MCM2003 Berlin Sep 1 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: A Transport Monte-Carlo Model for Ionic Channels Trudy van der Straaten Gulzar Kathawala Umberto Ravaioli Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign

MCM2003 Berlin Sep 2 Beckman Institute University of Illinois at Urbana-Champaign Resources National Science Foundation (Grant No.EEC ) Defense Advanced Research Projects Agency (DARPA SIMBIOSYS AF NA 0533) National Center for Supercomputing Applications (NCSA) Visualization Theoretical and Computational Biophysics Group Beckman Institute. Sanner, M.F., Spehner, J.-C., and Olsen, A.J. (1986) Reduced Surface: an efficient way to compute molecular surfaces. Biopolymers, 38 (3), ACKNOWLEDGEMENTS

MCM2003 Berlin Sep 3 Beckman Institute University of Illinois at Urbana-Champaign OUTLINE  Background: Ion Channels – Nature’s Nanodevices Physiological Functions Applications for BioDevices  Hierarchical Approach to Channel Simulation Molecular Dynamics  Monte Carlo  Continuum Models  Transport Monte-Carlo Simulations Description of Model Simulation of simple electrolytes Simulation of Gramicidin channel  Work in progress and future work Extension to OmpF Porin and other channels

MCM2003 Berlin Sep 4 Beckman Institute University of Illinois at Urbana-Champaign ION CHANNELS – Physiological Role  Proteins embedded in the membrane of all biological cells forming nanoscopic water-filled tunnels.  Regulate the passive transport of ions in and out of the cell.  Maintain correct intracellular ion composition and electrical potential which is crucial to cell survival and function.  Wide range of specialized functions e.g., control electrical signaling in the nervous system, muscle contraction.  Malfunctioning channels are linked to many diseases. Natural targets which viruses attack and use to enter cells  Many drugs used in clinical medicine act directly or indirectly through channels ~50Å

MCM2003 Berlin Sep 5 Beckman Institute University of Illinois at Urbana-Champaign ION CHANNELS – Natural Nanodevices  Selectivity – channels can transmit or block a particular ion species. e.g. Potassium channel selects K + over Na + by a factor of 10 4, despite their similar size – dehydration of Na + presents an energy barrier  Gating/Switching – Transition between conducting and non-conducting states in response to environmental triggers (pH, voltage, chemical and mechanical).  Strong charge density – critical to the open channel I-V characteristics. Charge density can be altered by mutation allowing channels to be ‘engineered’ with specific conductances, selectivities and functions.  Device elements that can self-assemble, perfectly reproducible.  Template for design of biodevices and biosensors. ~50Å ompF porin

MCM2003 Berlin Sep 6 Beckman Institute University of Illinois at Urbana-Champaign ION CHANNEL SIMULATION – Molecular Dynamics Biophysicists’ tool of choice  Includes all particles, free and bound. System evolves over time according to Newtonian mechanics.  Computationally intensive O(NlogN) N ~ 10 5  t ~ 1fs T sim ~ 1-10ns Run-times: CPU weeks-months hydrocarbon membrane electrolyte porin Figure: S. -W. Chiu and E. Jakobsson Computational Biology Group, Beckman Institute

MCM2003 Berlin Sep 7 Beckman Institute University of Illinois at Urbana-Champaign ION CHANNEL SIMULATION – Continuum Models  IV curves generated in mins-hours  Neglect of ion size leads to unphysically high ion densities in certain regions K + density > 0.75M 0M OmpF porin Poisson’s Equation Drift-diffusion Equation Continuity Equation

MCM2003 Berlin Sep 8 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: TRANSPORT MONTE CARLO SIMULATION insulator electrode membrane ion channel electrolyte bath 1 electrolyte bath 2  Water, membrane and protein are treated as continuum dielectric background media, each with a specific permattivity.  Ion trajectories are integrated in time and space using the leap-frog method.  Trajectories interrupted by random scattering events that represent the interaction with water.

