A frequency-resolved mutual information rate and its application to neural systems

Abstract

Bernardi D, Lindner B. A frequency-resolved mutual information rate and its application to neural systems. J Neurophysiol 113: 1342-1357, 2015. First published December 4, 2014 doi:10.1152/jn.00354.2014.-The encoding and processing of time-dependent signals into sequences of action potentials of sensory neurons is still a challenging theoretical problem. Although, with some effort, it is possible to quantify the flow of information in the model-free framework of Shannon's information theory, this yields just a single number, the mutual information rate. This rate does not indicate which aspects of the stimulus are encoded. Several studies have identified mechanisms at the cellular and network level leading to low-or high-pass filtering of information, i.e., the selective coding of slow or fast stimulus components. However, these findings rely on an approximation, specifically, on the qualitative behavior of the coherence function, an approximate frequency-resolved measure of information flow, whose quality is generally unknown. Here, we develop an assumption-free method to measure a frequency-resolved information rate about a time-dependent Gaussian stimulus. We demonstrate its application for three paradigmatic descriptions of neural firing: an inhomogeneous Poisson process that carries a signal in its instantaneous firing rate; an integrator neuron (stochastic integrate-and-fire model) driven by a time-dependent stimulus; and the synchronous spikes fired by two commonly driven integrator neurons. In agreement with previous coherence-based estimates, we find that Poisson and integrate-and-fire neurons are broadband and low-pass filters of information, respectively. The band-pass information filtering observed in the coherence of synchronous spikes is confirmed by our frequency-resolved information measure in some but not all parameter configurations. Our results also explicitly show how the response-response coherence can fail as an upper bound on the information rate. information transmission; information filter; neural variability; stochastic spike trains SENSORY SYSTEMS SEND INFORMATION about external stimuli to the brain in the form of spike trains (Rieke et al. 1996;Borst and Theunissen 1999). Identifying what features of signals are selected by a neuron or neural population is important for understanding the functional physiology of any neural circuit. A basic classification scheme arises in the frequency domain: how much information does a neuron encode about fast or slow components of a stimulus? Put differently, does a neuron select information about high-or low-frequency bands of a timedependent signal? Such a form of information filtering has been studied in the vestibular (Sadeghi et al. 2007; Massot et al.

Aplicações da teoria da informação à neurociência

“…O primeiro modelo considerado toma o sinal de entrada s(t) recebido pelo neurônio como a taxa de disparos de-Cordeiro e cols. e20180197-3 pendente do tempo r(t) de um processo de Poisson [19]. Para tal modelo, assumindo que r(t) não varia significativamente dentro de um intervalo de tempo curto ∆t, a probabilidade de que k disparos sejam gerados nesse intervalo de tempo é e −r(t)∆t [r(t)∆t]…”

“…Os parâmetros utilizados na implementação são os mesmos reportados em [19], sendo r 0 = 100 Hz, = 0, 2 e ∆t = 1 ms.…”

“…O modelo integra-e-dispara com vazamento (LIF, do inglês "leaky integrate-and-fire") é um modelo simples, mas amplamente utilizado em neurociência computacional [2]. A versão do modelo implementada neste trabalho é a mesma descrita em [19], a qual possui entrada e ruído gaussianos, sendo por isso chamada de modelo LIF estocástico. A dinâmica desse modelo é descrita pela equação (3).…”

Nicotinic modulation of hierarchal inhibitory control over prefrontal cortex resting state dynamics: modeling of genetic modification and schizophreniarelated pathology

“…Ultra-slow oscillations seen during quiet wakefulness [30,31,32,33] have also been shown to play a role in memory consolidation by controlling the flow of memory-related information from thalamus and hippocampus to the cortex [34,35]. Notably, the since transmission of such information appears to be proportional to PYR firing rates [36], the altered H-state activity in a5SNP PFC may imply a memory-consolidation pathology in a5-mutation schizophrenic population.…”

Closed-Loop Estimation of Retinal Network Sensitivity by Local Empirical Linearization

“…to estimate the spectrum of the information rate we compute its behavior within the linear theory (Van Hateren, 1992): $\text{MI}(\nu )=\frac{1}{2}\ln \left[1+C_{boldnormalS}(\nu )I(\nu )/\delta t^2\right]$ where $C_{boldnormalS}(\nu )$ is the power spectrum of the actual stimulus statistics (noisy damped oscillator), and $I(\nu )=(\delta t/L){\stackrel{true^}{boldnormalS}}^{\text{T}}(\nu )·I·\stackrel{true^}{boldnormalS}(\nu )$. Note that this decomposition in frequency of the transmitted information is valid because the system is linear and the stimulus is Gaussian distributed (Bernardi and Lindner, 2015). …”