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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.


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 ,


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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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