DOCSLIB.ORG

Computational Biophysics: Introduction

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Computational Biophysics: Introduction Computational Biophysics: Introduction Bert de Groot, Jochen Hub, Helmut Grubmüller Max Planck-Institut für biophysikalische Chemie Theoretische und Computergestützte Biophysik Am Fassberg 11 37077 Göttingen Tel.: 201-2308 / 2314 / 2301 / 2300 (Secr.) Email: [email protected] [email protected] [email protected] www.mpibpc.mpg.de/grubmueller/ Chloroplasten, Tylakoid-Membran From: X. Hu et al., PNAS 95 (1998) 5935 Primary steps in photosynthesis F-ATP Synthase 20 nm F1-ATP(synth)ase ATP hydrolysis drives rotation of γ subunit and attached actin filament F1-ATP(synth)ase NO INERTIA! Proteins are Molecular Nano-Machines ! Elementary steps: Conformational motions Overview: Computational Biophysics: Introduction L1/P1: Introduction, protein structure and function, molecular dynamics, approximations, numerical integration, argon L2/P2: Tertiary structure, force field contributions, efficient algorithms, electrostatics methods, protonation, periodic boundaries, solvent, ions, NVT/NPT ensembles, analysis L3/P3: Protein data bank, structure determination by NMR / x-ray; refinement L4/P4: Monte Carlo, normal mode analysis, principal components L5/P5: Bioinformatics: sequence alignment, Structure prediction, homology modelling L6/P6: Charge transfer & photosynthesis, electrostatics methods L7/P7: Aquaporin / ATPase: two examples from current research Overview: Computational Biophysics: Concepts & Methods L08/P08: MD Simulation & Markov Theory: Molecular Machines L09/P09: Free energy calculations: Molecular recognition L10/P10: Non-equilibrium thermodynamics: Molecular driving forces L11/P11: Quantum mechanics methods: Enzymatic catalysis L12/P12: Hartree-Fock, density functional theory L13/P13: Rate theory: Biomolecular efficiency a water molecule an ethanol molecule a water droplet a water droplet water vapor a salt crystal (NaCl) bovine pancreatic trypsin inhibitor (BPTI) 20 different amino acids Threonine Asparagine Glutamate Alanine Proline Histidine Isoleucine Arginine Valine Lysine Glycine Serine Phenylalanine Aspartate Leucine Glutamine Methionine Tyrosine Tryptophane Cysteine hexa-peptide alpha-helix beta sheet bovine pancreatic trypsin inhibitor (BPTI) myoglobin antibody IGG domain porin bacteriorhodopsin Four different nucleotides encode amino acids (à Uracil) ? hemagglutinin (influenza virus) hemagglutinin (influenza virus) Molecular Dynamics Simulations Interatomic interactions Molecular Dynamics Simulation Molecule: (classical) N-particle system Newtonian equations of motion: with Integrate numerically via the „leapfrog“ scheme: with Δt ≈ 1fs! (equivalent to the Verlet algorithm) MD-Experiments with Argon Gas Radial distribution function distance 300 K 70 K 10 K Molecular Dynamics Simulations Schrödinger equation i~@t (r, R)=H (r, R) Born-Oppenheimer approximation He e(r; R)=Ee(R) e(r; R) Nucleic motion described classically Empirical Force field 1 Molecular dynamics-(MD) simulations of Biopolymers • Motions of nuclei are described classically, • Potential function Eel describes the electronic influence on motions of the nuclei and is approximated empirically à „classical MD“: Covalent bonds Non-bonded interactions bond Ei approximated exact = K T { B R= ν0 |R| Molecular Dynamics Simulation Molecule: (classical) N-particle system Newtonian equations of motion: with Integrate numerically via the „leapfrog“ scheme: with Δt ≈ 1fs! (equivalent to the Verlet algorithm) „Force- Field“ Computational task: Solve the Newtonian equations of motion: BPTI: Molecular Dynamics (300K) 8 4 nm Molecular dynamics simulation, 1s = ^ 2 ·10 -11s.
