J Comput Neurosci (2006) 20: 77–84 DOI 10.1007/s10870-006-4770-0 Spike propagation in dendrites with stochastic ion channels Kamran Diba · Christof Koch · Idan Segev Received: 3 June 2005 / Revised: 29 July 2005 / Accepted: 1 September 2005 / Published online: 20 February 2006 C  Springer Science + Business Media, Inc. 2006 Abstract We investigate the effects of the stochastic na- ture of ion channels on the faithfulness, precision and repro- ducibility of electrical signal transmission in weakly active, dendritic membrane under in vitro conditions. The properties of forward and backpropagating action potentials (BPAPs) in the dendritic tree of pyramidal cells are the subject of intense empirical work and theoretical speculation (Larkum et al., 1999; Zhu, 2000; Larkum et al., 2001; Larkum and Zhu, 2002; Schaefer et al., 2003; Williams, 2004; Waters et al., 2005). We numerically simulate the effects of stochastic ion channels on the forward and backward propagation of den- dritic spikes in Monte-Carlo simulations on a reconstructed layer 5 pyramidal neuron. We report that in most instances there is little variation in timing or amplitude for a single BPAP, while variable backpropagation can occur for trains of action potentials. Additionally, we find that the genera- tion and forward propagation of dendritic Ca 2+ spikes are susceptible to channel variability. This indicates limitations on computations that depend on the precise timing of Ca 2+ spikes. Action Editor : Alain Destexhe K. Diba · C. Koch Division of Biology, 1200 E. California Blvd, Pasadena, CA 91125 K. Diba () Center for Molecular and Behavioral Neuroscience, Rutgers University, 197 University Ave, Newark, NJ 07102 e-mail: diba@andromeda.rutgers.edu I. Segev Life Sciences Institute and Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem, 91904 Israel Keywords temporal precision . spike reliability . coincidence detection Abbreviations: BAC: Backpropagation activated Ca 2+ spike; AP: Action potential; BPAP: Backpropagating action potential; ISI: Interstimulus interval; rp: Reference point 1. Introduction The effects of stochastic ion channel transitions in the cen- tral nervous system are not well understood (White et al., 2000; van Rossum et al., 2003; Diba et al., 2004; Jacobson et al., 2005). Whereas the effects of ion channels on mem- brane properties are often studied in the macroscopic limit of large membranes, the thermal environment of the brain leads to temperature-dependent, random (stochastic) changes in the configuration of individual channels (Hille, 2001). As a first order approximation, the variance of voltage noise from stochastic channels is proportional to N, the number of channels, and Z 2 , the square effective impedance (DeFe- lice, 1981; Manwani and Koch, 1999). From the viewpoint of voltage-gating, this means that when Z is small, channel stochasticity effects are negligible. At the cell body of pyra- midal neurons (in culture and in vitro), channel stochasticity leads to sub-millivolt fluctuations in the subthreshold mem- brane potential (Diba et al., 2004; Jacobson et al., 2005). What are the effects of stochasticity on suprathreshold be- havior? In the axon initial segment (or spike initiation zone at the first node of Ranvier), the density of Na + channels is quite large, estimated at around 1500/µm 2 (Mainen and Se- jnowski, 1998). Schneidman et al. (1998) showed numer- ically that for large impedance axonal patches, the spike firing time can jitter significantly in response to sustained, Springer