Modeling the Short-Term Dynamics of in Vivo Excitatory Spike Transmission

Abstract

Information transmission in neural networks is influenced by both short-term synaptic plasticity (STP) as well as nonsynaptic factors, such as after-hyperpolarization currents and changes in excitability. Although these effects have been widely characterized in vitro using intracellular recordings, how they interact in vivo is unclear. Here, we develop a statistical model of the short-term dynamics of spike transmission that aims to disentangle the contributions of synaptic and nonsynaptic effects based only on observed presynaptic and postsynaptic spiking. The model includes a dynamic functional connection with short-term plasticity as well as effects due to the recent history of postsynaptic spiking and slow changes in postsynaptic excitability. Using paired spike recordings, we find that the model accurately describes the short-term dynamics of in vivo spike transmission at a diverse set of identified and putative excitatory synapses, including a pair of connected neurons within thalamus in mouse, a thalamocortical connection in a female rabbit, and an auditory brainstem synapse in a female gerbil. We illustrate the utility of this modeling approach by showing how the spike transmission patterns captured by the model may be sufficient to account for stimulus-dependent differences in spike transmission in the auditory brainstem (endbulb of Held). Finally, we apply this model to large-scale multielectrode recordings to illustrate how such an approach has the potential to reveal cell type-specific differences in spike transmission in vivo Although STP parameters estimated from ongoing presynaptic and postsynaptic spiking are highly uncertain, our results are partially consistent with previous intracellular observations in these synapses.SIGNIFICANCE STATEMENT Although synaptic dynamics have been extensively studied and modeled using intracellular recordings of postsynaptic currents and potentials, inferring synaptic effects from extracellular spiking is challenging. Whether or not a synaptic current contributes to postsynaptic spiking depends not only on the amplitude of the current, but also on many other factors, including the activity of other, typically unobserved, synapses, the overall excitability of the postsynaptic neuron, and how recently the postsynaptic neuron has spiked. Here, we developed a model that, using only observations of presynaptic and postsynaptic spiking, aims to describe the dynamics of in vivo spike transmission by modeling both short-term synaptic plasticity (STP) and nonsynaptic effects. This approach may provide a novel description of fast, structured changes in spike transmission.

Keywords: functional connectivity; generalized linear models; short-term synaptic plasticity; spiking neurons.

Figure 1.

TM-GLM. Postsynaptic spiking probability before passing the spiking nonlinearity (yellow) changes as a linear combination of presynaptic coupling term with STP dynamics (blue), postsynaptic spiking history (green), the postsynaptic excitability (red). Transparent red curves show the bases of slow changes in postsynaptic probability at presynaptic spike times ($X_c$).

Figure 2.

Spike transmission probability depends on the presynaptic ISI and differs between synapses. A, Cross-correlograms between presynaptic and postsynaptic spiking at three different synapses show an increase in the postsynaptic spike count (or probability) after a short latency, indicative of a monosynaptic connection. The efficacy (Eff.) for each synapse is calculated as the ratio between the number postsynaptic spikes that are above baseline in the transmission interval (denoted by the horizontal bar) and the number of presynaptic spikes. B, ISI distributions (log-scale) for the presynaptic neurons. The distributions are color-coded into five quantiles with equal numbers of presynaptic spikes. C, We calculate a separate cross-correlogram using the subset of presynaptic spikes where the preceding spike fell within each ISI range. Colors correspond to B going from shorter presynaptic ISIs (left) to longer ISIs (right). Note that both the baseline firing rate and the synaptic peak for each connection change as a function of presynaptic ISI.

Figure 3.

A simulation of a simplified spiking model shows how spike transmission probability depends on multiple factors. A, For different types of STP, postsynaptic summation increases the amplitudes of the PSPs at shorter ISIs. Lines denote the membrane potential of a postsynaptic neuron in a simplified model as it responds to short (dark traces) and long (light) paired presynaptic pulses. Relative amplitudes of EPSPs increase or decrease under the simplified model depending on the type of STP. B, Spike generation changes with synaptic strength. In this paired-pulse stimulation paradigm, stronger synapses are more likely to generate a spike following the first presynaptic impulse which can then decrease the spiking probability following the second impulse if there are post-spike history effects. As in A, traces denote postsynaptic membrane potential responses to short (dark) and long (light) presynaptic ISIs. Dashes denote example postsynaptic spiking, with spike interference occurring for strong synapses and short ISIs. C, The pattern of spike transmission probability under the simplified model changes depending on the type of STP, the coupling strength, and presence of post-spike interference. Dashed lines show transmission probability without interference from previous postsynaptic spikes, while solid lines show how post-spike history effects can decrease the spike transmission probability.

Figure 4.

Including short-term dynamics substantially improves the model of spike transmission. A, Spike transmission patterns are diverse across different connections. For three different connections (between a pair of neurons in thalamus, a projection from VB-Barrel, and an auditory nerve fiber projection onto a SBC) transmission patterns are modeled by a combination of different factors. For each synapse, top panels show the presynaptic ISI distributions (log-spaced). In the second/third row, the observed spike transmission probability (red data points) and model predictions (blue with 95% confidence bands) for training and test set (2-fold cross-validation). We then used the estimated TM parameters for each synapse and simulated responses to paired presynaptic pulses. Blue curves denote the PPRs of the full model, and gray lines denote PPRs by taking synaptic summation out. Bottom row, TM-GLM (blue) are superior in predicting individual postsynaptic transmission events compared with GLM (orange, without STP) for each synapse type. For each individual presynaptic spike, we compare the model transmission probability with the observed binary outcome. ROC curves show the prediction accuracy with positive deviations from the diagonal indicating better performance. B, Estimates for the four STP parameters of the model for each synapse. Dots represent estimates from bootstrap sampled data. C, Model comparison for 6 different models (AIC relative to a model without plasticity). Models: (1) integration only, (2) facilitation only, (3) depression only, (4) three-parameter TM, (5) four-parameter TM without resetting integration, and (6) full model. Boxplots denote the difference in AIC values for bootstrap samples in B.

