8.4 Modeling cell assemblies  (Page 2/9)

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.

Cell models

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 $N{a}^{+}$ channels. Then $N{a}^{+}$ floods in (due to diffusion) causing a depolarization of the cell. When the voltage reaches the near peak depolarization $K^{+}$ gating channels open allowing $K^{+}$ 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 $C{a}^{2+}$ . $C{a}^{2+}$ levels are important because they open $C{a}^{2+}$ dependent $K^{+}$ channels. More $K^{+}$ channels lead to greater repolarization, increasing refractory times between firing and leading to lower activity. We will look at two different sources of $C{a}^{2+}$ . One, through voltage gated channels. The second from NMDA receptor channels, which will be discussed in further detail ahead.

Cell types

There are two basic types of cells: excitatory and inhibitory. When excitatory cells fire they increase the potential in the neurons they synapse onto. Whereas, inhibitory decrease the potential. For our purposes we will use different parameters to the two cells different characteristics.

Mathematical model

The excitatory cell model used has 4 compartments per cell. The first compartment represents the soma. The other three are a chain of dendrites, which represent a collapsed dendritic tree at different distances from the soma. In the case of an inhibitory cell there will only be 2 total compartments. Cells will synapse onto compartment 4 if it is a E (excitatory) to E connection. Compartment 1 if it is an I (inhibitory) to E connection. Compartment 2 if it is an E to I connection.

Below is the main differential equation that governs the cell voltage in a compartment. The first term in the fraction represents the leak current. The second term is the summation of current that comes in from neighboring compartments. The third term represents Ion channel currents; they are only present at the cell soma. The fourth term is current entering from synaptic input.