Conversely, postsynaptic expression of plasticity is reflected as a change in the regulation, turnover, or responsiveness of postsynaptic receptors (Sheng and Kim, 2002; MacDougall and Fine, 2014; Costa et al., 2017). The quantal size, q, depends upon the number and properties of postsynaptic receptors activated by a quantum as well as by the amount of transmitter contained in one vesicle (Korn and Faber, 1998). Although q may thus in principle be influenced by both pre- and postsynaptic factors, the quantal size is commonly assumed to relate to postsynaptic mechanisms. In other words, vesicle size and transmitter loading are assumed to be both stereotyped and not plastic (Bliss, 1990; Faber and Korn, 1991; Korn and Faber, 1998).

## Statistical Models Are Used to Estimate Synaptic Parameters

According to Del Castillo and Katz (1954) and many others (Johnson and Wernig, 1971; McLachlan, 1978; Korn et al., 1987; Bekkers and Stevens, 1990; Redman, 1990), the frequency distribution of evoked postsynaptic responses due to probabilistic presynaptic release follows binomial statistics. Poisson statistics may be more realistic in certain cases, for example in low Ca2+ to-Mg2+ conditions when p is very low (Del Castillo and Katz, 1954; Martin, 1966). However, binomial statistics are assumed in the majority of studies of release.

The choice of release statistics comes with inherent assumptions. When the binomial model is relied upon, it is for example implicitly assumed that the release probability, p, and quantal size, q, are uniform across all n release sites (**Box 1**). These assumptions have the added benefit of simplifying the relationships between the synaptic parameters n, p, and q (McLachlan, 1978; Redman, 1990; Faber and Korn, 1991; Korn and Faber, 1991; Costa et al., 2017). Another useful consequence is the binomial model provides a simple theoretical framework for identifying the locus of expression of longterm plasticity by analysis of the CV (**Box 2**; Bekkers and Stevens, 1990; Malinow and Tsien, 1990; Faber and Korn, 1991). However, even if the constraints for the binomial release model

#### BOX 2 | What is the point of using 1/CV2 instead of CV?

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It may seem counterintuitive and unnecessarily cumbersome to plot 1/CV2 , normalized, versus the normalized amplitude in CV analysis. The rationale for this practice stems from the fact that—if you assume a binomial model of vesicular release—the probability of release, p, is proportional to 1/CV2 . In other words, you can to a first approximation read off the change in release probability, p, from the y-axis when the CV analysis is represented in this manner, which is a handy advantage.

To show that p ∝ 1/CV2 , we combine the expected value E [X] (Eq. 1) and the variance Var [X] of the binomial distribution (Eq. 2), and plug these into the expression for the CV, which is the standard deviation over the mean.

$$\begin{cases} \mathsf{CV} = \frac{\sigma}{\mu} \\\\ \mathsf{E}\left[\mathsf{X}\right] = \mathsf{n}\mathsf{p}\mathsf{q} = \mu \\ \mathsf{V}\mathsf{s}\mathsf{r}\left[\mathsf{X}\right] = \mathsf{n}\mathsf{p}\left(1-\mathsf{p}\right)\mathsf{q}^{2} = \sigma^{2} \end{cases}$$

$$\Rightarrow \mathsf{CV}^{2} = \left(\frac{\sigma}{\mu}\right)^{2} = \frac{\mathsf{n}\mathsf{p}\left(1-\mathsf{p}\right)}{\left(\mathsf{n}\mathsf{p}\right)^{2}} = \frac{1-\mathsf{p}}{\mathsf{n}\mathsf{p}}$$

Here, the scaling resulting from the quantal amplitude, q, vanishes. Solving for p gives: 1

$$\rho = \frac{-}{\pi \text{C} \text{V}^2 + 1}$$

So, if we assume that the number of release sites, n, does not change after the induction of plasticity, it follows that:

$$
\therefore \rho \propto \frac{1}{\text{CV}^2}
$$

Although the number of release sites, n, may change in late LTP by growth of new synaptic connections (Geinisman et al., 1993; Bolshakov et al., 1997; Korn and Faber, 1998; Loebel et al., 2013), it is reasonable to assume that n does not change in early LTP (Box 1). This assumption, however, is a key caveat of assuming the binomial distribution in CV analysis.

#### What is special about the diagonal?

One additional advantage of plotting 1/CV2 versus the mean is that the diagonal line, 1y/1x = 1, can be used as a demarcation line to determine whether expression is pre- or postsynaptic (Figure 1). To show this, we again use the expressions for the expected value, E [X], and the variance, Var [X], of the binomial distribution (Eqs 1 and 2), and combine these with the expression for the CV.

$$\begin{cases} \mathsf{CV} = \frac{\sigma}{\mu} \\ \mathsf{E}\left[\mathsf{X}\right] = \mathsf{n}\mathsf{p}\mathsf{q} = \mu \\ \mathsf{V}\mathsf{s}\mathsf{r}\left[\mathsf{X}\right] = \mathsf{n}\mathsf{p}\left(1-\mathsf{p}\right)\mathsf{q}^{2} = \sigma^{2} \end{cases}$$

$$\Rightarrow \mathsf{CV}^{2} = \left(\frac{\sigma}{\mu}\right)^{2} = \frac{\mathsf{n}\mathsf{p}\left(1-\mathsf{p}\right)}{\left(\mathsf{n}\mathsf{p}\right)^{2}} = \frac{1-\mathsf{p}}{\mathsf{n}\mathsf{p}}$$

We solve for 1/CV2 and normalize with respect to the initial probability of release, p0. We also define a presynaptic change in synaptic strength due to altering the probability of release, cpre = p/p0, to explore what happens when expression is only presynaptic. In this scenario, the y coordinate in the CV analysis plot is:

$$\frac{1}{\text{CV}^2}\_{\text{CV}^2 \text{ com}} = \frac{\rho}{1-\rho} \frac{1-\rho\_{\text{O}}}{\rho\_{\text{O}}} = \frac{c\_{\text{O}\text{Po}}(1-\rho\_{\text{O}})}{1-c\_{\text{f}\text{Po}}\rho\_{\text{O}}}$$

Here, it is useful to note that this above expression does not depend on the quantal amplitude, q. Similarly, the x coordinate, µnorm, in the CV analysis plot is:

$$
\mu\_{\text{COR}} = \frac{n\rho\varrho}{n\rho\varrho\varrho\varrho\_0} = c\_{\text{fluoG}\text{pot}}
$$

where

$$n = n\_0

c\_{\text{f70}} = \frac{\rho}{\rho\_0}

c\_{\text{f8cut}} = \frac{Q}{Q\_{\odot}}$$

#### BOX 2 | Continued

As before, we assume that the number of release sites, n, remains unaltered. In the scenario where plasticity is solely presynaptic, cpost reduces to 1, so we are left with µnorm = cpre. Here, the end coordinate becomes:

$$\left(c\_{\text{ро}}, \frac{c\_{\text{ро}}\left(1-\rho\_{\text{�}}\right)}{1-c\_{\text{f}@0}\rho\_{\text{0}}}\right).$$

Therefore, the slope of an imagined line from the starting coordinate (1, 1) to this end point is:

$$\frac{\Delta\chi}{\Delta\chi} = \frac{\frac{c\_{\text{FO}}(1-\rho\_{\text{O}})}{1-c\_{\text{FO}}\rho\_{\text{O}}} - 1}{c\_{\text{PO}} - 1} = \frac{1}{1 - c\_{\text{PO}}\rho\_{\text{O}}}$$

Since both cpre and p0 are positive, non-zero numbers, it follows that 1y/1x > 1. Ergo, presynaptically expressed plasticity gives rise to data points above the unitary diagonal line 1y/1x = 1 for LTP. In the case of LTD, the scenario is the inverse; presynaptically expressed plasticity gives rise to data points below the diagonal (Figure 1).

In the case where plasticity is solely postsynaptically expressed, we are left with µnorm = cpost, so the final CV coordinate is now:

$$\left(\mathsf{C}\_{\mathsf{fect}}, \frac{\mathsf{C}\_{\mathsf{fect}} \left(\mathsf{1} - \mathsf{D}\_{\mathsf{0}}\right)}{\mathsf{1} - \mathsf{C}\_{\mathsf{fect} \mathsf{Q} \mathsf{D}}}\right) = \left(\mathsf{C}\_{\mathsf{fect}}, \frac{\mathsf{1} - \mathsf{D}\_{\mathsf{0}}}{\mathsf{1} - \mathsf{D}\_{\mathsf{0}}}\right) = \left(\mathsf{C}\_{\mathsf{fect}}, \mathsf{1}\right)$$

which implies a line parallel to the x-axis:

$$\frac{\Delta\mathcal{Y}}{\Delta\chi} = \frac{1 - 1}{c\_{\text{post}} - 1} = 0$$

This finding is in effect trivial, since we already observed above that 1/CV2 norm did not depend on the quantal amplitude, q. It is also consistent with the above observation that p ∝ 1/CV2 since a line parallel to the x-axis implies that the probability of release p remains unaltered as the mean µ is increased or decreased.

In practice, since CV analysis relies on a finite number of data points in the baseline and post-induction period, the slope of the line between the coordinate (1, 1) and the end point will suffer from inaccuracy, due to the noise inherent in the stochasticity of release. This means pre- and postsynaptically expressed plasticity will not always give rise to data points on opposite sides of the diagonal demarcation line (e.g., see Figures 4 and 5), especially for experiments with baseline period with relatively few responses. Plasticity can of course also be expressed as a mixture of pre- and postsynaptic mechanisms (Sjöström et al., 2007; Costa et al., 2015), in which case data points may consistently end up on or close to the diagonal line.

are not met, CV analysis may still work adequately (**Box 1**; Faber and Korn, 1991).

#### PRINCIPLES OF CV ANALYSIS

#### The Basis for CV Analysis in Intuitive Terms

In probability theory and statistics, the CV—which is defined as the standard deviation σ divided by the mean µ—is a general standardized measure of dispersion of a probability or frequency distribution. The CV is, in other words, an experimentally useful measure of noise, or normalized overall variability (Abdi, 2010). For this reason, the CV is also known as the relative standard deviation. Since the majority of the noise at a synapse is due to the stochastic nature of quantal neurotransmitter release (Otmakhov et al., 1993; Costa et al., 2017), changes in noise as indicated by alterations in the CV are useful, since such changes suggest

a presynaptic locus of that change, i.e., due to a change in p (Bekkers and Stevens, 1990; Malinow and Tsien, 1990; Faber and Korn, 1991). Conversely, an on-average alteration in synaptic strength without a concomitant change in the CV would by the same line of reasoning appear to be due to postsynaptic changes in q, e.g., by regulation of AMPA receptors (Kauer et al., 1988; Isaac et al., 1995; Liao et al., 1995; Barria et al., 1997; Nicoll and Malenka, 1999). This latter observation, however, assumes that vesicle neurotransmitter loading is fixed and stereotyped (**Box 1**). In summary, an overall intuitive understanding of CV analysis should thus be based on the observation that changes in synaptic noise are primarily due to presynaptic expression. Conversely, no changes in noise during long-term plasticity suggests that expression is postsynaptic.

