The passive properties of dendrites modulate the propagation of slowly-varying firing rate in feedforward networks (Q6072586)

The aim in this article is to investigate the way dendritic passive properties affect the propagation of the slowly -- varying firing rate in feedforward networks (FFNs). For the construction of an appropriate feedforward neural network, one uses the two-compartment model introduced in: [\textit{G. Yi} et al., Front. Cell. Neuroscience 11, 265 (2017; \url{doi:10.3389/fncel.2017.00265})]. The model is inspired from the Pinsky-Rinzel model, in [\textit{P. F. Pinsky} and \textit{J. Rinzel}, J. Comput. Neurosci. 1, No. 1--2, 39--60 (1994; \url{doi:10.1007/BF00962717})]. The two-compartment model consists of a dendritic chamber and a soma chamber separated by an internal coupling conductance $g_c$. Each layer consists of 100 neurons and the feedforward connectivity between adjacent layers is random with a synaptic connection probability $p_{\mathrm{inter}}$. Only long-range excitatory synapses take part to the interlayer communication. The mathematical model reads: \[ C_m \frac{d{V_S}}{dt}=-\frac {{g_c}{(}{V_S}-{V_D}{)}}{p}-I_{Na}-I_K-I_{SL} \] \[ C_m\frac{d{V_D}}{dt}=-\frac {{g_c}{(}{V_S}-{V_D}{)}}{1- p}-I_{DL}-I_{\mathrm{syn}}+I_{\mathrm{sim}}+I_{\mathrm{noise}} \] where $V_S$ is the transmembrane potential of the somatic chamber, $V_D$ is the transmembrane potential of dendritic chamber, $p$ is a dimensionless morphological parameter describing the portion of membrane area taken up by the soma, $I_{\mathrm{sim}}$ is the external input current to layer 1, $I_{\mathrm{syn}}$ is the synaptic current received by each neuron and $I_{\mathrm{noise}}$ is a noise. All other ionic currents are defined by specific expressions. Since neurons receive inputs from neurons in the previous layer, the total synaptic current to neuron $i$ is described by: \[ I_{i,\mathrm{syn}}(t)= \sum_{j}\omega_{ij}\sum_{f}\alpha(t-{t^f}_j) \] We denoted by $\omega_{ij}$ the weight on the synapse connecting neuron j to neuron i and by $\alpha(t)$ the postsynaptic current modelled by an exponential function. To stimulate the slow time-varying signals one uses a modified Ornstein-Uhlenbeck process for $I_{\mathrm{sim}}$. The detailed description of the model as well as the simulation procedure are shown in the second section of the article. The third section is devoted to the presentation of numerical results followed by a large analysis of them as well as a discussion on more recent achievements in domain.