jason crain school of physics, university of edinburgh, edinburgh uk
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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
.
.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)
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
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