Jason Crain School of Physics, University of Edinburgh, Edinburgh UK

1. Lengthscale Bridging in Biophysical Systems: Experiment and Simulation Jason Crain School of Physics, University of Edinburgh, Edinburgh UK National Physical Laboratory, London, UK

2. Project Outline Metal binding peptides Anti Microbial peptides TechnologyDrivers Viral inhibition Early amyloid formation Secondary structure control by solvent Models for membrane-mediated folding Design principles for compact domains Physical Science Questions Accuracy of empirical potential models Coarse-graining concepts in biology Structure – function relationships High-field NMR Replica Exchange MD Methodological Developments Synchrotron CD Quantum Drude MD Near and Intermediate Range Neutron diffraction

3. 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 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. Magainin activity against viruses, bacteria, protozoa, yeasts and fungi, and may be cytotoxic to cancer cells. Magainin

4. 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. Parallel Tempering Molecular Dynamics Metropolis Algorithm Local move MD Local move MD R4 R1 R3 R3 R2 R4 R2 R3 R1 R1 R4 R2

5. 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

6. 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

7. . . SPC SPC/E SPC/Fw PPC TIP3/4/5P +FQ SWFLEX GCPM SWM4-NDP POL5-TZ TTM-2 Six-site QCT . . 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

8. 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

9. Moments expansion for quantum harmonic atom: … for interaction • Polarizability to all orders • Non-additive induction beyond dipole limit • Dispersion included

10. 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 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 Harmonically-bound one electron pseudo-atom Accurately sampled QDO forcefield will intrinsically contain multipole and dispersion interactions converges to the ground state wave function regardless of the choice of the initial wave function

11. Implementation of Norm-conserving DMC for Quantum Drude Oscillators Wick rotation for Schrodinger Eqn t ! it Diffusion Equation • 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 PDF V(x)

12. Quantum Diffusion Monte Carlo Norm Conservation - Diagramatic  Expansions Application to solid Xe Jones, Mueser, Martyna & Crain Phys. Rev. B 2009, 79, 144119 FCC Solid Xenon Variational 32 atoms NC-DMC IBM Research

13. 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

14. Quantum Drude MD: Path integral sampling Discrete path integral and classical isomorphism Harmonic potential depending on Trotter index and T Potential energy from discretized path integral Energy estimators: 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

15. 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