# BCCN AG-Seminar

Tuesday, 14.07.2009 17 c.t.## On a novel rate theory for transport in narrow ion channels

*by Dr. Enrique Abad*

Contact person: Armin Biess

### Location

Seminarraum Haus 2, 4. Stock (Bunsenstr.)### Abstract

We present a novel rate theory based on the notions of splitting probability and mean first passage time to describe conduction of single ions in narrow (quasi 1D) channels. In contrast to traditional approaches such as classical transition state theory or Kramers theory, we describe ion transport via a Markovian hopping model with transition rates that depend on the full geometry of the potential of mean force (PMF) associated to the channel structure and a nonequilibrium constraint, e.g. an applied voltage. The above theoretical framework can be used to compute current-voltage curves from numerical PMFs obtained from atomistic molecular dynamics simulations, thereby bridging the gap between the atomistic level of description (channel protein structure) and the mesoscopic level (conductance properties obtained from experiments). In this context, the underlying question of how the structure of channel proteins has evolved to optimize transport is of significant interest. With this motivation in mind, we explore the role of geometric effects in a model where the equilibrium PMF is given by a symmetric sawtooth potential (this is a particular case of a piecewise linear PMF, in which explicit analytic solutions for both hopping rates and ion flux can be found). Despite its relative simplicity, the sawtooth model gives rise to a surprisingly rich phenomenology, e.g. the ion flux is maximized for an optimum value of the linear size associated to each ion binding site when the applied voltage exceeds a threshold value which depends on the characteristic binding energy. Finally, we show how the theory can be used to reproduce conductance vs. concentration curves for the gramicidin A channel. Possible extensions of the model to deal with the case of a fluctuating PMF and the case of multi-ion conductance are also discussed.