Figure 3. Simulation of membrane polarization and spike propagation in cable structures containing stochastic ion channels.

(A) Simulated uniform cable with recording and current injection sites. (B) Example membrane potential traces (left) from simulations using leak Na⁺ and K⁺ channels with the indicated single channel conductances. The membrane potential variance is plotted as a function of the single channel conductance (right). (C) Voltage responses to injection of a current step at one end of the cable. Simulated stochastic (Stoch) and deterministic (Det) responses are plotted along with the analytical solution (Ref). Insets show the voltage as the current responses approach their steady-state values. In each case the traces overlap. As a result the Ref and Det traces are obscured by the Stoch trace. (D) Simulated branched cable structure with recording and current injection sites. (E) Voltage responses to injection of a current step at the base of the tree. Insets show the voltage as the current responses approach their steady-state values. Labels are as in (C). Ref and Det traces are obscured by the Stoch trace. (F) Action potentials generated when Hodgkin-Huxley channels are inserted into the cable in A. The top panel compares results of deterministic simulations using NEURON or PSICS, with stochastic PSICS simulations using a single channel conductance of 0.01 pS. The lower panel shows the output of several stochastic PSICS simulations using a single channel conductance of 20 pS. Membrane potentials in (E) and (F) are labeled as in (C), except that the blue trace is data from a simulation using NEURON.