8.4 Modeling cell assemblies

Theory

One hypothesis on how ideas are structured in the brain is that groups of cells form a unit called a cell assembly. The cells within the assembly are connected with strong excitatory synapses. Thus, when enough activity occurs in the neurons within the assembly, then the entire assembly will have the ability to activate. An active assembly would meet the definition that the cells within the assembly are firing at a high rate in the same time frame. Successions of assembly activation could be the basis of how to form thoughts and give a mental representation for different concepts. This idea was introduced by Donald Hebb in The Organization of Behavior . The assembly will eventually shut down if the source of stimulation ceases or a competing assembly can provide inhibition. This theory can be extended to explain how learning occurs and possible phenomena such as perspective-rivalry. For instance, in optical illusions, such as the nectar cube shown below, there are two different possible interpretations of the perspective. It is possible that two different assemblies represent the different perspectives. In order to switch perspectives one must shut down the current perspective assembly and activate the alternate perspective. There could also be a hierarchy of assemblies. Sub-assemblies could give rise to larger assemblies. Due to synaptic plasticity different sub-assemblies that are activated in similar orders through repetition allows new larger Assemblies to form. If sufficient clues that are represented by smaller sub-assemblies are activated, the brain will be able to activate the larger assembly.

Module goal

To get some insight on whether this is plausible we want to construct biologically accurate computational models and test assembly activation and inhibition. This module will follow the paper Modeling Hebbian cell assemblies comprised of cortical neurons , by A Lanser and E Fransen. It will show how to reproduce the results contained in the paper and the mathematics involved.

Here is a brief summary of what is ahead:

1.) Go over the neuron models and the different ion channels.

2.) Show how synaptic input is modeled.

3.) Show how differential equations are solved with time stepping.

4.) Show how patterns which represent different assemblies are used to "train" a network and produce weights.