BioMOCA: A Transport Monte-Carlo Model for Ionic Channels Trudy van der Straaten

1. 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 Beckman Institute University of Illinois at Urbana-Champaign

2. ACKNOWLEDGEMENTS Resources National Science Foundation (Grant No.EEC-0228390) Defense Advanced Research Projects Agency (DARPA SIMBIOSYS AF NA 0533) National Center for Supercomputing Applications (NCSA) Visualization Theoretical and Computational Biophysics Group Beckman Institute. http://www.ks.uiuc.edu/Research/vmd Sanner, M.F., Spehner, J.-C., and Olsen, A.J. (1986) Reduced Surface: an efficient way to compute molecular surfaces. Biopolymers, 38 (3), 305-320. Beckman Institute University of Illinois at Urbana-Champaign

3. 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 Beckman Institute University of Illinois at Urbana-Champaign

4. 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 Beckman Institute University of Illinois at Urbana-Champaign

5. 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 104, 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 Beckman Institute University of Illinois at Urbana-Champaign

6. 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 ~ 105 • t ~ 1fs • Tsim ~ 1-10ns • Run-times: CPU weeks-months electrolyte hydrocarbon membrane porin Figure: S. -W. Chiu and E. Jakobsson Computational Biology Group, Beckman Institute Beckman Institute University of Illinois at Urbana-Champaign

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

8. membrane insulator electrolyte bath 2 + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - electrode electrode electrolyte bath 1 insulator ion channel BioMOCA: TRANSPORT MONTE CARLO SIMULATION • 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. Beckman Institute University of Illinois at Urbana-Champaign

9. BioMOCA: TRANSPORT MONTE CARLO SIMULATION • Ion trajectory flight times between collisions Tf 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 (P3M) 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. Neumann BCs Dirichlet BCs Beckman Institute University of Illinois at Urbana-Champaign

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

11. lipid bilayer open closed 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 lipid bilayer open closed Beckman Institute University of Illinois at Urbana-Champaign

12. membrane  = 2 X [Å] electrolyte bath = 80 electrolyte bath = 80 protein= 20 Z [Å] fixed BioMOCA: SIMULATION of GRAMICIDIN CHANNEL • 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 H2O (D+ = 1.334x10-9m2s-1, D- = 2.032x10-9m2s-1) Beckman Institute University of Illinois at Urbana-Champaign

13. 73Å [Na+] 24Å [Cl-] ~2M 0.58V  0.25V 0M -0.25V -0.72V Simulation of Na+, Cl- Transport in Gramicidin 1Molar NaCl Vbias = 250mV t =10fs Tsim=0.1s ~30 CPU hrs (Intel 2.2GHz) Increased ion diffusivities by factor of 10 15 Na+ ions crossed the channel Beckman Institute University of Illinois at Urbana-Champaign

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

15. t [ns] = 2 X [Å] = 20 = 80 Z [Å] Na+ TRAJECTORY - RARE EVENT Vbias = 250 mV 1Molar NaCl Tsim = 200ns + Beckman Institute University of Illinois at Urbana-Champaign

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

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

18. BioMOCA: SIMULATION of GRAMICIDIN CHANNEL • Measuring current: 1Molar NaCl Vbias = 250mV Tsim = 9 s 20-30 CPU hours per s (10 processors) 101 Na+ ions crossed channel from right bath to left bath i ~ 1.8 pA (1.8-2.2pA) • 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) 2.0M 1.0M 0.5M 0.2M 0.1M Single-channel I-V curves for gramicidin in DPhPC for varying bath concentrations of NaCl. Busath et al. Biophysical Journal 75, 1998 pp 2830-2844 Beckman Institute University of Illinois at Urbana-Champaign

19. 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. Beckman Institute University of Illinois at Urbana-Champaign

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

21. PORIN CHANNEL: K+, Cl– ion density K+ Cl- 10mM 100mM 1M 10M 100M Beckman Institute University of Illinois at Urbana-Champaign

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

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

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

25. PORIN CHANNEL: K+, Cl– trajectories Vbias = -200mV Beckman Institute University of Illinois at Urbana-Champaign

26. WORK IN PROGRESS: SIMULATION of PORIN CHANNEL Representation of porin trimer in BioMOCA Beckman Institute University of Illinois at Urbana-Champaign

27. PORIN CHANNEL: K+, Cl– ion density K+ Cl- 10mM 100mM 1M 10M 100M Beckman Institute University of Illinois at Urbana-Champaign