SMA5233 SMA5233 Particle Methods and Molecular DynamicsParticle Methods and Molecular Dynamics

Lecture 1:Lecture 1: Introduction Introduction

A/P Chen Yu ZongA/P Chen Yu Zong

Tel: 6516-6877Tel: 6516-6877Email: Email: phacyz@nus.edu.sgphacyz@nus.edu.sg

http://http://bidd.nus.edu.sgbidd.nus.edu.sgRoom 08-14, level 8, S16 Room 08-14, level 8, S16

National University of SingaporeNational University of Singapore

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What is expected: What is expected:

To learn basic theory, algorithm of molecular To learn basic theory, algorithm of molecular simulations and their applicationssimulations and their applications

To learn the fundamentals in molecular To learn the fundamentals in molecular modelingmodeling

To practice the installation and use of related To practice the installation and use of related softwaresoftware

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Labs, Exams and Textbook: Labs, Exams and Textbook:

Projects and labs of part 1:Projects and labs of part 1:

Molecular dynamics software (12%).Molecular dynamics software (12%).

Simulation of biomolecular motions and dynamics Simulation of biomolecular motions and dynamics (12%).(12%).

ExamsExams (part 1: 26%) (part 1: 26%)

Text and web: Text and web: http://bidd.nus.edu.sg/group/teach/sma5233/sma5233.htmhttp://bidd.nus.edu.sg/group/teach/sma5233/sma5233.htm

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Topics covered in part 1: Topics covered in part 1:

Lecture 1: IntroductionLecture 1: Introduction

Lecture 2: Physical Principles and Design Issues Lecture 2: Physical Principles and Design Issues of MDof MD

Lecture 3: Force FieldsLecture 3: Force Fields

Lecture 4: Integration MethodsLecture 4: Integration Methods

Lecture 5: Applications in Biomolecular Simulation Lecture 5: Applications in Biomolecular Simulation and Drug Designand Drug Design

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Topics covered in part 2: Topics covered in part 2:

Lecture 6, introduction to Monte Carlo method, Lecture 6, introduction to Monte Carlo method, random number generatorsrandom number generators

Lecture 7, Some applications of MC methodLecture 7, Some applications of MC method

Lecture 8, Advanced MC methods, such as parallel Lecture 8, Advanced MC methods, such as parallel temperingtempering

Lecture 9, Brownian dynamics, stochastic differential Lecture 9, Brownian dynamics, stochastic differential equationsequations

Lecture 10, dissipative particle methodLecture 10, dissipative particle method

Lecture 11, smoothed particle hydrodynamicsLecture 11, smoothed particle hydrodynamics

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Reference Books for Part 1: Reference Books for Part 1: ""Molcular Modelling. Principles and Applications". Andrew Leach. Publisher: Prentice Hall. ISBN: Molcular Modelling. Principles and Applications". Andrew Leach. Publisher: Prentice Hall. ISBN: 0582382106. This book has rapidly become the defacto introductory text for all aspects of simulation. 0582382106. This book has rapidly become the defacto introductory text for all aspects of simulation.

"Molecular Dynamics Simulation: Elementary Methods". J.M. Haile. Publisher: Wiley. ISBN: "Molecular Dynamics Simulation: Elementary Methods". J.M. Haile. Publisher: Wiley. ISBN: 047118439X. This text provides a more focus but slightly more old-fashioned view of simulation. It 047118439X. This text provides a more focus but slightly more old-fashioned view of simulation. It has some nice simple examples of how to code (in fortran) some of the algorithmshas some nice simple examples of how to code (in fortran) some of the algorithms

P.W. Atkins Physical Chemistry (any edition) Chapters 11-14) P.W. Atkins Physical Chemistry (any edition) Chapters 11-14)

Schlick, T. Molecular Modeling and Simulation: An Interdisciplinary Guide. Springer-Verlag, New Schlick, T. Molecular Modeling and Simulation: An Interdisciplinary Guide. Springer-Verlag, New York, NY: 2002. ISBN 0-387-95404-X. York, NY: 2002. ISBN 0-387-95404-X.

MacKerell, A.D., Jr., Empirical Force Fields for Biological Macromolecules: Overview and Issues, MacKerell, A.D., Jr., Empirical Force Fields for Biological Macromolecules: Overview and Issues, Journal of Computational Chemistry, 25: 1584-1604, 2004 Journal of Computational Chemistry, 25: 1584-1604, 2004

M. P. Allen, D. J. Tildesley (1989) Computer simulation of liquids. Oxford University Press. ISBN M. P. Allen, D. J. Tildesley (1989) Computer simulation of liquids. Oxford University Press. ISBN 0198556454. 0198556454.

