Chem. 860 Molecular Simulations with Biophysical Applications Qiang Cui Department of Chemistry and Theoretical Chemistry Institute University of Wisconsin, Madison Spring, 2009

Topics Basic ideas of biomolecular simulations Empirical Force Fields Equilibrium simulations: Basic Molecular Dynamics and (some) Monte Carlo Non-equilibrium (time-dependent) properties Some specialized techniques (Car-Parrinello; QM/MM, Transition path sampling...) Current challenges (Multi-scale simulations) Goal: learn how to design and carry out proper simulations for biophysical applications

(Bio)molecular Simulations Evaluate analytic theories (solvation, rate, spectroscopy) Help better interpret complex experimental data in structural and dynamical terms (spectra, diffraction, NMR) In the absence of direct experimental data, observe the behavior of the system for mechanistic investigations or predictions Equilibrium properties (thermodynamics, average structure and fluctuation) Time-dependent properties (chemical reactions, conformational transitions/folding, diffusion) Karplus, Petsko, Nature, 347, 631 (1991); Karplus, McCammon, Nat. Struct. Biol. 9, 646 (2002) Use physical based techniques to numerically simulate the behavior of molecular systems

Unique power of simulations High spatial and temporal resolution Facilitate analysis of important factors for mechanistic investigations - easy to turn on and off specific contribution “High-throughput” rational design of new ligands, biomolecules or (e.g., mutation) experiments Obtain insights into processes difficult (or devastating) to do experimentally (Nuclear meltdown, galaxy collision) Ultimately: stimulate new experiments Observe - analyze (model building) - design

Example 1. Water channel de Groot, Grubmuller, Science, 294, 2353 (2001); E. Tajkhorshid et al. Science, 296, 525 (2002) “State-of-the-art” all-atom simulation: 100,000 atoms; ~100 ns

Example 1.2 K + channel Berneche et al. Roux, Nature, 414, 73 (2001); 431, 830 (2004)

Example 1.3 Real-Time-dependence Barrier (re)crossing PSU Benkovic, Hammes-Schiffer, Science, 301, 1196 (2003)

Example 2. Solvent effect on protein dynamics Vitkup, Ringe, Petsko, Karplus, Nat. Struct. Biol. 7, 34 (2000)

Example 2.2 Solvent effect on protein-ligand dynamics Loring et al. J. Phys. Chem. B 105, 4068 (2001)

Example 2.3 Diffuse IR band and proton storage site in bR Gerwert et al. Nature, 439, 109 (2006) QC et al. PNAS, 105, (2008) XH + bR

Ex 3. Rational Design of proteins and ligands ab initio design of a Novel fold Kuhlman et al., Baker, Science, 302, 1364 (2003) Incorporate catalytic function into proteins Dwyer et al., Hellinga, Science, 304, 1967 (2004)

Basic elements Potential Function (force field): how atoms in biomolecules ( ) interact with each other and how biomolecules interact with the environment ( ). Equilibrium statistical mechanics Non-equilibrium statistical mechanics (MD only) Molecular Dynamics (MD) Monte Carlo (stochastic)

Limitations Potential Energy Function (force field; QM level) Limited conformational/chemical (e.g., titration) sampling (requires smart techniques!) System finite size (depending on the range of interaction) Bottom line: Design proper simulation for your question! "when one microsecond is a long time" Y. Duan, P. A. Kollman, Science, 282, 740 (1998) 1  s RMSD ~ 3 Å

Limitations Potential Energy Function (force field; QM level) Limited conformational/chemical (e.g., titration) sampling (requires smart techniques!) System finite size (depending on the range of interaction) Bottom line: Design proper simulation for your question! Coarse-grained modelshttp://md.chem.rug.nl/~marrink/MOV/index.html