025) in each tail.

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Two Tailed T Test

You may want to compare a sample mean to a given value of x with a t test . Let’s say your null hypothesis is that the mean is equal to 10 (μ = 10). A two tailed t test will test:

• Is the mean greater than 10?
• Is the mean less than 10?

If you choose an alpha level of 5%, and the f statistic is in the top 2.5% or bottom 2.5% of the probability distribution, then there is a significant difference in the means. That situation will also result in a p-value of less than 0.05. A small p-value gives you a reason to reject the null hypothesis .

Two tailed F test

To learn more watch the video below or keep reading.

Can’t see the video? Click here to watch it on YouTube.

An f test tells you if two population variances are equal. A two tailed f test is the standard type of f test which will tell you if the variances are equal or not equal. The two tailed version of test will test if one variance is greater than, or less than, the other variance. This is in comparison to the one tailed f test , which is used when you only want to test if one variance is greater than the other or that one variance is less than the other (but not both).

Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics , Cambridge University Press. Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial.

Two-Tailed Hypothesis Tests: 3 Example Problems

In statistics, we use hypothesis tests to determine whether some claim about a population parameter is true or not.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter = ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter , ≠ some value

There are two types of hypothesis tests:

• One-tailed test : Alternative hypothesis contains either or > sign
• Two-tailed test : Alternative hypothesis contains the ≠ sign

In a two-tailed test , the alternative hypothesis always contains the not equal ( ≠ ) sign.

This indicates that we’re testing whether or not some effect exists, regardless of whether it’s a positive or negative effect.

Check out the following example problems to gain a better understanding of two-tailed tests.

Example 1: Factory Widgets

Suppose it’s assumed that the average weight of a certain widget produced at a factory is 20 grams. However, one engineer believes that a new method produces widgets that weigh less than 20 grams.

To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses:

• H 0 (Null Hypothesis): μ = 20 grams
• H A (Alternative Hypothesis): μ ≠ 20 grams

This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal “≠” sign. The engineer believes that the new method will influence widget weight, but doesn’t specify whether it will cause average weight to increase or decrease.

To test this, he uses the new method to produce 20 widgets and obtains the following information:

• n = 20 widgets
• x = 19.8 grams
• s = 3.1 grams

Plugging these values into the One Sample t-test Calculator , we obtain the following results:

• t-test statistic: -0.288525
• two-tailed p-value: 0.776

Since the p-value is not less than .05, the engineer fails to reject the null hypothesis.

He does not have sufficient evidence to say that the true mean weight of widgets produced by the new method is different than 20 grams.

Example 2: Plant Growth

Suppose a standard fertilizer has been shown to cause a species of plants to grow by an average of 10 inches. However, one botanist believes a new fertilizer causes this species of plants to grow by an average amount different than 10 inches.

To test this, she can perform a one-tailed hypothesis test with the following null and alternative hypotheses:

• H 0 (Null Hypothesis): μ = 10 inches
• H A (Alternative Hypothesis): μ ≠ 10 inches

This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal “≠” sign. The botanist believes that the new fertilizer will influence plant growth, but doesn’t specify whether it will cause average growth to increase or decrease.

To test this claim, she applies the new fertilizer to a simple random sample of 15 plants and obtains the following information:

• n = 15 plants
• x = 11.4 inches
• s = 2.5 inches
• t-test statistic: 2.1689
• two-tailed p-value: 0.0478

Since the p-value is less than .05, the botanist rejects the null hypothesis.

She has sufficient evidence to conclude that the new fertilizer causes an average growth that is different than 10 inches.

Example 3: Studying Method

A professor believes that a certain studying technique will influence the mean score that her students receive on a certain exam, but she’s unsure if it will increase or decrease the mean score, which is currently 82.

To test this, she lets each student use the studying technique for one month leading up to the exam and then administers the same exam to each of the students.

She then performs a hypothesis test using the following hypotheses:

• H 0 : μ = 82
• H A : μ ≠ 82

This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal “≠” sign. The professor believes that the studying technique will influence the mean exam score, but doesn’t specify whether it will cause the mean score to increase or decrease.

To test this claim, the professor has 25 students use the new studying method and then take the exam. He collects the following data on the exam scores for this sample of students:

• t-test statistic: 3.6586
• two-tailed p-value: 0.0012

Since the p-value is less than .05, the professor rejects the null hypothesis.

She has sufficient evidence to conclude that the new studying method produces exam scores with an average score that is different than 82.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing What is a Directional Hypothesis? When Do You Reject the Null Hypothesis?

Statistics vs. Probability: What’s the Difference?

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Explaining two-tailed tests

I am looking for various ways of explaining to my students (in an elementary statistics course) what is a two tailed test, and how its P value is calculated.

How do you explain to your students the two- vs one- tailed test?

• hypothesis-testing

2 Answers 2

This is a great question and I'm looking forward to everyones version of explaining the p-value and the two-tailed v.s. one-tailed test. I've been teaching fellow orthopaedic surgeons statistics and therefore I tried to keep it as basic as possible since most of them haven't done any advanced math for 10-30 years.

My way of explaining calculating p-values & the tails

I start with a explaining that if we believe that we have a fair coin we know it should end up tails 50 % of the flips on average ($=H_0$). Now if you wonder what the probability of getting only 2 tails out of 10 flips with this fair coin you can calculate that probability as I've done in the bar graph. From the graph you can see that the probability of getting 8 out of 10 flips with a fair coin is about about $\approx 4.4\%$.

Since we would question the fairness of the coin if we got 9 or 10 tails we have to include these possibilities, the tail of the test. By adding the values we get that the probability now is a little more than $\approx 5.5\%$ of getting 2 tails or less.

Now if we would get only 2 heads, ie 8 heads (the other tail), we would probably be just as willing to question the fairness of the coin. This means that you end up with a probability of $5.4...\%+5.4...\% \approx 10.9\%$ for a two-tailed test .

Since we in medicine usually are interested in studying failures we need to include the opposite side of the probability even if our intent is to do good and to introduce a beneficial treatment.

Reflections slightly out of topic

This simple example also shows how dependent we are on the null hypothesis to calculate the p-value. I also like to point out the resemblance between the binomial curve and the bell curve. When changing into 200 flips you get a natural way of explaining why the probability of getting exactly 100 flips starts to lack relevance. The defining intervals of interest is a natural transition to probability density/mass function functions and their cumulative counterparts.

In my class I recommend them the Khan academy statistics videos and I also use some of his explanations for certain concepts. They also get to flip coins where we look into the randomness of the coin flipping - the thing that I try to show is that randomness is more random than what we usually believe inspired by this Radiolab episode .

I usually have one graph/slide, the R-code that I used to create the graph:

• $\begingroup$ Great answer Max - and thank you for recognizing the non-triviality of my question :) $\endgroup$ –  Tal Galili Commented Dec 1, 2011 at 12:31
• $\begingroup$ +1 nice answer, very thorough. Forgive me, but I'm going to nitpick on two things. 1) the p-value is understood as the probability of data being as extreme or more extreme as yours under the null, thus your answer is right. However, when using discrete data like your coin flips, this is inappropriately conservative. It's best to use what's called the "mid p-value", i.e. 1/2 the probability of data as extreme as yours + the probability of data being more extreme. An easy discussion of these issues can be found in Agresti (2007) 2.6.3. (cont.) $\endgroup$ –  gung - Reinstate Monica Commented Dec 2, 2011 at 5:48
• $\begingroup$ 2) You state that randomness is more random than we believe. I can guess what you might mean by that (I haven't had a chance to listen to the Radiolab episode you link, but I will). Curiously enough, I've always told students that randomness is less random than you believe. I'm referring here to the perception of streaks (e.g., in gambling). People believe that random events should alternate much more than random events actually do, and as a result believe they see streaks. See Falk (1997) Making sense of randomness Psych Rev 104,2. Again, you're not wrong--just food for thought. $\endgroup$ –  gung - Reinstate Monica Commented Dec 2, 2011 at 6:00
• $\begingroup$ Thank you @gung for your input. I've actually not heard of the mid-pvalue - it makes sense though. I'm not sure about if it's something I would mention when teaching basic statistics since it may give a feeling of loosing the hands-on feeling that I try to give. Concerning randomness we mean exactly the same - when seeing a truly random number we are fooled to think there's a pattern to it. I think I heard on the Freakonomics podcast folly of prediction that... $\endgroup$ –  Max Gordon Commented Dec 2, 2011 at 16:43
• $\begingroup$ ... the human mind has over the years learned that failing to detect a predator is costlier than thinking it's probably nothing. I like that analogy and I try to tell my colleagues that one of the primary reasons for using statistics is to help us with this defect that we're all born with. $\endgroup$ –  Max Gordon Commented Dec 2, 2011 at 16:47

Suppose that you want to test the hypothesis that the average height of men is "5 ft 7 inches". You select a random sample of men, measure their heights and calculate the sample mean. Your hypothesis then is:

$H_0: \mu = 5\ \text{ft} \ 7 \ \text{inches}$

$H_A: \mu \ne 5\ \text{ft} \ 7 \ \text{inches}$

In the above situation you do a two-tailed test as you would reject your null if the sample average is either too low or too high.

In this case, the p-value represents the probability of realizing a sample mean that is at least as extreme as the one we actually obtained assuming that the null is in fact true. Thus, if observe the sample mean to be "5 ft 8 inches" then the p-value will represent the probability that we will observe heights greater than "5 ft 8 inches" or heights less than "5 ft 6 inches" provided the null is true.

If on the other hand your alternative was framed like so:

$H_A: \mu > 5\ \text{ft} \ 7 \ \text{inches}$

In the above situation you would a one-tailed test on the right side. The reason is that you would prefer to reject the null in favor of the alternative only if the sample mean is extremely high.

The interpretation of the p-value stays the same with the slight nuance that we are now talking about the probability of realizing a sample mean that is greater than the one we actually obtained. Thus, if observe the sample mean to be "5 ft 8 inches" then the p-value will represent the probability that we will observe heights greater than "5 ft 8 inches" provided the null is true.

• 2 $\begingroup$ Formerly, for your second $H_A$ the null should read $H_0:\, \mu\le 5\ \text{ft}\ 7\ \text{inches}$, not $H_0:\, \mu = 5\ \text{ft}\ 7\ \text{inches}$. See one of @whuber's comments to this question, Do null and alternative hypotheses have be to exhaustive or not? . $\endgroup$ –  chl Commented Dec 1, 2011 at 10:23
• 2 $\begingroup$ @chl I agree. However, for a person who is just being introduced to statistical ideas, re-writing the null for a one-tailed test may be a distraction when the focus is on how and why things change with respect to interpretation of the p-value. $\endgroup$ –  varty Commented Dec 1, 2011 at 14:55
• 1 $\begingroup$ Fair enough. That's worth mentioning though, even for teaching purpose. $\endgroup$ –  chl Commented Dec 2, 2011 at 13:19

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MA121: Introduction to Statistics

Setting Up Hypotheses

One- and two-tailed tests, learning objectives.

• Define Type I and Type II errors
• Interpret significant and non-significant differences
• Explain why the null hypothesis should not be accepted when the effect is not significant

In the James Bond case study, Mr. Bond was given 16 trials on which he judged whether a martini had been shaken or stirred. He was correct on 13 of the trials. From the  binomial distribution , we know that the probability of being correct 13 or more times out of 16 if one is only guessing is 0.0106. Figure 1 shows a graph of the binomial distribution. The red bars show the values greater than or equal to 13. As you can see in the figure, the probabilities are calculated for the upper tail of the distribution. A probability calculated in only one tail of the distribution is called a " one-tailed probability ".

Figure 1. The binomial distribution. The upper (right-hand) tail is red.

Figure 2. The binomial distribution. Both tails are red.

Should the one-tailed or the two-tailed probability be used to assess Mr. Bond's performance? That depends on the way the question is posed. If we are asking whether Mr. Bond can tell the difference between shaken or stirred martinis, then we would conclude he could if he performed either much better than chance or much worse than chance. If he performed much worse than chance, we would conclude that he can tell the difference, but he does not know which is which. Therefore, since we are going to reject the null hypothesis if Mr. Bond does either very well or very poorly, we will use a two-tailed probability.

On the other hand, if our question is whether Mr. Bond is better than chance at determining whether a martini is shaken or stirred, we would use a one-tailed probability. What would the one-tailed probability be if Mr. Bond were correct on only 3 of the 16 trials? Since the one-tailed probability is the probability of the right-hand tail, it would be the probability of getting 3 or more correct out of 16. This is a very high probability and the null hypothesis would not be rejected.

You should always decide whether you are going to use a one-tailed or a two-tailed probability before looking at the data. Statistical tests that compute one-tailed probabilities are called  one-tailed tests ; those that compute two-tailed probabilities are called  two-tailed tests . Two-tailed tests are much more common than one-tailed tests in scientific research because an outcome signifying that something other than chance is operating is usually worth noting. One-tailed tests are appropriate when it is not important to distinguish between no effect and an effect in the unexpected direction. For example, consider an experiment designed to test the efficacy of a treatment for the common cold. The researcher would only be interested in whether the treatment was better than a  placebo  control. It would not be worth distinguishing between the case in which the treatment was worse than a placebo and the case in which it was the same because in both cases the drug would be worthless.

Some have argued that a one-tailed test is justified whenever the researcher predicts the direction of an effect. The problem with this argument is that if the effect comes out strongly in the non-predicted direction, the researcher is not justified in concluding that the effect is not zero. Since this is unrealistic, one-tailed tests are usually viewed skeptically if justified on this basis alone.

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S.3.2 hypothesis testing (p-value approach).

The P -value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis was true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the P -value is small, say less than (or equal to) \(\alpha\), then it is "unlikely." And, if the P -value is large, say more than \(\alpha\), then it is "likely."

If the P -value is less than (or equal to) \(\alpha\), then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P -value is greater than \(\alpha\), then the null hypothesis is not rejected.