#### Binomial Release Statistics

In the context of neurotransmission, the CV is represented by the standard deviation, σ, of a set of evoked synaptic responses divided by their mean, µ, taken over a given time period (Bekkers and Stevens, 1990; Malinow and Tsien, 1990; Faber and Korn, 1991; Costa et al., 2017):

$$\text{CV} = \frac{\sigma}{\mu} \tag{3}$$

To extract specific synaptic release parameters, it is useful to apply a specific statistical model. A typical choice is the binomial release model (**Box 1**), although it is important to understand that the CV is a general measure of noise and that the CV is not in and of itself linked to any particular statistical model.

In terms of binomial statistics, µ is the mean synaptic efficacy given by the expected value of the random variable X, which is E [X] = µ = npq (Eq. 1), and the standard deviation is derived from the variance (Eq. 2) as σ = √ Var [X] = q np 1 − p q 2 . These mathematical relationships have been described many times in greater detail in the previous literature, and we refer the reader to these papers for a more in-depth treatment (Johnson and Wernig, 1971; McLachlan, 1978; Faber and Korn, 1991).

Typically, 1/CV2 rather than CV is plotted in most studies (**Figure 1**). This perhaps counterintuitive practice can be explained by the fact that 1/CV2 is proportional to the probability of release (**Box 2**). This practice is furthermore justified by the observation that the unitary diagonal line in a 1/CV2 versus µ plot (**Figure 1**) is a handy demarcation line between pre- and postsynaptic expression (**Box 2**). In this context, it is worth noting that the analytical expression for the CV is independent of the quantal size, q (Bliss, 1990; Malinow and Tsien, 1990; Faber and Korn, 1991; Korn and Faber, 1991; Costa et al., 2017), as derived from Eqs 1–3:

$$\text{CV} = \left(\frac{\sigma}{\mu}\right) = \sqrt{\frac{1-p}{np}}$$

This fact reflects the observation in the above intuitive introduction to CV analysis that postsynaptic changes should not affect synaptic noise levels. Again, this is because the variation at individual release sites predominately stems from the stochastic nature of neurotransmitter release (Otmakhov et al., 1993; Costa et al., 2017) and the CV is a metric of noise (Abdi, 2010; Costa et al., 2017).

To ensure that the CV reflects synaptic noise, characteristic of stochastic release, it has been argued that it should be corrected for the background noise (Faber and Korn, 1991):

$$
\sigma^2 = \sigma\_{\text{measured}}^2 - \sigma\_{\text{background}}^2
$$

In practice, we find that subtracting the background noise has little or no impact on the locus of expression, as long as the background noise is stable across recordings.

## RESULTS

#### Expected Outcomes

Coefficient of variation analysis compares the relative change of synaptic parameters before and after induction of plasticity (Faber and Korn, 1991), which in practical terms means we work with normalized values of CV and mean synaptic strength, µ. In the standard CV analysis plot (**Figure 1**), the normalized change in synaptic strength, µ(norm), thus indicates

FIGURE 1 | Locus of expression areas in the CV analysis plot. Normalized 1/CV2 , a proxy for the probability of release p (Box 2), is plotted against the normalized mean µ(norm), which is a measure of synaptic strength. The solid horizontal line at y = 1 indicates 100% 1/CV2 (norm), or no change in p. The dotted vertical line at x = 1 delineates LTP (to the right) from LTD (to the left). The dashed diagonal line with slope 1y/1x = 1 demarcates presynaptic from postsynaptic expression of plasticity (Box 2). In other words, data that falls on or close to the continuous horizontal line should be considered to be postsynaptically expressed, whereas data that is above the dashed diagonal for LTP, or below it for LTD, should be considered presynaptically expressed. Mixtures of pre- and postsynaptic expression is also possible (Sjöström et al., 2007), which results in data points scattered between the dashed diagonal and the continuous horizontal lines.

whether LTP or LTD took place, while appreciable changes in 1/CV2 (norm) serve as a proxy for modifications in presynaptic release (Bekkers and Stevens, 1990; Malinow and Tsien, 1990; Faber and Korn, 1991; Costa et al., 2017), as outlined above. Whether a change in 1/CV2 (norm) is appreciable or not is determined by comparing the outcome to the diagonal line (**Figure 1** and **Box 2**; Sjöström et al., 2003, 2007; Buchanan et al., 2012; Abrahamsson et al., 2017).

If 1/CV2 (norm) changes at least to the same degree as the mean synaptic efficacy, µnorm, this supports a presynaptic locus of plasticity expression (**Figure 1**). On the contrary, if 1/CV2 (norm) remains relatively unaffected as the mean response µ(norm) changes, this is evidence to support a postsynaptic locus of plasticity expression (**Figure 1**; Korn and Faber, 1991; Reid and Clements, 1999). Of course, forms of plasticity may involve both pre- and postsynaptic modifications (Kullmann and Nicoll, 1992; Sjöström et al., 2007; Loebel et al., 2013; Costa et al., 2015).

Overall, CV analysis provides an estimate of the locus of plasticity expression without having to resolve precise changes in n, p, or q (Costa et al., 2017). This is useful, because quantifying changes in n, p, or q—known as quantal analysis is labor intensive and typically requires specific experimental conditions (Larkman et al., 1992, 1997a,b). Another approach for directly quantifying changes in n, p, or q, known as variance-mean analysis, requires sequential changes in cation composition (Clements and Silver, 2000; Clements, 2003). However, CV analysis can readily be performed following plasticity experiments without prior preparation (**Figure 2A**), but this relative simplicity comes at the cost of not knowing the precise changes in n, p, and q. The two sample pairedrecording experiments show how both LTP (**Figure 2A**) and LTD (**Figure 2B**) at L5 PC-PC connections are presynaptically expressed according to CV analysis (**Figure 2C**), in agreement with our prior findings (Sjöström et al., 2003, 2007).

To be able to draw robust conclusions about the locus of plasticity, it is essential to repeat across several long-term plasticity experiments (**Figure 3**). Here, the statistical significance of CV analysis can be assessed by comparing the angle ϕ of the outcome relative to the diagonal (**Figure 3C** and **Box 2**), as we have done before (Sjöström et al., 2003, 2007; Buchanan et al., 2012; Abrahamsson et al., 2017).

In summary, CV analysis is a straightforward method for estimating the locus of expression that can easily be implemented following a standard plasticity experiment without the need for any special preparations (Bekkers and Stevens, 1990; Malinow and Tsien, 1990; Sjöström et al., 2003, 2007). It is important, however, to be aware of the assumptions of the binomial distribution (**Box 1**) as well as several experimental pitfalls associated with CV analysis (see below).

#### Caveats of CV Analysis

Like any other method, CV analysis comes with caveats (Faber and Korn, 1991; Korn and Faber, 1991; Costa et al., 2017). As a consequence, CV analysis may be misleading in some cases

FIGURE 2 | Sample LTP and LTD experiments show presynaptic expression. (A) Sample spike-timing-dependent plasticity experiment with 1t = 10 ms temporal difference between pre- and postsynaptic spike trains evoked at 50 Hz (Sjöström et al., 2001) for which LTP was evoked (EPSP before, dark blue: 0.58 ± 0.03 mV versus after, light blue: 0.92 ± 0.02 mV, p < 0.001). Inset: average EPSP traces showed a change in paired-pulse ratio suggesting presynaptic expression (Sjöström et al., 2007). Scale bars: 0.5 mV, 20 ms. Bottom: membrane potential and input resistance of pre- and postsynaptic PCs were stable (red and blue, respectively). Right: flattened 2-photon imaging stack of Alexa-594-filled cells verified PC identity, with pre- and postsynaptic PCs denoted by 1 and 2, respectively. (B) Sample spike-timing-dependent plasticity experiment with 1t = −25ms temporal difference between pre- and postsynaptic spike trains evoked at 20 Hz (Sjöström et al., 2001, 2003) for which LTD was elicited (before: 2.0 ± 0.04 mV versus after: 1.0 ± 0.02 mV, p < 0.001. Inset: change in paired-pulse ratio suggested presynaptic expression (Sjöström et al., 2003, 2007). Scale bars: 0.5 mV, 20 ms. Bottom: membrane potential and input resistance of pre- and postsynaptic PCs were stable (red and blue, respectively). Right: pre- and postsynaptic PCs are indicated by 1 and 2, respectively. (C) Coefficient of variation analysis of LTP (right-side-up triangle) and LTD experiments (upside-down triangle) in (A,B) both indicated a presynaptic locus of expression, in keeping with prior findings (Markram and Tsodyks, 1996; Sjöström et al., 2003, 2007).

(Faber and Korn, 1991). Here, we show how to anticipate and circumvent some of the key shortcomings.

#### The Number of Activated Inputs Should Remain Constant

A constant number of afferents should be activated within and across trials (Redman, 1990; Faber and Korn, 1991; Saviane and Silver, 2007). Although it is possible to conduct CV analysis on synaptic responses evoked with extracellular stimulation (Bekkers and Stevens, 1990; Malinow and Tsien, 1990), there is with extracellular stimulation the potential for loss or gain of afferent fibers throughout the recording, which may complicate CV analysis by requiring corrections (Faber and Korn, 1991; Costa et al., 2017). This potential problem is not specific to CV analysis per se, but also applies to e.g., quantal analysis and variance-mean analysis. Furthermore, recordings that show evidence of polysynaptic connectivity violate the simple binomial model (McLachlan, 1978) and therefore complicate the interpretation of quantal parameters by precluding CV analysis (Faber and Korn, 1991; Korn and Faber, 1991; Costa et al., 2017) and require statistical adjustments (Faber and Korn, 1991; Reid and Clements, 1999).

Avoiding these problems can be achieved by interrogating monosynaptic connections using paired recordings (Korn and Faber, 1998; Saviane and Silver, 2007), which have been carried out e.g., in neocortex (**Figure 2**; Sjöström et al., 2003, 2007; Song et al., 2005; Lalanne et al., 2016) and hippocampus (Sayer et al., 1989; Bekkers and Stevens, 1990; Malinow, 1991; Debanne et al., 1999). However, identifying monosynaptic connections is technically challenging and time consuming, especially for synapse types with low connectivity rates. To alleviate this problem, multiple whole-cell recordings may be employed to increase the yield of identified monosynaptic connections (**Figures 2**, **3**), as previously described by us (Sjöström et al., 2003, 2007; Song et al., 2005; Lalanne et al., 2016) and others (Perin et al., 2011; Perin and Markram, 2013; Peng et al., 2019).

