We would like to solve for the information capacity and computational ability of a single neuron. The primary cellular apparatus for this appears to be the dendritic tree. In order to do this, we need to create a computer model which is simple enough to perform viable simulations, but complex enough to capture some element of the biology and shed light on how different dendritic morphologies change the computational natures of cells. We begin with the cable equation as a general boundary condition solution for potentials in the dendritic tree. Since this is not an analytically solvable task for any feasible neuronal model, we break up the dendritic tree into many compartments (a finite element model), and solve the resulting set of coupled differential equations for finite compartment widths and finite temporal step size. Spike timing dependent plasticity is used as a motif for synaptic learning, and dynamic membrane channels in the cellular membrane and synaptic bouton are used for synaptic input and active potential conductance. The model demonstrates that given fixed parameters in a set of compartments, different tree configurations (abstracted from cerebellar purkinje cell, cortical astrocyte, retinal ganglion, and simple linear dendritic morphologies) will have different efficacies eliciting spikes in the soma.
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