MCM2003 Berlin Sep 9 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: TRANSPORT MONTE CARLO SIMULATION  Ion trajectory flight times between collisions T f are generated statistically  Scattering thermalizes the ion - final state is selected from a Maxwellian distribution  Local field is evaluated using the particle-particle-particle-mesh (P 3 M) scheme.  Charge is associated to mesh using cloud-in-cell (CIC) scheme.  Mixed boundary conditions to model insulating walls and bias applied across the system  Open system: Ions enter and leave the buffer regions near the contacts. Ion population is maintained with an injection scheme. Dirichlet BCs Neumann BCs

MCM2003 Berlin Sep 10 Beckman Institute University of Illinois at Urbana-Champaign  Ion size effects are modeled with a Lennard-Jones pairwise potential which prevents ions coalescing. point-particle Coulomb potential Lennard-Jones potential BioMOCA: TRANSPORT MONTE CARLO SIMULATION + _ protein  Protein and membrane boundaries are treated as hard walls, ions are reflected diffusively.

MCM2003 Berlin Sep 11 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: SIMULATION of GRAMICIDIN CHANNEL  Small simple channel-forming molecule: radius ~ 2Å length ~25Å  15 amino acids folded into a helical structure.  Expressed by some bacteria to kill other microorganisms by collapsing ion gradients required for survival.  Selective for small cations H+, Li+, Na+  Well-studied, good choice for ion channel simulation prototype open closed lipid bilayer open closed lipid bilayer

MCM2003 Berlin Sep 12 Beckman Institute University of Illinois at Urbana-Champaign  PROTEIN DATA BANK – repository of 3-D biological macromolecular structure data  atomic coordinates and radii. (1MAG.pdb)  Define region on mesh accessible to finite-sized ion. Add slab representing membrane. Assign relative dielectric coefficient to each region.  Construct  fixed by assigning a fractional point charge to each atom and associating to mesh using cloud-in-cell (CIC) scheme. (gromos force-field)  Diffusivities: Na +, Cl - in bulk H 2 O (D + = 1.334x10 -9 m 2 s -1, D - = 2.032x10 -9 m 2 s -1 ) Z [Å] electrolyte bath  = 80 membrane  = 2 protein  = 20 X [Å] electrolyte bath  = 80  fixed BioMOCA: SIMULATION of GRAMICIDIN CHANNEL

MCM2003 Berlin Sep 13 Beckman Institute University of Illinois at Urbana-Champaign Simulation of Na+, Cl- Transport in Gramicidin 1Molar NaCl V bias = 250mV  t =10fs T sim =0.1  s ~30 CPU hrs (Intel 2.2GHz) Increased ion diffusivities by factor of Na + ions crossed the channel 0M ~2M [Na + ] [Cl - ] 73Å 24Å -0.72V 0.58V 0.25V -0.25V 

MCM2003 Berlin Sep 14 Beckman Institute University of Illinois at Urbana-Champaign AVERAGE POTENTIAL AND ION DENSITY V bias = 0 mV 1Molar NaCl T sim = 200ns single Na + crossing Z [Å]  [V] c [M] Na + Cl - Empty channel

MCM2003 Berlin Sep 15 Beckman Institute University of Illinois at Urbana-Champaign Z [Å] X [Å]  = 80  = 2  = 20 t [ns] Na + TRAJECTORY - RARE EVENT V bias = 250 mV 1Molar NaCl T sim = 200ns +

MCM2003 Berlin Sep 16 Beckman Institute University of Illinois at Urbana-Champaign AVERAGE POTENTIAL AND ION DENSITY V bias = 250 mV 1Molar NaCl T sim = 400ns 10 Na + crossings Z [Å]  [V] c [M] Na + Cl - zero bias

MCM2003 Berlin Sep 17 Beckman Institute University of Illinois at Urbana-Champaign residence time (ps) max displacement from contact [Å] Na + TRAJECTORY - RARE EVENT V bias = 250 mV 1Molar NaCl T sim = 200ns norm. units

