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.

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.

5.) Give parameters that are used and explain parameters that are dependent on simulations.

6.) Run simulations by going through the matlab prompt and display results.

Below is a quick description of the basic dynamics of neurons and how messages are relayed in neuronal networks. The mathematical model that is used in the simulations is given in detail.

The basic function of a neuron is the ability to relay information by means of an action potential. This is a quick depolarization burst which originates at the cell soma (main body) and travels down the axon reaching boutons. At a bouton the depolarization will cause neurotransmitters to be released into the synaptic cleft, a small space between the bouton and a spine of the target cell. The neurotransmitter then opens ion channels in the postsynaptic receptor area that can serve to excite or depress the post-synaptic neuron, depending on whether the sending neuron is excitatory or inhibitory. A cell achieves an action potential when it receive enough excitation from other cells. When the cell voltage reaches a certain threshold its firing mechanisms kick in and generate an action potential. The firing mechanism consists of voltage gated ion channels in the cell's soma membrane. These channels permability are dependent on voltage levels and are specialized to only allow specific ions to pass through. The standard action potential starts with stimuli which raises voltage sufficiently to open Na+Na+ channels. Then Na+Na+ floods in (due to diffusion) causing a depolarization of the cell. When the voltage reaches the near peak depolarization K+K+ gating channels open allowing K+K+ to rush out, lowering the potential back to rest. There are additional ions which have a role in cell dynamics. One important ion that helps regulate firing rates is Ca2+Ca2+. Ca2+Ca2+ levels are important because they open Ca2+Ca2+ dependent K+K+ channels. More K+K+ channels lead to greater repolarization, increasing refractory times between firing and leading to lower activity. We will look at two different sources of Ca2+Ca2+. One, through voltage gated channels. The second from NMDA receptor channels, which will be discussed in further detail ahead.