Specifically, the four steps involved in using the P -value approach to conducting any hypothesis test are:

• Specify the null and alternative hypotheses.
• Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. Again, to conduct the hypothesis test for the population mean μ , we use the t -statistic \(t^*=\frac{\bar{x}-\mu}{s/\sqrt{n}}\) which follows a t -distribution with n - 1 degrees of freedom.
• Using the known distribution of the test statistic, calculate the P -value : "If the null hypothesis is true, what is the probability that we'd observe a more extreme test statistic in the direction of the alternative hypothesis than we did?" (Note how this question is equivalent to the question answered in criminal trials: "If the defendant is innocent, what is the chance that we'd observe such extreme criminal evidence?")
• Set the significance level, \(\alpha\), the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the P -value to \(\alpha\). If the P -value is less than (or equal to) \(\alpha\), reject the null hypothesis in favor of the alternative hypothesis. If the P -value is greater than \(\alpha\), do not reject the null hypothesis.

Example S.3.2.1

Mean gpa section  .

In our example concerning the mean grade point average, suppose that our random sample of n = 15 students majoring in mathematics yields a test statistic t * equaling 2.5. Since n = 15, our test statistic t * has n - 1 = 14 degrees of freedom. Also, suppose we set our significance level α at 0.05 so that we have only a 5% chance of making a Type I error.

Right Tailed

The P -value for conducting the right-tailed test H 0 : μ = 3 versus H A : μ > 3 is the probability that we would observe a test statistic greater than t * = 2.5 if the population mean \(\mu\) really were 3. Recall that probability equals the area under the probability curve. The P -value is therefore the area under a t n - 1 = t 14 curve and to the right of the test statistic t * = 2.5. It can be shown using statistical software that the P -value is 0.0127. The graph depicts this visually.

The P -value, 0.0127, tells us it is "unlikely" that we would observe such an extreme test statistic t * in the direction of H A if the null hypothesis were true. Therefore, our initial assumption that the null hypothesis is true must be incorrect. That is, since the P -value, 0.0127, is less than \(\alpha\) = 0.05, we reject the null hypothesis H 0 : μ = 3 in favor of the alternative hypothesis H A : μ > 3.

Note that we would not reject H 0 : μ = 3 in favor of H A : μ > 3 if we lowered our willingness to make a Type I error to \(\alpha\) = 0.01 instead, as the P -value, 0.0127, is then greater than \(\alpha\) = 0.01.

Left Tailed

In our example concerning the mean grade point average, suppose that our random sample of n = 15 students majoring in mathematics yields a test statistic t * instead of equaling -2.5. The P -value for conducting the left-tailed test H 0 : μ = 3 versus H A : μ < 3 is the probability that we would observe a test statistic less than t * = -2.5 if the population mean μ really were 3. The P -value is therefore the area under a t n - 1 = t 14 curve and to the left of the test statistic t* = -2.5. It can be shown using statistical software that the P -value is 0.0127. The graph depicts this visually.

The P -value, 0.0127, tells us it is "unlikely" that we would observe such an extreme test statistic t * in the direction of H A if the null hypothesis were true. Therefore, our initial assumption that the null hypothesis is true must be incorrect. That is, since the P -value, 0.0127, is less than α = 0.05, we reject the null hypothesis H 0 : μ = 3 in favor of the alternative hypothesis H A : μ < 3.

Note that we would not reject H 0 : μ = 3 in favor of H A : μ < 3 if we lowered our willingness to make a Type I error to α = 0.01 instead, as the P -value, 0.0127, is then greater than \(\alpha\) = 0.01.

In our example concerning the mean grade point average, suppose again that our random sample of n = 15 students majoring in mathematics yields a test statistic t * instead of equaling -2.5. The P -value for conducting the two-tailed test H 0 : μ = 3 versus H A : μ ≠ 3 is the probability that we would observe a test statistic less than -2.5 or greater than 2.5 if the population mean μ really was 3. That is, the two-tailed test requires taking into account the possibility that the test statistic could fall into either tail (hence the name "two-tailed" test). The P -value is, therefore, the area under a t n - 1 = t 14 curve to the left of -2.5 and to the right of 2.5. It can be shown using statistical software that the P -value is 0.0127 + 0.0127, or 0.0254. The graph depicts this visually.

Note that the P -value for a two-tailed test is always two times the P -value for either of the one-tailed tests. The P -value, 0.0254, tells us it is "unlikely" that we would observe such an extreme test statistic t * in the direction of H A if the null hypothesis were true. Therefore, our initial assumption that the null hypothesis is true must be incorrect. That is, since the P -value, 0.0254, is less than α = 0.05, we reject the null hypothesis H 0 : μ = 3 in favor of the alternative hypothesis H A : μ ≠ 3.

Note that we would not reject H 0 : μ = 3 in favor of H A : μ ≠ 3 if we lowered our willingness to make a Type I error to α = 0.01 instead, as the P -value, 0.0254, is then greater than \(\alpha\) = 0.01.

Now that we have reviewed the critical value and P -value approach procedures for each of the three possible hypotheses, let's look at three new examples — one of a right-tailed test, one of a left-tailed test, and one of a two-tailed test.

The good news is that, whenever possible, we will take advantage of the test statistics and P -values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.

Statistics Tutorial

Descriptive statistics, inferential statistics, stat reference, statistics - hypothesis testing a mean (two tailed).

A population mean is an average of value a population.

Hypothesis tests are used to check a claim about the size of that population mean.

Hypothesis Testing a Mean

The following steps are used for a hypothesis test:

• Check the conditions
• Define the claims
• Decide the significance level
• Calculate the test statistic

For example:

• Population : Nobel Prize winners
• Category : Age when they received the prize.

And we want to check the claim:

"The average age of Nobel Prize winners when they received the prize is not 60"

By taking a sample of 30 randomly selected Nobel Prize winners we could find that:

• The mean age in the sample (\(\bar{x}\)) is 62.1
• The standard deviation of age in the sample (\(s\)) is 13.46

From this sample data we check the claim with the steps below.

1. Checking the Conditions

The conditions for calculating a confidence interval for a proportion are:

• The sample is randomly selected
• The population data is normally distributed
• Sample size is large enough

A moderately large sample size, like 30, is typically large enough.

In the example, the sample size was 30 and it was randomly selected, so the conditions are fulfilled.

Note: Checking if the data is normally distributed can be done with specialized statistical tests.

2. Defining the Claims

We need to define a null hypothesis (\(H_{0}\)) and an alternative hypothesis (\(H_{1}\)) based on the claim we are checking.

The claim was:

In this case, the parameter is the mean age of Nobel Prize winners when they received the prize (\(\mu\)).

The null and alternative hypothesis are then:

Null hypothesis : The average age was 60.

Alternative hypothesis : The average age is not 60.

Which can be expressed with symbols as:

\(H_{0}\): \(\mu = 60 \)

\(H_{1}\): \(\mu \neq 60 \)

This is a ' two-tailed ' test, because the alternative hypothesis claims that the proportion is different from the null hypothesis.

If the data supports the alternative hypothesis, we reject the null hypothesis and accept the alternative hypothesis.

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3. Deciding the Significance Level

The significance level (\(\alpha\)) is the uncertainty we accept when rejecting the null hypothesis in a hypothesis test.

The significance level is a percentage probability of accidentally making the wrong conclusion.

Typical significance levels are:

• \(\alpha = 0.1\) (10%)
• \(\alpha = 0.05\) (5%)
• \(\alpha = 0.01\) (1%)

A lower significance level means that the evidence in the data needs to be stronger to reject the null hypothesis.

There is no "correct" significance level - it only states the uncertainty of the conclusion.

Note: A 5% significance level means that when we reject a null hypothesis:

We expect to reject a true null hypothesis 5 out of 100 times.

4. Calculating the Test Statistic

The test statistic is used to decide the outcome of the hypothesis test.

The test statistic is a standardized value calculated from the sample.

The formula for the test statistic (TS) of a population mean is:

\(\displaystyle \frac{\bar{x} - \mu}{s} \cdot \sqrt{n} \)

\(\bar{x}-\mu\) is the difference between the sample mean (\(\bar{x}\)) and the claimed population mean (\(\mu\)).

\(s\) is the sample standard deviation .

\(n\) is the sample size.

In our example:

The claimed (\(H_{0}\)) population mean (\(\mu\)) was \( 60 \)

The sample mean (\(\bar{x}\)) was \(62.1\)

The sample standard deviation (\(s\)) was \(13.46\)

The sample size (\(n\)) was \(30\)

So the test statistic (TS) is then:

\(\displaystyle \frac{62.1-60}{13.46} \cdot \sqrt{30} = \frac{2.1}{13.46} \cdot \sqrt{30} \approx 0.156 \cdot 5.477 = \underline{0.855}\)

You can also calculate the test statistic using programming language functions:

With Python use the scipy and math libraries to calculate the test statistic.

With R use built-in math and statistics functions to calculate the test statistic.

5. Concluding

There are two main approaches for making the conclusion of a hypothesis test:

• The critical value approach compares the test statistic with the critical value of the significance level.
• The P-value approach compares the P-value of the test statistic and with the significance level.

Note: The two approaches are only different in how they present the conclusion.

The Critical Value Approach

For the critical value approach we need to find the critical value (CV) of the significance level (\(\alpha\)).

For a population mean test, the critical value (CV) is a T-value from a student's t-distribution .

This critical T-value (CV) defines the rejection region for the test.

The rejection region is an area of probability in the tails of the standard normal distribution.

Because the claim is that the population proportion is different from 60, the rejection region is split into both the left and right tail:

The student's t-distribution is adjusted for the uncertainty from smaller samples.

This adjustment is called degrees of freedom (df), which is the sample size \((n) - 1\)

In this case the degrees of freedom (df) is: \(30 - 1 = \underline{29} \)

Choosing a significance level (\(\alpha\)) of 0.05, or 5%, we can find the critical T-value from a T-table , or with a programming language function:

Note: Because this is a two-tailed test the tail area (\(\alpha\)) needs to be split in half (divided by 2).

With Python use the Scipy Stats library t.ppf() function find the T-Value for an \(\alpha\)/2 = 0.025 at 29 degrees of freedom (df).

With R use the built-in qt() function to find the t-value for an \(\alpha\)/ = 0.025 at 29 degrees of freedom (df).

Using either method we can find that the critical T-Value is \(\approx \underline{-2.045}\)

For a two-tailed test we need to check if the test statistic (TS) is smaller than the negative critical value (-CV), or bigger than the positive critical value (CV).

If the test statistic is smaller than the negative critical value, the test statistic is in the rejection region .

If the test statistic is bigger than the positive critical value, the test statistic is in the rejection region .

When the test statistic is in the rejection region, we reject the null hypothesis (\(H_{0}\)).

Here, the test statistic (TS) was \(\approx \underline{0.855}\) and the critical value was \(\approx \underline{-2.045}\)

Here is an illustration of this test in a graph:

Since the test statistic is between the critical values we keep the null hypothesis.

This means that the sample data does not support the alternative hypothesis.

And we can summarize the conclusion stating:

The sample data does not support the claim that "The average age of Nobel Prize winners when they received the prize is not 60" at a 5% significance level .

The P-Value Approach

For the P-value approach we need to find the P-value of the test statistic (TS).

If the P-value is smaller than the significance level (\(\alpha\)), we reject the null hypothesis (\(H_{0}\)).

The test statistic was found to be \( \approx \underline{0.855} \)

For a population proportion test, the test statistic is a T-Value from a student's t-distribution .

Because this is a two-tailed test, we need to find the P-value of a T-value bigger than 0.855 and multiply it by 2 .

The student's t-distribution is adjusted according to degrees of freedom (df), which is the sample size \((30) - 1 = \underline{29}\)

We can find the P-value using a T-table , or with a programming language function:

With Python use the Scipy Stats library t.cdf() function find the P-value of a T-value bigger than 0.855 for a two tailed test at 29 degrees of freedom (df):

With R use the built-in pt() function find the P-value of a T-Value bigger than 0.855 for a two tailed test at 29 degrees of freedom (df):

Using either method we can find that the P-value is \(\approx \underline{0.3996}\)

This tells us that the significance level (\(\alpha\)) would need to be smaller 0.3996, or 39.96%, to reject the null hypothesis.

This P-value is bigger than any of the common significance levels (10%, 5%, 1%).

So the null hypothesis is kept at all of these significance levels.

The sample data does not support the claim that "The average age of Nobel Prize winners when they received the prize is not 60" at a 10%, 5%, or 1% significance level .

Calculating a P-Value for a Hypothesis Test with Programming

Many programming languages can calculate the P-value to decide outcome of a hypothesis test.

Using software and programming to calculate statistics is more common for bigger sets of data, as calculating manually becomes difficult.

The P-value calculated here will tell us the lowest possible significance level where the null-hypothesis can be rejected.

With Python use the scipy and math libraries to calculate the P-value for a two tailed hypothesis test for a mean.

Here, the sample size is 30, the sample mean is 62.1, the sample standard deviation is 13.46, and the test is for a mean different from 60.

With R use built-in math and statistics functions find the P-value for a two tailed hypothesis test for a mean.

Left-Tailed and Two-Tailed Tests

This was an example of a left tailed test, where the alternative hypothesis claimed that parameter is smaller than the null hypothesis claim.

You can check out an equivalent step-by-step guide for other types here:

• Right-Tailed Test
• Two-Tailed Test

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4 One-tailed vs two-tailed test

To gain a deeper understanding of how to conduct a hypothesis test, this section will delve into the concepts of one-tailed and two-tailed tests. These tests are vital tools in statistical hypothesis testing, and the decision of which test to employ depends on the research question and hypothesis under examination. It is crucial to give careful thought to the suitable type of test to ensure that the hypothesis is thoroughly tested and precise conclusions are derived from the data. This section will elaborate on this topic in greater detail.

To commence, complete the following activity pertaining to the formulation of null and alternative hypotheses. This exercise may be somewhat challenging, but it serves as an excellent introduction to upcoming discussions – don’t be concerned if you find it difficult!

