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This report summarizes work done as part of the Hippocampus Neuroscience PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed round the study of a common problem. This module explains how to implement the conductance-based model for the dynamics of a network of single compartmental cells presented in the paper "Rate Models for Conductance-Based Cortical Neuronal Networks," by O. Shriki, D. Hansel, and H. Sompolinsky.

Introduction

In order to gain a better understanding of many biological processes, it is often necessary to implement a theoretical model of a neuronal network. In the paper Rate Models for Conductance-Based Cortical Neuronal Networks , Shriki et al. present a conductance-based model for simulating the dynamics of a neuronal network   [link] . The work done in this module is an implementation of their model. In his module Dynamics of the Firing Rate of Single Compartmental Cells , Yangluo Wang shows how to model the dynamics of an isolated cell using the Hodgkin and Huxley model. We will build on the work presented by Wang to model the dynamics of cells within a neuronal network driven by some external current. We then apply this model to a network of cells within a hypercolumn in primary visual cortex.

Network dynamics

The dynamics of cell i within a network of N neurons are given by

C m d V i d t = I i l e a k - I i a c t i v e + I i e x t + I i n e t ,

where the parameters for cell i are defined according to the following table:

Parameter Definitions
C m membrane capacitance
V i membrane potential
I i l e a k leak current
I i a c t i v e active ionic current
I i e x t externally applied current
I i n e t network current

Leak current and active current

The model of a cell within a network is very similar to the model of an isolated cell,

C m d V i d t = I i l e a k - I i a c t i v e + I i a p p ,

where

I i l e a k = g L ( E L - V i ) ,
I i a c t i v e = I i N a + I i K + I i A .

The leak current and active current for a cell within a network is defined exactly as it is for an isolated cell. For details on these two currents, see Yungluo Wang's module Dynamics of the Firing Rate of Single Compartmental Cells . The applied current in the isolated cell model is an abstract current that drives the cell. For the network model, we replace this applied current with the sum of the external and network currents.

Network current

The network current for cell i is induced by other cells within the network and is given by

I i n e t ( t ) = j = 1 N g i j ( t ) ( E j - V i ( t ) ) ,

where g i j is the synaptic conductance of cell i generated by action potentials of cell j , and E j is the reversal potential of the synapse from cell j to cell i . Note that E j depends only on the properties of the presynaptic cell j . If t j is a vector containing the spike times of cell j , the conductance at the synapse from cell j to cell i is given by

d g i j ( t ) d t = - g i j ( t ) τ i j + G i j R j ( t ) , t > 0 ,

where τ i j is the conductance decay constant, G i j is the peak synaptic conductance, and R j ( t ) is the firing rate of cell j given by

Questions & Answers

what is the stm
Brian Reply
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Damian
How we are making nano material?
LITNING Reply
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LITNING Reply
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LITNING
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Sahil
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Rafiq
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Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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Adin Reply
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Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
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Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Damian Reply
research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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absolutely yes
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
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Damian
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Tarell
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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