Organotypic hippocampal slices were prepared, as previously described, from P6-7 female and male Sprague Dawley rats and kept in culture for 6–13 days (Stoppini et al., 1991; Kessels et al., 2013). APP_CT100 was sparsely expressed using Sindbis viral vectors that were injected into CA1 20–30 h before recording. Sparse expression is relevant to avoid immune responses to viral particles (Uyaniker et al., 2019) and to ensure that the majority of synapses from control neurons are sufficiently separated from Aβ-producing neurons (Wei et al., 2010). On the day of recording a cut was made between CA3 and CA1 to prevent stimulus-induced bursting. Whole-cell recordings were obtained simultaneously from neighboring uninfected and infected CA1 neurons; infected neurons were identified by fluorescence using co-expression of GFP. Two stimulating electrodes were placed 100 μm apart laterally and 200 μm in opposite directions (e.g., 100 and 300 μm) along the apical dendrite in the stratum radiatum (Figure 5A). For the recordings 3- to 5-MΩ pipettes were used containing internal solution of 115 mM cesium methanesulfonate, 20 mM CsCl, 10 mM Hepes, 2.5 mM MgCl₂, 4 mM Na₂ATP, 0.4 mM Na₃GTP, 10 mM sodium phosphocreatine (Sigma), and 0.6 mM EGTA (Amresco), at pH 7.25. During recording, slices were perfused with artificial cerebrospinal fluid containing 119 mM NaCl, 2.5 mM KCl, 26 mM NaHCO₃, 1mM NaH₂PO₄, and 11 mM glucose (pH 7.4), and gassed with 5% CO2/95% O₂ at 27 °C with 4 mM MgCl₂, 4 mM CaCl₂, 4 μM 2-chloroadenosine (Sigma), and 100 μM picrotoxin (Sigma). During each recording, neurons received input from the two stimulating electrodes, sweeps from each individual electrode were 3 s apart. The resulting EPSCs were averaged and count as n = 1. AMPAR EPSCs were measured as peak inward currents at −60 mV.

Evoked whole-cell patch clamp experiments were simulated using MATLAB 2021a. To match the electrophysiological data, experimental groups always consisted of 27 in silico neurons. In these simulations, populations of neurons were given values for N, P_r, and Q. The number of synapses (N) differed between 5 and 25, depending on the experiment. Each synapse was assigned a release probability (P_r) between 0 and 1. In a uniform population all synapses had the same P_r, but in a non-uniform population, synapses were randomly assigned a value drawn from a beta distribution with a specific mean P_r and corresponding standard deviation (SD). An example of randomly drawn P_r values within such a distribution is depicted in Supplementary Figure 1 (i.e., 27 neurons with 15 synapses each). Regarding quantal response size (Q), each synapse was given a value between 5 and 25 pA, depending on the experiment. Again, in uniform populations Q was the same for each synapse, but in non-uniform populations Q was attributed randomly per synapse from the distribution in the Pearson system with mean, standard deviation, skewness (between 0.75 and 1) and kurtosis (4). An exemplar distribution of randomly drawn Q values for one experiment is depicted in Supplementary Figure 1 (i.e., 27 neurons with 15 synapses each).

Each simulated experiment consisted of 48 sweeps, based on the average number of sweeps used in the electrophysiological experiments (Figure 5A). Each sweep meant the stimulation of one population of synapses that was activated. However, to mimic the stochastic process of neurotransmitter release, a go/no go value was randomly drawn from a uniform distribution in the interval (0,1) for each synapse for each sweep. If this go/no go value was equal to or lower than the P_r of that synapse a “vesicle was released” and the EPSC amplitude of that synapse would be equal to its Q. If the go/no go value would lead to no release, the EPSC amplitude of that synapse would be 0. Per sweep, the currents of all the synapses in which release took place were summated giving the total EPSC amplitude of that sweep. Per neuron/recording this was done 48 times (i.e., nr. of sweeps), leading to a mean EPSC amplitude and its variance per neuron.

For the electrophysiological recordings, variance analysis was performed on the mean EPSC amplitudes and variance of responses to 30–80 sweeps, on average 48 sweeps, per neuron. For the in silico neurons, 48 sweeps were used. The EPSC amplitudes per sweep and variance per neuron were used to calculate their mean EPSC amplitude, 1/CV² and VMR (equations 2 and 3). These three values were averaged over 27 neurons per group and compared between conditions. Note that multiplying 1/CV² with VMR per neuron leads to its μ value. As a consequence, 1/CV² and VMR are negatively correlated for both simulated and recorded neurons (Supplementary Figure 2).

