Estimation of the synaptic conductance in a McKean-model neuron

Estimating the synaptic conductances impinging on a single neuron directly from its membrane potential is one of the open problems to be solved in order to understand the flow of information in the brain. Despite the existence of some computational strategies that give circumstantial solutions ([1-3] for instance), they all present the inconvenience that the estimation can only be done in subthreshold activity regimes. The main constraint to provide strategies for the oscillatory regimes is related to the nonlinearity of the input-output curve and the difficulty to compute it. In experimental studies it is hard to obtain these strategies and, moreover, there are no theoretical indications of how to deal with this inverse non-linear problem. In this work, we aim at giving a first proof of concept to address the estimation of synaptic conductances when the neuron is spiking. For this purpose, we use a simplified model of neuronal activity, namely a piecewise linear version of the Fitzhugh-Nagumo model, the McKean model ([4], among others), which allows an exact knowledge of the nonlinear f-I curve by means of standard techniques of non-smooth dynamical systems. As a first step, we are able to infer a steady synaptic conductance from the cell's oscillatory activity. As shown in Figure ¿Figure1,1, the model shows the relative errors of the conductances of order C, where C is the membrane capacitance (C<<1), notably improving the errors obtained using filtering techniques on the membrane potential plus linear estimations, see numerical tests performed in [5].Peer ReviewedPostprint (published version

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

Estimation of synaptic conductances in presence of nonlinear effects caused by subthreshold ionic currents

Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures for the models tested here.Peer ReviewedPostprint (published version

Sequential estimation of intrinsic activity and synaptic input in single neurons by particle filtering with optimal importance density

This paper deals with the problem of inferring the signals and parameters that cause neural activity to occur. The ultimate challenge being to unveil brain’s connectivity, here we focus on a microscopic vision of the problem, where single neurons (potentially connected to a network of peers) are at the core of our study. The sole observation available are noisy, sampled voltage traces obtained from intracellular recordings. We design algorithms and inference methods using the tools provided by stochastic filtering that allow a probabilistic interpretation and treatment of the problem. Using particle filtering, we are able to reconstruct traces of voltages and estimate the time course of auxiliary variables. By extending the algorithm, through PMCMC methodology, we are able to estimate hidden physiological parameters as well, like intrinsic conductances or reversal potentials. Last, but not least, the method is applied to estimate synaptic conductances arriving at a target cell, thus reconstructing the synaptic excitatory/inhibitory input traces. Notably, the performance of these estimations achieve the theoretical lower bounds even in spiking regimes.Postprint (published version

Inferring Trial-to-Trial Excitatory and Inhibitory Synaptic Inputs from Membrane Potential using Gaussian Mixture Kalman Filtering

Time-varying excitatory and inhibitory synaptic inputs govern activity of neurons and process information in the brain. The importance of trial-to-trial fluctuations of synaptic inputs has recently been investigated in neuroscience. Such fluctuations are ignored in the most conventional techniques because they are removed when trials are averaged during linear regression techniques. Here, we propose a novel recursive algorithm based on Gaussian mixture Kalman filtering for estimating time-varying excitatory and inhibitory synaptic inputs from single trials of noisy membrane potential in current clamp recordings. The Kalman filtering is followed by an expectation maximization algorithm to infer the statistical parameters (time-varying mean and variance) of the synaptic inputs in a non-parametric manner. As our proposed algorithm is repeated recursively, the inferred parameters of the mixtures are used to initiate the next iteration. Unlike other recent algorithms, our algorithm does not assume an a priori distribution from which the synaptic inputs are generated. Instead, the algorithm recursively estimates such a distribution by fitting a Gaussian mixture model. The performance of the proposed algorithms is compared to a previously proposed PF-based algorithm (Paninski et al., 2012) with several illustrative examples, assuming that the distribution of synaptic input is unknown. If noise is small, the performance of our algorithms is similar to that of the previous one. However, if noise is large, they can significantly outperform the previous proposal. These promising results suggest that our algorithm is a robust and efficient technique for estimating time varying excitatory and inhibitory synaptic conductances from single trials of membrane potential recordings

