Particle-Based Simulation of Bio-Electronic Systems Alex - - PowerPoint PPT Presentation

▶
particle based simulation of bio electronic systems
SMART_READER_LITE
LIVE PREVIEW

Particle-Based Simulation of Bio-Electronic Systems Alex - - PowerPoint PPT Presentation

Jan 13, 2024 732 likes •953 views

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

slide-1
SLIDE 1

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Particle-Based Simulation of Bio-Electronic Systems

Alex Smolyanitsky, and Marco Saraniti Center for Computational Nanoscience Arizona State University

slide-2
SLIDE 2

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

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

slide-3
SLIDE 3

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Complex field electrophoresis: system description

hole Top view 300 nm 300 nm

3 00 nm

Teflon slab

buried electrode (1.25 V)

20 nm 40 nm

  • α-Hemolysin protein molecules are

driven by DC electrophoresis.

  • 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.

  • 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).

slide-4
SLIDE 4

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

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
  • f 10 nm is successfully focused into

a 20 nm x 20 nm hole.

slide-5
SLIDE 5

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Constrained dynamics: basic constraints

dij

i j

φ

i j k i j k l

c) 3-D dihedral angle a) simple linear bond b) 2-D bond angle

slide-6
SLIDE 6

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Constrained dynamics: flowchart

Find potential distribution Calculate electrical fields and forces Update particle velocities and positions Find potential distribution Calculate electrical fields and forces Update particle velocities and positions Correct positions and velocities

  • f constrained particles

Flowchart of the Brownian dynamics simulation tool without (left) and with (right) the constrained dynamics corrections.

slide-7
SLIDE 7

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

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
slide-8
SLIDE 8

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Constrained dynamics: SHAKE algorithm

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.

number of bound particles

  • avg. number of SHAKE iterations

500 1000 1500 2000 2500 3000 3500 20 40 60

bonds, angles, dihedrals constrained bonds and angles constrained bonds constrained

slide-9
SLIDE 9

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Constrained dynamics: velocity correction

time, ns average bound atom energy, eV

0.02 0.04 0.06 0.08 0.1 0.02 0.04 0.06 0.08 0.1

Euler int, velocity correction off (1 fs st Euler int, velocity correction on (1 fs st Verlet int, velocity correction on & off ( Pred/corr int, velocity correction off (4 Pred/corr int, velocity correction on (4 BPTI protein constrained dynamics velo

simulated time [ns] average bound atom energy [eV]

0.02 0.04 0.06 0.08 0.1 0.02 0.03 0.04 0.05 0.06 0.07 Velocity correction off Velocity correction on

Euler unconstrained integrator, 2 fs timestep

simulated time [ns] average bound atom energy [eV]

0.02 0.04 0.06 0.08 0.1 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Velocity correction on Velocity correction off

Verlet unconstrained integrator, 8 fs timestep

simulated time [ns] average bound atom energy [eV]

0.02 0.04 0.06 0.08 0.1 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Velocity correction off Velocity correction on

Predictor-corrector unconstrained integrator, 8 fs timestep

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.

slide-10
SLIDE 10

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

OmpF ion channel simulation: general structure

  • 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

slide-11
SLIDE 11

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

OmpF ion channel simulation: system description

x [nm] y [nm]

2 4 6 8 10 12 14 2 4 6 8 10 12 14

xy-plane slice z = 6.5 nm

x [nm] y [nm]

2 4 6 8 10 12 14 2 4 6 8 10 12

xy-plane slice z = 7.5 nm

x [nm] y [nm]

2 4 6 8 10 12 14 2 4 6 8 10 12 14

xy-plane slice z = 8.5 nm

x [nm] y [nm]

2 4 6 8 10 12 14 2 4 6 8 10 12 14

xy-plane slice z = 7.0 nm

x [nm]

5 10 15

y [ n m ]

5 10 15

z [nm]

5 10 15

5 15 25 35 45 55 65 75

water ε=78.0 lipid membrane ε=4.0 protein region ε=6.0 bottom contact top contact dielectric constant

3-D dielectric map of the system (left) and dielectric contour planes at various z-coordinates (right).

slide-12
SLIDE 12

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

OmpF ion channel simulation: conductance and selectivity

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.

KCl concentration [M] OmpF trimer conductance [nS]

0.2 0.4 0.6 0.8 1 1 2 3 4 5

BD, εprotein=6.0 experimental data ***

KCl concentration [M] selectivity ratio

0.2 0.4 0.6 0.8 1 1 1.5 2 2.5 3 3.5 4

IK/ICl current ratio NK/NCl ion number ratio

slide-13
SLIDE 13

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

OmpF ion channel simulation: axial potential and ion distribution profiles

axial position [nm]

  • avg. potential [V]

2 4 6 8 10 12 14

  • 1.2
  • 1
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.2

0.25M KCl 0.5M KCl 1.0M KCl no ions, no bias

channel region Arg-168, Lys-80 constriction zone Asp-113, Glu-117 intracellular region extracellular region

axial position [nm]

  • avg. concentration [M]

2 4 6 8 10 12 14 0.5 1 1.5 2 2.5 3

0.25M KCl, cations 0.25M KCl, anions 0.5M KCl, cations 0.5M KCl, anions 1.0M KCl, cations 1.0M KCl, anions

channel region constriction zone Asp-113, Glu-117 Arg-168, Lys-80 intracellular region extracellular region

Simulated distributions of potential (left) and ionic concentration (right) along the axis of an OmpF monomer for various KCl concentrations.

slide-14
SLIDE 14

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

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.

slide-15
SLIDE 15

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

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

slide-16
SLIDE 16

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Kv1.2 potential profile (side)

XZ-plane slices at y = 5.0 nm of simulated distributions of potential (left) and dielectric constant (right). No added KCl, single Poisson step.

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. 2008.
slide-17
SLIDE 17

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

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.

slide-18
SLIDE 18

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Kv1.2 axial energy and potassium distribution

axial position [nm] K

+ ion energy [eV]

K

+ distribution [M]

2 4 6 8 10 12

  • 12
  • 11
  • 10
  • 9
  • 8
  • 7
  • 6
  • 5
  • 4
  • 3
  • 2
  • 1

1

  • 0.5

0.5 1 1.5 2

K

+ ion energy [eV]

axial K

+ [M]

selectivity filter 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.

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.

slide-19
SLIDE 19

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

Visualization: Chicken Villin Headpiece folding

200 ns simulated, starting from thermally unstable linear conformation. LINCS bond constraint algorithm with angle-constraining potentials used.

One of the few protein subdomains

  • btaining stable conformation within

microseconds (see, for example, RCSB code 1VII).

slide-20
SLIDE 20

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

ARIZONA INSTITUTE FOR NANO-ELECTRONICS

Center for Computational Nanoscience

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 man-

made and biological structures