Multiple t-tests with a Holm-Šídák correction were performed on log₂-normalized data to test whether they differed significantly from 0 or if there were differences between groups. One-way ANOVAs were used to test if there were differences between multiple groups. Paired t-tests were used to detect differences between two groups in the electrophysiological experiments and unpaired t-tests were used for two-group comparisons in the in silico experiments. For all experiments, p < 0.05 was considered significant.

To examine whether a uniform versus a non-uniform input variable distribution (N, P_r and Q) would lead to different outcomes in variance analysis output (i.e., μ, 1/CV² and VMR), we simulated whole-cell electrophysiological experiments in which excitatory postsynaptic currents are determined by stimulating a population of 27 neurons. In this simulation, for each in silico neuron 15 synapses were stimulated (N = 15). Release was set to be univesicular, indicating that in this model N represents the number of release sites and also the number of synapses. These in silico synapses had physiological values for the mean and standard deviation of the release probability (P_r = 0.3 ± 0.15) and quantal size (Q = 15 ± 4.5 pA) based on previous literature for Sc-CA1 hippocampal synapses that receive Schaffer collateral input (Hessler et al., 1993; Rosenmund et al., 1993; Dobrunz and Stevens, 1997; Hanse and Gustafsson, 2001; Oertner et al., 2002). In the non-uniform distributions, P_r ranged from 0.04 to 0.81 and Q values ranged from and 6 to 28 pA (Supplementary Figure 1). We used these values to design four populations with the same N, mean P_r and mean Q, but with different distributions for P_r and Q.

In the first population, all 15 synapses were uniform having an identical P_r and Q (Figure 1A; P_r = 0.3 ± 0; Q = 15 ± 0 pA). In the second set of in silico experiments, we tested groups of 15 synapses per neuron that varied in P_r but with Q uniform (Figure 1B; Pr = 0.3 ± 0.15; Q = 15 ± 0 pA). The third experiment used 15 synapses with uniform P_r and with different values for Q (Figure 1C; P_r = 0.3 ± 0; Q = 15 ± 4.5 pA). In the fourth experiment both P_r and Q were non-uniform in the 15 synapses (Figure 1D; P_r = 0.3 ± 0.15; Q = 15 ± 4.5 pA). Because the N of each neuron and the P_r and Q of the synapses were on average the same in all four experiments, the average EPSC amplitudes were also highly similar to each other (Figures 1A–D). We calculated the 1/CV² and VMR values for the 4 populations to assess whether the uniformity of the input variables affect the output (Figures 1A–D). We make a distinction between “predicted values” (i.e., 1/CV² and VMR) that result from variance analysis, and “expected values” that are calculated by input variables N, P_r and Q in equations 1, 3 and 4. Normalizing the predicted values of 1/CV² and VMR to their expected values showed that the prediction did not deviate significantly from the expected outcome for both the uniform and non-uniform populations of in silico synapses (Figure 1E). More importantly, these normalized values gave similar values when comparing between the four in silico experiments (Figure 1E). Furthermore, changing the distribution further by using either smaller or larger values as standard deviation for P_r and Q also did not affect the average EPSC amplitude, 1/CV² or VMR significantly (Supplementary Figure 3). These data indicate that the uniformity of a population of synapses did not affect the outcomes of variance analysis.

In the previous experiment, we simulated synaptic responses upon stimulation of 15 Sc-CA1 synapses per neuron. It may be possible that when stimulating a lower number of synapses, differences in variance between uniform and non-uniform populations of synapses become more apparent. To examine the effect of changing the number of synapses, we chose different numbers for N ranging from 5 to 25 with P_r (0.3) and Q (15 pA) kept constant (Figure 2). We compared synapses that were uniform in both P_r (0.3 ± 0) and Q (15 ± 0 pA) or non-uniform in both P_r (0.3 ± 0.15) and Q (15 ± 4.5 pA). The mean EPSC and 1/CV² changed linearly with a change in N (Figures 2A, B), whereas the VMR was not affected by changes in N (Figure 2C), indicating that changing N has the expected effects on the variance analysis parameters in both uniform and non-uniform populations of synapses. The values for average EPSC amplitude, 1/CV² and VMR normalized to their expected values showed that the uniform and the non-uniform populations did not deviate from each other (Figures 2A–C), indicating the number of stimulated synapses does not influence the reliability of variance analysis.