Sequential estimation of neural models by Bayesian filtering

Un dels reptes més difícils de la neurociència és el d'entendre la connectivitat del cervell. Aquest problema es pot tractar des de diverses perspectives, aquí ens centrem en els fenòmens locals que ocorren en una sola neurona. L'objectiu final és, doncs, entendre la dinàmica de les neurones i com la interconnexió amb altres neurones afecta al seu estat. Les observacions de traces del potencial de membrana constitueixen la principal font d'informació per a derivar models matemàtics d'una neurona, amb cert sentit biofísic. En particular, la dinàmica de les variables auxiliars i els paràmetres del model són estimats a partir d'aquestes traces de voltatge. El procés és en general costós i típicament implica una gran varietat de blocatges químics de canals iònics, així com una certa incertesa en els valors dels paràmetres a causa del soroll de mesura. D'altra banda, les traces de potencial de membrana també són útils per obtenir informació valuosa sobre l'entrada sinàptica, un problema invers sense solució satisfactòria a hores d'ara. En aquesta Tesi, estem interessats en mètodes d'estimació seqüencial, que permetin evitar la necessitat de repeticions que podrien ser contaminades per la variabilitat neuronal. En particular, ens concentrem en mètodes per extreure l'activitat intrínseca dels canals iònics, és a dir, les probabilitats d'obertura i tancament de canals iònics, i la contribució de les conductàncies sinàptiques. Hem dissenyat un mètode basat en la teoria Bayesiana de filtrat per inferir seqüencialment aquestes quantitats a partir d'una única traça de voltatge, potencialment sorollosa. El mètode d'estimació proposat està basat en la suposició d'un model de neurona conegut. Això és cert fins a cert punt, però la majoria dels paràmetres en el model han de ser estimats per endavant (això és valid per a qualsevol model). Per tant, el mètode s'ha millorat pel cas de models amb paràmetres desconeguts, incloent-hi un procediment per estimar conjuntament els paràmetres i les variables dinàmiques. Hem validat els mètodes d'inferència proposats mitjançant simulacions realistes. Les prestacions en termes d'error d'estimació s'han comparat amb el límit teòric, que s'ha derivat també en el marc d'aquesta Tesi

Identification of Dynamics, Parameters and Synaptic Inputs of a Single Neuron using Bayesian Approach

Revealing dynamical mechanisms of the brain in order to understand how it works and processes information has recently stimulated enormous interest in computational neuroscience. Understanding the behavior of a single neuron, the most important building block of the brain, is of core interest in the brain-related sciences. Application of the advanced statistical signal processing methods, e.g., Bayesian methods, in assessing the hidden dynamics and estimating the unknown parameters of a single neuron has been considered recently as of special interest in neuroscience. This thesis attempts to develop robust and efficient computational techniques based on Bayesian signal processing methods to elucidate the hidden dynamics and estimate the unknown parameters of a single neuron. In the first part of the thesis, Kalman filtering (KF)-based algorithms are derived for the Hodgkin-Huxley (HH) neuronal model, the most detailed biophysical neuronal model, to identify the hidden dynamics and estimate the intrinsic parameters of a single neuron from a single trace of the recorded membrane potential. The unscented KF (UKF) has already been applied to track the dynamics of the HH neuronal model in the literature. We extend the existing KF technique for the HH neuronal model to another version, namely, extended Kalman filtering (EKF). Two estimation strategies of the KF, dual and joint estimation strategies, are employed in conjunction with the EKF and UKF for simultaneously tracking the hidden dynamics and estimating the unknown parameters of a single neuron, leading to four KF algorithms, namely, joint UKF (JUKF), dual UKF (DUKF), joint EKF (JEKF) and dual EKF (DEKF). In the second part of this thesis, the problem of inferring excitatory and inhibitory synaptic inputs that govern activity of neurons and process information in the brain is investigated. The importance of trial-to-trial variations of synaptic inputs has recently been investigated in neuroscience. Such variations are ignored in the most conventional techniques because they are removed when trials are averaged during linear regression techniques. Here, we propose a novel recursive algorithm based on Gaussian mixture Kalman filtering for estimating time-varying excitatory and inhibitory synaptic inputs from single trials of noisy membrane potential. Unlike other recent algorithms, our algorithm does not assume an a priori distribution from which the synaptic inputs are generated. Instead, the algorithm recursively estimates such a distribution by fitting a Gaussian mixture model. Moreover, a special case of the GMKF when there is only one mixand, the standard KF, is studied for the same problem. Finally, in the third part of the thesis, inferring the synaptic input of a spiking neuron as well as estimating its dynamics and parameters is considered. The synaptic input underlying a spiking neuron can effectively elucidate the information processing mechanism of a neuron. The concept of blind deconvolution is applied to Hodgkin-Huxley (HH) neuronal model, for the first time in this thesis, to address the problem of reconstructing the hidden dynamics and synaptic input of a single neuron as well as estimating its intrinsic parameters only from a single trace of noisy membrane potential. The blind deconvolution is accomplished via a novel recursive algorithm based on extended Kalman filtering (EKF). EKF is then followed by the expectation-maximization (EM) algorithm which estimates the statistical parameters of the HH neuronal model. Extensive experiments are performed throughout the thesis to demonstrate the accuracy, effectiveness and usefulness of the proposed algorithms in our investigation. The performance of the proposed algorithms is compared with that of the most recent techniques in the literature. The promising results of the proposed algorithms confirm their robustness and efficiency, and suggest that they can be effectively applied to the challenging problems in neuroscience