Computational Issues in Modeling Ion Transport in Biological Channels: Self- Consistent Particle-Based Simulations S. Aboud 1,2, M. Saraniti 1,2 and R. Eisenberg 1 1 Molecular Biophysics Department, Rush University, Chicago IL 2 Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago IL

Outline Motivation Bulk Electrolyte Simulation Brownian Dynamics Field Equation: P 3 M Ion Channel Simulation Lipid Bilayer K + Channel Protein Future Work

Motivation

Ion Channel Device Application mature planar technology wild and mutant proteins extreme selectivity extreme sensitivity rapid response Design by R. Eisenberg, S.M. Goodnick*, M. Saraniti, T. J. Thornton* *EE Department and CSSER – Arizona State University

Brownian Dynamics Langevin Equation: Primitive model for water: continuum dielectric end simulation time ? NO YES calculate charge field equation calculate averages particle dynamics end initialization

Field Equation: P 3 M PM PP

frequent solutions use good initial guess 2D, 3D, mixed B.C. irregular rectangular grid spacing Requirements: Iterative multi-grid method Threshold definition: Poisson Solver

Boundary Conditions anion cation eject inject Dirichlet: Neumann:

Results: Conductivity specific conductivity: KCl [M] Λ [cm2 Ω-1mol-1] simulation experiment* * V. Lobo, Electrolyte Solutions: literature data on thermodynamic and transport properties, Vol. 2, Coimbra, 1975

Radial Distribution Function chemical potential: energy: pressure:

Potassium Channels inner pore outer pore selectivity filter

Potassium Channels KcsA MthK Doyle, D. A. et al. Science 280, (1998) Jiang, Y. et al. Nature 417, (2002)

Lipids POPC (palmitoyl-oleoyl-phosphatidylcholine) Phospholipid: phosphate alcohol glycerolglycerol fatty acid fatty acid C P O N C C C C O C C O C O O C C O O O hydrophobic hydrophilic

Lipid Bilayer

POPC and KcsA Channel M. F. Sanner, A.J. Olson, and J.C.Spehner, Biopolymers, vol. 38, pp , 1996.

POPC and KcsA Channel

POPC and MthK Channel

Computational Domain 40 x40 x 40 grid 0.3 nm cell

Channel Electrostatics

KcsA MthK

Conclusion and Future Work efficient simulation times simulate a wide range of geometries and ion concentrations concentration remains stable over long simulation times conductivity compares well with experiment calculate thermodynamics properties include explicit water model Bulk Electrolyte Simulation: Channel Simulation: explicit description of channel protein and lipid membrane electrostatic structure of potassium ion in channel pore investigate influence of multiple ions in channel include explicit water in channel simulate transport optimize atomic coordinates in channel