Activity 3 Hypotheses setting

Read the following statements and then develop a null hypothesis and an alternative hypothesis.

‘It is believed that OU students need to set aside no longer than, on average, 15 hours to study an entire session of an OU course. However, a researcher believes that OU students spend longer studying an entire session of an OU course.’

H 0 : OU students spend, on average, no more than 15 hours studying an entire session of OU course.

H a : OU students spend, on average, more than 15 hours studying an entire session of OU course.

They can also be written as:

H 0 : µ ≤ 15 hours studies

H a : µ > 15 hours studies

µ is a symbol for a population mean. Remember, H 0 and H a are always opposites.

Did you identify any differences between the hypotheses you developed in Activity 1 and Activity 3? The set of hypotheses in Activity 1 has an equal (=) or not equal (≠) supposition (sign) in the statement. However, in Activity 3, the set of hypotheses has less than or equal to (≤) and greater than (>) supposition (sign) in the statement. This creates different conditions that lead to acceptance or rejection of the null hypothesis.

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What Is a Two-Tailed Test?

Understanding a two-tailed test, special considerations, two-tailed vs. one-tailed test.

• Two-Tailed Test FAQs
• Corporate Finance
• Financial Analysis

What Is a Two-Tailed Test? Definition and Example

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

Investopedia / Joules Garcia

A two-tailed test, in statistics, is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. It is used in null-hypothesis testing and testing for statistical significance . If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.

Key Takeaways

• In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values.
• It is used in null-hypothesis testing and testing for statistical significance.
• If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.
• By convention two-tailed tests are used to determine significance at the 5% level, meaning each side of the distribution is cut at 2.5%.

A basic concept of inferential statistics is hypothesis testing , which determines whether a claim is true or not given a population parameter. A hypothesis test that is designed to show whether the mean of a sample is significantly greater than and significantly less than the mean of a population is referred to as a two-tailed test. The two-tailed test gets its name from testing the area under both tails of a normal distribution , although the test can be used in other non-normal distributions.

A two-tailed test is designed to examine both sides of a specified data range as designated by the probability distribution involved. The probability distribution should represent the likelihood of a specified outcome based on predetermined standards. This requires the setting of a limit designating the highest (or upper) and lowest (or lower) accepted variable values included within the range. Any data point that exists above the upper limit or below the lower limit is considered out of the acceptance range and in an area referred to as the rejection range.

There is no inherent standard about the number of data points that must exist within the acceptance range. In instances where precision is required, such as in the creation of pharmaceutical drugs, a rejection rate of 0.001% or less may be instituted. In instances where precision is less critical, such as the number of food items in a product bag, a rejection rate of 5% may be appropriate.

A two-tailed test can also be used practically during certain production activities in a firm, such as with the production and packaging of candy at a particular facility. If the production facility designates 50 candies per bag as its goal, with an acceptable distribution of 45 to 55 candies, any bag found with an amount below 45 or above 55 is considered within the rejection range.

To confirm the packaging mechanisms are properly calibrated to meet the expected output, random sampling may be taken to confirm accuracy. A simple random sample takes a small, random portion of the entire population to represent the entire data set, where each member has an equal probability of being chosen.

For the packaging mechanisms to be considered accurate, an average of 50 candies per bag with an appropriate distribution is desired. Additionally, the number of bags that fall within the rejection range needs to fall within the probability distribution limit considered acceptable as an error rate. Here, the null hypothesis would be that the mean is 50 while the alternate hypothesis would be that it is not 50.

If, after conducting the two-tailed test, the z-score falls in the rejection region, meaning that the deviation is too far from the desired mean, then adjustments to the facility or associated equipment may be required to correct the error. Regular use of two-tailed testing methods can help ensure production stays within limits over the long term.

Be careful to note if a statistical test is one- or two-tailed as this will greatly influence a model's interpretation.

When a hypothesis test is set up to show that the sample mean would be only higher than the population mean, this is referred to as a  one-tailed test . A formulation of this hypothesis would be, for example, that "the returns on an investment fund would be  at least  x%." One-tailed tests could also be set up to show that the sample mean could be only less than the population mean. The key difference from a two-tailed test is that in a two-tailed test, the sample mean could be different from the population mean by being  either  higher or lower than it.

If the sample being tested falls into the one-sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis. A one-tailed test is also known as a directional hypothesis or directional test.

A two-tailed test, on the other hand, is designed to examine both sides of a specified data range to test whether a sample is greater than or less than the range of values.

Example of a Two-Tailed Test

As a hypothetical example, imagine that a new  stockbroker , named XYZ, claims that their brokerage fees are lower than that of your current stockbroker, ABC) Data available from an independent research firm indicates that the mean and standard deviation of all ABC broker clients are $18 and $6, respectively.

A sample of 100 clients of ABC is taken, and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and the sample standard deviation is $6, can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?

• H 0 : Null Hypothesis: mean = 18
• H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)
• Rejection region: Z <= - Z 2.5  and Z>=Z 2.5  (assuming 5% significance level, split 2.5 each on either side).
• Z = (sample mean – mean) / (std-dev / sqrt (no. of samples)) = (18.75 – 18) / (6/(sqrt(100)) = 1.25

This calculated Z value falls between the two limits defined by: - Z 2.5  = -1.96 and Z 2.5  = 1.96.

This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker. Therefore, the null hypothesis cannot be rejected. Alternatively, the p-value = P(Z< -1.25)+P(Z >1.25) = 2 * 0.1056 = 0.2112 = 21.12%, which is greater than 0.05 or 5%, leads to the same conclusion.

How Is a Two-Tailed Test Designed?

A two-tailed test is designed to determine whether a claim is true or not given a population parameter. It examines both sides of a specified data range as designated by the probability distribution involved. As such, the probability distribution should represent the likelihood of a specified outcome based on predetermined standards.

What Is the Difference Between a Two-Tailed and One-Tailed Test?

A two-tailed hypothesis test is designed to show whether the sample mean is significantly greater than  or  significantly less than the mean of a population. The two-tailed test gets its name from testing the area under both tails (sides) of a normal distribution. A one-tailed hypothesis test, on the other hand, is set up to show only one test; that the sample mean would be higher than the population mean, or, in a separate test, that the sample mean would be lower than the population mean.

What Is a Z-score?

A Z-score numerically describes a value's relationship to the mean of a group of values and is measured in terms of the number of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score whereas Z-scores of 1.0 and -1.0 would indicate values one standard deviation above or below the mean. In most large data sets, 99% of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above and below the mean.

San Jose State University. " 6: Introduction to Null Hypothesis Significance Testing ."

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• Published: 09 September 2024

Oligodendroglial fatty acid metabolism as a central nervous system energy reserve

• Ebrahim Asadollahi   ORCID: orcid.org/0000-0003-4737-3587 1 ,
• Andrea Trevisiol 1 , 2 ,
• Aiman S. Saab   ORCID: orcid.org/0000-0003-3886-8369 1 , 3 ,
• Zoe J. Looser 3 ,
• Payam Dibaj 1 , 4 ,
• Reyhane Ebrahimi 1 ,
• Kathrin Kusch   ORCID: orcid.org/0000-0002-5079-502X 1 , 5 ,
• Torben Ruhwedel   ORCID: orcid.org/0000-0002-9535-9395 1 ,
• Wiebke Möbius   ORCID: orcid.org/0000-0002-2902-7165 1 ,
• Olaf Jahn   ORCID: orcid.org/0000-0002-3397-8924 6 , 7 ,
• Jun Yup Lee 8 ,
• Anthony S. Don   ORCID: orcid.org/0000-0003-1655-1184 8 ,
• Michelle-Amirah Khalil 9 ,
• Karsten Hiller 9 ,
• Myriam Baes 10 ,
• Bruno Weber   ORCID: orcid.org/0000-0002-9089-0689 3 ,
• E. Dale Abel 11 ,
• Andrea Balabio   ORCID: orcid.org/0000-0003-1381-4604 12 , 13 , 14 , 15 ,
• Brian Popko   ORCID: orcid.org/0000-0001-9948-2553 16 ,
• Celia M. Kassmann 1 ,
• Hannelore Ehrenreich   ORCID: orcid.org/0000-0001-8371-5711 17 , 18 ,
• Johannes Hirrlinger   ORCID: orcid.org/0000-0002-6327-0089 1 , 19 &
• Klaus-Armin Nave   ORCID: orcid.org/0000-0001-8724-9666 1  

Nature Neuroscience ( 2024 ) Cite this article

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• Cellular neuroscience
• Oligodendrocyte

Brain function requires a constant supply of glucose. However, the brain has no known energy stores, except for glycogen granules in astrocytes. In the present study, we report that continuous oligodendroglial lipid metabolism provides an energy reserve in white matter tracts. In the isolated optic nerve from young adult mice of both sexes, oligodendrocytes survive glucose deprivation better than astrocytes. Under low glucose, both axonal ATP levels and action potentials become dependent on fatty acid β-oxidation. Importantly, ongoing oligodendroglial lipid degradation feeds rapidly into white matter energy metabolism. Although not supporting high-frequency spiking, fatty acid β-oxidation in mitochondria and oligodendroglial peroxisomes protects axons from conduction blocks when glucose is limiting. Disruption of the glucose transporter GLUT1 expression in oligodendrocytes of adult mice perturbs myelin homeostasis in vivo and causes gradual demyelination without behavioral signs. This further suggests that the imbalance of myelin synthesis and degradation can underlie myelin thinning in aging and disease.

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Oligodendrocyte–axon metabolic coupling is mediated by extracellular K + and maintains axonal health

Aerobic glycolysis is the predominant means of glucose metabolism in neuronal somata, which protects against oxidative damage

Fatty acid oxidation organizes mitochondrial supercomplexes to sustain astrocytic ROS and cognition

In the central nervous system of vertebrates, oligodendrocytes make myelin to enable saltatory impulse conduction 1 . Myelinating oligodendrocytes also provide fast spiking axons with lactate or pyruvate 2 , 3 , 4 for the generation of ATP 5 . This metabolic support of axonal projections by the associated glial cells has preceded the evolution of myelin in vertebrates 6 , 7 , but is most important when myelin deprives axons from access to metabolites of the extracellular milieu. In nonmyelinating species, axon-associated glial cells also harbor lipid droplets 8 , which can serve as local energy reserves by mobilizing fatty acids (FAs) under starvation conditions 9 .

Vertebrate myelin is a multilayered, highly lipid-rich membrane compartment 10 that is more dynamic than previously thought. Maintaining myelin maintenance throughout adult life requires its constant turnover, including high-level expression of myelin proteins and their incorporation into the myelin sheath 11 , 12 . Similarly, myelin lipids are subject to rapid turnover, which has been difficult to quantify by metabolic labeling studies 13 , because FAs and their breakdown products are efficiently reutilized.

In oligodendrocytes, FA β-oxidation takes place in mitochondria and peroxisomes, the latter being prevalent within the myelin compartment 14 . Mitochondrial acetyl-CoA can be either metabolized for the generation of ATP (oxidative phosphorylation (OXPHOS)) or released to the cytoplasm via the citric acid shuttle 15 and locally recycled in FA synthesis. Mitochondrial acetyl-CoA can also be used for ketogenesis 16 .

Conceivably, reduced glucose availability lowers acetyl-CoA and FA synthesis and should affect lipid metabolism and myelin turnover. In a range of neurodegenerative disorders, including Alzheimer’s disease, the reduction of brain glucose metabolism correlates with white matter abnormalities 17 . To address the question of whether myelin lipid synthesis, FA turnover and oligodendroglial energy metabolism are indeed interconnected, we chose the acutely isolated optic nerve from young adult mice (Fig. 1a ) as a model system. We assessed axonal conductivity and ATP levels in myelinated optic nerves under defined metabolic conditions, including low glucose, and in the presence of specific metabolic inhibitors, complemented by oligodendrocyte-specific, gene-targeting experiments in vivo. The latter allowed us to detect a gradual loss of myelin membranes when oligodendrocytes have reduced glucose availability. More importantly, in the present study we show that oligodendroglial FA metabolism can be an energy reserve for white matter axons, supporting their function.

a , Schematic representation of the experimental pipeline. Below, myelinated optic nerves from Cnp-mEOS reporter mice, maintained ex vivo ( n  = 5). Left, longitudinal section showing mEOS + oligodendrocytes (black on white). Right, all DAPI + cell nuclei (black on white). b , Higher magnification of DAPI + (blue) optic nerve glia and PI + (white) dying cells (arrows). Left, cells surviving in 10 mM glucose (Glc). Right, without glucose, cells surviving up to 16 h, but many dying after 24 h (quantified in c ). c , Cell survival quantified by subtracting (PI + DAPI + ) dying cells from total (DAPI + ) cells including data from d – f (16 h: N  =  n  = 8; 24 h: N  =  n  = 12; mean ± s.e.m., Kruskal–Wallis test, Dunn’s multiple comparison). d , Different vulnerabilities of glial subtypes to 24-h glucose withdrawal. Optic nerve longitudinal sections are labeled by DAPI (all cells), PI (dying cells) and genetically expressed cell-specific markers (oligodendrocytes: Cnp -PTS1-mEOS; OPCs: Ng2 -YFP; microglia: Cxcr1 -GFP; astrocytes: Aldh1l1 -GFP). Note the shrunken cell nuclei in glucose-free medium and lack of overlap between oligodendrocytes and dying cells. e , Frequency of glial subtypes after 24-h incubation in 10 mM or 0 mM glucose (oligodendrocytes: 10 mM, N  =  n  = 5; 0 mM, N  =  n  = 4; microglia: 10 mM, N  =  n  = 3; 0 mM, N  =  n  = 5; OPCs and astrocytes: N  =  n  = 3, both) with data from d . f , Survival rate of glial subtypes after 24 h in 10 mM or 0 mM glucose, normalized to cells in glucose-containing aCSF (100%) with data from e (mean ± s.e.m., one-way ANOVA, Tukey’s multiple comparison). g , Glial cells that survive 16-h glucose deprivation dying under hypoxia (bottom), demonstrating oxidation of an endogenous energy reserve other than glucose ( N  =  n  = 3, each). h , 4-Br (a mitochondrial β-oxidation inhibitor) treatment of glucose-deprived optic nerves causing widespread cell death, demonstrating FAs as an energy reserve ( N  =  n  = 3). Note that 4-Br is not cytotoxic by itself (mean ± s.e.m., unpaired, two-tailed Student’s t -test, heteroscedastic). i , Thio (a peroxisomal β-oxidation inhibitor) treatment not increasing glial death which indicates mitochondrial β-oxidation sufficient for glial survival ( N  =  n  = 3). Animals, both sexes, are aged 2 months. Percentages (in g – i ) were calculated relative to overall survival for 16 h with glucose under normoxia (in c ). N , individual optic nerves; n , independent experiments. Error bars in e , g and i : mean ± s.e.m., unpaired, two-tailed Student’s t -test.