MCM2003 Berlin Sep 18 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: SIMULATION of GRAMICIDIN CHANNEL Single-channel I-V curves for gramicidin in DPhPC for varying bath concentrations of NaCl. Busath et al. Biophysical Journal 75, 1998 pp M 0.1M 0.2M 0.5M 1.0M  Measuring current: 1Molar NaCl V bias = 250mV T sim = 9  s CPU hours per  s (10 processors) 101 Na + ions crossed channel from right bath to left bath i ~ 1.8 pA( pA)  Cl - ions are never observed inside the channel  Zero bias: far fewer ions cross channel, crossings in both directions  Increasing Diffusivity increases current (number of ions crossing the channel)

MCM2003 Berlin Sep 19 Beckman Institute University of Illinois at Urbana-Champaign WORK IN PROGRESS: SIMULATION of PORIN CHANNEL  ompF porin is a trimeric protein found in the outer membrane of e-coli.  Net charge of ~ -30|e|. Highly charged pore constriction.  Moderately selective for cations.  Gating mechanism still unknown.  Well-known, very stable structure which can be mutated.  Good choice for experimental and simulation studies of ion permeation.

MCM2003 Berlin Sep 20 Beckman Institute University of Illinois at Urbana-Champaign WORK IN PROGRESS: SIMULATION of PORIN CHANNEL Representation of porin trimer in BioMOCA

MCM2003 Berlin Sep 21 Beckman Institute University of Illinois at Urbana-Champaign PORIN CHANNEL: K +, Cl – ion density 10mM100mM1M100M10M K+K+ Cl -

MCM2003 Berlin Sep 22 Beckman Institute University of Illinois at Urbana-Champaign PORIN CHANNEL: Current-voltage characteristic 100mM KCl Drift-diffusion (PROPHET) Monte-Carlo (BioMOCA)

MCM2003 Berlin Sep 23 Beckman Institute University of Illinois at Urbana-Champaign PORIN CHANNEL: Current-voltage characteristic 100mM KCl

MCM2003 Berlin Sep 24 Beckman Institute University of Illinois at Urbana-Champaign PORIN CHANNEL: Ion occupancies 100mM KCl Drift-diffusion (PROPHET) Monte-Carlo (BioMOCA) Drift-diffusion overestimates ion densities inside channel

MCM2003 Berlin Sep 25 Beckman Institute University of Illinois at Urbana-Champaign PORIN CHANNEL: K +, Cl – trajectories V bias = -200mV

MCM2003 Berlin Sep 26 Beckman Institute University of Illinois at Urbana-Champaign PORIN CHANNEL: Current-voltage characteristic 100mM KCl Drift-diffusion (PROPHET) Monte-Carlo (BioMOCA)

MCM2003 Berlin Sep 27 Beckman Institute University of Illinois at Urbana-Champaign ION-ION PAIR CORRELATION FUNCTION  The ion-ion pair correlation function g(r) plays a central role in describing the microscopic structure and thermodynamic state of a system.  For homogeneous systems g(r) is proportional to the probability of finding two atoms separated by a distance  Thermodynamic quantities that depend on the pair potential approximation can be extracted directly from g(r). Reproducing g(r) properly is a necessary prerequisite to obtaining the correct thermodynamic properties of the system.  g(r) can be measured from x-ray and neutron diffraction experiments and is readily computed from trajectories using a counting procedure.

