Intensity Coding in Two-Dimensional Excitable Neural Networks

In the light of recent experimental findings that gap junctions are essential for low level intensity detection in the sensory periphery, the Greenberg-Hastings cellular automaton is employed to model the response of a two-dimensional sensory network to external stimuli. We show that excitable elements (sensory neurons) that have a small dynamical range are shown to give rise to a collective large dynamical range. Therefore the network transfer (gain) function (which is Hill or Stevens law-like) is an emergent property generated from a pool of small dynamical range cells, providing a basis for a "neural psychophysics". The growth of the dynamical range with the system size is approximately logarithmic, suggesting a functional role for electrical coupling. For a fixed number of neurons, the dynamical range displays a maximum as a function of the refractory period, which suggests experimental tests for the model. A biological application to ephaptic interactions in olfactory nerve fascicles is proposed.Comment: 17 pages, 5 figure

An excitable electronic circuit as a sensory neuron model

An electronic circuit device, inspired on the FitzHugh-Nagumo model of neuronal excitability, was constructed and shown to operate with characteristics compatible with those of biological sensory neurons. The nonlinear dynamical model of the electronics quantitatively reproduces the experimental observations on the circuit, including the Hopf bifurcation at the onset of tonic spiking. Moreover, we have implemented an analog noise generator as a source to study the variability of the spike trains. When the circuit is in the excitable regime, coherence resonance is observed. At sufficiently low noise intensity the spike trains have Poisson statistics, as in many biological neurons. The transfer function of the stochastic spike trains has a dynamic range of 6 dB, close to experimental values for real olfactory receptor neurons.Comment: 10 pages, 6 figure

Electrical coupling in the retina ganglion cell layer increases the dynamic range

CAPESCNPqFrom The Twenty Third Annual Computational Neuroscience Meeting: CNS*2014 Québec City, Canada. 26-31 July 201

A Computational Study on the Role of Gap Junctions and Rod Ih Conductance in the Enhancement of the Dynamic Range of the Retina

Recent works suggest that one of the roles of gap junctions in sensory systems is to enhance their dynamic range by avoiding early saturation in the first processing stages. In this work, we use a minimal conductance-based model of the ON rod pathways in the vertebrate retina to study the effects of electrical synaptic coupling via gap junctions among rods and among AII amacrine cells on the dynamic range of the retina. The model is also used to study the effects of the maximum conductance of rod hyperpolarization activated current Ih on the dynamic range of the retina, allowing a study of the interrelations between this intrinsic membrane parameter with those two retina connectivity characteristics. Our results show that for realistic values of Ih conductance the dynamic range is enhanced by rod-rod coupling, and that AII-AII coupling is less relevant to dynamic range amplification in comparison with receptor coupling. Furthermore, a plot of the retina output response versus input intensity for the optimal parameter configuration is well fitted by a power law with exponent . The results are consistent with predictions of more theoretical works and suggest that the earliest expression of gap junctions along the rod pathways, together with appropriate values of rod Ih conductance, has the highest impact on vertebrate retina dynamic range enhancement

Physics of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality

Psychophysics try to relate physical input magnitudes to psychological or neural correlates. Microscopic models to account for macroscopic psychophysical laws, in the sense of statistical physics, are an almost unexplored area. Here we examine a sensory epithelium composed of two connected square lattices of stochastic integrate-and-fire cells. With one square lattice we obtain a Stevens's law $\rho \propto h^m$ with Stevens's exponent $m = 0.254$ and a sigmoidal saturation, where $\rho$ is the neuronal network activity and $h$ is the input intensity (external field). We relate Stevens's power law exponent with the field critical exponent as $m = 1/\delta_h = \beta/\sigma$. We also show that this system pertains to the Directed Percolation (DP) universality class (or perhaps the Compact-DP class). With stacked two layers of square lattices, and a fraction of connectivity between the first and second layer, we obtain at the output layer $\rho_ 2 \propto h^{m_2}$, with $m_2 = 0.08 \approx m^2$, which corresponds to a huge dynamic range. This enhancement of the dynamic range only occurs when the layers are close to their critical point.Comment: 22 pages, 7 figures, accepted by Physical Review Researc

Active dendrites enhance neuronal dynamic range

Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the last decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of active dendritic trees is a highly non-linear function of their afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease of dynamic range.Comment: 20 pages, 6 figure

Dynamic Range of Vertebrate Retina Ganglion Cells: Importance of Active Dendrites and Coupling by Electrical Synapses

