Particle-Based Simulation of Bio-Electronic Systems Alex Smolyanitsky, and Marco Saraniti Center for Computational Nanoscience Arizona State University A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
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 A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
Complex field electrophoresis: system description Top view hole • α -Hemolysin protein molecules are driven by DC electrophoresis. 00 nm •Protein modeled as charged rigid sphere Teflon slab (r = 5 nm) suspended in water ( ε = 78.0). 3 •External field, stokesian drag, stochastic contribution explicitly included in the buried electrode (1.25 V) simulation. •Driving fields obtained via application of 300 nm 20 nm constant potentials, not constant fields. 300 nm •Electric charge calculated from 40 nm 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). A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
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. A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
Constrained dynamics: basic constraints d ij i j φ i k j a) simple linear bond b) 2-D bond angle l j k i c) 3-D dihedral angle A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
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 Calculate electrical fields and forces fields and forces Update particle velocities Update particle velocities and positions and positions Correct positions and velocities of constrained particles A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
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 A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
Constrained dynamics: SHAKE algorithm bonds, angles, dihedrals constrained bonds and angles constrained 60 avg. number of SHAKE iterations bonds constrained 40 20 0 500 1000 1500 2000 2500 3000 3500 number of bound particles Average number of SHAKE iterations vs. number of bound particles required for convergence to relative SHAKE tolerance of 0.001 for various types of constraints. Verlet unconstrained integrator with free flight timestep of 8 fs used. A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
Constrained dynamics: velocity correction BPTI protein constrained dynamics velo 0.05 0.1 0.05 Euler int, velocity correction off (1 fs st Predictor-corrector unconstrained Verlet unconstrained average bound atom energy [eV] average bound atom energy [eV] Euler int, velocity correction on (1 fs st integrator, 8 fs timestep Pred/corr int, velocity correction off (4 integrator, 8 fs timestep Pred/corr int, velocity correction on (4 average bound atom energy, eV 0.045 0.045 0.08 Verlet int, velocity correction on & off ( Velocity correction off Velocity correction on Velocity correction on Velocity correction off 0.04 0.04 0.06 0.035 0.035 0.04 0.03 0.03 0.02 0.025 0.025 0 0 0.02 0.04 0.06 0.08 0.1 0.02 0.02 0 0.02 0.04 time, ns 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 simulated time [ns] simulated time [ns] 0.07 Euler unconstrained average bound atom energy [eV] integrator, 2 fs timestep Time evolution of the average energy of the 0.06 Velocity correction off bound atoms for various unconstrained Velocity correction on 0.05 integrator algorithms. After velocity correction, avg. kinetic energy 0.04 around 30meV for all algorithms. 0.03 No spurious heating/cooling of molecule. 0.02 0 0.02 0.04 0.06 0.08 0.1 simulated time [ns] A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
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 A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
OmpF ion channel simulation: system description 14 14 xy-plane slice xy-plane slice 12 z = 6.5 nm 12 z = 7.0 nm protein region lipid membrane 10 10 ε =6.0 ε =4.0 y [nm] y [nm] 8 8 top 6 6 contact 4 4 15 2 2 water 2 4 6 8 10 12 14 2 4 6 8 10 12 14 10 x [nm] x [nm] ε =78.0 z [nm] 14 5 xy-plane slice xy-plane slice 12 z = 7.5 nm 12 z = 8.5 nm 0 10 0 0 10 5 5 x [nm] y bottom y [nm] y [nm] [ 10 10 n m 8 8 ] 15 15 contact 6 6 4 dielectric 4 constant 2 2 5 15 25 35 45 55 65 75 2 4 6 8 10 12 14 2 4 6 8 10 12 14 x [nm] x [nm] 3-D dielectric map of the system (left) and dielectric contour planes at various z-coordinates (right). A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
OmpF ion channel simulation: conductance and selectivity 5 4 OmpF trimer conductance [nS] BD, ε protein =6.0 I K /I Cl current ratio 3.5 experimental data *** N K /N Cl ion number ratio 4 selectivity ratio 3 3 2.5 2 2 1 1.5 0 1 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 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 silicon- based platform. Journal of Physics Conference Series , 37(1):21-24, 2006. A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS A RIZONA I NSTITUTE FOR N ANO -E LECTRONICS C enter for C omputationa l N anoscience C enter for C omputationa l N anoscience
Recommend
More recommend
