Jason Crain

School of Physics, University of Edinburgh, Edinburgh UK

National Physical Laboratory, London, UK

Lengthscale Bridging in Biophysical Systems: Experiment and Simulation

Viral inhibition

Anti Microbial peptides

Metal binding peptides

Early amyloid formationSecondary structure control by solvent

Models for membrane-mediated folding

Design principles for compact domainsAccuracy of empirical potential modelsCoarse-graining concepts in biology

High-field NMRReplica Exchange MD

Near and Intermediate Range Neutron diffraction

Synchrotron CDQuantum Drude MD

Structure – function relationships

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Project Outline

Antimicrobial peptidesThese evolutionarily conserved peptides are usually positively charged and have both a hydrophobic and hydrophilic side that

enables the molecule to be soluble in aqueous environments yet also enter lipid-rich membranes.

Magainin

Magaininactivity against viruses, bacteria, protozoa, yeasts and fungi, and may be cytotoxic to cancer cells.

ThanatinPotent bacteriocide and fungicide anti-parallel beta-sheet structure from residue 8 to the C-terminus, including the disulfide bridge. In spite of the presence of two proline residues, there is a large degree of structural variability in the N-terminal segment.

Parallel Tempering Molecular DynamicsAccelerating configurational sampling in slowly-relaxing systems with rugged energy landscapes such as peptides. Prone to become trapped in meta-stable configurations on timescales that are long compared to the simulation time.

Metropolis Algorithm

R1

R2

R3

R4

R4

R3

R2

R1

R4

R3

R1

R2

Local move MD Local move MD

Conformational Plasticity in Human HIV-1 Membrane proximal fusion peptide: Parallel

Tempering MD and Synchrotron Circular Dichroism

•64 Replicas; •CHARMM22 ; •TIP3P Water

•PTMD implemented on Blue Gene

T=300K T=800K

GP41657-671

In H20And TFE mixed solvent

Many situations where the polarization (induction) and dispersion interactions are important

Elusive interactions:Polarization and dispersion in condensed matter

•Liquids•Interfaces•Charged groups•Biological systems

Classical force fields: One charge fits all

•Simple to implement – scaleable to large system size •Additive•No Polarization / Van der Waals

fit the mean field of the liquid by •Manipulating dipole moments •Introducing phantom charges•Deforming molecular geometry.

• Transferability beyond paramaterization regime is questionable

- eg gas to condensed phases in noble gases - water

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.SPC

SPC/ESPC/Fw

PPCTIP3/4/5P

+FQSWFLEX

GCPMSWM4-

NDPPOL5-TZ

TTM-2Six-site

QCT..

Textbook treatment of the classical harmonic atom:

-qi

•Only dipole polarizability•Non-additive induction only in dipole limit•No Dispersion in the ground state

Original ideas : Drude 1900; Kirkwood / Onsager < 1940’s; Bade 1957

+

Moments expansion for quantum harmonic atom:

… for interaction

•Polarizability to all orders•Non-additive induction beyond dipole limit •Dispersion included

VARIATIONAL MONTE CARLOOptimization of trial wavefunction Easiest to implementLimited to accuracy of trial choiceGround state T = 0

PROJECTOR/DIFFUSION MONTE CARLORepeated operations to project/diffuse a trial state to the ground state via stochastic trajectoryLeads to exact ground state (T=0) in principle PATH INTEGRALQM-Classical Stat Mech isomorphismTrace of thermal density matrix computed. Finite temperature propertiesPossible implementation with forces

Harmonically-bound one electron pseudo-

atomAccurately sampled QDO forcefield will

intrinsically contain multipole and

dispersion interactions

The Halfway House: Quantum Drude Oscillators as one-electron model potentials

converges to the ground statewave function regardless of the choice of the initial wave function

Wick rotation for Schrodinger Eqn t ! it

Diffusion Equation

V(x)

PDF

Implementation of Norm-conserving DMC for Quantum Drude Oscillators

•Initial wavefunction represented by N “walkers”

•V-E is a walker survival operator

•Gaussian response requires short range cutoffs

•Diffusion/branching processes generates walker distribution representative of ground state wavefunction

•Walker number is strictly conserved to give stable trajectories - Introduction of a flux-matching branch operator

QDO paramaterized to reproduce BWLSL gas phase for Xenon

Quantum Diffusion Monte Carlo Norm Conservation - Diagramatic Expansions Application to solid XeJones, Mueser, Martyna & Crain Phys. Rev. B 2009, 79, 144119

FCC Solid Xenon

IBM Research

Variational

NC-DMC

32 atoms

Ground state energy and bulk modulus for FCC Xenon

IBM Research

BWLSL

Expt.E ¼ ZPE

Bulk modulus within 3-10 % of experimental value (depending on estimates of nuclear quantum effects) BWLSL potential is > 22% too high

Full QDO with NC-DMC + all pair multipole trial

Quantum Drude MD: Path integral sampling

IBM Research

Discrete path integral and classical isomorphism

Isomorphic to classical ring of P particlesClassical MD can be used to obtain quantum behaviorBeads are harmonically coupled by springs with chain frequency P . Potential must not vary much over Rms bond length.

Harmonic potentialdepending on Trotter indexand T

Potential energy

Energy estimators: from discretized path integral

Path Integral formulation for Quantum Drude MD

IBM Research

Full Quantum Drude Xenon MeltMolecular Dynamics With Path integral Sampling

•Dispersion included

•Many body polarization included