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Glial cells in glucose-deprived optic nerves rely on fa β-oxidation.

We analyzed fully myelinated transgenic mice (both sexes) at age 2 months, expressing fluorescent proteins in mature oligodendrocytes ( Cnp-mEos2-PTS1 ) 14 or astrocytes ( Aldh1L1-GFP ). Optic nerves were incubated at 37 °C in artificial cerebrospinal fluid (aCSF) containing 10 mM glucose, 0 mM glucose (termed ‘glucose free’) or low glucose (termed ‘starved’; Methods ). After 24 h, the total number of cells (DAPI + ), the number of dying cells (propidium iodide positive (PI + )) and the identity of surviving cells were determined by fluorescence analysis of sectioned nerves. Surprisingly, the large majority (>97%) of oligodendrocytes appeared healthy after 24 h in glucose-free medium, whereas >70% of astrocytes had died (Fig. 1b-f ). Oligodendrocyte precursor cells (OPCs) and microglia were also not reduced. Next, we compared earlier time points and found no cell death at 16 h (Fig. 1c ). This suggests that all glial cells in the myelinated optic nerve can principally survive in the absence of glucose by utilizing a pre-existing energy reserve.

In the presence of 1 mM glucose, a concentration insufficient to maintain axonal conduction (see also below for nerve function), all cells of the optic nerve stayed alive for at least 24 h. Glucose is essential for the pentose phosphate pathway and the synthesis of nucleotides. To rule out glucose-free medium being detrimental independent of the reduced energy metabolism, we incubated optic nerves in aCSF containing as little as 1.5 mM 3-hydroxybutyrate as an alternative energy source and detected no cell death after 24 h (Extended Data Fig. 1a,b ). Moreover, optic nerves that were kept glucose free in the presence of a reactive oxygen species (ROS) inhibitor (S3QEL-2) and a mitochondrial ROS scavenger (MitoTEMPO) did not show enhanced cell survival, suggesting that cell death is not caused by the generation of ROS (Extended Data Fig. 1c,d ).

Our hypothesis that alternative metabolites and FA metabolism provide an energy reserve for OXPHOS was supported by experiments, in which optic nerves were incubated for 16 h in glucose-free aCSF in combination with severe hypoxia (N 2 atmosphere). Under hypoxia, cell death was extensive with 76% PI-labeled cells, suggesting that all cell types are affected (Fig. 1g ). Thus, in the absence of glucose, virtually all glial cells appeared to have survived by OXPHOS.

We next asked directly whether FAs metabolized by β-oxidation comprise the postulated energy reserve. Optic nerves were incubated without glucose and under normoxia, but in the presence of 25 µM 4-bromocrotonic acid (4-Br), a nonspecific thiolase inhibitor of mitochondrial FA β-oxidation and ketolysis. Application of this drug dramatically reduced the rate of overall cell survival to 30% at 16 h (Fig. 1h ). Importantly, 4-Br had no effect on glial survival in the presence of glucose (Fig. 1h ), ruling out unspecific toxicity. Next, we tested 5 µM thioridazine (Thio), an inhibitor of peroxisomal β-oxidation that also claimed to block mitochondrial β-oxidation 18 . However, Thio had no obvious effect in the absence of glucose (Fig. 1i ). This suggests that with respect to cell death peroxisomal β-oxidation is sufficiently compensated by mitochondrial β-oxidation (but see below for the effect on axonal conduction).

Energy scarcity causes myelin thinning and vesicular demyelination

If FAs of the white matter were the main source of metabolic energy, starvation might even lead to a visible loss of myelin membranes. To directly determine this, we maintained optic nerves in low (0.5 mM) or regular (10 mM) glucose medium and analyzed them 24 h later (that is, before major glial cell death; Fig. 1c ) by electron microscopy (EM) and quantitative morphometry (Fig. 2a–c ). Starvation led to increased g -ratios (Fig. 2a–c ). However, these numbers were not conclusive because acute starvation caused nonspecific swelling of the axonal and myelin compartments. Compatible with active demyelination was the emergence of vesicular structures underneath the myelin sheaths in starved nerves (Extended Data Fig. 2a,b ), possibly caused by autophagy of myelin as reported 19 (but see LC3 + puncta in oligodendrocyte somata further below). Most probably, the vesiculation of the innermost myelin layer is caused by the detachment of myelin basic protein (MBP) 20 .

a , Electron microscopic images of optic nerve cross-sections (wild-type mice aged 2 months), taken after 24 h of incubation in medium with 10 mM glucose (top: N  =  n  = 3) or 0.5 mM glucose (bottom: N  =  n  = 3). b , Scatter plot of calculated g -ratios (outer fiber diameter/axon diameter) as a function of axon caliber, revealing myelin loss when optic nerves are exposed to low glucose (red dots, bottom) compared with 10 mM glucose-containing medium (black dots, top). c , Bar graph with calculated mean g -ratios (same data as in b ) ( N  =  n  = 3 for both 0 mM and 10 mM; error bars: mean ± s.e.m.; unpaired, two-tailed Student’s t -test). d , Schematic depiction of the pCNP-mTagRFP-mWasabi-LC3 transgene used for oligodendrocyte-specific expression of the LC3 fusion protein. The two fluorophores (red and green) give LC3 a yellow color and reveal diffuse cellular distribution. Note that mTagRFP-mWasabi-LC3 becomes an autophagosome-specific marker, when LC3 is translocated to the membrane of newly formed autophagophore/autophagosomes (green puncta). e , Live imaging of optic nerves (ex vivo) from a mTagRFP-mWasabi-LC3 transgenic mouse, incubated in aCSF with 10 mM (left) or 0 mM (middle) glucose. Note the ubiquitous expression of the LC3 fusion protein. Specific labeling of autophagosomes (green puncta, arrows on image inset) occurs only in the absence of glucose with an all-or-none difference. Right, the accumulation of autophagosomes also in oligodendrocytes in the presence of 10 mM glucose (Glc) after applying the specific inhibitor, Lys05 (10 µM). f , Quantification of the data in e , normalized to the number of cell bodies (adult mice, aged 2–5 months; N  =  n  = 4 for 10 mM Glc, N  =  n  = 5 for 10 mM Glc + Lys05 and N  =  n  = 3 for 0 mM Glc; error bars: mean ± s.e.m.; one-way ANOVA, Tukey’s test).

When kept in 10 mM glucose for 24 h, optic nerve axons appeared morphologically normal by EM, whereas those at 0.5 mM glucose revealed loss of integrity of cytoskeletal elements (Fig. 2a ). This raises the possibility that axonal degeneration rather than glucose deprivation causes myelin thinning. Although the dissection of axons will invariably cause their Wällerian degeneration, which is itself triggered by loss of NAD + and ATP 21 , we also analyzed the ‘intact’ nerves for signs of axonal degeneration. As predicted, when immunostained for a proteolysis-dependent NF-L epitope, a very specific marker for neurodegeneration 22 , the molecular signature of Wällerian degeneration was also detected in nerves kept in 10 mM glucose for 24 h (Extended Data Fig. 2c ). Thus, starvation rather than axonal degeneration triggers the observed demyelination.

A basal level of autophagy in oligodendrocytes

We also subjected entire optic nerves to quantitative proteome analysis after either 16 h in glucose-free medium (when all cells survive) or 24 h in 1 mM glucose-containing medium, both in comparison to a regular medium (10 mM glucose). It is interesting that we noticed a minor trend toward higher myelin protein abundance (Extended Data Fig. 3a,b ), perhaps because autophagy liberates proteins from compact myelin that are otherwise not solubilized. In these nerve lysates, the abundance of some glycolytic enzymes was reduced (for example, PFKAM (phosphofructokinase, muscle)) whereas fatty acid-binding proteins (FABP3) and enzymes of FA metabolism (acyl-COA dehydrogenase 9 (ACAD9)) were increased. A higher steady-state level of some autophagy-related proteins was detected, but only when nerves were maintained in low (1 mM) glucose (Extended Data Fig. 3b ), most probably because some glucose is required for the pentose phosphate pathway, nucleotide synthesis and a transcriptional response. When assessed by EM (Fig. 2a–c ), compact myelin appeared decreased, which would imply a greater loss of lipids than proteins. After 16 h in glucose-free medium, western blotting revealed a significant increase of acetyl-CoA acetyltransferase 1 (ACAT1) and 3-hydroxybutyrate dehydrogenase 1 (BDH1), enzymes involved in FA and ketone body metabolism, respectively (Extended Data Fig. 3c,d ).

In adult mice, food withdrawal induces LC3 + autophagosomes in neuronal perikarya but not in axons 23 . Nevertheless, it is possible that myelin degradation is mediated by autophagy. To study autophagy in optic nerves, we generated a new line of pCNP-mTagRFP-mWasabi-LC3 transgenic mice that express a tandem (pH-sensitive) fluorescent tag 24 in oligodendrocytes (Fig. 2d ). Indeed, 8.5 h after glucose withdrawal from optic nerves, we observed the accumulation of autophagosomes (Fig. 2e,f ) in oligodendrocyte somata and processes as reported before 19 . In glucose-containing medium (10 mM), however, these organelles were detectable only when their degradation was specifically inhibited, for example, by Lys05 (Fig. 2e (right column) ,f ). This suggests that in oligodendrocytes a basal level of autophagy always exists that increases only on glucose deprivation. This may explain why transcriptional upregulation of autophagy genes by its master regulator TFEB (transcription factor EB) is not essential for utilizing FAs from the myelin compartment (see also below for nerve recordings), as evidenced by the unaltered cell survival of glucose-deprived optic nerves from oligodendrocyte-specific TFEB conditional knockout (cKO) mice (Extended Data Fig. 3e–f ).

Oligodendrocyte lipid metabolism supports axonal function in starved optic nerves

As axonal conduction is energy dependent, we asked whether FA metabolism can support axon function under low glucose conditions. As a readout in acutely isolated optic nerves, we determined the size of the evoked compound action potential (CAP) after electrical stimulation 4 (Fig. 3a,b ). These recordings were performed in combination with real-time monitoring of the axonal ATP levels in the same nerves, using a genetically encoded ATP sensor expressed in the axonal compartment 5 (Fig. 3c ).

a , Stimulating (Stim.) and recording (Rec.) CAPs from isolated optic nerves and monitoring axonal ATP by ratiometric FRET analysis. b , Top, typical CAP at 10 mM glucose with the CAPA shaded in red below. Bottom, recording of a stable CAPA, normalized to 1.0 (at 10 mM glucose, normoxia, low spiking rate (1 per 30 s)). Note a 5-min glucose withdrawal step to deplete astroglial glycogen. a.u., arbitrary units. c , Ratiometric FRET analysis using transgenically expressed 5 ATP sensor ATeam1.03 YEMK (Ex and Em depict maximum excitation and emission wavelength respectively). d , Optic nerves, maintained functionally stable at 2 mM glucose and low spiking activity (0.2 Hz), exposed to 4-Br (25 µM; N  =  n  = 5), an inhibitor of mitochondrial FA β-oxidation. Note the progressive decline of optic nerve conductivity ( N  =  n  = 7). e , Optic nerves exposed to Etox (5 µM, N  = 6, n  = 6), an inhibitor of long-chain FA uptake into mitochondria. Note the faster declining CAPA ( N  =  n  = 7). f , Same as in d , demonstrating a progressive loss of axonal ATP. Note the faster and stronger effect on the axonal ATP levels ( N  =  n  = 4) compared with controls ( N  =  n  = 5). g , Axonal ATP in Etox-treated nerves ( N  =  n  = 3) and controls ( N  =  n  = 5) as before. h , Optic nerves stimulated as before but in the presence of Thio (5 µM, N  = 5, n  = 5), an inhibitor of peroxisomal β-oxidation ( N  =  n  = 7). Note the difference to cell survival which is independent of peroxisomal β-oxidation (in Fig. 1i ). i , Axonal ATP in Thio-treated nerves ( N  =  n  = 5) and controls ( N  =  n  = 5) as before. j , Optic nerves from Cnp-Cre +/- ::Mfp2 flox/flox mice, lacking peroxisomal β-oxidation in oligodendrocytes 27 and controls, at 2.7 mM glucose with increasing stimulation frequency ( N  =  n  = 7 each). Stronger CAPA decline in mutant nerves (7 Hz) confirms the role of oligodendrocytes in metabolic support. k , Optic nerves from Cnp-Cre +/− ::Tfeb flox/flox mice ( N  =  n  = 9) and controls ( N  =  n  = 6), showing that FA mobilization does not depend on de novo autophagy induction. All mice are aged 2 months (from both sexes). Bar graphs are mean ± s.e.m. (unpaired, two-tailed Student’s t -test) of data recorded in the last 5 min at each frequency. Controls are shared across d , e and h .

