Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Protein Folding&BiospectroscopyLecture 5,F14PFB,David Robinson,Protein Folding,Introduction,Protein Structure,Interactions,Protein Folding Models,Biomolecular Modelling,Bioinformatics,Classical Molecular Dynamics Simulations of Proteins,“everything that living things do can be understood in terms of the jigglings and wigglings of atoms.,The Feynman Lectures in Physics vol.1,3-6(1963),What is Molecular Dynamics?,“The science of simulating the motions of a system of particles(Karplus&Petsko),From systems,As small as an atom,As large as a galaxy,Equations of motion,Time evolution,Why?,Essential Elements,Knowledge of the interaction potential for the particles Forces,Classical Newtonian equations of motion,Many particle systems simulation,Maxwell-Boltzmann averaging process for thermodynamic properties:time averaging,One particle,easy analytically,Many particles impossible analytically,Basis:Molecular Mechanics,Theoretical foundation,Potential energy functions,Energy minimization,Molecular dynamics,Uses of simulation&modelling,Conformational searching with MD and minimization,Exploration of biopolymer fluctuations and dynamics&kinetics,MD as an ensemble sampler,Free energy simulations,Example applications,Energy minimization as an estimator of binding free energies,Protein stability,Approximate association free energy of molecular assemblies,Approximate pKa calculations,Theoretical Foundations,Force field parameters for families of chemical compounds,System modelled using Newtons equations of motion,Examples:hard spheres simulations(Alder Villin headpiece(Duan&Kollman,1998),Protein Motion,Protein motions of importance are torsional oscillations about the bonds that link groups together,Substantial displacements of groups occur over long time intervals,Collective motions either local(cage structure)or rigid-body(displacement of different regions),What is the importance of these fluctuations for biological function?,Effect of fluctuations,Thermodynamics:equilibrium behaviour important;e.g.,energy of ligand binding,Dynamics:displacements from average structure important;e.g.,local sidechain motions that act as conformational gates in oxygen transport myoglobin,enzymes,ion channels,Local Motions,0.01-5,1 fs-0.1s,Atomic fluctuations,Small displacements for substrate binding in enzymes,Energy“source for barrier crossing and other activated processes(e.g.,ring flips),Sidechain motions,Opening pathways for ligand(myoglobin),Closing active site,Loop motions,Disorder-to-order transition as part of virus formation,Rigid-Body Motions,1-10,1 ns 1 s,Helix motions,Transitions between substates(myoglobin),Hinge-bending motions,Gating of active-site region(liver alcohol dehydrogenase),Increasing binding range of antigens(antibodies),Large Scale Motion,5,1 microsecond 10000 s,Helix-coil transition,Activation of hormones,Protein folding transition,Dissociation,Formation of viruses,Folding and unfolding transition,Synthesis and degradation of proteins,Role of motions sometimes only inferred from two or more conformations in structural studies,Typical Time Scales.,Bond stretching:10,-14,-10,-13,sec.,Elastic vibrations:10,-12,-10,-11,sec.,Rotations of surface sidechains:10,-11,-10,-10,sec.,Hinge bending:10,-11,-10,-7,sec.,Rotation of buried side chains:10,-4,-1 sec.,Protein folding:10,-6,-10,2,sec.,Timescale in MD:,A Typical timestep in MD is 1 fs(10,-15,sec)(ideally 1/10 of the highest frequency vibration),http:/ time for simulation 10,4,seconds,Typical time-step size 10,15,seconds,Number of MD time steps 10,11,Atoms in a typical protein and water simulation 32,000,Approximate number of interactions in force calculation 10,9,Machine instructions per force calculation 1000,Total number of machine instructions 10,23,BlueGene capacity(floating point operations per second)1 petaflop(,10,15,),Ab initio,protein folding simulation,Blue Gene will need 3 years to simulate 100,sec.,Empirical Force Fields and Molecular Mechanics,describe interaction of atoms or groups,the parameters are“empirical,i.e.they are dependent on others and have no direct intrinsic meaning,Bond stretching,Approximation of the Morse potential by an“elastic spring model,Hookes law as reasonable approximation close to reference bond length l0,l,k,:Force constant,l,:distance,Angle Bending,Deviation from angles from their reference angle,0,often described by Hookes law:,k,:Force constant,:bond angle,Force constants are much smaller than those for bond stretching,Torsional Terms,V,n,:barrier height,n,:multiplicity(e.g.n=3),:torsion angle,:phase factor,Need to include higher terms for non-symmetric bonds,(i.e.to distinguish trans,gauche conformations),Hypothetical potential function for rotation around a chemical bond:,Electrostatic interactions,Electronegative elements attract electrons more than less electronegative elements,Unequal charge distribution is