It is also possible to circumvent the problem of accidental loss or gain of afferent inputs by using more direct optical methods such as 2-photon glutamate uncaging (Ellis-Davies, 2019; Mitchell et al., 2019) or optical quantal analysis (Oertner et al., 2002; Emptage et al., 2003; MacDougall and Fine, 2019; Padamsey et al., 2019). However, even with paired recordings or these more direct optical methods, it is still possible for the number of release sites n to change (**Box 1**).

#### Outlier Synaptic Responses Distort CV Analysis

The variation at single synaptic contacts—primarily driven by the stochastic and probabilistic nature of presynaptic release (Otmakhov et al., 1993; Costa et al., 2017)—significantly influences the overall observed variability i.e., fluctuations in evoked potentials between neuronal connections in the brain (Otmakhov et al., 1993; Crochet et al., 2005). This makes the CV an excellent proxy for presynaptic changes in release (Malinow and Tsien, 1990; Faber and Korn, 1991; Costa et al., 2017). However, it also indicates that the CV is sensitive to the variation and stability of synaptic parameters at each release site and is therefore vulnerable to measurement error in the presence of additional sources of variation (Faber and Korn, 1991; Korn and Faber, 1991).

Extraneous sources of variation—for e.g., outliers due to stimulus failure or electrical artifacts (Oleskevich et al., 2000) and baseline trends and/or rundown (Reid and Clements, 1999) significantly affect the CV and may mask the true locus of expression (**Figures 4**, **5**). A straightforward solution to this caveat is to carefully inspect experiments for outlier responses and then individually exclude them from the CV analysis (**Figures 4D,E**). However, careful selection criteria for removing data points should be applied, otherwise bias will certainly be introduced. For example, electrical artifacts or spurious spiking (**Figure 4D**) are quite striking and useful selection criteria for identifying outliers. In other words, outliers should not be removed merely on the basis of being an outlier. Outliers should only be removed based on evidence for a cause of it being an outlier, such as spurious spiking (**Figure 4D**). Nevertheless, bias is a concern so removal of data points should be rare.

#### Unstable Baseline Distorts CV Analysis

Recordings should be evaluated for any trends resulting from rundown or instability, which may inflate estimates of the standard deviation, σ (McLachlan, 1978; Scheuss and Neher, 2001). The effect of baseline drift is illustrated in **Figure 5**; note that it is quite substantial even for relatively small baseline trends. Such trends can arise from gradual changes in cell input resistance, resting membrane potential, et cetera (**Figure 5Di**). It is therefore important to continuously monitor such parameters throughout long-term plasticity experiments (**Figures 2A,B**).

One solution to this problem is to systematically eliminate experiments above a threshold trend value, using a numerical selection criterion based on e.g., linear regression or bisection of the baseline period (Lalanne et al., 2016). By applying the same selection criteria to condition as well as control experiments (e.g., **Figure 3**), bias is avoided. We advise against detrending data, as it may introduce bias depending on the assumptions underlying the detrending algorithm. It is possible, however, to remove a portion

FIGURE 4 | A single outlier response may corrupt CV analysis. (A) Sample Monte-Carlo simulation of an individual presynaptically expressed LTD experiment in which a single EPSP was shifted by 3.2 mV (z-score: 8.2) to produce a striking outlier (red dots). To enable comparison with experimental data (Figures 2, 3), the number of EPSPs, interstimulus intervals, background noise levels, amount of LTD, initial EPSP amplitude, et cetera were set to representative values (see section "Materials and Equipment"). (B) With a single outlier in the baseline period (z-score 8.2 as in A), CV analysis of LTD was on average biased to erroneously indicate post-instead of presynaptic expression (arrow). In the case of LTP, CV analysis would instead be biased toward presynaptic expression (not shown, but possible to simulate in downloadable code, see section "Materials and Equipment"), because the outlier would still artificially elevate the y-axis coordinate, just as for LTD. However, if the outlier is in the post-induction period, the bias is in the opposite direction. (C) As in (A), 150 individual simulations (gray circles) were systematically repeated for single outliers of increasing z-score values (0, 4.1, and 8.2 shown in Ci–iii). The increasing outlier values systematically biased outcome toward a postsynaptic interpretation (summarized in B). (D) Sample LTD experiment (Di, 1t = −25ms and 20 Hz as in Figures 2, 3) for which a spurious presynaptic spike (arrow, Dii, top red trace) resulted in undesirable short-term depression of subsequent EPSP (\* in Dii, compare top to bottom blue sample traces), leading to an outlier EPSP in the time course (\* in Di). (E) By including the outlier (\* in Di,ii), CV analysis was biased toward postsynaptic interpretation (arrow). Here, this pitfall was avoided by removing the outlier (arrow starting point).

of the baseline period that is unstable (**Figure 5D**), especially if doing so is supported by some independent selection criterion such as change in input resistance, resting membrane potential, or similar (Lalanne et al., 2016).

Gradual trends in variance or mean may also be addressed by binning 1/CV2 over time (Scheuss and Neher, 2001). For simplicity, we do not show this here, but we have relied on this approach before (Sjöström et al., 2003).

FIGURE 5 | Baseline trends may corrupt CV analysis. (A) Sample Monte-Carlo simulation of an individual presynaptically expressed LTD experiment that was suffering from a strong baseline run-up (115.2 µV/min, see section "Materials and Equipment"). (B) With baseline trend (115.2 µV/min as in A), CV analysis was on average biased to erroneously indicate post-instead of presynaptic expression (arrow). In the case of LTP, CV analysis would instead be biased toward presynaptic expression (not shown, but possible to simulate in downloadable code, see section "Materials and Equipment"), because the baseline trend artificially elevates the y-axis coordinate. However, if the baseline trend is in the post-induction period, the bias is in the opposite direction. (C) As in (A), 150 individual simulations (gray circles) were systematically repeated for different baseline trends (0, 57.6, and 115.2 µV/min shown in Ci–iii). The increasing baseline trend systematically biased outcome toward a postsynaptic interpretation (summarized in B). (D) Sample LTD experiment (Di, 1t = −25ms and 20 Hz as in Figures 2, 3) at PC1 → PC2 connection (Dii) that suffered from an increasing baseline trend, coincident with a significant change in postsynaptic input resistance (bottom: blue circles, asterisk). Presynaptic input resistance and membrane potential are indicated in red. (E) By including the entire baseline period, CV analysis was biased toward postsynaptic interpretation (arrow). Here, this pitfall was avoided by removing the unstable baseline period, which was further supported by a significant change in input resistance (\* in Di).

#### Alternative Interpretations Are Possible

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Even under the best of circumstances, the results of CV analysis should be interpreted while considering the structure and function of the synapse type under investigation (Costa et al., 2017). To illustrate this point, consider NMDAreceptor-dependent LTP in hippocampal area CA1. Some studies have found that this form of plasticity is expressed as an increase in the probability of release, p, suggesting a presynaptic locus (Kullmann and Nicoll, 1992). However, this apparent change in the release probability may in fact be achieved postsynaptically by the conversion of silent to functional synapses (Glasgow et al., 2019). In this scenario, postsynaptic insertion of AMPA receptors may be erroneously interpreted as a presynaptic increase in the probability of release (Isaac et al., 1995, 1996; Liao et al., 1995; Kerchner and Nicoll, 2008). Synaptic unsilencing at the neuromuscular junction, on the other hand, is a mechanistically distinct presynaptic phenomenon (Wojtowicz et al., 1994).

In summary, alternative interpretations are often possible. This pitfall, however, is not limited to CV analysis as such but is a general caveat. Nevertheless, this means CV analysis should generally be supported by other methods for localizing the expression locus, such as analysis of failure rate (Malinow and Tsien, 1990; Faber and Korn, 1991), paired-pulse ratio (**Figures 2A,B**; Poncer and Malinow, 2001; Sjöström et al., 2007; Abrahamsson et al., 2017), NMDA:AMPA ratio (Watt et al., 2004; Sjöström et al., 2007), FM1-43 dye loading (Murthy et al., 1997; Zakharenko et al., 2001), spontaneous release (changes in frequency versus amplitude; Malgaroli and Tsien, 1992; Manabe et al., 1992; Abrahamsson et al., 2017), etc. Of these approaches, evaluating the paired-pulse ratio is likely the most straightforward option, as it can be readily performed in parallel with CV analysis, provided the experiments were carried out with paired pulses (**Figures 2A,B**). Since it relies on two responses rather than one as for CV analysis, pairedpulse ratio analysis is furthermore mathematically independent from CV analysis. Failure-rate and CV analyses, however, are essentially relying on the same theoretical framework and so are not independent methods, which means the corroborative power is limited. For further information regarding these techniques, we invite the reader to the review by Glasgow et al. (2019) in this research topic. Furthermore, modern techniques enable more direct measurements of locus of expression, e.g., using 2-photon glutamate uncaging (Ellis-Davies, 2019; Mitchell et al., 2019), optical glutamate sensors (Jensen et al., 2017, 2019; Durst et al., 2019), or optical quantal analysis (Oertner et al., 2002; Emptage et al., 2003; MacDougall and Fine, 2019; Padamsey et al., 2019). These more advanced methods may however require expensive specialized equipment.

#### DISCUSSION

We have provided a practical guide to using CV analysis for the purposes of investigating the locus of expression of long-term plasticity. We primarily directed this guide to beginners in the field, so we have tried to simplify key concepts to make them more accessible. We acknowledge that others have delved into the mathematical background with greater detail and rigor than we have here (McLachlan, 1978; Faber and Korn, 1991; Quastel, 1997); this was intentional.

Binomial statistics have been successfully applied to the study of quantal release at peripheral and central synapses for decades (Johnson and Wernig, 1971; McLachlan, 1978; Korn et al., 1987; Bekkers and Stevens, 1990; Malinow and Tsien, 1990). Nonetheless, the simplifying assumptions inherent in this model may not hold in all cases. Therefore, if resolving precise changes in synaptic parameters is required, it is possible to use alternative albeit more laborious approaches to accommodate potential non-uniformities in p and q (Silver et al., 1998; Reid and Clements, 1999; Saviane and Silver, 2007). However, it appears that the locus of plasticity expression can be reliably and easily estimated with CV analysis—using alternative methods such as analysis of NMDA:AMPA ratio, paired-pulse ratio, or quantal analysis in parallel with CV analysis generally give rise to the same interpretation (Reid and Clements, 1999; Sjöström et al., 2007). Modern and more direct methods based on optical activation or readout are especially attractive alternatives (Jensen et al., 2017, 2019; Durst et al., 2019; Ellis-Davies, 2019; MacDougall and Fine, 2019; Mitchell et al., 2019; Padamsey et al., 2019), since they in many cases are virtually free of assumptions. Still, all methods come with their own advantages and caveats, e.g., analysis of pairedpulse ratio may erroneously suggest presynaptic expression for NMDA-only silent synapses that undergo postsynaptic expression (Poncer and Malinow, 2001), glutamate uncaging can necessarily only explore postsynaptic expression, and dyes used with optical methods may distort plasticity mechanisms by buffering calcium (MacDougall and Fine, 2019). It therefore remains important to use several methods in parallel. Classical CV analysis is one method that is both straightforward and inexpensive to use.