Load more

Recommended publications
  • Using Constrained Density Functional Theory to Track Proton Transfers and to Sample Their Associated Free Energy Surface
    Using Constrained Density Functional Theory to Track Proton Transfers and to Sample Their Associated Free Energy Surface Chenghan Li and Gregory A. Voth* Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, University of Chicago, Chicago, IL, 60637 Keywords: free energy sampling, proton transport, density functional theory, proton transfer ABSTRACT: The ab initio molecular dynamics (AIMD) and quantum mechanics/molecular mechanics (QM/MM) methods are powerful tools for studying proton solvation, transfer, and transport processes in various environments. However, due to the high computational cost of such methods, achieving sufficient sampling of rare events involving excess proton motion – especially when Grotthuss proton shuttling is involved – usually requires enhanced free energy sampling methods to obtain informative results. Moreover, an appropriate collective variable (CV) that describes the effective position of the net positive charge defect associated with an excess proton is essential for both tracking the trajectory of the defect and for the free energy sampling of the processes associated with the resulting proton transfer and transport. In this work, such a CV is derived from first principles using constrained density functional theory (CDFT). This CV is applicable to a broad array of proton transport and transfer processes as studied via AIMD and QM/MM simulation. 1 INTRODUCTION The accurate and efficient delineation of proton transport (PT) and
    [Show full text]
  • Molecular Dynamics Simulations in Drug Discovery and Pharmaceutical Development
    processes Review Molecular Dynamics Simulations in Drug Discovery and Pharmaceutical Development Outi M. H. Salo-Ahen 1,2,* , Ida Alanko 1,2, Rajendra Bhadane 1,2 , Alexandre M. J. J. Bonvin 3,* , Rodrigo Vargas Honorato 3, Shakhawath Hossain 4 , André H. Juffer 5 , Aleksei Kabedev 4, Maija Lahtela-Kakkonen 6, Anders Støttrup Larsen 7, Eveline Lescrinier 8 , Parthiban Marimuthu 1,2 , Muhammad Usman Mirza 8 , Ghulam Mustafa 9, Ariane Nunes-Alves 10,11,* , Tatu Pantsar 6,12, Atefeh Saadabadi 1,2 , Kalaimathy Singaravelu 13 and Michiel Vanmeert 8 1 Pharmaceutical Sciences Laboratory (Pharmacy), Åbo Akademi University, Tykistökatu 6 A, Biocity, FI-20520 Turku, Finland; ida.alanko@abo.fi (I.A.); rajendra.bhadane@abo.fi (R.B.); parthiban.marimuthu@abo.fi (P.M.); atefeh.saadabadi@abo.fi (A.S.) 2 Structural Bioinformatics Laboratory (Biochemistry), Åbo Akademi University, Tykistökatu 6 A, Biocity, FI-20520 Turku, Finland 3 Faculty of Science-Chemistry, Bijvoet Center for Biomolecular Research, Utrecht University, 3584 CH Utrecht, The Netherlands; [email protected] 4 Swedish Drug Delivery Forum (SDDF), Department of Pharmacy, Uppsala Biomedical Center, Uppsala University, 751 23 Uppsala, Sweden; [email protected] (S.H.); [email protected] (A.K.) 5 Biocenter Oulu & Faculty of Biochemistry and Molecular Medicine, University of Oulu, Aapistie 7 A, FI-90014 Oulu, Finland; andre.juffer@oulu.fi 6 School of Pharmacy, University of Eastern Finland, FI-70210 Kuopio, Finland; maija.lahtela-kakkonen@uef.fi (M.L.-K.); tatu.pantsar@uef.fi
    [Show full text]
  • Molecular Dynamics Study of the Stress–Strain Behavior of Carbon-Nanotube Reinforced Epon 862 Composites R
    Materials Science and Engineering A 447 (2007) 51–57 Molecular dynamics study of the stress–strain behavior of carbon-nanotube reinforced Epon 862 composites R. Zhu a,E.Pana,∗, A.K. Roy b a Department of Civil Engineering, University of Akron, Akron, OH 44325, USA b Materials and Manufacturing Directorate, Air Force Research Laboratory, AFRL/MLBC, Wright-Patterson Air Force Base, OH 45433, USA Received 9 March 2006; received in revised form 2 August 2006; accepted 20 October 2006 Abstract Single-walled carbon nanotubes (CNTs) are used to reinforce epoxy Epon 862 matrix. Three periodic systems – a long CNT-reinforced Epon 862 composite, a short CNT-reinforced Epon 862 composite, and the Epon 862 matrix itself – are studied using the molecular dynamics. The stress–strain relations and the elastic Young’s moduli along the longitudinal direction (parallel to CNT) are simulated with the results being also compared to those from the rule-of-mixture. Our results show that, with increasing strain in the longitudinal direction, the Young’s modulus of CNT increases whilst that of the Epon 862 composite or matrix decreases. Furthermore, a long CNT can greatly improve the Young’s modulus of the Epon 862 composite (about 10 times stiffer), which is also consistent with the prediction based on the rule-of-mixture at low strain level. Even a short CNT can also enhance the Young’s modulus of the Epon 862 composite, with an increment of 20% being observed as compared to that of the Epon 862 matrix. © 2006 Elsevier B.V. All rights reserved. Keywords: Carbon nanotube; Epon 862; Nanocomposite; Molecular dynamics; Stress–strain curve 1.