We first determined empirically the (set-up-specific) threshold level of glucose concentration (Extended Data Fig. 4a,b ), at which acutely isolated optic nerves, after 5 min of glycogen depletion, remained sufficiently energized. This was defined as maintaining a low firing rate (0.2 Hz) for 2 h without decline of the CAP area (CAPA) (Fig. 3d ; here: 2.7 mM glucose in aCSF). A subsequent gradual increase of the stimulation frequency (to 1 Hz, 3 Hz and 7 Hz) caused a gradual decline of the CAP, that is, an increasing fraction of axons with conduction blocks. Both preservation and decline of axon function could be quantified by calculating the curve integral, with the CAPAs plotted as a function of time. Similar to the cell survival experiments (Fig. 1h ), we inhibited FA catabolism under starvation conditions. Importantly, when recordings were done in the presence of 4-Br, an inhibitor of thiolase (Fig. 3d ) or etomoxir (Etox), an inhibitor of mitochondrial carnitine palmitoyltransferase 1 (CPT1) (Fig. 3e ), these blockers of the mitochondrial FA β-oxidation caused a much more rapid decay of CAPA, that is, loss of conductivity. When applied in the presence of 10 mM glucose, these drugs had no toxic effects (Extended Data Fig. 4c–h ). Under all conditions, we also monitored axonal ATP levels, which revealed strong parallels to the electrophysiological recordings (Fig. 3f,g ). Thus, when glucose is limiting, the functional integrity of spiking axons is supported by FA degradation.

To confirm that the decline of the CAP, as observed under starvation, was not the result of ROS production, we repeated our recordings in the presence of ROS inhibitors and scavengers. Indeed, these drugs could not ‘rescue’ the CAP decline (Extended Data Fig. 4i,j ). To also rule out the possibility that inhibition of β-oxidation interferes with degradation of toxic FAs generated in hyperactivated neurons 25 leading to the decline of CAPs, we compared optic nerve conduction in the presence of 10 mM glucose. Indeed, high-frequency (5–20 Hz) conduction of these nerves remained the same in the presence or absence of 4-Br (Extended Data Fig. 5a,b ).

Next, we applied 5 µM Thio, an inhibitor of peroxisomal β-oxidation. It is interesting that, and different from cell survival assays in the complete absence of glucose (Fig. 1i ), in the electrophysiological experiments at low glucose similar results were obtained when inhibiting β-oxidation in mitochondria or peroxisomes (Fig. 3h,i ). This may reflect the different energy requirements of basic survival and axonal conduction and also the extensive periaxonal localization of peroxisomes.

As our pharmacological treatments lacked cell-type specificity, we used genetics to selectively perturb β-oxidation in oligodendrocytes. Unfortunately, that was not possible for mitochondria, because even a triple-KO of all CPT1 genes would not block uptake of short-/medium-chain FAs and lead to the accumulation of neurotoxic acyl-carnitine 26 . However, peroxisomal FA β-oxidation could be specifically targeted in Cnp-Cre +/− ::Mfp2 flox/flox mutant mice 27 . Indeed, increasing the axonal spiking frequency in these mutant nerves caused the same increase in conduction blocks (that is, decrease of CAPA) as seen in Thio-treated nerves (Fig. 3j ). In agreement with earlier studies, there were no underlying structural abnormalities of Cnp-Cre +/− ::Mfp2 flox/flox optic nerves, including the number of axons, number of unmyelinated axons, number of ultrastructural axonal defects and number of microglia 27 . Also, basic electrophysiological properties of the nerves, including excitability and nerve conduction velocity, were unaltered (Extended Data Fig. 5c–j ). This demonstrates directly a role for oligodendrocytes in the support of starving axons, with a important role for β-oxidation in peroxisomes, many of which reside in the myelin compartment 14 .

We further investigated whether autophagy plays a role in myelin turnover and FA metabolism under starvation conditions. TFEB activates autophagy-related genes and lysosomal functions 28 also in oligodendrocyte lineage cells 29 . We generated Cnp-Cre::TFEB flox/flox mice for oligodendrocyte-specific ablation, but found that mutant optic nerve conduction remains indistinguishable from wild-type nerves with respect to the ex vivo CAP decline (Fig. 3k ) and conduction velocity. In contrast, application of the autophagy inhibitor Lys05 to wild-type nerves under limiting glucose concentrations caused a faster CAP decline (Extended Data Fig. 6a,b ). This suggests a contribution of pre-existing autophagy to axonal energy metabolism. In turn, the autophagy inducer 3,4‐dimethoxychalcone (DMC), an activator of TFEB and TFE3, improved nerve function, but failed to do so in nerves from Cnp-Cre::TFEB flox/flox mice (Extended Data Fig. 6c,d ). Taken together, these observations suggest that autophagy pre-exists in oligodendrocytes and that the master regulator TFEB is not critical for the utilization of FAs in energy metabolism. We also detected the upregulation of autophagy in brain lysates of mice with reduced glucose availability to oligodendrocytes (see below; Fig. 4i,j ).

a , Targeting GLUT1 expression in oligodendrocytes. Plp-CreERT2::Slc2a1 flox/flox mice received tamoxifen at age 2 months for phenotype analysis 5 months later. b , Western blot (WB) analysis of purified myelin membranes from whole-brain lysates. Note the decrease (quantified in c – e ) of (oligodendroglial) GLUT1 ( c ), but not (neuronal) GLUT3 ( d ) or panglial MCT1 ( e ); CA2 (for control (CTR), N  = 4; for icKO, N  = 4; error bars: mean ± s.e.m., unpaired, two-tailed Student’s t -test). Rel., Relative. TUBA, α-tubulin. f , Electron micrographs of optic nerve cross-section from GLUT1 mutant icKO ( N  = 4; CTR: N  = 4). Note the thinning of myelin in the absence of axonal degeneration. g , Scatter plot of calculated g -ratios (fiber diameter/axon diameter) from optic nerve EM data, with regression lines as a function of axon diameter. h , Myelin thinning in GLUT icKO mice ( N  = 4) compared with controls ( N  = 3). Error bars: mean ± s.e.m., unpaired, two-tailed Student’s t -test. i , j , Western blots of brain lysates from GLUT1 icKO mice ( i ) and quantification ( j ), normalized to protein input (fast green) ( N  = 4 for CTR and icKO; mean ± s.e.m., heteroscedastic for BDH1; Student’s t -test). k , Proposed working model of glycolytic oligodendrocytes with a myelin compartment that constitutes a lipid-based energy buffer. During normal myelin turnover, the degradation of myelin lipids in lysosomes liberates FAs for β-oxidation (β-Ox) in mitochondria (MT) and peroxisomes (PEX), leading to new myelin lipid synthesis. When glucose availability is reduced, as modeled in GLUT1 icKO mice, myelin synthesis drops and FA-derived acetyl-CoA begins, supporting mitochondrial respiration for oligodendroglial survival. This shift of normal myelin turnover to lipid-based ATP generation allows oligodendrocytes to share relatively more glucose-derived pyruvate/lactate with the axonal compartment to support ATP generation and prevent axon degeneration. Note that glucose is never absent in vivo and that myelin-associated peroxisomes 14 are better positioned than mitochondria to support axons with the products of FA β-oxidation. Whether oligodendrocytes also use ketogenesis to metabolically support axons and other cells is not known.

Ablating GLUT1 from mature oligodendrocytes in vivo reduces myelin thickness

Acute glucose deprivation of white matter in short-term ex vivo experiments showed proof of principle for the role of FAs as energy reserves. However, this model differs from long-lasting, chronic hypoglycemia, which can occur in real life, for example, on starvation. Starvation experiments are obviously not possible and have difficulty controlling side effects, such as ketosis and gluconeogenesis. To circumvent these and to only ‘glucose starve’ oligodendrocytes, we generated a line of tamoxifen-inducible Plp1 CreERT2/+ ::Slc2a1 flox/flox conditional mutant mice. These lack glucose transporter 1 (GLUT1) expression specifically in mature oligodendrocytes after tamoxifen administration at the age of 2 months (Fig. 4a ). We expected only a slow decline of glucose import, because GLUT1 is associated with myelin 4 and should have a slow turnover similar to myelin structural proteins. Moreover, mutant oligodendrocytes remain gap junction coupled to astrocytes and Plp1 CreERT2 recombination efficacy is not 100%. When testing purified myelin by western blot analysis 5 months after tamoxifen administration, we determined a significant but still incomplete decrease of GLUT1. In contrast, GLUT3, monocarboxylate transporter 1 (MCT1), α-tubulin and oligodendroglial carbonic anhydrase 2 (CA2) were unaltered in abundance (Fig. 4b–e ).

Importantly, Slc2a1 conditional mutants from both sexes showed no obvious behavioral defects and lacked visible neuropathological changes (Extended Data Fig. 7a–c ). However, when the myelin sheath thickness was quantified by EM (Fig. 4f ), g -ratio analysis of the optic nerve revealed significant loss of myelin membranes in the absence of obvious axonal pathology (Fig. 4g,h and Extended Data Fig. 7d–i ). There were also no signs of inflammation or altered electrophysiological properties (Extended Data Fig. 7j–m ). In addition, CC1 and Plin2 immunostaining failed to show oligodendrocyte loss or the abnormal formation of lipid droplets in the optic nerve, respectively (Extended Data Fig. 8a,b,f ). Whether the fraction of the recently identified immune oligodendrocytes 30 changes on chronic starvation awaits a more detailed single-nucleus RNA sequencing analysis, but the number of oligodendrocytes expressing the relevant marker gene IL33 was not increased (Extended Data Fig. 8c–e ). Western blot analysis of mutant brain lysates showed elevated levels of LC3b I and II and BDH1, and a tendency for more mitochondrial ACAT1 (Fig. 4i,j ). These data demonstrate that myelin metabolism continues when oligodendrocytes lack normal glucose uptake, suggesting that the mechanism of myelin loss during starvation is the ongoing catabolic arm of myelin turnover.

Our in vitro and in vivo data, when combined, led to a model of myelin dynamics that extends the model of glycolytic oligodendrocytes delivering metabolic support to fast spiking axons 2 , 3 , 4 , 5 (Fig. 4k ). Our key experiment was the direct analysis of both axonal conductivity and ATP levels in myelinated optic nerves under defined metabolic conditions, including low glucose, and in the presence of specific metabolic inhibitors, complemented by oligodendrocyte-specific, gene-targeting experiments in vivo. The latter allowed us to detect even a gradual loss of myelin membranes when oligodendrocytes have reduced glucose availability. Distinguishing the contribution of mitochondrial and peroxisomal β-oxidation in vivo remains difficult, but, regardless of the subcellular origin of FAs, membrane lipids are in constant horizontal flux between compartments, which also includes, for oligodendrocytes, myelin membranes that emerge as a large ‘lipid store’.

Myelin sheaths are wrapped within hours and days 31 , 32 and continue to turn over in adult life when myelin synthesis and degradation are in equilibrium 11 , 33 . The anabolic arm of myelin membrane synthesis is well known and has been studied in the context of developmental myelination by the impact of nutritional deprivation. Studies in undernourished newborn rats were first performed in the late 1940s and in the following decades by radiolabeling studies. These data have shown the suppression of myelin synthesis under caloric restriction, which can be rescued by refeeding 34 . We propose likewise that, in our system, continued myelin synthesis comes to a halt on glucose deprivation.

However, the catabolic arm of myelin turnover 35 , which includes myelin degradation and FA breakdown, continues. This was shown directly in adult mice, in which the tamoxifen-induced loss of MBP, a protein required for myelin membrane incorporation, causes demyelination 11 . Importantly, after energy deprivation, mitochondrial FA β-oxidation can feed acetyl-coA without temporal delay into the tricarboxylic acid cycle and OXPHOS. In fact, this would be the fastest utilization of readily available metabolic energy. We note that, under real-life conditions, there can be transient hypoglycemia but no aglycemia. Thus, oligodendroglial FAs must only partially compensate for glucose, most probably sparing available glycolysis products for anaplerotic reactions or export and axonal support.

Alternatively, oligodendrocytes may use FA-derived acetyl-CoA to generate ketone bodies in the cholesterol pathway (by 3-hydroxy-3-methylglutaryl-CoA lyase or direct deacylation of acetoacetyl-CoA) 36 , 37 . This would match recent findings in Drosophila spp., where glycolytically impaired glial cells use FA β-oxidation in combination with ketogenesis to support neuronal metabolism 9 , 38 . In mammalian brains, ketone bodies increase with age 39 and can spread horizontally 40 such as pyruvate or lactate through the monocarboxylate transporter MCT1. All these metabolites can also pass via gap junctions to other glial cells in the ‘panglial’ syncytium 41 . Horizontal flux of FAs may also lead to their β-oxidation in other glial cells. Mice with cell-type-specific deletions of MCT1 (ref. 42 ), connexins and pannexins will help define these pathways in the future. The higher vulnerability of astrocytes to glucose deprivation is thus puzzling and may reflect an irreversible metabolic switch to glycolysis and therefore glucose dependency. Our experiments with specific inhibitors suggest that the toxic effects of ROS, as reported for astrocytes 43 , are less likely.

Unlike glycogen mobilization by astrocytes, FA β-oxidation by oligodendrocytes (or ketone body supplementation) cannot support rapid axonal firing, even for a short time 44 . Thus, on severe hypoglycemia, conduction blocks appear unavoidable once glycogen stores have been depleted 45 . However, in the absence of axonal spiking, oligodendroglial FA metabolism might suffice to prevent a more severe ATP decline that leads to irreversible axon loss 46 .

A limitation of our study is the lack of direct in vivo evidence that oligodendroglial β-oxidation supports axon function and survival under real starvation conditions. Starvation experiments are illegal and real hypoglycemia (also insulin induced) would initially introduce physiological responses (gluconeogenesis, ketogenesis) that interfere with and mask the paradigm itself. However, nature provides supporting evidence: hibernating animals have severely reduced blood glucose levels over a period of months 47 , 48 , but lack obvious neurodegeneration. It is interesting that, after hibernation, Syrian hamsters exhibit substantial changes of myelin lipids, with phospholipids but not cholesterol being lost 49 .

