Inferring and validating mechanistic models of neural microcircuits based on spike-train data

Abstract

The interpretation of neuronal spike-train recordings often relies on abstract statistical models that allow for principled parameter estimation and model-selection but provide only limited insights into underlying microcircuits. On the other hand, mechanistic neuronal models are useful to interpret microcircuit dynamics, but are rarely quantitatively matched to experimental data due to methodological challenges. We present analytical methods to efficiently fit spiking circuit models to single-trial spike trains. Using the maximallikelihood approach, we statistically infer the mean and variance of hidden inputs, neuronal adaptation properties and connectivity for coupled integrate-and-fire neurons. Parameter estimation is found to be very accurate, even for highly sub-sampled networks. We apply our methods to recordings from cortical neurons of awake ferrets to reveal properties of the hidden synaptic inputs, in particular underlying population-level equalization between excitatory and inhibitory inputs. The methods introduced here open the door to a quantitative, mechanistic interpretation of recorded neuronal population activity.

Inferring the collective dynamics of neuronal populations from single-trial spike trains using mechanistic models

“…The membrane voltage can be scaled such that the remaining parameters of interest for inference are those for the input together with the membrane time constant (see Methods section 1). Moreover, a change of τ m can be well compensated for in terms of spiking dynamics by appropriate changes ofμ i and σ i [25]. Therefore, we focus on the following parameters for inference C i ,μ i , σ i for i ∈ {1, .…”

“…p(s k |µ k , ϑ) is the ISI probability density of the leaky I&F neuron exposed to Gaussian white noise input (with mean µ k and standard deviation σ), evaluated at ISI s k . This density can be accurately computed by solving a Fokker-Planck partial differential equation, which can be achieved numerically in efficient ways [25]. p(x k |x k−1 , τ ) is the transition probability density for x(t), from state x k−1 to state x k , which depends on the time constant τ and on the time duration between states x k−1 and x k .…”

“…Setting τ m instead to a wrong value within a biologically plausible range affects the maximal likelihood only very little (see Fig S1), because a change of τ m can be well compensated for in terms of spiking dynamics by suitable changes of the input parameters (cf. [25]). We, therefore, keep τ m fixed for the rest of this study.…”

“…At the core of our methodology we exploit efficient numerical schemes to compute the ISI probability density of an I&F neuron exposed to Gaussian white noise input with high precision. The ability to rapidly compute this density allows to evaluate the likelihood of observed spike trains, which has been previously used for inference purposes using single stochastic I&F neurons [25,38] and networks [25]. The nonstationarity considered here (doubly-stochastic population model) constitutes a relevant and highly nontrivial extension.…”

“…We present a statistically principled approach based on derived likelihood functions to fit this type of model to single-trial spike trains and quantitatively compare different model variants, including simpler phenomenological models. Specifically, we efficiently compute the likelihood of a given spike train by exploiting analytical methods for stochastic I&F neuron models [25] combined with inference techniques for hidden Markov models [26]. This allows us to infer the model parameters by likelihood maximization, classify the latent dynamics via likelihood-based model selection, and estimate hidden time series from the time-varying probability density over the latent state.…”