MCM2003 Berlin Sep 28 Beckman Institute University of Illinois at Urbana-Champaign EVALUATING g(r) USING BioMOCA Simple electrolyte: Modified (shifted-truncated) Lennard-Jones potential Compute g(r) using three different simulation methods 1. Equilibrium Monte Carlo (EMC) 2. Molecular Dynamics (MD) 3. Transport Monte Carlo (BioMOCA) } L=69.251Å L=96Å

MCM2003 Berlin Sep 29 Beckman Institute University of Illinois at Urbana-Champaign EVALUATING g(r) USING BioMOCA Simple electrolyte: Modified (shifted-truncated) Lennard-Jones potential Magnified view

MCM2003 Berlin Sep 30 Beckman Institute University of Illinois at Urbana-Champaign SIMULATION PARAMETERS Simulation cell L  L  L MD, EMC: L=69.251Å BTMC: L=96Å divalent Compute g(r) using three different simulation methods 1. Equilibrium Monte Carlo (EMC) 2. Molecular Dynamics (MD) 3. Transport Monte Carlo (BioMOCA)

MCM2003 Berlin Sep 31 Beckman Institute University of Illinois at Urbana-Champaign Bulk 5: divalent,  + = 1.9Å  - = 3.62Å 0.75Molar  Coarse mesh (  = 4Å )

MCM2003 Berlin Sep 32 Beckman Institute University of Illinois at Urbana-Champaign Bulk 1: monovalent,  + =  - = 3Å Particle-Mesh scheme on progressively coarser meshes. Distortions to g(r) at larger mesh spacing due to truncation of short-range Coulomb forces are recovered using the P 3 M scheme

MCM2003 Berlin Sep 33 Beckman Institute University of Illinois at Urbana-Champaign SIMULATION OF NA+, CL- CONDUCTIVITY L=200Å 20  20  20 1Volt 300K Equivalent conductivity applied field current density concentration (Mol) E = j = c = For c > 10mM BioMOCA results compare satisfactorily with the published experimental data, given the uncertainties in the ion transport and pair potential parameters. At very low concentrations Debye length is too long to be resolved on mesh g [Scm 2 mol -1 ] c [mol]

MCM2003 Berlin Sep 34 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: SIMULATION of GRAMICIDIN CHANNEL  Small simple channel-forming molecule  Each monomer is made up of 15 amino acids folded into a helical structure.  Pore radius ~ 2Å length ~25Å  Expressed by some bacteria to kill other microorganisms by collapsing the ion gradients that are required for their survival.  Selective for small cations H+, Li+, Na+  Well-studied experimentally and theoretically  Good choice for developing ion channel simulation prototype open closed lipid bilayer ~25Å hydrophilic hydrophobic

MCM2003 Berlin Sep 35 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: SIMULATION of GRAMICIDIN CHANNEL Visualization: Theoretical and Computational Biophysics Group Beckman Institute.

MCM2003 Berlin Sep 36 Beckman Institute University of Illinois at Urbana-Champaign Simulation of Na+, Cl- Transport in Gramicidin 1Molar NaCl V bias = 250mV Z [Å]  [V] c [M] Na + Cl -

MCM2003 Berlin Sep 37 Beckman Institute University of Illinois at Urbana-Champaign Na + TRAJECTORY - RARE EVENT V bias = 0 mV Z [Å] X [Å]  = 80  = 2  = 20 t [ns] 1Molar NaCl T sim = 200ns

MCM2003 Berlin Sep 38 Beckman Institute University of Illinois at Urbana-Champaign BioMOCA: SIMULATION of GRAMICIDIN CHANNEL 40 simulations 400ns duration 250mV 1Molar NaCl avg = 4.5 SD = 2.2

MCM2003 Berlin Sep 39 Beckman Institute University of Illinois at Urbana-Champaign For realistic ion channel simulations there exists a trade-off between computational cost and model complexity. contacts BioMOCA: SIMULATION of GRAMICIDIN CHANNEL

MCM2003 Berlin Sep 40 Beckman Institute University of Illinois at Urbana-Champaign WORK IN PROGRESS: SIMULATION of PORIN CHANNEL Representation of porin trimer in BioMOCA

MCM2003 Berlin Sep 41 Beckman Institute University of Illinois at Urbana-Champaign 10mM100mM1M100M10M PORIN CHANNEL: K +, Cl – ion density K+K+ Cl -