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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

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
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.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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