    [Show full text]
  • FORCE FIELDS for PROTEIN SIMULATIONS by JAY W. PONDER
    FORCE FIELDS FOR PROTEIN SIMULATIONS By JAY W. PONDER* AND DAVIDA. CASEt *Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 51. Louis, Missouri 63110, and tDepartment of Molecular Biology, The Scripps Research Institute, La Jolla, California 92037 I. Introduction. ...... .... ... .. ... .... .. .. ........ .. .... .... ........ ........ ..... .... 27 II. Protein Force Fields, 1980 to the Present.............................................. 30 A. The Am.ber Force Fields.............................................................. 30 B. The CHARMM Force Fields ..., ......... 35 C. The OPLS Force Fields............................................................... 38 D. Other Protein Force Fields ....... 39 E. Comparisons Am.ong Protein Force Fields ,... 41 III. Beyond Fixed Atomic Point-Charge Electrostatics.................................... 45 A. Limitations of Fixed Atomic Point-Charges ........ 46 B. Flexible Models for Static Charge Distributions.................................. 48 C. Including Environmental Effects via Polarization................................ 50 D. Consistent Treatment of Electrostatics............................................. 52 E. Current Status of Polarizable Force Fields........................................ 57 IV. Modeling the Solvent Environment .... 62 A. Explicit Water Models ....... 62 B. Continuum Solvent Models.......................................................... 64 C. Molecular Dynamics Simulations with the Generalized Born Model........
    [Show full text]
  • Force Fields for MD Simulations
    Force Fields for MD simulations • Topology/parameter files • Where do the numbers an MD code uses come from? • How to make topology files for ligands, cofactors, special amino acids, … • How to obtain/develop missing parameters. • QM and QM/MM force fields/potential energy descriptions used for molecular simulations. The Potential Energy Function Ubond = oscillations about the equilibrium bond length Uangle = oscillations of 3 atoms about an equilibrium bond angle Udihedral = torsional rotation of 4 atoms about a central bond Unonbond = non-bonded energy terms (electrostatics and Lenard-Jones) Energy Terms Described in the CHARMm Force Field Bond Angle Dihedral Improper Classical Molecular Dynamics r(t +!t) = r(t) + v(t)!t v(t +!t) = v(t) + a(t)!t a(t) = F(t)/ m d F = ! U (r) dr Classical Molecular Dynamics 12 6 &, R ) , R ) # U (r) = . $* min,ij ' - 2* min,ij ' ! 1 qiq j ij * ' * ' U (r) = $ rij rij ! %+ ( + ( " 4!"0 rij Coulomb interaction van der Waals interaction Classical Molecular Dynamics Classical Molecular Dynamics Bond definitions, atom types, atom names, parameters, …. What is a Force Field? In molecular dynamics a molecule is described as a series of charged points (atoms) linked by springs (bonds). To describe the time evolution of bond lengths, bond angles and torsions, also the non-bonding van der Waals and elecrostatic interactions between atoms, one uses a force field. The force field is a collection of equations and associated constants designed to reproduce molecular geometry and selected properties of tested structures. Energy Functions Ubond = oscillations about the equilibrium bond length Uangle = oscillations of 3 atoms about an equilibrium bond angle Udihedral = torsional rotation of 4 atoms about a central bond Unonbond = non-bonded energy terms (electrostatics and Lenard-Jones) Parameter optimization of the CHARMM Force Field Based on the protocol established by Alexander D.