Here, we have listed a set of key pitfalls and shortcomings of the CV analysis method, which we have also illustrated in the form of simple downloadable computer simulations (see GitHub link in section "Materials and Equipment"). We have also provided a number of straightforward solutions for the most obvious issues. From this simple guide, it should be clear that CV analysis is a powerful and easy-to-use method, especially when combined with other approaches such as analysis of pairedpulse ratio or NMDA:AMPA ratio (Watt et al., 2000, 2004; Sjöström et al., 2007).

#### DATA AVAILABILITY STATEMENT

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation, to any qualified researcher.

#### ETHICS STATEMENT

The animal study was reviewed and approved by the Montreal General Hospital Faculty Animal Care Committee (MGH FACC).

#### AUTHOR CONTRIBUTIONS

fnsyn-12-00011 March 25, 2020 Time: 17:9 # 13

JB and AW carried out the experiments. SL carried out the mathematical derivations. PS wrote the custom software. JB, PS, and AT wrote the manuscript with input from AW.

#### FUNDING

This work was supported by CFI LOF 28331 (PS), CIHR OG 126137 (PS), CIHR NIA 288936 (PS), FRSQ CB 254033 (PS), NSERC DG 418546-2 (PS), NSERC DG 2017-04730 (PS), and NSERC DAS 2017-507818 (PS). JB was in receipt of the McGill University Max Stern Recruitment Award and the

#### REFERENCES

McGill University Integrated Program in Neuroscience (IPN) Recruitment Award. AW was supported by the McGill University Grad Excellence Award, the Research Institute of the McGill University Health Centre (RI-MUHC) Studentship, and the Healthy Brains, Healthy Lives (HBHL) Master's Fellowship. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

#### ACKNOWLEDGMENTS

We thank Alanna Watt and members of the Sjöström Lab for help and useful discussions. We are also grateful for the constructive feedback from the reviewers.

Martin, A. R. (1966). Quantal nature of synaptic transmission. Physiol. Rev. 46, 51–66. doi: 10.1152/physrev.19<IP_ADDRESS>

**Conflict of Interest:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2020 Brock, Thomazeau, Watanabe, Li and Sjöström. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Autaptic Cultures: Methods and Applications

#### John M. Bekkers\*

Eccles Institute of Neuroscience, The John Curtin School of Medical Research, The Australian National University, Canberra, ACT, Australia

Neurons typically form daisy chains of synaptic connections with other neurons, but they can also form synapses with themselves. Although such self-synapses, or autapses, are comparatively rare in vivo, they are surprisingly common in dissociated neuronal cultures. At first glance, autapses in culture seem like a mere curiosity. However, by providing a simple model system in which a single recording electrode gives simultaneous access to the pre- and postsynaptic compartments, autaptic cultures have proven to be invaluable in facilitating important and elegant experiments in the area of synaptic neuroscience. Here, I provide detailed protocols for preparing and recording from autaptic cultures (also called micro-island or microdot cultures). Variations on the basic procedure are presented, as well as practical tips for optimizing the outcomes. I also illustrate the utility of autaptic cultures by reviewing the types of experiments that have used them over the past three decades. These examples serve to highlight the power and elegance of this simple model system, and will hopefully inspire new experiments for the interrogation of synaptic function.

#### Edited by:

Dirk Feldmeyer, Helmholtz Association of German Research Centers (HZ), Germany

#### Reviewed by:

Michael Beierlein, University of Texas Health Science Center at Houston, United States Kimberly M. Huber, University of Texas Southwestern Medical Center, United States

> \*Correspondence: John M. Bekkers<EMAIL_ADDRESS>
Received: 21 December 2019 Accepted: 01 April 2020 Published: 30 April 2020

#### Citation:

Bekkers JM (2020) Autaptic Cultures: Methods and Applications. Front. Synaptic Neurosci. 12:18. doi: 10.3389/fnsyn.2020.00018 Keywords: autapse, culture, methods, review, synapse

## INTRODUCTION

The brain achieves its astonishing feats of information processing in part because of the complexity of its synaptic connections. Many synaptic circuit motifs have been elucidated, including feedforward, feedback, recurrent and lateral inhibition and excitation (Douglas and Martin, 2007; Yuste, 2015). Perhaps surprisingly, one of the most simple circuit motifs of all—that in which a neuron makes a synaptic connection with itself—was relatively late to come to the attention of neuroscientists. The term ''autapse'' entered the neuroscience lexicon only in 1972 when it was first coined to describe putative self-synapses on Golgi-stained pyramidal neurons in rabbit neocortex (Van der Loos and Glaser, 1972). Since then, both anatomical and physiological evidence for autapses in vivo has accumulated steadily (Karabelas and Purpura, 1980; Park et al., 1980; Peters and Proskauer, 1980; Preston et al., 1980; Lübke et al., 1996; Cobb et al., 1997; Tamás et al., 1997; Pouzat and Marty, 1998, 1999; Pawelzik et al., 2003; Bacci and Huguenard, 2006; Connelly and Lees, 2010; Manseau et al., 2010; Jiang et al., 2012, 2015; Yin et al., 2018; Deleuze et al., 2019). Today there is no question that autapses exist in the brain, albeit in much smaller numbers than (hetero-) synapses. However the importance of autapses for the normal operation of neural circuits remains a matter for speculation (Bekkers, 1998, 2003, 2009; White et al., 1998; Li et al., 2010; Connelly, 2014; Deleuze et al., 2014; Guo et al., 2016; Wiles et al., 2017).

In parallel with these discoveries about autapses in intact brain tissue, it was found that, under the right conditions, autapses in neuronal cultures are surprisingly common. When constrained to grow in isolation on ''microislands'' or ''microdots'' a few tens of microns across (Furshpan et al., 1976, 1986; Landis, 1976), cultured neurons readily form autapses (Segal and Furshpan, 1990; Bekkers and Stevens, 1991). The presence of two or more neurons on the microisland does not seem to curtail autapse formation (Tarsa and Goda, 2002; Wierda and Sørensen, 2014), suggesting that neurons are just as likely to form autapses as synapses when given the opportunity. It is possible that the 2-dimensional geometry of cultures, with the greater likelihood that an axon will encounter its dendrites, is an important reason why autapses are so prevalent in culture (Ikeda and Bekkers, 2006).

Although initially a curiosity, autaptic cultures have proven to be a valuable model system for addressing a range of important questions in cellular neuroscience. By providing a homogeneous population of synaptic contacts on a single, isolated neuron, autaptic cultures offer the ultimate in synaptic reductionism. Their functional simplicity has enabled many important and elegant experiments that would not have been possible in more complex systems.

The goals of this article are, first, to show how to prepare and utilize these cultures and, second, to give an overview of their many applications, with an emphasis on neurophysiological experiments. An alternative method for studying single neurons in isolation is to use very-low-density cultures, which have been described in detail elsewhere (e.g., Goslin et al., 1998; Ventimiglia and Lindsay, 1998; Fath et al., 2009); I will not be discussing this approach here. I will also not be discussing the use of similar cultures to study neurite growth on patterned substrates, which is of interest to the design of brain-machine interfaces (e.g., Jang et al., 2016; Gautam et al., 2017).

#### METHODS FOR PREPARING AUTAPTIC CULTURES

Autaptic cultures are prepared in essentially the same way as conventional dissociated primary cultures (''mass cultures''), the main difference being the preparation of the culture plates. Several excellent articles about preparing autaptic cultures have been published (Segal et al., 1998; Allen, 2006; Fasano et al., 2008; Rost et al., 2010; Burgalossi et al., 2012; Lu et al., 2016) and the guidance below draws upon all of these, as well as my own experience (Bekkers and Stevens, 1991; Bekkers, 2005). It should be kept in mind that cell culture is often laced with superstition. The best advice is to start simple and elaborate only if necessary.

The methods presented here will focus on general-purpose hippocampal or cortical cultures prepared from newborn mice or rats. Others have described how to prepare cultures from embryos (Fath et al., 2009; Lu et al., 2016), older tissue (Ogata and Tatebayashi, 1991; Brewer, 1997; Allen, 2006) and other brain areas (Johnson, 1994; Shi and Rayport, 1994; Sulzer et al., 1998; Michel and Trudeau, 2000; Moechars et al., 2006). There is even a protocol for preparing autaptic cultures from human induced pluripotent stem cells (Fenske et al., 2019). Whatever the tissue source, it goes without saying that all procedures must be approved by the local ethics committee.

#### Overview of the Procedure

**Figure 1** shows the basic steps in preparing autaptic cultures, and the detailed requirements are listed in **Tables 1**–**4**. Briefly, the key initial step is to prepare coverslips with spots of permissive growth substrate (e.g., collagen, poly-D-lysine) dispersed across a coating of non-permissive substrate (agarose). Dissociated primary neurons are then added to the coverslips, usually (but not always) after first growing a monolayer of glial cells (astrocytes) on the spots to provide trophic support for the neurons. Autaptic neurons are typically ready for use after 1–2 weeks in vitro. The entire procedure will take at least 2–3 weeks, depending on the exact method used.

#### TABLE 1 | Solutions for preparing plates.

#### Permissive coating solution

#### Stock solutions:

• Aim for final concentrations of ∼0.1 mg/ml poly-D-lysine and ∼0.5 mg/ml collagen

Keep the coating solution for several weeks at 4◦C.

Notes: 1. Poly-L-lysine, and either the hydrobromide or hydrochloride salt, should work as well, but some experimentation may be required. 2. Some investigators recommend preparing the poly-D/L-lysine stock in borate buffer (1.24 g of boric acid, 1.9 g of sodium tetraborate, 400 ml of H2O).

#### Dissection solution

This can be standard mammalian Ringer containing (in mM): 125 NaCl, 3 KCl, 2 CaCl2, 1 MgCl2, 25 HEPES @ pH 7.4 adjusted with NaOH, 10 glucose, 25 sorbitol to give 315 mOsm/kg, 0.22 µm filtered to sterilize.

#### Enzyme solution

#### Mix in a 15 ml tube:

Add about 10 µl of 1 M NaOH to adjust pH to about 7 (i.e., a pale pink color).

Keep in 37◦C bath for 10–15 min to dissolve papain, then 0.22 µm filter into another sterile 15 ml tube and return the tube to the 37◦C bath until required.

#### Preparation of Plates

#### TABLE 3 | Culture media.

#### Classic serum-containing medium

To prepare 100 ml:

Filter (0.22 µm) into a sterile bottle. Keep in the dark at 4◦C for about 2 weeks.