The vertebrate retina has a very high dynamic range. This is due to the concerted action of its diverse cell types. Ganglion cells, which are the output cells of the retina, have to preserve this high dynamic range to convey it to higher brain areas. Experimental evidence shows that the firing response of ganglion cells is strongly correlated with their total dendritic area and only weakly correlated with their dendritic branching complexity. On the other hand, theoretical studies with simple neuron models claim that active and large dendritic trees enhance the dynamic range of single neurons. Theoretical models also claim that electrical coupling between ganglion cells via gap junctions enhances their collective dynamic range. In this work we use morphologically reconstructed multi-compartmental ganglion cell models to perform two studies. In the first study we investigate the relationship between single ganglion cell dynamic range and number of dendritic branches/total dendritic area for both active and passive dendrites. Our results support the claim that large and active dendrites enhance the dynamic range of a single ganglion cell and show that total dendritic area has stronger correlation with dynamic range than with number of dendritic branches. In the second study we investigate the dynamic range of a square array of ganglion cells with passive or active dendritic trees coupled with each other via dendrodendritic gap junctions. Our results suggest that electrical coupling between active dendritic trees enhances the dynamic range of the ganglion cell array in comparison with both the uncoupled case and the coupled case with cells with passive dendrites. The results from our detailed computational modeling studies suggest that the key properties of the ganglion cells that endow them with a large dynamic range are large and active dendritic trees and electrical coupling via gap junctions.Fundacao de Amparo a Pesquisa do Estado de Sa Paulo (FAPESP)Fundacao de Amparo a Pesquisa do Estado de SA Paulo FAPESPCNPq (Brazil)CNPq (Brazil

Sincronização, transições de fase, criticalidade e subamostragem em redes de neurônios formais

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-Graduação em FísicaPara estudar neurônios computacionalmente, pode-se escolher entre, pelo menos, duas abordagens diferentes: modelos biológicos do tipo Hodgkin e Huxley ou modelos formais (ex. o de Hindmarsh e Rose (HR), o de Kinouchi e Tragtenberg estendido (KTz), etc). Neurônios formais podem ser representados por equações diferenciais (ex. HR) ou por mapas, que são sistemas dinâmicos com variáveis de estado contínuas e dinâmica temporal discreta (ex. KTz). Poucos mapas foram propostos para descrever neurônios. Tais mapas provêem diversas vantagens computacionais, já que não há necessidade de ajustar nenhuma precisão arbitrária em variáveis de integração, o que leva a uma melhor performance nos cálculos e a resultados mais precisos. Acoplamos mapas KTz em redes regulares e complexas através de um mapa de sinapse química. Em redes regulares, verificamos que o modelo exibe diferentes tipos de sincronização (tais como sincronia em fase e em antifase e através de ondas que se propagam nas diagonais da rede); estudamos o efeito das sinapses na sincronização e nos intervalos entre disparos: sinapses muito lentas, em certas condições iniciais da rede, podem travar os neurônios em um comportamento de disparos rápidos, mesmo eles tendo sido ajustados em regime de bursting. A excitabilidade do neurônio KTz foi estudada. Redes regulares de neurônios KTz excitáveis apresentaram ondas espirais e mudança no intervalo dinâmico ao mudar o parâmetro de acoplamento. Redes regulares e complexas excitáveis com acoplamento homogêneo apresentaram transições de fase de primeira ordem. Propomos a adição de um ruído uniforme no acoplamento, o que torna as transições de fase contínuas e gera distribuições críticas de avalanches temporais e espaciais, apontando para um modelo criticamente auto-organizado, com expoentes ~ 1.6 e ~ 1.4, respectivamente. Estudamos a influência de alguns comportamentos dinâmicos dos neurônios na estabilidade das avalanches. Finalmente, analisamos os efeitos da subamostragem dos dados através de dois métodos, comparando as distribuições críticas de uma amostra completa com as de uma subamostra, ou amostra parcial, da rede. Constatamos que um dos métodos mantém a lei de potência com expoente ~ 1.35, enquanto o outro gera uma distribuição log-normal.To study neurons with computational tools, one may call upon, at least, two different approaches: Hodgkin-Huxley like neurons (i.e. biological models) or formal models (e.g. Hindmarsh-Rose (HR) model, extended Kinouchi-Tragtenberg model (KTz), etc). Formal neurons may be represented by differential equations (e.g. HR), or by maps, which are dynamical systems with continuous state variables and discrete time dynamics (e.g. KTz). A few maps had been proposed to describe neurons. Such maps provide one with a number of computational advantages, since there is no need to set any arbitrary precision on the integration variable, which leads to better performance in the calculations and to more precise results. We coupled KTz maps within regular lattices and complex networks through a chemical synapse map. In regular lattices, the model exhibits different kinds of synchronization (such as phase and antiphase synchronization and linear wave fronts propagating over the network's diagonals); we studied the effect of synapses in the synchronization patterns and in the interspike interval times: slow synapses, under certain network's initial conditions, can lock down neurons into fast spiking behavior, even though they had been set into a bursting regime. The excitability of KTz neurons was studied. Excitable regular lattices and complex networks subjected to homogeneous coupling presented first order phase transitions. We propose the addition of uniform noise in the coupling, transforming the transitions into continuous phase transitions and generating critical avalanches' distributions in time and space, pointing towards a self-organized critical model, with exponents ~ 1.6 and ~ 1.4, respectively. We studied the influence of some dynamical behaviors of the neurons over the stability of the avalanches. Finally, we analyzed the data subsampling effect by two different methods, comparing the critical distributions of a full sample with those of a subsample, or partial sample, of the network. We found that one of the methods keep the power-law shape with exponent ~ 1.35 whereas the other generates a log-normal distribution