Particle-Based Simulation of Bio-Electronic Systems

Transcription

1 Particle-Based Simulation of Bio-Electronic Systems Alex Smolyanitsky, and Marco Saraniti Arizona State University

2 Outline Particle-based Brownian dynamics simulations for bioelectronic systems Complex-field DC-electrophoresis of charged proteins Simulations of molecule: constraints and general computational framework SHAKE and LINCS algorithms RATTLE and general velocity correction Results and discussion for OmpF ion channel Preliminary results for Kv1.2 ion channel Visualization of simple protein folding Conclusions and future work

3 Complex field electrophoresis: system description hole Top view α-hemolysin protein molecules are driven by DC electrophoresis. 300 nm Teflon slab buried electrode (1.25 V) Protein modeled as charged rigid sphere (r = 5 nm) suspended in water (ε = 78.0). External field, stokesian drag, stochastic contribution explicitly included in the simulation. 300 nm 300 nm 20 nm 40 nm Driving fields obtained via application of constant potentials, not constant fields. Electric charge calculated from protonation states of individual residues in α-hemolysin at a given ph value. T = 300K, q = +65 e at ph = 5.0; diffusion coefficient, mobility, and settling time used in simulation, respectively: The simulation setup is a 300 nm x 300 nm x 300 nm water-filled box split by a 30 nm thick teflon membrane (ε = 2.0).

4 Complex field electrophoresis: visualization The distance from the protein s initial position is calculated at approx. 115 nm. Total focusing time is about 4 microseconds. The protein with effective diameter of 10 nm is successfully focused into a 20 nm x 20 nm hole.

5 Constrained dynamics: basic constraints d ij i j i φ k j a) simple linearbond b) 2-D bond angle l j k i c) 3-D dihedral angle

6 Constrained dynamics: flowchart Flowchart of the Brownian dynamics simulation tool without (left) and with (right) the constrained dynamics corrections. Find potential distribution Find potential distribution Calculate electrical fields and forces Calculate electrical fields and forces Update particle velocities and positions Update particle velocities and positions Correct positions and velocities of constrained particles

7 Constraint algorithm review General Framework Based on Lagrange multiplier method For a system containing N particles requires inversion of N x N matrix at every timestep SHAKE algorithm Approximate iterative method to avoid direct matrix inversion Guaranteed to converge within 50 iterations with timesteps up to 10 fs LINCS algorithm Non-iterative, uses matrix form of Taylor expansion to avoid direct matrix inversion Timesteps up to 20 fs, twice as large compared to SHAKE Applicable only to systems with low connectivity, limiting use for constraining the angles using artificial bonds and demanding use of angle-constraining potentials rather than artificial bonds RATTLE and general velocity correction Removes bond strain by minimizing relative velocity along the constraint Applied sequentially Improves SHAKE convergence

8 Constrained dynamics: SHAKE algorithm avg. number of SHAKE iterations bonds, angles, dihedrals constrained bonds and angles constrained bonds constrained number of bound particles Average number of SHAKE iterations vs. number of bound particles required for convergence to relative SHAKE tolerance of for various types of constraints. Verlet unconstrained integrator with free flight timestep of 8 fs used.

9 Constrained dynamics: velocity correction average bound atom energy [ev] average bound atom energy, ev BPTI protein constrained dynamics velo Euler int, velocity correction off (1 fs st Euler Verlet int, unconstrained velocity correction on (1 fs st Pred/corr integrator, int, 8 fs velocity timestep correction off (4 Pred/corr int, velocity correction on (4 Verlet int, velocity correction on & off ( Velocity correction on Velocity correction off time, ns simulated time [ns] average bound atom energy [ev] Predictor-corrector unconstrained integrator, 8 fs timestep Velocity correction off Velocity correction on simulated time [ns] average bound atom energy [ev] Euler unconstrained integrator, 2 fs timestep Velocity correction off Velocity correction on simulated time [ns] Time evolution of the average energy of the bound atoms for various unconstrained integrator algorithms. After velocity correction, avg. kinetic energy around 30meV for all algorithms. No spurious heating/cooling of molecule.

10 OmpF ion channel simulation: general structure A Three 16-strand barrel subunits (340 residues each) Permeation region constricted to 7 x 11 Å Transverse fields in permeation region due to charged residues Cation-selective, depending on salt concentration selectivity ratio 1.5 to 2.5

11 OmpF ion channel simulation: system description 15 protein region ε=6.0 lipid membrane ε=4.0 top contact y[nm] xy-plane slice z=6.5nm y[nm] xy-plane slice z=7.0nm z [nm] 10 5 water ε= xy-plane slice z=7.5nm x[nm] xy-plane slice z=8.5nm x[nm] 0 5 y [nm] x [nm] bottom contact y[nm] y[nm] dielectric constant x[nm] x[nm] 3-D dielectric map of the system (left) and dielectric contour planes at various z-coordinates (right).