We note reports of white matter lesions being detectable by magnetic resonance imaging in patients in diabetic hypoglycemic coma 50 or in severe anorexia nervosa 51 , 52 , which has been mechanistically unexplained. Thus, if nutritional stress is prolonged, the lack of normal myelin synthesis despite continued FA catabolism by oligodendroglia becomes macroscopically visible. Also the peripheral nervous system is involved because individuals with obesity who underwent gastric bypass (bariatric) surgery develop encephalopathy and peripheral neuropathy 53 . Similarly, physically starved rats 54 showed peripheral demyelination by Schwann cells that share functions with oligodendrocytes in myelin lipid metabolism 2 , 17 , 55 .

Our findings have relevance for human neurodegenerative diseases. In pathological conditions with chronic hypometabolism, lack of normal myelin synthesis in oligodendrocytes (but continued FA catabolism) should become macroscopically visible, which may be the case in small-vessel disease. Also, in multiple sclerosis, axon degeneration has been attributed to energy failure 56 which could by itself contribute to demyelination. Many neuropsychiatric diseases, including Alzheimer’s disease, have been associated with hypometabolism 17 and white matter abnormalities 57 , 58 , 59 or unexplained myelin abnormalities 60 , 61 . Long axons in the white matter are clearly a bottleneck of neuronal integrity. In a prolonged metabolic crisis, maintaining the oligodendrogial FA metabolism possibly being the key to prevent irreversible axon degeneration.

All mice were bred on a C57BL/6 background (except Aldh1l1-GFP) and kept under a 12 h:12 h day:night cycle with free access to food and water (temperature of 22 °C, 30–70% humidity). Experimental procedures were approved and performed in accordance with Niedersächsisches Landesamt für Verbraucherschutz und Lebensmittelsicherheit (LAVES; license no. 18/2962).

Transgenic mice were generated in-house by routine procedures, as previously described 14 . To visualize autophagosome in oligodendrocytes, a mTagRFP-mWasabi-LC3 construct 24 was placed under the control of the Cnp promoter. Genotyping was with forward (5′-CAAATAAAGCAATAGCATCACA-3′) and reverse (5′-GCAGCATCCAACCAAAATCCCGG-3′) primers, using the following PCR program: (30× 58 °C: 30 sec; 72 °C: 45 sec; 95 °C: 30 sec).

Eight other mouse lines were genotyped as previously published: (1) Aldh1l1-GFP for labeling astrocytes 62 ; (2) Cxcr-GFP for microglia 63 ; (3) Cnp-mEos2 for oligodendrocytes 14 ; (4) Ng2-YFP for OPC 64 ; (5) Mfp2 flox/flox ::Cnp-Cre , targeting peroxisomal β-oxidation in myelinating glia 27 , 65 ; (6) Slc2a1 flox/flox ::Plp1 CreERT2 , targeting GLUT1 in myelinating glia 66 , 67 ; (7) Tfeb flox/flox ::Cnp-Cre , targeting autophagy in myelinating glia 28 , 65 ; and (8) Thy1-Ateam , encoding a neuronal ATP sensor 5 .

The following control genotypes were used in combination with the corresponding homozygous mutants: Cnp +/+ ::Mfp2 flox/flox , Slc2a1 flox/flox  + tamoxifen and Cnp +/+ ::Tfeb flox/ flox .

Reagents were purchased from Merck unless otherwise stated.

Artificial CSF solution for optic nerve incubation and recording

Optic nerve incubation and electrophysiological recordings were done under constant superfusion with aCSF containing (in mM): 124 NaCl, 23 NaHCO 3 , 3 KCl, 2 MgSO 4 , 1.25 NaH 2 PO 4 and 2 CaCl 2 . The aCSF was constantly bubbled with carbogen (95% O 2 , 5% CO 2 ). A concentration of 10 mM glucose (Sigma-Aldrich, ≥99%) was used as the standard (control). Incubation experiments were done with 0 mM glucose (‘glucose free’). For EM and proteomics experiments, 0.5 mM and 1 mM glucose (‘starvation’) were applied, respectively. For electrophysiological recordings, 2.7 mM glucose was applied as a starvation condition unless otherwise stated. Whenever a lower glucose concentration than 10 mM was applied, the difference was substituted by sucrose (which cannot be metabolized) to maintain osmolarity.

Specific inhibitors for—(1) mitochondrial β-oxidation, 4-Br 68 (TCI, ≥98%); (2) peroxisomal β-oxidation, Thio (Sigma-Aldrich, ≥99%); (3) mitochondrial β-oxidation of long-chain FAs, Etox 69 (Tocris, ≥98%); (4) ROS inhibitor, S3QEL-2 (ref. 70 ) (Sigma-Aldrich); (5) ROS scavenger, MitoTEMPO 71 (Sigma-Aldrich); and (6) autophagy inhibitor, Lys05 (ref. 72 ) (Sigma-Aldrich, ≥98%)—were prepared freshly and added to the aCSF at a concentration of 25, 5, 5, 10, 10 and 10 μM, respectively. To block mitochondrial OXPHOS, 5 mM sodium azide was added to aCSF containing 0 mM glucose and 119 mM NaCl. The autophagy inducer, DMC 73 (AdipoGen), was applied at 40 μM.

Mouse optic nerve preparation and incubation

After cervical dislocation, optic nerves were dissected before the optic chiasma and each nerve were gently removed. The prepared nerves (attached to the eyeball) were transferred into a six-well plate containing 10 ml of aCSF adjusted to 37 °C. Another 90 ml of aCSF was circulating during the incubation period. To study the effects of anoxia, aCSF was bubbled with nitrogen (95% N 2 , 5% CO 2 ; Air Liquide) instead of carbogen (95% O 2 , 5% CO 2 ). To minimize the diffusion of oxygen into aCSF, the wells were sealed with parafilm.

Determining glial cell survival

To label dying cells, optic nerves were exposed to PI (12 µM; Sigma-Aldrich) during the last hour of incubation. Nerves were subsequently washed (10 min) in 7 ml of aCSF. After 1 h fixation with 4% paraformaldehyde (PFA in 0.1 M phosphate buffer), the nerves were detached from the eyeball and frozen blocks were prepared in Tissue-Tek O.C.T compound (SAKURA). Sections (8 μm) were obtained by cryosectioning (Leica) and kept in the dark at −20 °C until further staining. Sections were washed in phosphate-buffered saline (PBS, 10 min) and stained with DAPI (1:20,000 of 1 mg per ml of stock), washed again in PBS (2× for 5 min) and mounted.

All images were taken with an inverted epifluorescent microscope (Zeiss Axio Observer Z1). Illumination and exposure time settings for PI and DAPI were kept constant for all images. For the fluorescent reporter lines, different exposure times were used, according to the observed signal intensity of each fluorophore. Sections (2–3) of optic nerves were imaged and tiled arrays were stitched by the microscope software (Zen, Zeiss) for quantification.

To determine the percentage of dying cells, Fiji software and Imaris software (v.8.1.2) were used. Stitched images were loaded in Fiji to trim areas of the optic nerves that contain dying cells unrelated to the experiment (that is, resulting from normal handling). After adjusting the thresholds for each channel, single cells were automatically marked over the nucleus, manually double-checked and corrected. In the last step, co-localization of signals was calculated and data were exported (Excel files) for statistical analysis. The percentage of dying cells was obtained by dividing the number of PI over DAPI + nuclei (PI/DAPI). For determining the frequency of each cell type, the number of fluorescent cells (green fluorescent protein (GFP), yellow FP (YFP) or monomeric fluorescent protein Eos 2 (mEOS2)) was divided by the number of DAPI + cells. To calculate the relative survival of each cell type, the percentage of each fluorophore-positive cell type was determined (astrocytes: Aldh1l1 -GFP; microglia: Cxcr1 -GFP; OPCs: NG2 -YFP; oligodendrocytes: Cnp -mEOS2) after the corresponding PI/DAPI + cells had been subtracted. The obtained values were normalized to the results for control conditions (10 mM glucose) and expressed as ‘cell survival rate’. To minimize the effect of signal intensity differences between different experiments, we adjusted the threshold for quantifications based on respective controls in each experiment. As we had dramatic cell death in starved nerves, blinding was not applicable.

Myelin preparation

GLUT1-inducible cKO (icKO) mice were sacrificed 5 months after tamoxifen injection (age 7 months). A light-weight membrane fraction enriched in myelin was obtained from frozen half-brains, using a sucrose density gradient centrifugation as previously described 74 . Briefly, after homogenizing the brains in 0.32 M sucrose solution containing protease inhibitor (cOmplete, Roche), a crude myelin fraction was obtained by density gradient centrifugation over a 0.85 M sucrose cushion. After washing and two osmotic shocks, the final myelin fraction was purified by sucrose gradient centrifugation. Myelin fractions were washed, suspended in Tris-buffered saline (137 mM NaCl, 20 mM Tris-HCl, pH 7.4, 4 °C) and supplemented with protease inhibitor (Roche).

Western blotting

Western blotting and Fast Green staining were performed as previously described 75 using the following primary and secondary antibodies: ACAT1 (1:3,000, cat. no. 16215-1-AP, Proteintech), BDH1 (1:500, cat. no. 15417-1-AP, Proteintech), LC3B (1:2,000, cat. no. NB100-2220, Novusbio), Na + /K + ATPase α1 (1:1,000, cat. no. ab7671, Abcam), GLUT1 (1:1,000) 76 , GLUT2 (1:1,000, cat. no. ab54460, abcam), GLUT3 (1:1,000, cat. no. ab191071, abcam), GLUT4 (1:1,000, cat. no. 07-1404, Millipore), MCT1 (1:1,000) 77 , CA2 (1:1,000) 78 and α-tubulin (1:1,000, cat. no. T5168, Sigma-Aldrich), mouse immunoglobulin G heavy and light (IgG H&L) Antibody Dylight 680 Conjugated (1:10,000, cat. no. 610-144-002); rabbit IgG H&L Antibody DyLight 800 Conjugated (1:10,000, cat. no. 611-145-002, Rockland); horseradish peroxidase-conjugated secondary antibodies (1:5,000, cat. nos. 115-03-003 and 111-035-003, Dianova). Signal intensities, analyzed with the Image Studio software Licor or Fiji, were normalized to the corresponding total protein load, which was quantified by Fast Green staining. Obtained values were normalized to the mean of the respective values from control mice.

Proteome analysis and western blots

Optic nerves were collected after incubation in aCSF with 10 mM glucose (control), 0 mM or 1 mM glucose, transferred to microtubes and kept at −80 °C until further analysis. To minimize variability, one nerve from a mouse was incubated under starvation or glucose-deprivation conditions and the other under control conditions. Nerves from two mice were pooled for protein extraction, homogenized in 70 μl of radioimmunoprecipitation analysis buffer (50 mM Tris-HCl; Sigma-Aldrich), sodium deoxycholate (0.5%; Sigma-Aldrich), NaCl (150 mM), sodium dodecylsulfate (SDS) (0.1%; Serva), Triton X-100 (1%; Sigma-Aldrich), EDTA (1 mM) and complete protease inhibitor cocktail (Roche) by using ceramic beads in a Precellys homogenizer (for 3× 10 s at 6,500 rpm) (Precellys 24, Bertin Instruments). After a 5-min centrifugation at 15,626 g and 4 °C, the supernatant was used for protein determination (DC Protein Assay reagents, BioRad) according to the manufacturer’s protocol, with the absorbance of samples at 736 nm (Eon microplate spectrophotometer, Biotek Instruments). Proteins (0.5 µg) were separated on 12% SDS–polyacrylamide gel electrophoresis gels and subjected to silver staining 79 .

Proteome analysis of purified myelin was performed as recently described 74 , 75 and adapted to optic nerve lysates 11 . Briefly, supernatant fractions corresponding to 10 μg of protein were dissolved in lysis buffer (1% ASB-14, 7 M urea, 2 M thiourea, 10 mM dithiothreitol and 0.1 M Tris, pH 8.5). After removal of the detergents and protein alkylation, proteins were digested overnight at 37 °C with 400 ng of trypsin. Tryptic peptides were directly subjected to liquid chromatography–tandem mass spectrometry (LC–MS/MS) analysis. For quantification according to the TOP3 approach 80 , aliquots were spiked with 10 fmol μl −1 of Hi3 E. coli Standard (Waters Corp.), containing a set of quantified synthetic peptides derived from Escherichia coli . Peptide separation by nanoscale reversed-phase ultraperformance LC was performed on a nanoAcquity system (Waters Corp.) as described 11 . MS analysis on a quadrupole time-of-flight mass spectrometer with ion mobility option (Synapt G2-S, Waters Corp.) was performed in ultra-definition (UD-MS E ) 81 and MS E mode, as established for proteome analysis of purified myelin 75 , 82 , to ensure correct quantification of myelin proteins that are of high abundance. Processing of LC–MS data and searching against the UniProtKB/Swiss-Prot mouse proteome database were performed using the Waters ProteinLynx Global Server v.3.0.3 with published settings 75 . For post-identification analysis including TOP3 quantification of proteins, the freely available software ISOQuant 81 ( www.isoquant.net ) was used. False discovery rate for both peptides and proteins was set to a 1% threshold and only proteins reported by at least two peptides (one of which was unique) were quantified as parts per million (p.p.m.) abundance values (that is, the relative amount (w:w) of each protein in respect to the sum over all detected proteins). The Bioconductor R packages ‘limma’ and ‘ q value’ were used to detect significant changes in protein abundance using moderated Student’s t -test statistics as described 83 . Optic nerve fractions from five animals per condition (10 mM glucose versus 1 mM glucose/9 mM sucrose; 10 mM glucose versus 0 mM glucose/10 mM sucrose) were processed with replicate digestion, resulting in two technical replicates per biological replicate and, thus, in a total of 20 LC–MS runs to be compared per individual experiment.

