Estimation of Synaptic Activity during Neuronal Oscillations

In the study of brain connectivity, an accessible and convenient way to unveil local functional structures is to infer the time trace of synaptic conductances received by a neuron by using exclusively information about its membrane potential (or voltage). Mathematically speaking, it constitutes a challenging inverse problem: it consists in inferring time-dependent parameters (synaptic conductances) departing from the solutions of a dynamical system that models the neuron’s membrane voltage. Several solutions have been proposed to perform these estimations when the neuron fluctuates mildly within the subthreshold regime, but very few methods exist for the spiking regime as large amplitude oscillations (revealing the activation of complex nonlinear dynamics) hinder the adaptability of subthreshold-based computational strategies (mostly linear). In a previous work, we presented a mathematical proof-of-concept that exploits the analytical knowledge of the period function of the model. Inspired by the relevance of the period function, in this paper we generalize it by providing a computational strategy that can potentially adapt to a variety of models as well as to experimental data. We base our proposal on the frequency versus synaptic conductance curve (f−gsyn), derived from an analytical study of a base model, to infer the actual synaptic conductance from the interspike intervals of the recorded voltage trace. Our results show that, when the conductances do not change abruptly on a time-scale smaller than the mean interspike interval, the time course of the synaptic conductances is well estimated. When no base model can be cast to the data, our strategy can be applied provided that a suitable f−gsyn table can be experimentally constructed. Altogether, this work opens new avenues to unveil local brain connectivity in spiking (nonlinear) regimes.

The Neurobiological Bases for the Computational Theory of Mind

The language of thought hypothesis is one of Fodor’s seminal contributions to cognitive science. Prominent among the objections to it has been the argument that there is no neurobiological evidence for materially realized symbols in the brain. If memory is materially realized by enduring alterations in synaptic conductances, then this is true, because the synaptic-conductance hypothesis is simply the ancient associative learning hypothesis couched in neurobiological language. Associations are not symbols and cannot readily be made to function as such, thus neurobiologists are unable to say how simple information—for example, the durations of intervals in simple Pavlovian conditioning paradigms—are stored in altered synaptic conductances. Recent results from several laboratories converge, strongly suggesting that memories do not reside in altered synaptic conductances but rather at the molecular level inside neurons. The chapter reviews the experimental evidence for this revolutionary conclusion, as well as the plausibility arguments for it.

Estimating Excitatory and Inhibitory Synaptic Conductances from Spike Trains using a Recursive Bayesian Approach

Inference of excitatory and inhibitory synaptic conductances (SCs) from the spike trains is poorly addressed in the literature due to the complexity of the problem. As recent technological advancements make recording spikes from multiple (neighbor) neurons of a behaving animal (in some rare cases from humans) possible, this paper tackles the problem of estimating SCs solely from the recorded spike trains. Given an ensemble of spikes corresponding to population of neighbor neurons, we aim to infer the average excitatory and inhibitory SCs underlying the shared neural activity. In this paper, we extended our previously established Kalman filtering (KF)–based algorithm to incorporate the voltage-to-spike nonlinearity (mapping from membrane potential to spike rate). Having estimated the instantaneous spike rate using optimal linear filtering (Gaussian kernel), our proposed algorithm uses KF followed by expectation maximization (EM) algorithm in a recursive fashion to infer the average SCs. As the dynamics of SCs and membrane potential is included in our model, the proposed algorithm, unlike other related works, considers different sources of stochasticity, i.e., the variabilities of SCs, membrane potential, and spikes. Moreover, it is worth mentioning that our algorithm is blind to the external stimulus, and it performs only based on observed spikes. We validate the accuracy and practicality of our technique through simulation studies where leaky integrate and fire (LIF) model is used to generate spikes. We show that the estimated SCs can precisely track the original ones. Moreover, we show that the performance of our algorithm can be further improved given enough number of trials (spikes). As a rule of thumb, 50 trials of neurons with the average firing rate of 5 Hz can guarantee the accuracy of our proposed algorithm.