#### Alternative serum-containing medium

To prepare 100 ml:

• 50 ml DMEM with HEPES: Weigh out 870 mg Dulbecco's Modified Eagle's Medium (DMEM) with high glucose (powder), add <50 ml distilled water (dH2O) while stirring. Make up to 50 ml with dH2O.

• Mix the 50 ml prepared in step 1 with 50 ml of DMEM with high glucose (liquid).

Filter (0.22 µm) into a sterile bottle. Keep in the dark at 4◦C for about 2 weeks.

#### Complete Neurobasal medium (serum-free)

To prepare 100 ml, mix aseptically:

• 98 ml of Neurobasal or Neurobasal Plus medium

Keep in the dark at 4◦C for about 2 weeks.

Notes: 1. To heat-inactivate FBS, heat @ 56◦C for 30 min in a water bath. 2. MEM without phenol red may be preferred for cultures that will be used for imaging experiments to minimize background fluorescence. 3. For suppressing the overgrowth of glial cells, prepare a 2.5 mM stock solution of cytosine arabinoside, free base (Sigma–Aldrich, C-1768) in dH2O and store the stock at −20◦C. Dilute this in warmed culture medium to achieve a final concentration of 5 µM in the culture plate after feeding. 4. Glial cells grow more readily in medium supplemented with FBS, so an alternative for suppressing glial growth, particularly if plating onto an astrocyte feeder layer, is to replace the FBS with twice the concentration of horse serum.

atomizer or airbrush to spray a mist of permissive substrate onto the agarose-coated coverslips, which requires judgment and experience to achieve a satisfactory distribution of small, discrete spots (Segal and Furshpan, 1990; Bekkers and Stevens, 1991; Fasano et al., 2008). A more recent method is to fabricate a stamping tool that imprints a regular pattern of permissive substrate solution onto the coverslips (Moulder et al., 2007; Sgro et al., 2011; Burgalossi et al., 2012; Ricoult et al., 2012).

(i) Microatomizer method. Obtain a small glass reagent sprayer or artist's airbrush (see **Table 4** for suggested

#### TABLE 4 | Other requirements.

See "Preparation of Plates" section for more details.

13 mm round glass coverslips, No. 1 (0.13–0.17 mm thickness), cleaned as described 24 well culture plates 56 mm sterile culture dish (for coarse dissection of tissue) 35 mm sterile culture dish (for fine dissection of tissue, if required) 15 ml sterile plastic centrifuge tubes (for preparing solutions, incubating in enzyme, trituration) 50 ml sterile plastic centrifuge tubes (for working aliquots of culture medium) 0.22 µm pore 25 mm diameter sterile syringe filters (for sterilizing solutions) 10 ml syringes (for use with syringe filters) 10 ml sterile pipettes (for dispensing medium and adding cell suspension to plates) Sterile Pasteur pipettes plugged at the wide end with cotton wool (for dispensing solutions during dissection and doing trituration) Hemocytometer and access to a microscope (for counting cells) Dissection instruments: e.g., dissection scope, medium scissors for decapitation, small scissors for opening the skull, small flat spatula for removing the brain and doing coarse dissection, one pair fine forceps, one scalpel blade for mincing tissue 80% v/v ethanol in distilled water (for sterilizing the dissection instruments and work area) Sterile bottles (for storing the culture medium and solutions used in the preparation) Small atomizer (for spraying the culture plates). We have the most experience with a small glass reagent sprayer (e.g., Kimble 5 ml thin layer chromatography sprayer, kimble-chase.com) but a small recycled perfume spray bottle might work as well, or an artist's airbrush (e.g., Aztec airbrush from www.testors.com).

Stamping tool for applying spots of permissive substrate. This is an alternative to the atomizer. The stamping tool yields more reproducible microislands but the tool needs to be fabricated. See "Preparation of Plates" section for more details.

Notes: 1. Quantities depend on the number of cultures. We find that one newborn animal is sufficient to yield enough hippocampal neurons for one or two 24-well plates. 2. The composition of the glass used in the coverslips may affect the health of the cultures. Be prepared to test coverslips from different suppliers.

sources). A small perfume bottle may also work. Sterilize the sprayer by spraying 80% ethanol and allowing it to dry in the culture hood. Load the substrate solution into the atomizer and spray the coating solution onto the dry agarose-coated plates. The spraying pressure, spraying duration, and distance from the plate need to be optimized so that small, discrete spots (∼200 µm diameter) of the substrate solution settle on the coverslip. Here are some tips to guide mastery of this critical step (see also ''Troubleshooting'' section below).

A variation on the above is to use the ''sandwich'' method, in which the coverslip containing the neurons is opposed to and separate from an astrocyte feeder culture that provides diffusible growth factors to the medium (Brewer and Cotman, 1989). A simple way to prepare plates for this method is to simply scratch the bottom of each well with a needle (Lu et al., 2016). This raises small protuberances of plastic that will hold the coverslip just above the bottom of the well. Another method is to briefly touch the bottom of each well in three places with a hot soldering iron, raising small plastic welts. The coverslips for ''sandwich'' cultures are prepared by first distributing them in large (e.g., 60 mm) culture dishes. They are then coated with agarose and sprayed with a permissive substrate, as described above for the standard method. Finally, they are sterilized and stored in the large culture dishes until needed for the cell preparation. See ''Alternative Plating Method'' section below for further details.

#### Plating Procedure

Broadly speaking, primary neuronal cultures can be prepared in two different ways (**Figure 1**):

	- (a) Low-density: The dissociated cell suspension is directly added to the microisland plates at a low enough density that only the astrocytes survive.
	- (b) Passaging: The astrocytes are grown and passaged separately before adding them to the microisland plates.

For both the one-step and two-step procedures the cultures are more likely to be successful when prepared from embryonic or newborn tissue, e.g., from rodents aged between embryonic day 16 (E16) and postnatal days 0–3 (P0–3). If cultures need to be prepared from older animals, more elaborate procedures are required (Kay and Wong, 1986; Kaneda et al., 1988; Ogata and Tatebayashi, 1991; Brown et al., 1993; Magistretti et al., 1996; Brewer, 1997; Allen, 2006). The steps presented below assume that newborn rodent tissue is being used. Methods for using embryonic tissue are described elsewhere (Goslin et al., 1998; Fath et al., 2009).

Unless otherwise stated, all of the following steps are done in a sterile laminar flow hood.

(1) Prepare instruments and solutions. Assemble the dissection instruments (**Table 4**) in the hood and sterilize them with 80% ethanol. Prepare the enzyme solution (**Table 2**), chill the dissection solution (**Table 2**) and warm the culture medium (**Table 3**). Papain is most commonly used in the enzyme solution because it is regarded as gentler than trypsin for dissociating fragile neural tissue (Goslin et al., 1998). However, if preparing astrocytes for passaging (see Step 8 below) then trypsin is suitable and more economical. The choice of the culture medium is critical. For growing neurons under defined conditions, serum-free medium (e.g., Neurobasal medium; **Table 3**) is preferred. On the other hand, astrocytes grow better in serum-containing medium (**Table 3**, Rost et al., 2010; Burgalossi et al., 2012). Thus, unless the neurons are being plated onto a confluent monolayer of astrocytes (see Steps 6 and 8 below), it is advisable to start with a serum-containing medium to promote astrocyte division. If desired, the culture can be switched to a serum-free medium after the astrocytes have reached confluence. A disadvantage of using serum is that there may be batch-to-batch variability in the properties of the serum, and so it may be advisable to test small amounts of different batches before placing a larger order.

stage during this procedure. Being very gentle and careful is the key to success. You should finish with 6–10 ml of single-cell suspension.

stick to the substrate within an hour or two. They should begin to extend processes within 24 h, or sooner if plated on astrocytes.

(8) Passaging method for preparing astrocyte monolayers. Passaging provides an ample supply of pure astrocytes that can be plated out on new culture dishes at a higher density than in Step 6 above, which means that a confluent astrocytic ''lawn'' will grow more quickly. On the other hand, this approach is more complex. Briefly, neural tissue is dissociated as in Steps 1–4 above, except that harsher enzymes (e.g., trypsin) and more vigorous trituration are used to favor the more hardy astrocytes over neurons. The cells are grown in culture flasks under conditions that suit astrocytes and are passaged until required (Ullian et al., 2001).

## Feeding

Following the plating of neurons, it is normal for significant neuronal death and accumulation of debris to occur over the first 24 h. The debris should be removed as much as possible by feeding the culture the day after the dissociation. If using 24-well plates, this is done by removing 0.15 ml of the old medium from each well (i.e., about 1/3 the well volume) and adding the same quantity of fresh, warmed medium.

A general rule of thumb is that autaptic cultures do better with minimal feeding, say, once every 1–2 weeks using the 0.15 ml off/on protocol above. However, there are several important exceptions to this rule.

yellow color, indicative of an accumulation of acidic waste products. This change is often seen in older, denser cultures. If this occurs, feeding should be done more frequently to minimize damage to the neurons.

Particularly in older cultures, it may help to add blockers of synaptic transmission to the culture medium to reduce excitotoxicity. For example, after 7–10 days in vitro we sometimes add kynurenic acid (1 mM final concentration in each well), CNQX or DNQX (10 µM) to inhibit non-NMDA ionotropic glutamate receptors, or D, L-APV (40 µM) to inhibit NMDA receptors. We find that cultures typically survive much better for longer periods (>3–4 weeks) in the presence of one of these blockers. However, it should be kept in mind that chronic blockade of excitatory synaptic transmission may affect synapse maturation (Murthy et al., 2001).

#### Alternative Plating Method

The ''sandwich'' culture is an elegant method for exposing neurons to astrocyte-conditioned medium without physical contact with the astrocytes (Brewer and Cotman, 1989; Goslin et al., 1998; Lu et al., 2016). Because the autaptic neurons are resting on coated glass rather than an astrocytic lawn, the quality of the optics is improved, which is beneficial for certain experiments. In this method, dissociated cells are plated in wells that do not contain coverslips but which have small plastic protuberances on the bottom, as described in the ''Preparation of Plates'' section. After 1–2 weeks a confluent mixed neuron-glia feeder culture is obtained. At this time another dissociation is done and the isolated cells are plated onto coverslips that had previously been agarose-coated and sprayed in large culture dishes (see ''Preparation of Plates'' section and Goslin et al., 1998). These large culture dishes are placed in the incubator for a few hours to allow the neurons to settle and attach, then each coverslip is taken out, inverted, and placed neuron side down in each well in the plate containing the feeder culture. The plastic protuberances hold the coverslip and adherent neurons just above the glia, allowing access to secreted growth factors without direct contact.

## Troubleshooting

from the coverslips, and size of the spray nozzle. For example, with our glass microatomizer (Kimble-Chase; see **Table 4**) we use airflow (from a reticulated air supply) at 3–4 L min−1 , burst duration 0.5–1 s and spray distance ∼10–15 cm.