Electron microscopy

Freshly prepared or incubated optic nerves were immersion fixed in 4% formaldehyde, 2.5% glutaraldehyde (EM-grade, Science Services) and 0.5% NaCl in phosphate buffer, pH 7.4 overnight at 4 °C. Fixed samples were embedded in EPON after dehydration with acetone as previously described 84 . Sections of 50- to 60-nm thickness were obtained with the Leica UC7 ultramicrotome equipped with a diamond knife (Histo 45° and Ultra 35 °C, Diatome) and imaged using an LEO EM 912AB electron microscope (Zeiss) equipped with an on-axis 2048 × 2048-CCD-camera (TRS).

EM analysis

EM images from optic nerves were imported into the Fiji software. As a result of overt ultrastructural differences in incubated nerves under starvation, blinding to the conditions was not applicable here. However, analysis of GLUT1 optic nerve images was performed blinded. To create an unbiased selection of axons for which the g -ratio was calculated, a grid consisting of 1-μm 2 squares for ex vivo and 4-μm 2 squares for in vivo experiments was overlaid on each image, and axons that were crossed by the intersecting lines were selected for quantification, with the requisites of: (1) the axon being in focus and (2) the axon shape being not evidently deformed. For each axon, three circles were manually drawn around the axonal membrane, the inner layer and the outer layer of myelin. When myelin was not evenly preserved, the myelin thickness of the adjacent, preserved area was used as a proxy and the circle was corrected accordingly. The obtained area ( A ) of each circle was converted into the corresponding diameter using the formula A  = π r 2 and the g -ratio (outer diameter/axon diameter) was calculated. In ex vivo experiments, the obtained data from the axons with a diameter <2 μm were used for further analysis. The mean g -ratio for axons from one nerve was used for statistical analysis and presented as a data point in the bar graphs.

To determine the axonal size distribution in the optic nerves, axons were binned by increasing caliber and the number of counted axons for each caliber bin was divided by the total numbers of counted axons per nerve and presented as a single data point.

In optic nerves, the total number of axons and the number of degenerating and unmyelinated axons were counted in microscopic subfields of 1,445 µm 2 . Using these data, the percentage of degenerating and unmyelinated axons was calculated.

For nerves incubated in vitro, the percentage of axons containing vesicle-like structures in glial cytoplasm underneath their myelin sheath was also determined.

Electrophysiological recording

All mice used for optic nerve electrophysiology were aged 8–12 weeks (unless otherwise stated). Recordings were performed as described previously 4 , 5 , 85 . Briefly, optic nerves were carefully dissected and quickly transferred into the recording chamber (Harvard Apparatus) and continuously superperfused with aCSF. A temperature controller (TC-10, NPI Electronic) maintained the temperature at 37 °C.

To assure the optimal stimulation and recording condition, custom-made suction electrodes were back-filled with aCSF containing 10 mM glucose. To achieve supramaximal stimulation, a battery (Stimulus Isolator 385; WPI) was used to apply a current of 0.75 mA at the proximal end of the optic nerve, to evoke a CAP at the distal end acquired by the recording electrode at 100 kHz connected to an EPC9 amplifier (Heka Elektronik). The signal was pre-amplified 10× using an Ext 10-2F amplifier (NPI Electronic) and further amplified (20–50×) and filtered at 30 kHz, using a low-noise voltage preamplifier SR560 (Stanford Research System). All recordings were done after nerve equilibration for 2 h (except for excitability and nerve conduction velocity (NCV) measurements) in aCSF containing 10 mM glucose, during which the CAP was monitored every 30 s until a stable waveform had been reached.

To measure the excitability of nerves, CAPs were evoked with currents starting from 0.05 mA and (using 0.05-mA steps) increased to 0.75 mA. The analyzed CAPA for each current was normalized to the obtained CAP at 0.75 mA. NCVs of optic nerves were determined by dividing the length of each nerve by the latency of the second peak for each nerve.

Confocal imaging acquisition

An upright confocal laser scanning microscope (Zeiss LSM 510 META/NLO) equipped with an argon laser and a ×63 objective (Zeiss 63x IR-Achroplan, 0.9 W) was used for live imaging of the optic nerve for ATP measurement, as reported previously 5 , 86 . The immersion objective was placed into superfusing aCSF on top of the clamped optic nerve, with electrodes and images acquired with the time resolution of 30 s. A frame size of 114.21 ×1,33.30 μm 2 (pinhole opening: 168 μm, pixel dwell time: 3.66 μs) was scanned (2× averaging) for cyan FP (CFP; Ex 458 nm; Em 470–500 nm), fluorescence resonance energy transfer (FRET; Ex 458 nm; Em long pass 530 nm) and YFP (Ex 514 nm; Em long pass 530 nm) channel and the focus was adjusted manually based on eye estimation of the nerve movement. To image autophagosome formation in the mouse optic nerve (aged 2–5 months), suction electrodes were used for fixing the nerve. A frame size of 133.45 × 76.19 μm 2 was scanned for the red FP (Ex 543 nm; Em 565–615 nm) and Wasabi (Ex 488 nm; Em BP 500–550 nm) channels with the pinhole adjusted at 384 μm and the pixel dwell time: 58.4 μs.

CAP analysis

Optic nerve function can be measured quantitatively by calculating the area underneath the evoked waveform. This CAPA represents the conduction of nearly all optic nerve axons. The evoked waveform from the optic nerve includes three peaks that represent different axons with different rates of signal speed 4 , 85 .

Exported CAP waveforms were analyzed for area using a customized script (available on GitHub: https://github.com/Andrea3v/CAP-waveform-analysis ) in MATLAB2018b. The time between the first peak of the CAP waveform (at ∼ 1.2 ms after the stimulation, depending on the electrodes used) and the end of third peak (depending on the nerve length) at the last few minutes of the baseline recording was defined as the time range for CAPA integration. This window was kept constant for all recorded traces for each nerve. The calculated CAPA was then normalized to the average obtained from the last 30 min of baseline recordings. The results from several nerves were pooled, averaged and after binning plotted against time. Bar graphs depict the average CAPA for short time windows or the calculated CAPA for larger time windows. Overall, nerve conductivity was determined from the ‘CAPA area’, that is, the area under multiple CAPA curves obtained for the nerves in the experimental arm after normalizing these readings to the corresponding mean values from control nerves.

ATP quantification

The relative level of ATP was calculated as previously reported 5 . Images were loaded in Fiji and the area of the nerve that was stable during the imaging was selected for measuring the mean intensity for three different channels: FRET, CFP and YFP. The FRET:CFP ratio was calculated to give a relative ATP concentration. The ratio was normalized to 0 and 1.0 by using the values obtained during the phase of mitochondrial blockade + glucose deprivation (5 mM azide, 0 mM glucose) and baseline (10 mM glucose), respectively. Bar graphs were obtained by averaging the values obtained at the last 5 min of each step of applied protocol for electrophysiology recordings of each nerve.

Immunohistology

Immunostaining was performed as previously described 87 . Longitudinal cryosections of the optic nerve were fixed in 4% PFA (10–20 min) followed by washing in PBS (3× for 5 min). After 30 min of permeabilization with 0.4% Triton in PBS at room temperature (RT), blocking was performed for 30 min at RT in blocking solution (4% horse serum, 0.2% Triton in PBS). Incubation with primary antibody (Iba1 (1:1,000, cat. no. 019-19741, Wako), interleukin (IL)-33 (1:150, cat. no. AF3626, R&D Systems), Plin2 (1:150, cat. no. 15294-1-AP, Proteintech), CC1 (1:150, cat. no. OP80, Merck) and NF-L (1:150, cat. no. MCA-1D44, EnCor)) was performed in blocking solution (1% high sensitivity buffer, 0.02% Triton in PBS) at 4 °C. After washing with PBS (3× for 10 min), sections were incubated with secondary antibody in PBS/bovine serum albumin-containing DAPI (1:2,000, stock 1 mg ml −1 ) for 1 h at RT. The washed sections (3× for 10 min) in PBS were mounted and microscopy was performed.

Autophagosome quantification

Microscopy images were processed with Fiji software and the number of autophagosomes (appearing as puncta) and cell bodies in each image were manually quantified. The total numbers of counted autophagosomes were divided by the total numbers of cell bodies in the same images. At least three images from different regions of the nerve were analyzed for each nerve and the average of the obtained values was presented as a single data point.

Mouse behavior

All measurements were performed by the same experimenter, blinded to the animals’ genotype. Mice were trained weekly for 6 weeks before actual testing. For the Rotarod test, mice were placed on the horizontal rod. Rotation started with 1 rpm and 1 unit (rpm) was added every 10 s. The rpm value at which mice fell was recorded and the average of three repeats was reported for each mouse.

For grip strength measurements, mice were allowed to grasp a metal bar that connected to the grip strength meter. Holding on with their forelimbs, mice were slowly pulled backward until the grip was lost. The average of three measurements was reported as a data point.

Data presentation and statistics

All data are presented as mean ± s.e.m. For cell death measurements in the optic nerve, quantifications of two to three sections from the same nerve were combined and the mean was taken as one data point (in Fig. 1c , the 16-h incubation point was determined with one to three sections). The N and n numbers indicate the total number of mice used for each condition and the total number of independently incubated/recorded optic nerves or samples that were analyzed, respectively. For proteomics after incubations at 1 mM and 10 mM glucose, two optic nerves were pooled. Statistical analysis of the data was performed in excel or Graphpad Prism 9. The experiments with big sample size were tested for data normality using D’Agostino and Pearson’s omnibus normality test and, for groups with small size, normal distribution of the data was assumed. For experiments with more than two groups ordinary one-way analysis of variance (ANOVA) or the Kruskal–Wallis test with an appropriate post-hoc test was applied for intergroup comparison. For experiments with two groups, the difference in the variance of each group of data was tested and, based on the outcome, the appropriate Student’s t -test (unpaired, two-tailed distribution, two-sample equal variance/homoscedastic or unequal variance/heteroscedastic) was performed. All reported P values in the figures are related to unpaired, homoscedastic, two-tailed Student’s t -test unless otherwise stated.

Animals with blindness, optic nerves with dissection artifact and unstable baseline recordings were excluded in the present study. Data collection and analysis were not performed blind to the conditions of the experiments unless otherwise stated.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

All relevant data to the manuscript will be available upon a reasonable request to corresponding authors. The MS proteomics data have been deposited to the ProteomeXchange Consortium via the PRIDE 88 partner repository with the dataset accession no. PXD053960 . Source data are provided with this paper.

Code availability

MATLAB script for CAP analysis is available on GitHub ( https://github.com/Andrea3v/CAP-waveform-analysis ).

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Acknowledgements

We thank A. Fahrenholz, B. Sadowski, D. Hesse, G. Fricke-Bode and U. Kutzke for technical help, and the institute’s animal facility, the light microscopy facility and the mechanical workshop for expert support. We also thank U. Suter and the KAGS team for helpful discussions. E.A. was supported by a fellowship of the German Academic Exchange Service. Work in the authors’ laboratory was supported by grants from the German Research Council, including nos. SPP1757 and TRR-274. A.S.S. received support from the Cloëtta Foundation and the Swiss National Science Foundation (grant no. PCEFP3_187000). B.P. and K.A.N. acknowledge support by the Dr. Myriam and Sheldon Adelson Medical Foundation. K.A.N. was supported by a European Research Council Advanced Grant (MyeliNANO, 671048).

Open access funding provided by Max Planck Society.

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Max Planck Institute for Multidisciplinary Sciences, Department of Neurogenetics, Göttingen, Germany

Ebrahim Asadollahi, Andrea Trevisiol, Aiman S. Saab, Payam Dibaj, Reyhane Ebrahimi, Kathrin Kusch, Torben Ruhwedel, Wiebke Möbius, Celia M. Kassmann, Johannes Hirrlinger & Klaus-Armin Nave

University of Toronto, Sunnybrook Health Sciences Centre, Department of Physical Sciences, North York, Ontario, Canada

Andrea Trevisiol

University of Zurich, Institute of Pharmacology and Toxicology, Zurich, Switzerland

Aiman S. Saab, Zoe J. Looser & Bruno Weber

Center for Rare Diseases Göttingen, Department of Pediatrics and Pediatric Neurology, Georg August University Göttingen, Göttingen, Germany

Payam Dibaj

University of Göttingen Medical School, Institute for Auditory Neuroscience and Inner Ear Lab, Göttingen, Germany

Kathrin Kusch

Max Planck Institute for Multidisciplinary Sciences, Department of Molecular Neurobiology, Neuroproteomics Group, Göttingen, Germany

University Medical Center Göttingen, Department of Psychiatry and Psychotherapy, Translational Neuroproteomics Group, Göttingen, Germany

School of Medical Sciences and Charles Perkins Centre, The University of Sydney, Camperdown, New South Wales, Australia

Jun Yup Lee & Anthony S. Don

Department for Bioinformatics and Biochemistry, Braunschweig Integrated Center of System Biology, Technische Universität Braunschweig, Braunschweig, Germany

Michelle-Amirah Khalil & Karsten Hiller

Lab of Cell Metabolism, Department of Pharmaceutical and Pharmacological Sciences, KU Leuven, Leuven, Belgium

Myriam Baes

Department of Medicine, David Geffen School of Medicine at UCLA, Los Angeles, CA, USA

E. Dale Abel

Telethon Institute of Genetics and Medicine, Naples, Italy

Andrea Balabio

Department of Translational Medical Sciences, Federico II University, Naples, Italy

Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, TX, USA

Jan and Dan Duncan Neurological Research Institute, Texas Children’s Hospital, Houston, TX, USA

Feinberg School of Medicine, Northwestern University, Chicago, IL, USA

Brian Popko

Max Planck Institute for Multidisciplinary Sciences, Clinical Neuroscience, Göttingen, Germany

Hannelore Ehrenreich

Central Institute of Mental Health, Mannheim, Germany

Carl-Ludwig-Institute for Physiology, Faculty of Medicine, University of Leipzig, Leipzig, Germany

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Contributions

E.A., C.K. and K.A.N. conceptualized and designed the study. E.A., Z.J.L., P.D., K.K., J.Y.L., M.A.K., R.E. and T.R. performed experiments. A.T., A.S.S., B.W., P.D., W.M., O.J., H.E. and J.H. supervised trainees, contributed to data analysis and provided conceptual input. A.S.D., K.H., M.B., E.D.A., B.P. and A.B. provided mouse mutants and critical experimental advice. E.A. and K.A.N. wrote the manuscript with input from the coauthors.

