Boundary solution based on rescaling method: recoup the first and second-order statistics of neuron network dynamics

Cecilia Romaro, Antonio Carlos Roque, Jose Roberto Castilho Piqueira

There is a strong nexus between the network size and the computational resources available, which may impede a neuroscience study. In the meantime, rescaling the network while maintaining its behavior is not a trivial mission. Additionally, modeling patterns of connections under topographic organization presents an extra challenge: to solve the network boundaries or mingled with an unwished behavior. This behavior, for example, could be an inset oscillation due to the torus solution; or a blend with/of unbalanced neurons due to a lack (or overdose) of connections. We detail the network rescaling method able to sustain behavior statistical utilized in Romaro et al. (2018) and present a boundary solution method based on the previous statistics recoup idea.

Conductance-based models and the fragmentation problem: A case study based on hippocampal CA1 pyramidal cell models and epilepsy

Iara Frondana, Rodrigo R.S. Carvalho, Florencia Leonardi

Epilepsy has been a central topic in computational neuroscience, and in silico models have shown to be excellent tools to integrate and evaluate findings from animal and clinical settings. Among the different languages and tools for computational modeling development, NEURON stands out as one of the most used and mature neurosimulators. However, despite the vast quantity of models developed with NEURON, a fragmentation problem is evident in the great majority of models related to the same type of cell or cell properties. This fragmentation causes a lack of interoperability between the models because of differences in parameters.

A Numerical Study of the Time of Extinction in a Class of Systems of Spiking Neurons

Cecilia Romaro, Fernando Araujo Najman, Morgan André

In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of neurons linked together in a network, each of them having a membrane potential taking value in the integers, and each of them spiking over time at a rate which depends on the membrane potential through some rate function Ď•. Beside being affected by a spike each neuron can also be affected by leaking. At each of these leak times, which occurs for a given neuron at a fixed rate γ, the membrane potential of the neuron concerned is spontaneously reset to 0.

A system of interacting neurons with short term synaptic facilitation

Antonio Galves, Eva Löcherbach, Christophe Pouzat, Errico Presutti

In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium concentration within the cell at a given time. Neurons spike at a rate depending on their membrane potential. When spiking, the residual calcium concentration of the spiking neuron increases by one unit. Moreover, an additional amount of potential is given to all other neurons in the system. This amount depends linearly on the current residual calcium concentration within the cell of the spiking neuron. In between successive spikes, the potentials and the residual calcium concentrations of each neuron decrease at a constant rate.

A Result of Metastability for an Infinite System of Spiking Neurons

Morgan André

In 2018, Ferrari et al. wrote a paper called “Phase Transition for Infinite Systems of Spiking Neurons” in which they introduced a continuous time stochastic model of interacting neurons. This model consists in a countable number of neurons, each of them having an integer-valued membrane potential, which value determine the rate at which the neuron spikes. This model has also a parameter 𝛾, corresponding to the rate of the leak times of the neurons, that is, the times at which the membrane potential of a given neuron is spontaneously reset to its resting value (which is 0 by convention). As its title says, it was proven in this previous article that this model presents a phase transition phenomenon with respect to 𝛾. Here we prove that this model also exhibits a metastable behavior. By this we mean that if   đť›ľ  is small enough, then the re-normalized time of extinction of a finite version of this system converges toward an exponential random variable of mean 1 as the number of neurons goes to infinity.

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