    [Show full text]
  • The Fip35 WW Domain Folds with Structural and Mechanistic Heterogeneity in Molecular Dynamics Simulations
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Biophysical Journal Volume 96 April 2009 L53–L55 L53 The Fip35 WW Domain Folds with Structural and Mechanistic Heterogeneity in Molecular Dynamics Simulations Daniel L. Ensign and Vijay S. Pande* Department of Chemistry, Stanford University, Stanford, California ABSTRACT We describe molecular dynamics simulations resulting in the folding the Fip35 Hpin1 WW domain. The simulations were run on a distributed set of graphics processors, which are capable of providing up to two orders of magnitude faster compu- tation than conventional processors. Using the Folding@home distributed computing system, we generated thousands of inde- pendent trajectories in an implicit solvent model, totaling over 2.73 ms of simulations. A small number of these trajectories folded; the folding proceeded along several distinct routes and the system folded into two distinct three-stranded b-sheet conformations, showing that the folding mechanism of this system is distinctly heterogeneous. Received for publication 8 September 2008 and in final form 22 January 2009. *Correspondence: [email protected] Because b-sheets are a ubiquitous protein structural motif, tories on the distributed computing environment, Folding@ understanding how they fold is imperative in solving the home (5). For these calculations, we utilized graphics pro- protein folding problem. Liu et al. (1) recently made a heroic cessing units (ATI Technologies; Sunnyvale, CA), deployed set of measurements of the folding kinetics of 35 three- by the Folding@home contributors. Using optimized code, stranded b-sheet sequences derived from the Hpin1 WW individual graphics processing units (GPUs) of the type domain.
    [Show full text]
  • Introduction to Computational Chemistry: Molecular Dynamics
    Introduction to Computational Chemistry: Molecular Dynamics Alexander B. Pacheco User Services Consultant LSU HPC & LONI [email protected] LSU HPC Training Series Louisiana State University April 27, 2011 High Performance Computing @ Louisiana State University - http://www.hpc.lsu.edu April 27, 2011 1/39 Outline 1 Tutorial Goals 2 Introduction 3 Molecular Dynamics 4 Fundamentals of Molecular Dynamics 5 Ab Initio Molecular Dynamics Theory 6 Computational Chemistry Programs 7 Example Jobs High Performance Computing @ Louisiana State University - http://www.hpc.lsu.edu April 27, 2011 2/39 Tutorial Goals Cover the fundamentals of Molecular Dynamics Simulation: Ab-Initio and Classical. Expose researchers to the theory and computational packages used for MD simulations. Worked out examples for various computational packages such as CPMD, Gaussian, GAMESS and NWCHEM. Linux machines, LONI and LSU HPC at /home/apacheco/CompChem. Go ahead with the examples if you want but hold off all questions until tutorial is complete. My Background: Ab-Initio Molecular Dynamics. Questions about examples/tutorials and/or using Electronic Structure codes for AIMD, email me at [email protected] or [email protected] High Performance Computing @ Louisiana State University - http://www.hpc.lsu.edu April 27, 2011 3/39 What is Computational Chemistry Computational Chemistry is a branch of chemistry that uses principles of computer science to assist in solving chemical problems. Uses the results of theoretical chemistry, incorporated into efficient computer programs. Application to single molecule, groups of molecules, liquids or solids. Calculates the structure and properties such as relative energies, charge distributions, dipole and multipole moments, spectroscopy, reactivity, etc.