J. A. McCammon, S. C. Harvey (1987) Dynamics of Proteins and Nucleic Acids. Cambridge J. A. McCammon, S. C. Harvey (1987) Dynamics of Proteins and Nucleic Acids. Cambridge University Press. ISBN 0-52-135652-0 (paperback); ISBN 0-52-130750 (hardback). University Press. ISBN 0-52-135652-0 (paperback); ISBN 0-52-130750 (hardback).

D. C. Rapaport (1996) The Art of Molecular Dynamics Simulation. ISBN 0521445612. D. C. Rapaport (1996) The Art of Molecular Dynamics Simulation. ISBN 0521445612.

Daan Frenkel, Berend Smit (2001) Understanding Molecular Simulation. Academic Press. ISBN Daan Frenkel, Berend Smit (2001) Understanding Molecular Simulation. Academic Press. ISBN 0122673514. 0122673514.

J. M. Haile (2001) Molecular Dynamics Simulation: Elementary Methods. ISBN 047118439X J. M. Haile (2001) Molecular Dynamics Simulation: Elementary Methods. ISBN 047118439X

Oren M. Becker, Alexander D. Mackerell Jr, Benoît Roux, Masakatsu Watanabe (2001) Oren M. Becker, Alexander D. Mackerell Jr, Benoît Roux, Masakatsu Watanabe (2001) Computational Biochemistry and Biophysics. Marcel Dekker. ISBN 082470455X. Computational Biochemistry and Biophysics. Marcel Dekker. ISBN 082470455X.

Tamar Schlick (2002) Molecular Modeling and Simulation. Springer. ISBN 038795404X. Tamar Schlick (2002) Molecular Modeling and Simulation. Springer. ISBN 038795404X.

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Molecular Modeling: Goals, Problems, Molecular Modeling: Goals, Problems, PerspectivesPerspectives

1. 1. GoalGoal

simulate/predict simulate/predict processesprocesses such as such as

1.1. DNA migration in nanofluidic tubeDNA migration in nanofluidic tube

2.2. polypeptide foldingpolypeptide folding thermodynamic thermodynamic

3.3. biomolecular associationbiomolecular association equilibria governedequilibria governed

4.4. partitioning between solventspartitioning between solvents by by weakweak (nonbonded)(nonbonded)

5.5. membrane/micelle formationmembrane/micelle formation forcesforces

6.6. drug conformationdrug conformation

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Example of MD Application:Example of MD Application:How can an enzyme metabolite escape?How can an enzyme metabolite escape?

The enzyme acetylcholinesterase generates a strong electrostatic field that can attract the cationic substrate acetylcholine to the active site.

However, the long and narrow active site gorge seems inconsistent with the enzyme's high catalytic rate.

E + S E + P

How does the metabolite P escape?

Acetylcholinesterase (AChE) is the enzyme responsible for the termination of signaling in cholinergic synapses (such as the neuromuscular junction) by degrading the neurotransmitter acetylcholine. AChE has a gorge, 2 nm deep, leading to the catalytic site

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How can an enzyme metabolite escape?How can an enzyme metabolite escape?

Metabolite unlikely escape from the entrance

How can it escape?

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How can an enzyme metabolite escape?How can an enzyme metabolite escape?

How can it escape?

Can you tell which of the following possibilities is likely or unlikely, and why?

Protein unfolding

Condensation of ions on protein surface to counter-balance the force

Change of electric charge on metabolite

Alternative escape route

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How can an enzyme metabolite escape?How can an enzyme metabolite escape?

Alternative route

An “open back door” policy:

Transient opening of a channel to allow the metabolite to escape

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MD simulation of acetylcholinesterase MD simulation of acetylcholinesterase

MD simulation clearly reveals transient opening of a channel “back door”

Science 263, 1276-1278 (1994)

The open “back door”allows the metabolite Pto escape

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Molecular Modeling: Goals, Problems, Molecular Modeling: Goals, Problems, PerspectivesPerspectives

1. 1. GoalGoal Common characteristics:Common characteristics:

- Degrees of freedom:Degrees of freedom: atomic, coarse-grain atomic, coarse-grain

(solute + solvent) (solute + solvent) Hamiltonian orHamiltonian or - Equations of motion:Equations of motion: classical dynamicsclassical dynamics force fieldforce field- Governing theory:Governing theory: statistical mechanicsstatistical mechanics entropyentropy

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Processes: Thermodynamic EquilibriumProcesses: Thermodynamic EquilibriumFolding Micelle Formation

Complexation Partitioning

folded/native denatured micelle mixture

bound unbound in membrane in water in mixtures

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Definition of a model for molecular simulation