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Correspondence to Ebrahim Asadollahi or Klaus-Armin Nave .

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A.B. is cofounder and shareholder of Casma Therapeutics and an advisory board member of Avilar Therapeutics and Amplify Therapeutics. The other authors declare no competing interests.

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Extended data

Extended data fig. 1 death of glucose-deprived optic nerve glial cells is not caused by oxidative stress..

a , Acutely isolated mouse optic nerves (age 2 months) were maintained for 24 h either in the presence of low (1 mM) glucose or 1.5 mM beta-hydroxybutyrate (HB). Longitudinal nerve sections were stained with DAPI (blue) and propidium iodide (in white). b , Bar graphs showing the percentage of viable cells for each condition (compare to Fig. 1c ). Normal survival is possible in the presence of 1 mM glucose or 1.5 mM HB, indicating the critical role of glucose in energy production (N = n = 3 for both conditions; mean ± SEM, unpaired two-sided t-test). c , Longitudinal sections of optic nerves stained with PI and DAPI after 24 h incubation in glucose-free aCSF and in the presence of 10 μM of S3qel-2 (inhibitor for ROS production in complex III of electron transport chain) and 10 μM MitoTEMPO (mitochondrial ROS scavenger) or vehicle (DMSO) as control. d , Quantified cell survival (PI/DAPI) indicates that ROS do not contribute to cell death (N = n = 4 for control and N = n = 5 for ROS inhibitor/scavenger; wild type mice, 8-10 weeks old; mean ± SEM, unpaired two-sided t-test). N and n indicate the total number of optic nerves used for each condition and the total number of independent experiments, respectively.

Extended Data Fig. 2 Vesicle formation in the myelin compartment is independent of ongoing axonal degeneration in metabolically stressed optic nerves.

a , Electron micrographs of wildtype optic nerves (age 2 months), incubated for 24 in 10 mM glucose (left) or 0.5 mM glucose (right). Note periaxonal vesicular structures (white arrows) indicating myelin degradation under low glucose. b , Quantification of the data in ( a ) comparing percentage of myelinated axon cross sections with periaxonal vesicular structures (N = n = 3 for both conditions; mean ± SEM, unpaired two-tailed Welch’s t-test). c , longitudinal optic nerve section prepared freshly (0 h, left), after 24 h in 10 mM glucose (middle) or 0.5 mM glucose (right), immunostained for NF-L (green) and counter-stained with DAPI (blue). Yellow arrowheads point to degenerating axons (N = n = 3-4 for each condition).

Extended Data Fig. 3 Increased autophagy and lipid metabolism in metabolically stressed optic nerves.

a , Left: silver stained gels of optic nerve lysates from 2 month old wildtype mice (both genders), prepared after 24 h incubation in 10 mM glucose or 1 mM glucose (two nerves pooled per lane; one lane is equivalent to one sample). N = n = 5 for both conditions. Right: optic nerve lysates prepared after 16 h in 10 mM glucose or 0 mM glucose. Note the lack of major protein degradation. N = n = 5 for both conditions. b , Relative abundance of selected proteins in optic nerve lysates after 24 h in 1 mM glucose (left, N = n = 5) or 16 h in 0 mM glucose (right, N = n = 5). Note that enzymes of glucose and lipid metabolism show only moderate changes in abundance. Autophagy related proteins are increased in the presence of 1 mM glucose only, indicating a requirement of glucose for RNA synthesis and protein expression (N = n = 5, two technical replicates each; moderated t-statistics (more details in methods section)); Statistical significance (q-value) depicted on the right side of each panel. c, d , Western blots of lysates from wildtype optic nerves, incubated in 10 mM or 0 mM glucose for 16 h (age 8-12 weeks old, N = n = 5 for each condition) ( c ) and quantification of ACAT1 and BDH1 ( d ). Normalized to protein input (mean ± SEM, unpaired two-tailed t-test). e , Cell survival of 24 h glucose-deprived optic nerves from TFEB cKO mice (N = n = 4) and controls (N = n = 4; age 8-12 weeks). Images from longitudinal sections were stained with PI and DAPI. f , Quantified data from ( e ). There is no difference of cell survival (mean ± SEM, unpaired two-tailed Welch’s t-test). N and n indicate the total number of independent samples for each condition and the total number of independent experiments, respectively.

Extended Data Fig. 4 Decline in starved nerve function upon beta-oxidation inhibition is not caused by inhibitors cytotoxcicity or mitochondrial ROS generation.

a , Empirical determination of the minimal glucose concentration at which optic nerves can spike at low frequency (1/30 s) for 3 hours without loss of compound action potential area (CAPA), normalized to control values with 10 mM glucose. b , Bar graphs of the CAPA summation (CAPA area) calculated for the time window (yellow box in a ) for different glucose concentrations (N = n = 3 for 10, 3.7, 3 and 2.7 mM glucose condition, N = n = 3 for 2 mM and N = n = 5 for 3.3 mM glucose condition, one-way ANOVA, Tukey’s test). c , Recordings in aCSF+10 mM glucose ±25 μM 4-Br (N = n = 7 for control and N = n = 5 for 4-Br treated nerves). d , Bar graph of the CAPA summation for the defined time window (dashed lines) in ( c ). Values normalized to control. e , Normal conduction in aCSF with 10 mM glucose and 5 μM Etomoxir (Etox; N = n = 4) in comparison to 10 mM glucose control (same data as in c ; N = n = 7). f , Bar graph comparing the calculated CAPA summation for the time window between the dash lines in ( e ). obtained values were normalized to control condition. g , Normal conduction in aCSF with 10 mM glucose and 5 μM Thioridazine (Thio; N = n = 4 in comparison to 10 mM glucose (same data as in c ; N = n = 7)). h , Bar graph comparing the calculated CAPA summation for the depicted time window (dash lines) in ( g ). Obtained values were normalized to control. i , Conductivity under low glucose (aCSF+2.7 mM glucose +/-4-Br(25 μM)) in the presence of the ROS production inhibitor (S3qel-2, 10 μM) and mitochondrial ROS scavenger (MitoTEMPO, 10 μM). N = n = 5 for control (without 4-Br) and N = n = 7 (plus 4-Br). j , Bar graph comparing calculated CAPA from the data in (N &n the same as in ( i )) for the average of CAPA recorded during the last 5 min of each step of the RAMP protocol. All nerves from wild type mice (age 8-12 weeks, from both genders) unless mutants specified. All error bars: mean ± SEM, unpaired two-tailed t-test, unless indicated. N and n indicate the total number of optic nerves for each condition and the total number of independent experiments, respectively.

Extended Data Fig. 5 Inhibition of beta-oxidation in 10 mM glucose or peroxisomal beta-oxidation in oligodendrocytes does not affect optic nerves at histological and electrophysiological level at young adult mice.

a , Spiking at high frequencies. Recordings were in aSCF (10 mM glucose) ± 25 μM 4-Br, using a RAMP protocol of increasing frequencies between 5 and 20 Hz (N = 3, n = 4 for control and N = 2, n = 3 for 4-Br treated nerves). b , Bar graphs of CAPA, calculated for each nerve over 5 min at the indicated frequencies (from a ). c , EM images of MFP2 cKO optic nerves. d , Axon numbers in MFP2 cKO (N = 2, n = 3) versus controls (N = n = 3). e , Unmyelinated axon numbers (in m ) in MFP2 cKO (N = 2, n = 3) versus controls (N = n = 3). f , Percentage of axons with abnormal morphology in MFP2 cKO (N = 2, n = 3) versus controls (N = n = 3). g , Longitudinal optic nerve section of MFP2 cKO and controls, immunostained for Iba1 (counterstained with DAPI). h , Number of Iba1+ microglia normalized to DAPI+ nuclei (N = n = 4 for control and MFP2 cKO). i , Normal excitability of optic nerves (N = 6, n = 11 for CTR and N = 4, n = 7 for MFP2 cKO). j , Optic nerve conduction velocity (NCV) in controls (N = 7, n = 11) and MFP2 cKO (N = 6, n = 9). All nerves from wild type mice (age 8-12 weeks, male and female) unless mutants specified. All error bars: mean ± SEM, unpaired two-tailed t-test. N and n indicate the total number of used mice for each condition and the total number of independently recorded/analyzed optic nerves, respectively.

Extended Data Fig. 6 Preexisting autophagy contributes to oligodendroglial support of axonal conduction in starved optic nerves.

a , CAP recordings from wild type optic nerves kept under low glucose condition (aCSF with 2.7 mM glucose) in the presence or absence of 10 μM autophagy inhibitor Lys05 (8-12 weeks old, male and female; N = n = 5 each condition). b , Bar graph representing the average CAPA during the last 5 min of each stimulation step (same data in a ; mean ± SEM, unpaired two-tailed t-test). c , Effect of the autophagy inducer DMC (40 μM) on nerve conduction under low glucose condition. Note that the inducer improves CAPA in wildtype optic nerves but in nerves from TFEB cKO mice. d , Quantification of the data in ( c ) with a comparison of CAPA at 9 h (average of 5 min recordings). Statistics: N = n = 3 for control ( + DMSO), N = n = 3 for control +DMC, and N = n = 4 for TFEB + DMC, 3-5 months old mice from both genders, (mean ± SEM, one-way ANOVA, Tukey’s test).

Extended Data Fig. 7 Hypomyelinated optic nerves in normally behaving GLUT1 icKO mice lack histological signs of pathology or gliosis.

a , Normal body weight of GLUT1 icKO mice at the age of 7 months (5 months post tamoxifen). (N = 6, CTR and icKO). b , Normal rotarod performance of GLUT1 icKO mice shown as the speed (rpm) at which the mice fall (same mice in a ). c , Normal forelimb grip strength of GLUT1 icKO mice (same mice as in a ). d , Quantification of the inner tongue size as a function of axon caliber, by plotting the axon diameter (ax) by the respective diameter of a circle defined by the inner surface of the compacted myelin sheath (il), analogous to g-ratios (same images in Fig. 4f ). e , Tendency for smaller average inner tongue sizes in GLUT1 icKO mice. (same data as in d ; CTR, N = n = 3; icKO, N = n = 4). f , Normal number (density) of optic nerve axons in GLUT1 icKo mice normalized to controls (same images from Fig. 4f ). g , Normal axon size distribution in optic nerve from GLUT1 icKo mice (same images from Fig. 4f ; CTR, N = n = 3; icKO mice, N = n = 4). h , Normal percentage of unmyelinated axons in GLUT1 icKO mice (same images from Fig. 4f ). i , Normal percentage of axons showing morphological abnormalities by EM analysis (from images in Fig. 4f ). j , Normal excitability of optic nerves from GLUT1 icKO mice, recorded with increasing current of stimulation. Calculated CAPA for each current was normalized to recorded CAPA at 0.75 mA (CTR, N = n = 9; icKO, N = n = 15). k , Normal optic nerve conduction velocity (NCV) of GLUT1 icKO mice, calculated by dividing latency of the second CAP peak to the length of the nerve (common data with j ; CTR, N = n = 6; icKO, N = n = 12). l , Longitudinal sections of GLUT1 icKO optic nerves immunostained for Iba1 and counterstained with DAPI. m , Normal number of Iba1+ microglia in optic nerve from GLUT1 icKO mice, normalized to the number of DAPI+ nuclei in the same area (same images in l ). CTR N = 3, n = 4, icKO N = n = 5. All animals (both genders) were analyzed 4-5 months post tamoxifen injections. All error bars: mean ± SEM, unpaired two-tailed t-test. CTR, Control.

Extended Data Fig. 8 Optic nerves in GLUT1 icKO mice lack histological signs of changes in inflammatory/oligodendrocyte population or lipid droplets.

a , Longitudinal sections of GLUT1 icKO optic nerves immunostained for CC1 (orange) and counterstained with DAPI (blue). b , Oligodendrocytes population in optic nerve from GLUT1 icKO mice calculated by dividing the DAPI spots positive for CC1 to total number of DAPI+ nuclei (DAPI + CC1 + /DAPI + ) in the same area. Data points were normalized to the mean of CTR; N = 4 for both CTR and icKO. c , Longitudinal sections of GLUT1 icKO optic nerves immunostained for CC1 (orange), IL-33 (green) and counterstained with DAPI (blue). d-e , Bar graphs showing percentage of oligodendrocytes were positive for inflammatory marker, IL-33, (CC1 + IL-33 + ) divided to total number of oligodendrocytes (DAPI + CC1 + ) ( d ) and percentage of oligodendrocytes exhibiting high expression of inflammatory marker, IL-33 ( e ). (data points were normalized to the mean of CTR; N = 4 for both CTR and icKO). f , GLUT1 icKO optic nerve longitudinal sections were immunostained for Plin2 (red) and counterstained with DAPI (blue). Note lipid droplets are barely detectable in optic nerve cells (N = 3 for both control and icKO nerves). All animals (from both genders) were analyzed at the age of 6-7 months (4-5 months post tamoxifen). An unpaired two-tailed t-test was performed for comparing different groups. Error bars indicate mean ± SEM, and individual data points displayed. CTR, Control.

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Supplementary Fig. 1 Raw western blots in the present study.

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Source Data Fig. 1 Plotted source data for Fig. 1. Source Data Fig. 2 Plotted source data for Fig. 2. Source Data Fig. 3 Plotted source data for Fig. 3. Source Data Fig. 4 Plotted source data for Fig. 4.

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Asadollahi, E., Trevisiol, A., Saab, A.S. et al. Oligodendroglial fatty acid metabolism as a central nervous system energy reserve. Nat Neurosci (2024). https://doi.org/10.1038/s41593-024-01749-6

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DOI : https://doi.org/10.1038/s41593-024-01749-6

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