12 OmpF ion channel simulation: conductance and selectivity 5 4 OmpF trimer conductance [ns] BD, ε protein =6.0 experimental data *** selectivity ratio I K /I Cl current ratio N K /N Cl ion number ratio KCl concentration [M] KCl concentration [M] Simulated OmpF conductance vs. KCl concentration compared to experimental data, and simulated ionic selectivity based on currents and ion numbers (right). *** S. J. Wilk, S. Aboud, L. Petrossian, M. Goryll, J. M. Tang, R. S. Eisenberg, M.Saraniti, S. M. Goodnick, and T. J. Thornton. Ion channel conductance measurements on a siliconbased platform. Journal of Physics Conference Series, 37(1):21-24, 2006.

13 OmpF ion channel simulation: axial potential and ion distribution profiles 3 avg. potential [V] intracellular region 0.25M KCl 0.5M KCl 1.0M KCl no ions, no bias channel region constriction zone Asp-113, Glu-117 Arg-168, Lys-80 extracellular region axial position [nm] avg. concentration [M] intracellular region channel region constriction zone Asp-113, Glu M KCl, cations 0.25M KCl, anions 0.5M KCl, cations 0.5M KCl, anions 1.0M KCl, cations 1.0M KCl, anions Arg-168, Lys-80 extracellular region axial position [nm] Simulated distributions of potential (left) and ionic concentration (right) along the axis of an OmpF monomer for various KCl concentrations.

14 OmpF ion channel simulation: visualization of conduction through isolated monomer The potassium and chlorine ions are shown in grey and green, respectively. The OmpF monomer is shown as semi-transparent, inserted in lipid membrane (impermeable dielectric slab, not shown). The transmembrane potential is 100mV.

15 Kv1.2 voltage-dependent potassium channel Belongs to large family of voltage-dependent potassium channels Regulates potassium flow across cell membrane in neuron synapse of mammals Transmembrane portion is a tetramer, each subunit consisting of six helices S1-S6 forming voltage sensor (S1-S4) and pore domain (S5 and S6) Channel can be in open and closed conformations, depending on transmembrane voltage, the exact electromechanical process still unknown Conformation transition on millisecond timescale Top view (RCSB code 2R9R) Side view

16 Kv1.2 potential profile (side) Dielectric constant of protein region and implicit lipid membrane set to 2.0. Dielectric smoothing of the protein-water contact using the results in [1]. 1. Cyril Azuara, Henri Orland, Michael Bon, Patrice Koehl, and Marc Delarus, Incorporating Dipolar Solvents in Poisson- Boltzmann Electrostatics, Biophysical Journal, Vol. 95, Dec XZ-plane slices at y = 5.0 nm of simulated distributions of potential (left) and dielectric constant (right). No added KCl, single Poisson step.

17 Kv1.2 potential profile (top) 4eV-deep potential well in the selectivity filter. Considerable positive charge in the voltage sensor domains. XY-plane slice at z = 6.5 nm of simulated distribution of potential. No added KCl, single Poisson step.

18 Kv1.2 axial energy and potassium distribution K + ion energy [ev] K + ion energy [ev] axial K + [M] selectivity filter axial position [nm] accumulation at the mouth Potential energy of a potassium ion and potassium ion distribution along the channel axis. Bulk KCl concentration 1mM, 40 ns simulation, results averaged over the last 20 ns K + distribution [M] Ion distribution consistent with molecular dynamics simulation results revealing two potassium ions inside the selectivity filter and one at the mouth of KcsA channel with similar selectivity filter [2]. Peaks in ion distribution spatially coincide with near-zero axial field regions. 2. Simon Berneche and Benoit Roux, Molecular Dynamics of the KcsA K+ Channel in a Bilayer Membrane, Biophysical Journal, Vol 78, June 2000.

19 Visualization: Chicken Villin Headpiece folding One of the few protein subdomains obtaining stable conformation within microseconds (see, for example, RCSB code 1VII). 200 ns simulated, starting from thermally unstable linear conformation. LINCS bond constraint algorithm with angle-constraining potentials used.

20 Conclusions and future work Constrained dynamics with velocity correction implemented Conduction in OmpF ion channel studied, good agreement with experiment OmpF selectivity reveals combination of electrostatic and steric effects Preliminary data on Kv1.2 voltage-dependent potassium channel obtained, consistent with experimental data and MD simulations Future work Developing a Monte-Carlo based mechanism mimicking ion adsorption by chemically active solid surfaces in aqueous environment Moving closer to MD and electrically polarizable forcefield Modeling ionic conduction in nanostructures, including manmade and biological structures