# Cable Theory - Inside.Trinity.edu Cable Theory CSCI 2323-1 Last time What did we do last time? Does anyone remember why our model last time did not work (other than getting infinity due to Rene's

inabililty to check his units)? From old --> new Our last model assumed that the axon is either a small area (nm2) or it has a large are, but of uniform potential difference (V). This is not how axons work. The action potential propagates down the

length of the axon via saltatory conduction. Linear Cable Equation The neuron as a circuit Nelson, Philip. (2004). Biological Physics. New York: Freeman & Company.

What is cable theory? Mathematical Model used to calculate the flow of electric current along passive neuronal fibers. Regards axons as cables with

capacitance and resistance. Whats different is that now the individual segments of membrane can be viewed as parallel circuits, not the flow of ions. Useful variables

rm=Rm/2aa Membrane Resistance cm=Cm2aa Capacitance due to electrostatics Rl=Rl/ aa2 Longitudinal Resistance All these variables have been already calculated, so they are constants in our program. Getting to the equation

Ohms Law: Current across the membrane:

V=IlRlx il=-imx Displacement current: Ic=cm(V/t) im=ir+ic Constants

Space Constant How far a current will spread along the inside of the axon, thereby influencing the voltage along that distance. Time Constant

How fast the membrane potential Vm of the axon is changing in response to changes in the current injected into the cytosol. Potential Vo is the potential that we get at the injection site. Vlambda is the potential

that is due to lambda (the space constant). Vlambda is always 36.8% of V o. PDE What we are going to need to work with is the PDE solver. Let's go to MATLAB help.

Linear Cable Equation (Again!) Modeling the Action Potential http://openwetware.org/wiki/ BIO254:AP Nonlinear Cable Equation

The linear cable equation fails to relate how the action potential gains access to the free energy generated by sodium pumps. A nonlinear version exists to solve this problem, but we won't get into it because it frightens Rene.