    [Show full text]
  • Molecular Dynamics Simulations
    LECTURE 6 : BASICS FOR MOLECULAR SIMULATIONS - Historical perspective - Skimming over Statistical Mechanics - General idea of Molecular Dynamics - Force calculations, structure of MD, equations of motion - Statistical Ensembles [email protected] Atomic modeling of glass – LECTURE4 MD BASICS What we want to avoid … Computing the radial distribution function of vitreous SiO 2 from a ball and stick model Bell and Dean, 1972 [email protected] Atomic modeling of glass – LECTURE4 MD BASICS 1972 … and the historical perspective of molecular simulations ~1900 Concept of force field in the analysis of spectroscopy 1929 Model vibrationl excitations: atomic potentials (P.M. Morse and J.E. Lennard- Jones ) 1937 London dispersion forces due to polarisation (origin Van der Waals forces), 1946 Molecular Mechanics: use of Newton’s equations and force fields for the caracterization of molecular conformations 1953 Monte Carlo simulations after the Manhattan project (1943): computation of thermodynamic properties (Metropolis, Van Neuman, Teller, Fermi ) 1957 Hard sphere MD simulations (Alder-Wainwright) : Potential non-differentiable, no force calculations, free flight during collisions, momentum balance. Event-driven algorithms [email protected] Atomic modeling of glass – LECTURE4 MD BASICS 1964 LJ MD of liquid Argon (Rahman): differentiable potential, solve Newton’s equation of motion, accurate trajectories. Contains already the main ingredients of modern simulations 1970s Simulation of liquids (water, molten salts and metals,…)
    [Show full text]
  • Molecular Dynamics Simulation of Proteins: a Brief Overview
    Chem cal ist si ry y & h P B f i o o Patodia et al., J Phys Chem Biophys 2014, 4:6 p l h a Journal of Physical Chemistry & y n s r DOI: 10.4172/2161-0398.1000166 i u c o s J ISSN: 2161-0398 Biophysics ReviewResearch Article Article OpenOpen Access Access Molecular Dynamics Simulation of Proteins: A Brief Overview Sachin Patodia1, Ashima Bagaria1* and Deepak Chopra2* 1Centre for Converging Technologies, University of Rajasthan, Jaipur 302004, Rajasthan, India 2Department of Chemistry, Indian Institute of Science Education and Research, Bhopal 462066, India Abstract MD simulation has become an essential tool for understanding the physical basis of the structure of proteins and their biological functions. During the current decade we witnessed significant progress in MD simulation of proteins with advancement in atomistic simulation algorithms, force fields, computational methods and facilities, comprehensive analysis and experimental validation, as well as integration in wide area bioinformatics and structural/systems biology frameworks. In this review, we present the methodology on protein simulations and recent advancements in the field. MD simulation provides a platform to study protein–protein, protein–ligand and protein–nucleic acid interactions. MD simulation is also done with NMR relaxation timescale in order to get residual dipolar coupling and order parameter of protein molecules. Keywords: Molecular dynamics simulation; Force field; Residual dynamics simulations provide connection between structure and dipolar coupling; Orders
    [Show full text]
  • Unified Approach for Molecular Dynamics and Density-Functional Theory
    VOLUME 55, NUMBER 22 PHYSICAL REVIEW LETTERS 25 NOVEMBER 1985 Unified Approach for Molecular Dynamics and Density-Functional Theory R. Car International School for Advanced Studies, Trieste, Italy and M. Parrinello Dipartimento di Fisica Teorica, Universita di Trieste, Trieste, Italy, and International School for Advanced Studies, Trieste, Italy (Received 5 August 1985) We present a unified scheme that, by combining molecular dynamics and density-functional theory, profoundly extends the range of both concepts. Our approach extends molecular dynamics beyond the usual pair-potential approximation, thereby making possible the simulation of both co- valently bonded and metallic systems. In addition it permits the application of density-functional theory to much larger systems than previously feasible. The new technique is demonstrated by the calculation of some static and dynamic properties of crystalline silicon within a self-consistent pseu- dopotential framework. PACS numbers: 71.10.+x, 65.50.+m, 71.45.Gm Electronic structure calculations based on density- very large and/or disordered systems and to the com- functional (DF) theory' and finite-temperature com- putation of interatomic forces for MD simulations. puter simulations based on molecular dynamics (MD) We wish to present here a new method that is able have greatly contributed to our understanding of to overcome the above difficulties and to achieve the condensed-matter systems. MD calculations are able following results: (i) compute ground-state electronic to predict equilibrium and nonequilibrium properties properties of large andlor disordered systems at the of condensed systems. However, in all practical appli- level of state-of-the-art electronic structure calcula- cations MD calculations have used empirical intera- tions; (ii) perform ah initio MD simulations where the tomic potentials.
