Variance analysis as a method to predict the locus of plasticity at populations of non-uniform synapses

Abstract

Our knowledge on synaptic transmission in the central nervous system has often been obtained by evoking synaptic responses to populations of synapses. Analysis of the variance in synaptic responses can be applied as a method to predict whether a change in synaptic responses is a consequence of altered presynaptic neurotransmitter release or postsynaptic receptors. However, variance analysis is based on binomial statistics, which assumes that synapses are uniform. In reality, synapses are far from uniform, which questions the reliability of variance analysis when applying this method to populations of synapses. To address this, we used an in silico model for evoked synaptic responses and compared variance analysis outcomes between populations of uniform versus non-uniform synapses. This simulation revealed that variance analysis produces similar results irrespectively of the grade of uniformity of synapses. We put this variance analysis to the test with an electrophysiology experiment using a model system for which the loci of plasticity are well established: the effect of amyloid-β on synapses. Variance analysis correctly predicted that postsynaptically produced amyloid-β triggered predominantly a loss of synapses and a minor reduction of postsynaptic currents in remaining synapses with little effect on presynaptic release probability. We propose that variance analysis can be reliably used to predict the locus of synaptic changes for populations of non-uniform synapses.

Keywords: amyloid–beta; excitatory postsynaptic current (EPSC); hippocampus; synapse; uniformity; variance.

FIGURE 1

Non-uniform in silico populations of synapses do not affect variance analysis outcomes. (A–D) Left panel: example traces of summated EPSC amplitudes of 15 stimulated synapses per sweep of one in silico neuron. Right panels: average EPSC, 1/CV² and VMR (n = 27 neurons). (A) Both P_r (0.3 ± 0) and Q (15 ± 0 pA) uniform across synapses (grey). (B) P_r (0.3 ± 0.15) non-uniform and Q uniform (15 ± 0 pA) across synapses (yellow). (C) P_r (0.3 ± 0) uniform and Q (15 ± 4.5 pA) non-uniform across synapses (orange). (D) Both P_r (0.3 ± 0.15) and Q (15 ± 4.5 pA) non-uniform across synapses (red). (E) Log₂ values of 1/CV² and VMR for all four conditions normalized to their expected values. Statistics: normalized values were compared to 0 using multiple t-tests with a Holm-Šídák correction and to each other by one-way ANOVAs. Error bars indicate SEM.

FIGURE 2

Changes in N lead to similar variance analysis outcomes in both uniform and non-uniform in silico populations of synapses. (A–C) Left panels: effects of changes in number of synapses (N) on average EPSC (A), 1/CV² (B), and VMR (C) in uniform (grey circles) and non-uniform (red squares) populations. Right panel: average log₂ values of EPSC (A), 1/CV² (B), and VMR (C) normalized to expected values of uniform (grey circles) and non-uniform populations (red squares). For uniform populations P_r = 0.3 ± 0 and Q = 15 ± 0 pA; for non-uniform populations P_r = 0.3 ± 0.15 and Q = 15 ± 4.5 pA (n = 27). Statistics: effect of number of synapses on average EPSC, 1/CV² and VMR values (left panels) were tested using one-way ANOVAs. Normalized values were compared to 0 and between uniform and non-uniform using multiple t-tests with a Holm-Šídák correction. Error bars indicate SEM; ^****p < 0.0001.

FIGURE 3

Changes in P_r lead to similar variance analysis outcomes in both uniform and non-uniform in silico populations of synapses. (A–C) Left panels: effects of changes in release probability (P_r) on average EPSC (A), 1/CV² (B), and VMR (C) in uniform (grey circles) and non-uniform (red squares) populations. Right panel: average log₂ values of EPSC (A), 1/CV² (B), and VMR (C) normalized to expected values of uniform (grey circles) and non-uniform populations (red squares). For all populations N = 15 and Q = 15 pA; in uniform populations SDs of P_r and Q were 0; in non-uniform populations SDs of P_r were 0.15 (0.14 for P_r = 0.2 and 0.8) and SDs of Q were 4.5 pA (n = 27). Statistics: effect of release probability on average EPSC, 1/CV² and VMR values (left panels) were tested using one-way ANOVAs. Normalized values were compared to 0 and between uniform and non-uniform using multiple t-tests with a Holm-Šídák correction. Error bars indicate SEM; ^**p < 0.01, ^****p < 0.0001.

FIGURE 4

Changes in Q lead to similar variance analysis outcomes in both uniform and non-uniform in silico populations of synapses. (A–C) Left panels: effects of changes in quantal size (Q) on average EPSC (A), 1/CV² (B), and VMR (C) in uniform (grey circles) and non-uniform (red squares) populations. Right panel: average log₂ values of EPSC (A), 1/CV² (B), and VMR (C) normalized to expected values of uniform (grey circles) and non-uniform (red squares) populations. For all populations N = 15 and P_r = 0.3; in uniform populations SDs of Pr and Q were 0; in non-uniform populations SDs of P_r were 0.15 and SDs of Q were 4.5 pA (2.5 pA for Q = 5 pA) (n = 27). Statistics: effect of quantal size on average EPSC, 1/CV² and VMR values (left panels) were tested using one-way ANOVAs. Normalized values were compared to 0 and between uniform and non-uniform using multiple t-tests with a Holm-Šídák correction. Error bars indicate SEM; ^****p < 0.0001.

FIGURE 5

Variance analysis predicts the effects of Aβ on synapses. (A) Left panel: example traces of EPSCs from uninfected neuron (black circles) and infected neighboring neuron expressing APP_CT100 (yellow squares). Middle panels: with averages of EPSC, 1/CV² and VMR in uninfected neurons and their neighboring APP_CT100-infected neurons. Right panel: schematic representation of two CA1 neurons (uninfected and infected) that are recorded simultaneously. (B–E) Left panel: example traces of in silico control neuron (grey circles; N = 10, P_r = 0.46 ± 0.23, Q = 15 ± 4.5 pA) and test neuron in which N, P_r, and Q are changed to achieve a ∼47% reduction in EPSC amplitude (orange squares). Middle panels: averages of EPSC, 1/CV² and VMR between control and test neurons (n = 27). Right panel: simulations were run 1,000 times and differences in EPSC, 1/CV² and VMR were assessed using t-tests and checked for statistical significance. (B) N is reduced by ∼47% (N = 5); P_r and Q are unchanged compared to control. (C) P_r is reduced by 47% (P_r = 0.24 ± 0.15); N and Q are unchanged compared to control. (D) Q is reduced by 47% (Q = 7.95 ± 4.5 pA); N and P_r are unchanged compared to control. (E) N is decreased by 30% (N = 7) and Q is decreased by 24% (Q = 11.36 ± 4.5 pA), P_r is unchanged compared to the control. Statistics: paired t-test (A); unpaired t-test (B–D). Error bars indicate SEM; *p < 0.05; ^**p < 0.01, ^****p < 0.0001.