FIGURE 2 | Rat hippocampal neurons in dissociated culture (2–3 weeks in vitro). (A) Phase-contrast image of an isolated neuron in a mass culture showing the phase-bright soma, thick tapering dendrites, and thin untapered axons. Confluent astrocytes are visible beneath the neuron. A patch electrode, entering from the right, is positioned on the soma. (B) "Microdot" or "microisland" of astrocytes occupied by a single neuron (red arrow). This is a comparatively large island. (C) A microisland of more typical size, occupied by a single neuron imaged using phase contrast (Ca) and bright-field (Cb) microscopy after processing with a synapsin antibody to reveal autapses (dark spots on the processes in Cb). (D) Example of a microisland occupied by two neurons (red arrows). (E) Example of a microisland with multiple neurons. The scale bar in all panels is 50 µm.

If the neurons still die on plastic, they may require an astrocyte feeder layer, particularly if using mouse tissue or tissue from older (e.g., >P5) animals. Ideally, the astrocyte feeder layer should form a homogeneous extent of flat cells without too many gaps or overgrowth (e.g., **Figure 2A**). This is normally achieved by treating with an antimitotic agent (e.g., araC) as they approach confluence. The astrocyte cultures should also not be too old. We find that <3–4 weeks is preferred. Finally, the culture medium is probably the most important determinant of healthy cultures. Commercially available formulations are constantly evolving and some experimentation may be required to find the optimum for your application. Generally speaking, the serum-containing medium is better for growing astrocytes but it may be compromised by unpredictable variability between different lots of serum. Serum-free medium has the advantage of greater consistency but not all cell types may thrive in the absence of serum. Whatever the choice of medium, a universal precaution is that it should be fresh, sterile and adjusted to the correct pH and osmolarity.

#### ELECTROPHYSIOLOGICAL RECORDINGS FROM AUTAPSES

In this section, I will give tips for performing the most basic kind of electrophysiology experiment with autaptic cultures, i.e., a whole-cell patch-clamp recording of autaptic current from a single, isolated neuron under physiological conditions. These techniques are readily extended to more elaborate experiments of the kind that are summarized in later sections.

#### Choosing a Neuron

Broadly speaking, cultures can be used for electrophysiology experiments after ∼7 days in vitro (DIV), although autaptic currents are expected to be small at that stage (Gomperts et al., 2000). Longer time in culture typically leads to a greater number of autaptic connections and larger currents per neuron (Gomperts et al., 2000), but there is also a progressive loss of neurons with culture age. We find that ∼14–21 DIV is a good compromise for measuring large autaptic currents from healthy rodent neurons.

It is common to perform autaptic culture experiments in a HEPES-buffered bath solution at room temperature without bubbling or perfusion (e.g., Bekkers, 2005). Other standard bath solutions could also be used, for example, a perfused, carbogen-bubbled, bicarbonate-buffered bath solution warmed to physiological temperature, as in slice experiments (e.g., Ikeda et al., 2018). A phase-contrast microscope provides the best optics for observing neurites in culture (**Figure 2**). This may be important if one wishes to ensure, for example, that axons are not crossing the space between microislands. However, other types of contrast enhancement, such as differential interference contrast (DIC) or Hoffman modulation contrast, are acceptable for most studies with autaptic cultures.

After placing a whole coverslip in the chamber, the entire coverslip should be scanned at low magnification (e.g., 10× objective) to find potential microislands occupied by a single neuron. The shapes and sizes of these islands can be very diverse (**Figure 2**). In many cases it is unambiguous that a single neuron is present; in other cases, the identification is less clear. For example, glial overgrowth may obscure the view, or the soma of a glial cell (e.g., an oligodendrocyte) might be mistaken for that of a neuron. At other times the putative single neuron may occupy a very small island and it can be difficult to know if another neuron is hidden underneath the first. In these cases, the electrophysiology must be called upon to provide a definitive answer (see next section).

Identification of the type of neuron (e.g., glutamatergic, GABAergic, subtypes of these) can be inconclusive if simply based upon morphology. Dendritic morphology is often altered in culture, and in any case, the confinement of a neuron to a small island can make its dendrites hard to see. The best strategy is to prepare cultures from transgenic tissue in which the neurons of interest are fluorescently labeled (e.g., Ikeda et al., 2008).

During this initial scan, it is important to establish the health of the culture. The underlying layer of astrocytes should uniformly cover the islands of the permissive substrate, and the larger islands on the plate should be occupied by significant numbers of healthy-looking neurons (e.g., **Figure 2E**). There should be no sign of detachment of the astrocytes from the substrate, or of the agarose coating (which looks like a thin, transparent membrane) from the glass. If the culture contains clumps of many neuronal somata, perhaps extending thick fascicles of neurites between the clumps, then the plating density was too high. If there are healthy astrocytes but few neurons, then the plating density may have been too low.

Incidentally, cultures sometimes contain cells with vigorously waving cilia. These are ependymal cells from the meninges. They do not seem to interfere with experiments.

#### Whole-Cell Patch-Clamp

Standard patch-clamp techniques can be used with autaptic cultures, with a few precautions that are discussed below. After obtaining a stable whole-cell recording from the soma of an isolated neuron, the cell is voltage-clamped at a hyperpolarized holding potential (e.g., −60 mV) and a 1 ms-long depolarizing voltage-clamp step to 0 mV is applied (**Figure 3A**; this shows a hyperpolarizing test pulse followed by two depolarizing steps in succession). Each depolarizing step produces, in sequence, an outward capacitance transient (labeled 1 in **Figure 3B**), an inward ''action current'' (unclamped action potential; 2 in **Figure 3B**) and an inward capacitance transient (3 in **Figure 3B**). The action current escapes into the axon as a propagating action potential and, if autapses are present, a voltage-clamped autaptic current appears after a delay (4 in **Figure 3B**). In this example the neuron is glutamatergic and a fast inward excitatory autaptic current is observed. This autaptic current is selectively blocked by an inhibitor of AMPA receptors (**Figure 3B**, cyan trace). A similar experiment with an isolated GABAergic neuron shows an inhibitory autaptic current with slower kinetics, as expected for a current mediated by GABAA receptors (**Figure 3C**; in this example the pipette solution contained high Cl−).

Experiments can also be performed in current-clamp mode, in which case autaptic potentials would be recorded (Bekkers and Stevens, 1991). However, voltage-clamp recordings are generally more convenient because the repeated firing of self-exciting neurons can generally be more effectively controlled; thus, most investigators use voltage clamp.

This basic autapse experiment illustrates some precautions to keep in mind when measuring autaptic currents. First, the internal solution should allow the neuron to fire brief action potentials, i.e., it should typically be a high-K+ solution to enable rapid spike repolarization. This is necessary to ensure the presynaptic action potential and the postsynaptic autaptic response are temporally dissociated, given that both are recorded in the same electrode (**Figure 3**). An internal solution that blocks K + channels, such as a high-Cs+ solution of the kind commonly

FIGURE 3 | Example autaptic postsynaptic currents recorded from isolated rat hippocampal neurons. (A) Membrane current (Im, blue trace) recorded in response to a voltage clamp command (Vc, red trace) in an isolated glutamatergic neuron. In this example, two depolarizing stimuli (each a 2 ms-long step from −60 mV holding potential to 0 mV) were applied at a 50 ms interval. A hyperpolarizing test pulse (20 ms-long step from −60 to −70 mV) preceded the depolarizing stimuli. (B) Same data shown on an expanded time scale to illustrate the phases of the Im response. Also shown (Continued)

#### FIGURE 3 | Continued

(cyan trace) is Im from the same cell immediately after switching to a flow pipe containing 20 µM CNQX (6-cyano-7-nitroquinoxaline-2,3-dione) to block the excitatory postsynaptic current (EPSC). Labeled traces are (1) "on" capacitance transient, (2) action current (INa and IK), (3) "off" capacitance transient, and (4) autaptic EPSC. (C) Similar recording from an isolated GABAergic interneuron, showing an autaptic inhibitory postsynaptic current (autaptic IPSC) in response to a single stimulus. Same time scale as in panel (A); note the slower kinetics. In this experiment the pipette solution contained high Cl−, giving an inward current at −60 mV holding potential. Experiments in this figure were done at room temperature without series resistance compensation.

chosen to improve voltage clamp at depolarized potentials, should not be used.

A second precaution is that care must be taken to minimize voltage clamp errors. Autaptic currents can be large (up to 10 nA) and voltage escape could lead to uncontrolled action potentials and a reverberating feedback response in the neuron (Segal and Furshpan, 1990; Segal, 1991). Lower-resistance patch electrodes should generally be selected (e.g., <3–4 MΩ) to facilitate the achievement of low (<10–15 MΩ) electrode series resistance (Rs). In addition to improving voltage control, low Rs enables fast whole-cell capacitance transients (labeled 1 and 3 in **Figure 3B**) which are less likely to merge with and obscure the closely following autaptic current. If merging does occur and is a concern, a workaround is to pharmacologically isolate the transients and action current by briefly superfusing a blocker of postsynaptic receptors (e.g., CNQX for glutamatergic autapses; **Figure 3B**, cyan trace), then digitally subtracting the blocked trace from the unblocked trace. This procedure should yield the pure autaptic current with minimal contamination from transients. In any case, electronic series resistance compensation should generally be used when measuring autaptic currents to minimize voltage clamp errors (Williams, 2004). Some investigators further reduce voltage clamp errors by applying a low concentration of blocker of postsynaptic receptors to reduce the amplitude of the autaptic current (Otsu et al., 2004).

A related precaution is to ensure that Rs remains as stable as possible throughout the experiment. It is common for Rs to increase steadily over time, which destabilizes the Rs compensation and causes an apparent rundown in the amplitude of the autaptic current. We have found that this increase in Rs can be much reduced by using internal solutions with a higher osmolarity (e.g., 330 mOsm/kg cf 310 mOsm/kg for the external solution; Bekkers, 2005). Higher internal osmolarity causes the neuron to swell slightly, possibly reducing a tendency of intracellular organelles to block the electrode tip.

Finally, autaptic currents sometimes exhibit delayed peaks without a preceding action current. This is often a sign that there is more than one neuron on the microdot, giving rise to a polysynaptic circuit. For some kinds of experiments, the delayed polysynaptic currents may not be a concern, particularly if the early autaptic current dominates. Another strategy, if the second neuron is visible, is to destroy the first neuron using the patch electrode (e.g., by aspirating the soma) then lower a new electrode to record from the second neuron. This strategy is only useful if the presence on the second neuron of remnant synapses from the first neuron is not a concern.