    [Show full text]
  • Dynamics of Proteins Predicted by Molecular Dynamics Simulations and Analytical Approaches: Application to ␣-Amylase Inhibitor
    PROTEINS: Structure, Function, and Genetics 40:512–524 (2000) Dynamics of Proteins Predicted by Molecular Dynamics Simulations and Analytical Approaches: Application to ␣-Amylase Inhibitor Pemra Doruker, Ali Rana Atilgan, and Ivet Bahar* Polymer Research Center, School of Engineering, Bogazici University, and TUBITAK Advanced Polymeric Materials Research Center, Bebek, Istanbul, Turkey ABSTRACT The dynamics of ␣-amylase inhibi- INTRODUCTION tors has been investigated using molecular dynam- ics (MD) simulations and two analytical approaches, The biological function of proteins is generally controlled the Gaussian network model (GNM) and anisotropic by cooperative motions or correlated fluctuations involving 1–5 network model (ANM). MD simulations use a full large portions of the structure. There exists a multitude atomic approach with empirical force fields, while of computational methods in the literature for identifying 1,3,6–17 the analytical approaches are based on a coarse- the dominant correlated motions in macromolecules. grained single-site-per-residue model with a single- The basic approach common in these studies is to decom- parameter harmonic potential between sufficiently pose the dynamics into a collection of modes of motion, close (r < 7 Å) residue pairs. The major difference remove the “uninteresting” (fast) ones, and focus on a few between the GNM and the ANM is that no direc- low frequency/large amplitude modes which are expected tional preferences can be obtained in the GNM, all to be relevant to function. residue fluctuations being theoretically isotropic, A classical approach for determining the modes of while ANM does incorporate directional prefer- motion is the normal mode analysis (NMA). NMA has ences. The dominant modes of motions are identi- found widespread use in exploring proteins’ dynamics fied by (i) the singular value decomposition (SVD) of starting from the original work of Go and collaborators, the MD trajectory matrices, and (ii) the similarity two decades ago.
    [Show full text]
  • Download (PDF)
    Short Course on Molecular Dynamics Simulation Lecture 1: Basic Concepts Professor A. Martini Purdue University Course Objectives Awareness of the opportunities and limitations of MD simulation for scientific and engineering research Understanding of the compromise between model complexity/realism and computational expense Background that enables interpretation of MD studies reported in the literature Physical understanding of the theoretic basis of MD modeling Molecular Dynamics Simulation A. Martini Last Updated 8/2009 High Level Course Outline 1. MD Basics 2. Potential Energy Functions 3. Integration Algorithms 4. Temperature Control 5. Boundary Conditions 6. Neighbor Lists 7. Initialization and Equilibrium 8. Extracting Static Properties 9. Extracting Dynamic Properties 10. Non-Equilibrium MD Molecular Dynamics Simulation A. Martini Last Updated 8/2009 MD Basics Molecular dynamics (MD) simulation = computational tool used to describe how positions, velocities, and orientations of molecules change over time. The simulation is based on a set of models that describe molecular-scale interactions. These models relate energy/force to configuration which are be used to calculate acceleration via Newton’s law. Numerical integration yields particle velocities, and then each particle is moved through a distance equal to its calculated velocity multiplied by the simulation time step. So, MD is used as a computational “experiment” where a system is defined, allowed to evolve, and then observations made based on its evolution. Molecular Dynamics Simulation A. Martini Last Updated 8/2009 MD Basics Experiment MD Simulation Prepare Sample System of particles Connect Sample to Measuring Solve equations of motion Instrument Measure Property of Interest for Set Extract position and velocity data Time Interval Average to Minimize Use statistical mechanics to extract properties Statistical Noise Molecular Dynamics Simulation A.
    [Show full text]