Lengthscale Bridging in Biophysical
Systems: Experiment and
Simulation
Jason Crain
School of Physics, University of Edinburgh, Edinburgh UK
National Physical Laboratory, London, UK
Methodological
Developments
Physical Science Questions
Technology
Drivers
Project Outline
Anti Microbial
peptides
Metal binding
peptides
Early amyloid formation
Viral
inhibition
Secondary structure control by solvent
Models for membrane-mediated folding
Design principles for compact domains
Accuracy of empirical potential models
Coarse-graining concepts in biology
Structure – function relationships
High-field NMR
Replica Exchange MD
Quantum Drude MD
Synchrotron CD
Near and Intermediate Range
Neutron diffraction
Antimicrobial peptides
These 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.
Thanatin
Potent bacteriocide and fungicide
anti-parallel beta-sheet structure
Magainin
from residue 8 to the C-terminus,
activity against viruses, bacteria,
including the disulfide bridge. In spite
protozoa, yeasts and fungi, and may
of the presence of two proline
be Magainin
cytotoxic to cancer cells.
residues, there is a large degree of
structural variability in the N-terminal
segment.
Parallel Tempering Molecular Dynamics
Accelerating 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
Local move MD
Local move MD
R4
R3
R1
R3
R4
R2
R2
R1
R3
R1
R2
R4
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 H20
And TFE mixed solvent
Elusive interactions:
Polarization and dispersion in condensed matter
Many situations where the
polarization (induction) and
dispersion interactions are
important
•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
.
.
SPC
SPC/E
SPC/Fw
PPC
TIP3/4/5P
+FQ
SWFLEX
GCPM
SWM4NDP
POL5-TZ
TTM-2
Six-site
QCT
.
.
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
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
The Halfway House: Quantum Drude Oscillators as
one-electron model potentials
VARIATIONAL MONTE CARLO
Optimization of trial wavefunction
Easiest to implement
Limited to accuracy of trial choice
Ground state T = 0
Harmonically-bound one
electron pseudo-atom
Accurately sampled QDO
forcefield will intrinsically
contain multipole and
dispersion interactions
PROJECTOR/DIFFUSION MONTE CARLO
Repeated operations to project/diffuse a trial state
to the ground state via stochastic trajectory
Leads to exact ground state (T=0) in principle
PATH INTEGRAL
QM-Classical Stat Mech isomorphism
Trace of thermal density matrix computed.
Finite temperature properties
Possible implementation with forces
converges to the ground state
wave function regardless of the choice of the
initial wave function
Implementation of Norm-conserving DMC for Quantum Drude Oscillators
Wick rotation for Schrodinger Eqn t ! it
Diffusion Equation
•Initial wavefunction represented by N “walkers”
PDF
•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
V(x)
FCC Solid Xenon
Variational
32 atoms
NC-DMC
IBM Research
Quantum Diffusion Monte Carlo
Norm Conservation - Diagramatic  Expansions
Application to solid Xe
Jones, Mueser, Martyna & Crain
Phys. Rev. B 2009, 79, 144119
Ground state energy and bulk modulus for FCC Xenon
Bulk modulus within 3-10 % of experimental value (depending
on estimates of nuclear quantum effects)
BWLSL potential is > 22% too high
Expt.
 E ¼ ZPE
BWLSL
Full QDO with NC-DMC + all pair multipole trial
IBM Research
Quantum Drude MD: Path integral sampling
Discrete path integral and classical isomorphism
Harmonic potential
depending on Trotter index
and T
Energy estimators:
from discretized path integral
Isomorphic to classical ring of P particles
Classical MD can be used to obtain quantum behavior
Beads are harmonically coupled by springs with
chain frequency P . Potential must not vary much over
Rms bond length.
IBM Research
Potential energy
Path Integral formulation for Quantum Drude MD
Full Quantum Drude
Xenon Melt
Molecular Dynamics
With Path integral
Sampling
•Dispersion included
•Many body
polarization included
IBM Research