## APPLICATIONS OF AUTAPTIC CULTURES

In this section, I will illustrate the utility of autaptic cultures by giving an overview of studies that have made use of them over the past three decades. I will organize my survey to highlight the unique technical advantages of autapses while paying less attention to the specific research questions being addressed. Most of the examples will be electrophysiology experiments using hippocampal and neocortical cultures, but some use autaptic cultures from other brain areas, including the thalamus (Moechars et al., 2006), basal forebrain (Allen, 2006), nucleus accumbens (Shi and Rayport, 1994), raphé nucleus (Johnson, 1994) and ventral tegmental area (Sulzer et al., 1998; Michel and Trudeau, 2000). First, I will make general comments about the advantages and disadvantages of autaptic cultures.

#### Advantages

Like any dissociated culture model, autaptic cultures provide the convenience of a simplified two-dimensional structure: easy access to individual cells for making electrical recordings, and excellent visibility for imaging experiments. Also, however, autaptic cultures offer unique advantages (**Figure 4**).

FIGURE 4 | Schematic diagrams summarizing some of the experimental configurations possible with autaptic cultures. (A) Electrical recording from assured monosynaptic connections in a homogeneous set of autapses using a single electrode, and control of both pre- and postsynaptic intracellular solutions using a single electrode. (B) Ability to rapidly and uniformly apply extracellular solutions or light stimulation to all autaptic connections received by that neuron. (C) Study of signaling between a neuron and an underlying astrocyte, using two recording electrodes. (D) Study of competition between two or more neurons confined to a microisland. This also allows simultaneous comparison of synaptic and autaptic responses in the same neuron.

properties of a defined population of synaptic boutons can be studied, with no ambiguity about the origin of evoked or spontaneous synaptic events.

Examples of studies that explicitly draw upon these advantages are given in later sections.

#### Disadvantages

Autaptic cultures are susceptible to disadvantages that apply to culture models in general. For instance, cultured neurons commonly lose the dendritic and axonal morphologies that characterize their appearance in vivo. Their intrinsic functional properties might also be modified, and this must be checked or stated as a proviso (see next section). In addition to these general concerns about cultures, however, autaptic cultures have some specific disadvantages. Because the same neuron provides both the presynaptic and postsynaptic compartment, it may be impossible to separate processes that occur both preand postsynaptically. For example, Ca2+ signals that originate from the presynaptic action potential and the postsynaptic response may be entangled because of dendritic backpropagation (Otsu and Murphy, 2004). It is also difficult to depolarize the postsynaptic membrane without affecting presynaptic excitability (Bekkers and Stevens, 1991). When performing whole-cell patch-clamp experiments, one must be aware of the possibility of ''washout'' of key intracellular components, which might be a greater concern for autaptic cultures because both preand postsynaptic components could be vulnerable. That said, stable autaptic responses can generally be obtained, provided the electrode series resistance and other recording conditions are carefully controled (see ''Whole-Cell Patch-Clamp'' section). Lastly, the setting up of autaptic cultures is more fickle and labor intensive than that of conventional cell cultures, chiefly because more elaborate substrate preparation is required.

## Comparison of Autapses With Synapses in Other Model Systems

As a prelude to discussing the applications of autaptic cultures, I will briefly comment on comparisons between the electrical properties of autapses and synapses in two other widely-used model systems, mass cultures, and acute brain slices.

#### Comparison With Interneuronal Synapses in Mass Cultures

The basic biophysical features of autapses and synapses in mass cultures are reported to be the same (Bekkers and Stevens, 1991) or similar (Shi and Rayport, 1994; Mennerick et al., 1995; Liu et al., 2009, 2013). Autaptic EPSCs have somewhat larger amplitudes and readily-releasable vesicle pool sizes than their mass-culture counterparts (Mennerick et al., 1995; Liu et al., 2013), and differences in short-term plasticity have also been reported (Liu et al., 2013). Overall, however, autapses and interneuronal synapses in culture appear to function similarly.

#### Comparison With Synapses in Acute Slices

Dissociated cultures—including autaptic cultures—are less able to preserve the synaptic ''microenvironment'' than are more intact preparations, like acute slices, and this raises questions about the wider applicability of findings made in the culture setting. Nevertheless, many experimental findings made with autapses have translated well to the intact brain. For example, detailed molecular studies of the synaptic vesicle cycle at autapses (see ''A Homogeneous Population of Modified Synapses'' section) have been confirmed more generally (Chamberland and Tóth, 2016; Dittman and Ryan, 2019). Certain types of synaptic plasticity that have been studied in slices are also faithfully replicated in autaptic cultures. For instance, depolarizationinduced suppression of excitation (DSE; Straiker and Mackie, 2009) and inhibition (DSI; Straiker and Mackie, 2005; Kellogg et al., 2009) are present at autapses, as is long-term depression (LTD; Goda and Stevens, 1996; Tong et al., 1996; Kumura et al., 2000). Cultured dentate granule cells form autapses that resemble mossy fiber inputs to CA3 pyramidal cells, including expression of a presynaptic form of long-term potentiation (Rost et al., 2010). On the other hand, studies have also highlighted the potential risks of using cultures. For example, reports on the co-release of neurotransmitters (Hnasko and Edwards, 2012) and the efficacy of neuromodulators (Bekkers et al., 1996) show that the exact experimental conditions in culture can have an impact on the findings. All of this reinforces the point that, as for any model system, effective use of autaptic cultures must balance convenience and caution.

I will now turn to a survey of applications of autaptic cultures, organized under the five major advantages listed above in the ''Advantages'' section.

#### Examples of Applications

#### The Convenience of a Single Electrode

By providing access to large, monosynaptic currents that can be stably measured with a single electrode, autaptic cultures have been used in many key experiments on the biophysics of synaptic transmission. Early examples include studies of multivesicular release at glutamatergic synapses (Tong and Jahr, 1994b), how transporters shape neurotransmission (Tong and Jahr, 1994a; Diamond and Jahr, 1997), and how the kinetics of EPSCs are determined by asynchronous vesicle release and temperature (Diamond and Jahr, 1995; Pyott and Rosenmund, 2002). The role of presynaptic Ca2+ in determining neurotransmission has also been examined using autapses (Reid et al., 1998; Lee et al., 2000; Ikeda et al., 2008).

A different application has been to use autaptic cultures to study neuromodulation, again taking advantage of their convenience as an assay system. Modulators that have been characterized with autapses include histamine (Bekkers, 1993), adrenoceptor agonists (Raman et al., 1996), calcineurin (Tong et al., 1995), somatostatin (Boehm and Betz, 1997), clozapine (Michel and Trudeau, 2000), cyclic AMP (Gekel and Neher, 2008), amyloid α protein (Ripoli et al., 2013) and GABA acting via GABAB receptors (Valente et al., 2016). Several reports have also used autaptic cultures to examine short-term synaptic plasticity and its modulation (Mennerick and Zorumski, 1995a; Brody and Yue, 2000; Straiker and Mackie, 2007; Straiker et al., 2018). Lastly, autapses have been used as a convenient testbed for developing new molecular tools for the study of synaptic function (e.g., pHoenix, Rost et al., 2015).

#### A Single Axon

An autaptic neuron in culture is innervated by a single afferent (from itself) and thus provides access to a uniquely homogeneous population of presynaptic terminals—reliably stimulated—that can be used for the study of neurotransmitter release (Otsu and Murphy, 2004). For example, autaptic cultures have been utilized to measure the nonuniform probability of glutamate release from different boutons on the same axon (Rosenmund et al., 1993), the variable distribution of presynaptic Ca channel subtypes on a single afferent (Reid et al., 1997), and the differential invasion of glutamate-releasing terminals by action potentials (Prakriya and Mennerick, 2000). Autapses are also convenient for studying the synaptic vesicle cycle, for example, by using pharmacological approaches to count the number of releasable vesicles (Ikeda and Bekkers, 2009) or optical methods based on the styryl dyes (e.g., FM1–43) to follow vesicles through the cycle (Murthy et al., 1997; Murthy and Stevens, 1998). Experiments that load ''false'' neurotransmitters into synaptic vesicles have also been used to probe vesicle dynamics at autapses (Pan et al., 1993; Bekkers, 2005).

Another kind of experiment that relies on having a single axon takes advantage of the fact that both evoked and spontaneous postsynaptic currents originate from the same population of autaptic terminals, removing the ambiguity that typifies other kinds of synaptic circuits. For example, autaptic cultures been used to identify presynaptically silent synapses that give spontaneous but not evoked transmitter release (Kimura et al., 1997), and postsynaptically silent synapses that express only NMDA receptors (Gomperts et al., 1998). Autapses also allow the unambiguous study of phasic and asynchronous release from the same population of boutons (Otsu et al., 2004; Chang and Mennerick, 2010).

Lastly, the presence of a single axon enables definitive experiments showing the co-release of neurotransmitters from one neuron. For instance, autaptic cultures have been used to demonstrate the co-release of glutamate and serotonin from raphé neurons (Johnson, 1994) and of glutamate and dopamine from neurons in the ventral tegmental area (Sulzer et al., 1998).

#### A Homogeneous Population of Modified Synapses

Perhaps the most widely used application of autaptic cultures has been in structure-function studies, which take advantage of the ability to genetically modify a single isolated neuron and to examine the consequences of that modification for synaptic transmission, secure in the knowledge that all autapses received by that neuron are identically modified. The use of this culture system also enables the study of mutations that are postnatal lethal.

Genetically-modified autaptic cultures have been used to answer fundamental questions about the SNARE proteins, including SNAP-25 and SNAP-23 (Delgado-Martínez et al., 2007; Weber et al., 2014), syntaxin-1 (Gerber et al., 2008) and synaptobrevin-1 (Young, 2005; Zimmermann et al., 2014). Key experiments on the presynaptic Ca2+ sensor, synaptotagmin, have also been performed using autapses. For example, mutational analyses of synaptotagmin-1 (Fernández-Chacón et al., 2001; Stevens and Sullivan, 2003; Han et al., 2004; Nishiki and Augustine, 2004; Schupp et al., 2016; Chang et al., 2018) and synaptotagmin-4 (Ting et al., 2006) have elaborated details of the Ca2+ binding and synaptic vesicle fusion processes.  A number of these experiments took advantage of another convenient feature of autaptic cultures—the ability to completely superfuse a single neuron—to look for changes in the size of the readily-releasable pool (RRP) of synaptic vesicles. This feature will be further discussed in the next section.

Other researchers have used autapses and molecular genetic approaches to study the involvement of vesicular glutamate transporters in synaptic transmission (Fremeau et al., 2004; Wojcik et al., 2004; Zimmermann et al., 2015), as well as the properties of presynaptic voltage-gated Ca2+ channels (Few et al., 2012; Nanou et al., 2016). Lastly, a variety of disease models have been explored using this strategy. For example, genetic models of Alzheimer's disease (Pratt et al., 2011), autism (Weston et al., 2014) and epilepsy (Heeroma et al., 2009) have been implemented and studied in autaptic cultures.