It was previously suggested that variance analysis outcomes for non-uniform populations of synapses would deviate more from expected values at high release probability than at low release probabilities (Silver et al., 1998). We therefore asked whether variance analysis comparisons between uniform and non-uniform populations of synapses depend on average release probability. The effects of changes in release probability were assessed by selecting five values for P_r ranging from 0.2 to 0.8 (Figure 3). Note that we avoided including in silico synapses with a P_r lower than 0 or higher than 1 by setting the standard deviation for non-uniform populations to 0.14 instead of 0.15 for P_r = 0.2 and 0.8. In accordance with the prediction, the mean EPSC increased proportionally with an increase in P_r for both uniform and non-uniform groups of synapses (Figure 3A). However, only for a low average release probability (P_r = 0.2), the average EPSC amplitude was significantly lower for non-uniform synapses compared with uniform synapses (p = 0.001; Figure 3A). This result was unexpected, since the average EPSC should be similar when average N, P_r and Q are the same. Repeating this in silico experiment did give similar average EPSC amplitudes for changes at P_r = 0.2 (p = 0.924; Supplementary Figure 4) and for all other outcome values, which supports the notion that statistical differences can be based on chance. Nevertheless, irrespectively of having obtained a significant difference in EPSC amplitude at average P_r = 0.2, 1/CV² increased exponentially with an increase in P_r without differences between the uniform and non-uniform populations of synapses (Figure 3B). In addition, increases in P_r lead to the expected linear decrease in VMR and also here no differences were found between uniform and non-uniform populations (Figure 3C). This simulation indicates that changes in average P_r resulted in expected changes in 1/CV² and VMR in both uniform and in non-uniform populations of in silico synapses.

We next selectively varied the quantal response size by varying the Q from 5 to 25 pA in steps of 5 pA, with a standard deviation of 0 (uniform) or 4.5 (non-uniform) (Figure 4). We chose these values of average Q (15 pA) and standard deviation (4.5 pA) based on previous literature (Dobrunz and Stevens, 1997; Hanse and Gustafsson, 2001). To prevent the inclusion of synapses with negative values for Q, in the non-uniform populations the SD for the lowest value (Q = 5 pA) was set to 2.5 instead of 4.5. The average EPSC of synaptic responses increased proportionally with an increase in Q and did not differ between uniform and non-uniform populations for any of the Q values (Figure 4A). The 1/CV² is expected to be independent of Q, which was indeed reflected by variance analysis of both uniform and non-uniform populations of synapses (Figure 4B). VMR values increased linearly with Q and similarly for uniform and non-uniform populations of in silico synapses (Figure 4C), which is in line with the expectation that changes in Q are reflected in altered VMR values.

Combined, these results indicate that variance analysis correctly predicts changes in N, P_r and Q for non-uniform groups of in silico synapses.

To validate variance analysis as a predictor for the locus of synaptic plasticity, we previously demonstrated in electrophysiological experiments that changing a single parameter, i.e. either N, P_r or Q individually, resulted in the expected changes in 1/CV² and VMR (van Huijstee and Kessels, 2020). To further investigate the value of variance analysis in a more complex situation where potentially more than one parameter may be altered, we compared our in silico model to a previously published ex vivo whole-cell patch clamp experiment in which synaptic transmission is affected by the production of Aβ (Kessels et al., 2013). To induce elevated Aβ levels in CA1 pyramidal neurons, organotypic hippocampal slices were injected with viral vectors expressing APP_CT100, the β-secretase product of APP and substrate for Aβ after γ-secretase cleavage. Dual whole-cell recordings from pairs of neighboring uninfected and infected neurons were performed, and AMPAR currents at Sc-CA1 synapses were evoked by stimulating the same axonal input to both neurons. Excitatory transmission was on average 47% lower in APP_CT100-infected CA1 neurons compared with their neighboring control neurons (p < 0.0001; Figure 5A). We subsequently tested whether variance analysis could predict a synaptic locus of the observed synaptic depression. We found that the 1/CV² decreased significantly in these recordings by 40% (p = 0.0056; Figure 5A). The VMR also tended to decrease by on average 23%, but did not reach statistical significance (p = 0.058; Figure 5A).

