A Coupled 3 D PNPECP Model for Ion

A Coupled 3 -D PNP/ECP Model for Ion Transport in Biological Ion Channels Zhicheng Yang, Trudy. A. van der Straaten and Umberto. Ravaioli Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign

What are ion channels? § Natural nanotubes in § § biological cells Made of proteins With highly localized charge inside the channel Controls the flow of ions and water in and out the cells Selectivity and Gating 2/22/2021 Porin trimer A porin monomer filled with water University of Illinois at Urbana-Champaign 2

Why PNP? § Molecular Dynamics (MD) § Most popular and accurate § Limits simulation times to ~100 ns § Steady-state conduction occurs over much longer timescales § Poisson-Nernst-Planck (PNP) § Known as Drift-Diffusion theory § Continuum model § Widely used in device simulation § Much less computational cost 2/22/2021 University of Illinois at Urbana-Champaign 3

Conventional PNP model § Poisson equation § Nernst-Planck equation: § Above coupled equations are solve self-consistently 2/22/2021 University of Illinois at Urbana-Champaign 4

Problem with PNP § Continuum model treat ions as a continuum fluid of point particles § Ignores the size of ions and water molecules § Ignores non-singular distribution of charge on the ion Result: § Overestimate Coulomb screening and ion packing § Cannot describe ion selectivity 2/22/2021 University of Illinois at Urbana-Champaign 5

Free Energy Model for Inhomogeneous Fluid Mixtures: Yukawa-Charged Hard Sphere, General Interactions, and Plasmas Yaakov. Rosenfeld, J. Chem. Phys, 98, 8126 (1993). & D. Gillespie, W. Nonner, and R. S. Eisenberg, J. Phys. 14 12129 (2002). 2/22/2021 University of Illinois at Urbana-Champaign 6

Excess Chemical Potential (ECP) § ECP is introduced to add these additional effects to the PNP model § Modified Nernst-Planck equation: Where 2/22/2021 University of Illinois at Urbana-Champaign 7

Excess Chemical Potential (ECP) § Two components of ECP § Hard Sphere (HS) § Finite-sized ions § Present of water molecules § Electrostatic component (ES) § Non-singular charge distribution on the ion § ECP is a function of ion and water densities and can be calculated by DFT 2/22/2021 University of Illinois at Urbana-Champaign 8

Coupled PNP/ECP equations Modified Nernst-Planck equation with the ECP correction: Here is a function of Next slide shows how to calculate in detail Poisson equation: 2/22/2021 University of Illinois at Urbana-Champaign 9

Flow chart for PNP/ECP model Initial guess of water density Solve conventional PNP model for ion densities Add ECP correction to PNP model Outside iteration for coupled PNP/ECP Update water density Inside iteration for ECP correction Calculate ECP correction Final solution for potential, ion and water densties 2/22/2021 University of Illinois at Urbana-Champaign 10

Inside Iteration for ECP correction , Converge? , 2/22/2021 , University of Illinois at Urbana-Champaign 11

3 D test structure § Dimension of 96 x 96 Å § Membrane in the X-Y plane with length 28 Å in Z direction § Rectangular channel of 8 x 8 x 28 Å on the protein wall along Z direction § Ion concentration at bath region is 1 M/L 2/22/2021 University of Illinois at Urbana-Champaign Y Z X 12

Cation density without fixed charge Result from test structure without permanent charge PNP model without ECP correction PNP model with ECP correction 2 M/L 0 2/22/2021 University of Illinois at Urbana-Champaign 13

Anion density without fixed charge Result from test structure without permanent charge PNP model without ECP correction PNP model with ECP correction 2 M/L 0 2/22/2021 University of Illinois at Urbana-Champaign 14

Ion densities without fixed charge 2/22/2021 University of Illinois at Urbana-Champaign 15

Cation density Comparison Result from test structure with positive permanent charge PNP model without ECP correction PNP model with ECP correction 20 M/L 0 2/22/2021 University of Illinois at Urbana-Champaign 16

Anion density Comparison Result from test structure with positive permanent charge PNP model without ECP correction PNP model with ECP correction 20 M/L 0 2/22/2021 University of Illinois at Urbana-Champaign 17

Ion densities with fixed charge 2/22/2021 University of Illinois at Urbana-Champaign 18

Future Work § Comparisons with particle simulations § Implementation of a realistic biological ion channel § More efficient computational procedure 2/22/2021 University of Illinois at Urbana-Champaign 19