#### Control Over the Extracellular Environment

The ability to uniformly perfuse extracellular solution over an isolated autaptic neuron brings obvious advantages in pharmacological experiments, like the neuromodulation studies mentioned earlier (''The Convenience of a Single Electrode'' section). However, uniform perfusion also enables other kinds of experiments that are difficult or impossible to achieve using other systems. Two main types of such experiments have been performed: measurements of synaptic vesicle pools using the application of hypertonic sucrose solution, and studies that disentangle subsynaptic (strictly, ''sub-autaptic'') and extrasynaptic receptors by exploiting the unique configuration of autaptic cultures.

Sucrose experiments depend on the classical finding that hypertonic solution causes the direct release of synaptic vesicles without electrical stimulation (Fatt and Katz, 1952). By applying pulses of sucrose solution to the entire dendritic arbor of an isolated neuron on a small island, all presynaptic vesicle pools can be identically stimulated with a hypertonic challenge and the resulting postsynaptic electrical response can be recorded at the soma. Critically, spontaneous or electrically-evoked release from those same pools can also be recorded, allowing a comparison between the postsynaptic responses to the different release mechanisms. For example, by measuring the total charge carried by the (multi-vesicle) sucrose-evoked response, then dividing this by the mean charge of the (single-vesicle) spontaneous ''miniature'' synaptic response measured in the same neuron, one can estimate the total size of the RRP of synaptic vesicles across all release sites on that neuron (Rosenmund and Stevens, 1996; Stevens and Williams, 2007).

This method has been widely used to measure changes in the RRP size following genetic mutations, as mentioned in the previous section (''A Homogeneous Population of Modified Synapses''). The approach has also been used to study changes in RRP size following different kinds of plasticity, for example, long-term depression (Goda and Stevens, 1998), short-term depression (Stevens and Wesseling, 1998, 1999b) and augmentation (Stevens and Wesseling, 1999a; Garcia-Perez and Wesseling, 2008), as well as other factors that alter the RRP size at autapses (Stevens and Sullivan, 1998; Moulder et al., 2004; Moulder and Mennerick, 2005).

The second main type of experiment that exploits the ease of autapse superfusion is a method for distinguishing subsynaptic and extrasynaptic NMDA receptors. This experiment depends on the fact that electrical stimulation (e.g., via a whole-cell electrode at the soma) selectively activates subsynaptic NMDA receptors, whereas superfusing the entire neuron with glutamate activates both sub- and extrasynaptic NMDA receptors. Hence, by comparing these two responses one can infer the distinct properties of both pools of NMDA receptors (Tovar and Westbrook, 1999). In an elegant variation on this experiment, subsynaptic NMDA receptors are ''tagged'' by blocking them with an activity-dependent antagonist (MK-801) while electrically stimulating at the soma; the subsequent response to whole-cell application of glutamate must then be entirely due to unblocked extrasynaptic NMDA receptors (Tovar and Westbrook, 2002).

This approach has been used in several interesting studies. For example, the mobility and turnover of the different pools of NMDA receptors have been measured (Li et al., 2002; Tovar and Westbrook, 2002), as well as their subunit composition (Tovar and Westbrook, 1999; Thomas et al., 2006), pharmacology (Xia et al., 2010; Vyklicky et al., 2016) and desensitization properties (Li et al., 2003).

Lastly, the compact dendritic arbor of autaptic cultures facilitates the use of optical techniques for the study of synaptic function. For example, autaptic cultures permit the uniform elevation of intracellular Ca2+ in calcium uncaging experiments (Burgalossi et al., 2012). However, optogenetic techniques have not been used with autaptic cultures and provide an opportunity for interesting experiments in the future.

#### A Defined Neighborhood

The applications described so far have highlighted the isolation of autaptic neurons, but this final application takes advantage of microislands as a useful model for studying intercellular interactions in the local neighborhood. These experiments fall into two broad classes: signaling between an autaptic neuron and the underlying glial cells, and competition between neurons on microislands occupied by two or more neurons.

Neuron/glia signaling has been studied by making dual whole-cell recordings from an isolated autaptic neuron and an underlying glial cell (Mennerick and Zorumski, 1994, 1995a; Mennerick et al., 1996). These experiments have shown, for example, how transporters in the glia modulate the timecourse of the autaptic EPSC in the neuron (Mennerick and Zorumski, 1995b; Mennerick et al., 1999), and how autaptic neurons grown without glial contact exhibit more asynchronous neurotransmitter release (Sobieski et al., 2015). Culturing without contact with glia has also been shown to reduce the number of autapses that form (Ullian et al., 2001).

For studying interactions between neurons, microislands with two or more neurons are selected (**Figure 4D**). Early work used microislands with small numbers of neurons to study epileptiform activity, which tends to be very strong when neurons are spatially constrained in this way (Segal and Furshpan, 1990; Segal, 1991, 1994). More recent work, however, has tended to focus on two-neuron microislands for ''mix and match'' experiments. For example, it has been shown that chronically silencing one of a pair of isolated excitatory neurons leads to characteristic changes in the postsynaptic AMPA receptor subunit composition in each neuron (Harms et al., 2005). Other work has explored the competition between glutamatergic and GABAergic neurons when grown as mixed or homotypic pairs (Rao et al., 2000; Chang et al., 2014; Wierda and Sørensen, 2014), or between wildtype and mutant neurons that lack presynaptic proteins involved in transmitter release (Tarsa and Goda, 2002; García-Pérez et al., 2015). Finally, two-cell microislands with different combinations of striatal, cortical and thalamic neurons have been used to examine the effect of

#### REFERENCES

glutamatergic input on refining striatal output (Paraskevopoulou et al., 2019).

## CONCLUSION

Autaptic cultures provide the ultimate in synaptic simplicity: a one-neuron circuit. Despite a current tendency to study complex and preferably in vivo neural networks, autaptic cultures still have an important place in the toolbox of cellular neuroscientists because they enable straightforward, elegant experiments that address fundamental questions about synaptic transmission. The examples of applications given in this review provide a taste of the diversity of experiments that are possible with autaptic cultures, and will hopefully inspire novel applications, perhaps involving new-generation optical technologies. Of course, like all model systems, autaptic cultures have advantages and disadvantages, and these must be carefully weighed up when deciding whether autapses are the right tool for the job. It is hoped that this review has provided enough information to make that decision easier, and will assist in the implementation of autaptic culture experiments with the minimum pain and maximum prospect of success.

#### DATA AVAILABILITY STATEMENT

The datasets generated for this study are available on request to the corresponding author.

#### AUTHOR CONTRIBUTIONS

JB wrote the manuscript and prepared the figures.

#### FUNDING

This work was supported by Project Grant 1128320 from the National Health and Medical Research Council of Australia and Discovery Project Grant DP 180101034 from the Australian Research Council.

#### ACKNOWLEDGMENTS

I thank Jane Sullivan for comments on the manuscript. I also thank the reviewers for helpful suggestions.

J. Neurosci. 19, 9242–9251. doi: 10.1523/JNEUROSCI.19-21-09242.1999

the clamping phenotype of synaptotagmin-1. J. Neurosci. 34, 2100–2110. doi: 10.1523/JNEUROSCI.3934-13.2014

**Conflict of Interest**: The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2020 Bekkers. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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**5. Activity control based on the electron transfer**

Electron transfer can be controlled by the surrounding environment. For example, pH is an important factor to control the photoinduced electron transfer [29, 30, 48, 80, 81]. Since it has been reported that cancer cells are slightly acidic (pH 6 ~ 7) against normal tissues (pH 7 ~ 7.4) [82–85], control of the electron transfer of the photosensitizer by pH can be applied for the development of cancer-selective PDT. In the cases of pH-dependent 1 O2 photosensitizers, the redox control [30, 86–88], the structure change [89], and the control of intersystem crossing [90] by pH have been reported as the important concepts. Several types of pH-activatable-porphyrin photosensitizers [30, 88], including a phosphorus(V) porphyrin [48, 81], have been reported. In addition, a self-quenching of the photoexcited molecules can be also used to control the activity [47]. In this section, several examples about the activity control of electron transfer-photosensitizers are introduced.


*4.1. Kirchhoff Index*

" The Kirchhoff index of a connected graph *G* is defined as the sum of resistance distances between all pairs of vertices, mathematically:"

$$Kf(G(t)) \ = \sum\_{i$$

where *rij*(*G*) represents the resistance distance between a pair of vertices. In terms of eigenvalues for a connected network *G* of order *N* with all its nonzero eigenvalues represented by *νi*; *i* = 2, ... , *N*, a well-known identity Kirchhoff index is defined as:

$$Kf(G(t)) \ = \ \ N\_t \sum\_{k=2}^{N\_t} \frac{1}{\nu\_k} = N\_t \sum\_{i=0}^{t-1} \sum\_{j=0}^{n-1} \frac{1}{\nu\_{i,j}} \quad (i,j) \neq (0,0)$$

The Kirchhoff index for the categorical path-path product network:"

$$\begin{aligned} \mathcal{K}f(G(t)) &= \ & \text{at} \sum\_{i=0}^{t-1} \sum\_{j=0}^{n-1} \frac{1}{\left( (2 - 2\cos\frac{j\pi}{n})d\_{i+1} + d\_{j+1}(2 - 2\cos\frac{i\pi}{t}) - (2 - 2\cos\frac{j\pi}{n})(2 - 2\cos\frac{i\pi}{t}) \right)} \\ (i, j) & \neq & (0, 0) \end{aligned}$$

The Kirchhoff index for the categorical cycle-path product network:

$$\mathcal{K}f(G(t)) \quad = \ \text{at} \\ \sum\_{i=0}^{t-1} \sum\_{j=0}^{n-1} \frac{1}{(2 - 2\cos\frac{2j\pi}{n})d\_{i+1} + d\_{j+1}(2 - 2\cos\frac{i\pi}{t}) - (2 - 2\cos\frac{2j\pi}{n})(2 - 2\cos\frac{i\pi}{t})}$$

The Kirchhoff index for the categorical cycle-cycle network:

$$\begin{array}{rcl} Kf(G(t)) &=& n(t+2) \sum\_{i=0}^{t+1} \sum\_{j=0}^{n-1} \frac{1}{(2-2\cos\frac{2j\pi}{n})d\_{i+1} + d\_{j+1}(2-2\cos\frac{2j\pi}{t+2}) - (2-2\cos\frac{2j\pi}{n})(2-2\cos\frac{2j\pi}{t+2})} \end{array}$$


**2. Pathogenesis of Chagas' myocarditis**

Milei et al. proposed a combined theory that could explain the pathogenic mechanism in chronic chagasic myocarditis (Milei, et al., 1996a, Storino & Milei, 1994). This theory is based on three ingredients: the parasite, host immune system and fibrosis. These ingredients are proposed as being the primary causative agents of damage on myocardial tissue, conduction system, autonomic ganglia and nerves and microvasculature.