To further entangle the prediction for a synaptic locus, we reproduced the 47% decrease of the EPSC amplitude in silico by lowering N, P_r and Q separately by ∼47% (Figures 5B–D). In these experiments, we attempted to use values for N, P_r, and Q that would match the electrophysiological experiments in organotypic slices of the rat hippocampus. An important factor here is that the ex vivo slice recordings were conducted with 4 mM extracellular Ca²⁺ and P_r is known to depend strongly on extracellular Ca²⁺ concentration (Dodge and Rahamimoff, 1967; Rosenmund et al., 1993; Dobrunz and Stevens, 1997; Oertner et al., 2002). To estimate P_r in our in silico experiments, we used the VMR of the uninfected neurons (Figure 5A) and assumed that Q was on average 15 pA, since Q is not affected by changing Ca²⁺ concentrations when Mg²⁺ levels are kept high at 4 mM (Hardingham et al., 2006). By using this VMR (8.13) and Q (15 pA) in equation 4, we calculated a P_r of ∼0.46. This value is approximately in line with the relationship between Ca²⁺ concentration and P_r reported in literature (Rosenmund et al., 1993; Dobrunz and Stevens, 1997; Oertner et al., 2002). A factor that was considered to influence variance analysis when comparing EPSC recordings with in silico results is random electrical noise. When we included noise with a bandwidth of 10 pA to the in silico model by adding a random value between +5 pA and −5 pA to the amplitude generated by each sweep, the 1/CV² and VMR values are minimally affected except for recordings with low average EPSC amplitudes (Supplementary Figure 5).

To simulate a loss of functional synapses as the cause of ∼47% decrease in EPSC, we analyzed the effect of lowering N from 10 to 5 synapses per neuron, which resulted in a 43% decrease in the 1/CV² while the VMR remained unchanged (Figure 5B). Decreasing P_r from 0.46 ± 0.23 to 0.24 ± 0.15 to achieve a 47% decrease in EPSC amplitude led to a 65% decrease in 1/CV² and a 49% increase in VMR (Figure 5C), which particularly for VMR does not match experimental results. When decreasing Q by 47% from 15 to 7.96 pA, we found that 1/CV² decreased by 20% and VMR decreased by 33% (Figure 5D). This result is partially in line with expectation, since the significant change in 1/CV² (p = 0.029) unexpectedly predicts a decrease in N or P_r. An advantage of in silico experiments over electrophysiology experiments is that they can be effortlessly repeated many times. To assess the probability of finding statistically significant differences, we ran experiments of Figures 5B–D and subsequent statistics for each parameter (EPSC, 1/CV², VMR) 1,000 times. Whereas comparisons were either statistically significant or non-significant in nearly all repetitions for Figures 5B, C, the change in 1/CV² upon a decrease in Q reached significance in only 239 out of 1,000 repetitions (Figure 5D). In conclusion, this variance analysis predicts that APP_CT100 expression predominantly causes a loss of functional release sites, with possibly also a contribution of a decrease in quantal size at remaining functional release sites, and little change in presynaptic release probability.

For a more tailored reproduction, we based our in silico parameters on previous findings in similar models to the experiment described here (Kessels et al., 2013). APP and APP_CT100 expression consistently cause a ∼30% spine loss in CA1 dendrites across different studies (Hsieh et al., 2006; Kessels et al., 2010; Reinders et al., 2016). APP expression was reported not to affect presynaptic release probability in Sc-CA1 synapses, shown by an absence of change in paired-pulse facilitation (Kamenetz et al., 2003). There is also evidence that APP expression causes AMPAR removal in remaining Sc-CA1 synapses. Specifically, a ∼25% spine surface reduction of GluA1-expressing AMPARs was found (Hsieh et al., 2006), which predominantly contribute to AMPAR currents (Renner et al., 2017). This observation indicates a decrease in Q in the remaining synapses that did not undergo spine loss. Based on these findings we decided to decrease N by 30% (from 10 to 7 synapses) and cover the remaining EPSC amplitude reduction by lowering Q by 24% (from 15 to 11.36 ± 4.5 pA) (Figure 5E). With these manipulations, 1/CV² decreased significantly by 39% (p = 0.019) and VMR decreased by 15%, without reaching statistical significance (p = 0.097). Repeating this in silico experiment a 1,000 times, 1/CV² lowered significantly in 798/1,000 repetitions and the VMR lowered significantly in 667/1,000 repetitions (Figure 5E). These results obtained by in silico simulations approach the biological electrophysiology data (Figure 5A), demonstrating the validity of variance analysis for predicting the locus of synaptic changes.