Figure 5.

Presynaptic and postsynaptic spiking history determine transmission probability. A, Schematic of four different patterns of presynaptic spike triplets with a fixed interval between the two most recent presynaptic spikes (spikes denoted by black lines separated by ISI₁). B, We then split the presynaptic ISI distribution into eight quantiles, denoted by the different colors. C, We then assess how ISI₂ influences the spike transmission previously described for ISI₁. Using the natural occurrence of different ISI₁ and ISI₂ in the data, each data point shows the observed spike transmission probability for each pattern (colors correspond to ISI₂ quantiles). Lines denote the average estimated transmission probability for each pattern under the model (based on the natural sequence of observed spikes). To examine the influence of serial correlations, we then simulate model responses to the isolated triplet pattern, assuming the synapse is initially in an average state (bottom panels). D, Synaptic transmission patterns change depending on the history of postsynaptic spiking, as well. E, Note that the postsynaptic ISI distributions need not match the presynaptic distributions. F, Here, each data point in the scatter plots shows the spike transmission probability following different combinations of ISI₁ and ISI_post. Here, colors denote quantiles of the postsynaptic ISI distribution. Solid lines show the estimated transmission probability for each pattern under the model (based on the natural sequence of observed spikes). The bottom panels show model responses to isolated patterns using the estimated STP parameters and fixing the excitability from the model fits to their average values.

Figure 6.

The TM-GLM captures stimulus-dependent changes in spike transmission probability at the ANF-SBC synapse. A, The TM-GLM captures stimulus-dependent spike transmission probability patterns better than a static model without STP. Dots show spike transmission probability for (log-spaced) presynaptic ISIs during two types of auditory stimuli and during spontaneous activity: natural sounds (yellow), spontaneous activity (red), and tuning stimuli (blue). Solid lines and 95% confidence bands show model predictions for each stimulus type. Corresponding ISI distributions are shown on the right. B, The TM-GLM captures changes in extracellularly recorded PSPs. Here, the observed PSP slope (dots) approximately matches the coupling term in the TM-GLM (solid lines) for each three stimuli. Although the spike transmission probability of the static GLM can vary as a function of presynaptic ISI due to nonsynaptic factors, the coupling term is fixed. C, Estimates of individual PSP amplitudes predicted by the model and their PSP slopes in the juxtacellular recording. Black lines denote linear fits and the bar plot shows the corresponding Spearman correlations. D, After fitting each stimuli condition separately, in each column we plotted the estimated spike transmission probability of each type using the estimated STP parameters of others. E, Distribution of parameters from bootstrap samples with the TM-GLM fit for individual stimuli and all stimuli combined.

Figure 7.

Distinctive short-term dynamics for spike transmission in connections between excitatory neurons to putative RS and FS inhibitory neurons. A, Here, we examine putative synapses between excitatory neurons and inhibitory neurons (identified by their cross-correlations) and separate the putative inhibitory neurons into two classes: FS, which have narrow spike waveforms and high rates (left), and RS (right), which have wide waveforms and lower rates. Identifying these synapses requires both finding both a putative excitatory input and a putative inhibitory output for the same neuron. B, Half-widths (of the trough) of the spike waveforms and firing rates for the FS (orange) and RS (blue) inhibitory neurons, as well as, their excitatory inputs (gray). Individual blue and orange waveforms (maximum amplitude across the MEA) are shown for all nine putative inhibitory neurons. C, Estimated depression, facilitation, and membrane time constants for excitatory-RS and excitatory-FS connections, along with the release probability (right). The purple error-bar next to the membrane time-constant estimations show the median and standard deviations from in vitro experiments (Perrenoud et al., 2013). D, Simulated PSP amplitudes estimated from TM model of STP using estimated parameters. For each synapse, PSPs are estimated in response to a pulse train with interpulse intervals set to their corresponding average presynaptic ISIs. Dots and error bars denote the median and interquartile range for excitatory-RS (blue) and excitatory-FS (red) connections. These responses include the effect of membrane potential integration. E, Spike transmission probability patterns for individual synapses of excitatory-RS (blue) and excitatory-FS (red) connections normalized by long interval probabilities as a function of the presynaptic ISI. F, AUC of postsynaptic spiking prediction using the static GLM without STP (green) and the TM-GLM with STP (blue). G, H, Spike-transmission probabilities (left) and corresponding cross-correlograms (right) of four putative excitatory inputs to putative FS (G) and RS (H) inhibitory neurons show cell type-specific similarities.

Figure 8.

Short-term changes in spike probability for neurons that are not monosynaptically connected. A, In a simulated circuit, we generated a spurious connection between two neurons (Post₁ and Post₂) receiving common excitatory drive from a single presynaptic neuron (Pre) with different delays (orange cross-correlogram). B, Scatter plots show normalized spike transmission probabilities from different sets of simulations where the true connections to the postsynaptic neurons have different types of STP (both depressing, both facilitating, and one depressing; one facilitating). Lines with same colors as scatter plots show the estimated spike probability from the TM-GLM. Here, the data and model fits are averaged across 150 rounds of simulations (50 for each combination) and are normalized to have a spiking probability of 1 for the longest ISIs. C, We then fit spike transmission probability for 38 pairs of neurons from the MEA recording where there was no clear monosynaptic connection (putative non-connections). Observed (left) spike transmission probabilities show relatively little variation as a function of one neuron's ISIs, but the TM-GLM (right) does describe what variation there is. Insets show example cross-correlograms from two of these putative non-connections.