MOLECULARMODEL

Degrees of freedom: atoms are the elementary particles

Forces or interactions between atoms Boundary conditions

Methods for generating

configurations of atoms: Newton

systemtemperature

pressure

Every molecule consists of atoms that are very strongly bound to each other

Force Field =physicochemical

knowledge

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Molecular Modeling: Goals, Problems, Molecular Modeling: Goals, Problems, PerspectivesPerspectives

Four ProblemsFour Problems

1.1. Force fieldForce field

AA very small (free) energy very small (free) energy differencesdifferences

BB entropic effects entropic effects

CC size problem size problem

2.2. Search problemSearch problem

AA the search problem alleviatedthe search problem alleviated

BB the search problem aggravatedthe search problem aggravated

3.3. Ensemble problemEnsemble problem

4.4. Experimental problemExperimental problem

AA averaging averaging

BB insufficient accuracy insufficient accuracy

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Four ProblemsFour Problems1.1. The Force Field ProblemThe Force Field Problem

A A very small (free) energy differences (k very small (free) energy differences (kBBT = 2.5 kJ/mol)T = 2.5 kJ/mol)

resulting from summation over very many contributions (atoms)resulting from summation over very many contributions (atoms)

101066 – 10 – 1088 must be very accuratemust be very accurate

BB accounting for entropic effects accounting for entropic effects

not only energy minima are of not only energy minima are of

importance but whole range of importance but whole range of

xx-values-valueswith energies ~with energies ~kkBBTT

must be included in the must be included in the

force field parameter calibrationforce field parameter calibration

may have higher energybut lower free energythan

energyE(x)

coordinate x

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Four ProblemsFour ProblemsC C size problemsize problem

The larger the system, the more accurate the individual energy The larger the system, the more accurate the individual energy contributions (from atoms) must be to reach the same overall contributions (from atoms) must be to reach the same overall accuracyaccuracy

CCalibrate force field using alibrate force field using thermodynamicthermodynamic data for data for smallsmall molecules in molecules in the the condensedcondensed phase keep force field physical + simple phase keep force field physical + simple

transferable transferable

computablecomputable

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Choice of Model, Force Field, SamplingChoice of Model, Force Field, Sampling

3. 3. Scoring Function, Energy Function, Force FieldScoring Function, Energy Function, Force Field- Continuous Continuous Lattice Lattice - Basis for force field or scoring function:Basis for force field or scoring function:

1. 1. Structural dataStructural data

-- Large Large molecules: molecules: crystal structurescrystal structures

solution structures of proteinssolution structures of proteins

2. 2. Thermodynamic dataThermodynamic data

-- Small Small molecules:molecules: heat of vaporization, density heat of vaporization, density

in in condensed phasecondensed phase partition coefficients partition coefficients

, D, , D, etc.etc.

3. 3. Theoretical dataTheoretical data

- - SmallSmall molecules: molecules: electrostatic potential and gradientelectrostatic potential and gradient

in in gas phasegas phase torsion–angle rotation profilestorsion–angle rotation profiles

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Determination of Force Field ParametersDetermination of Force Field Parameters

2. 2. Polar MoleculesPolar Molecules

ethers, alcohols, esters, ketones,ethers, alcohols, esters, ketones,

acids, amines, amides, aromatics,acids, amines, amides, aromatics,

sulfides, thiols sulfides, thiols

methanol

ethanol

2-propanol

butanol

Calibration sets of small molecules

1. Non-polar molecules 2. Polar molecules 3. Ionic molecules

Calibration set: 28 compounds

diethylether

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Determination of Force Field ParametersDetermination of Force Field Parameters

Calibration set: 28 compounds

ethylamine

1-butylamine

ethyldiamine

diethylamine

n-methylacetamide

acetone

2-butanone

3-pentanone

acetic acid

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Applications of Molecular Simulation in Applications of Molecular Simulation in (Bio)Chemistry and Physics(Bio)Chemistry and Physics

1.1. Types of SystemsTypes of Systems- liquidsliquids- solutionssolutions- electrolyteselectrolytes- polymerspolymers

- proteinsproteins- DNA, RNADNA, RNA- sugarssugars- other polymersother polymers

- membranesmembranes- crystalscrystals- glassesglasses- zeoliteszeolites- metalsmetals- ……

2. 2. Types of ProcessesTypes of Processes

- meltingmelting

- adsorptionadsorption

- segregationsegregation

- complex formationcomplex formation

- protein foldingprotein folding

- order-disorder order-disorder transitionstransitions

- crystallisationcrystallisation

- reactionsreactions

- protein stabilisationprotein stabilisation

- membrane membrane permeationpermeation

- membrane formationmembrane formation

- ……

3. 3. Types of PropertiesTypes of Properties

- structuralstructural

- mechanicalmechanical

- dynamicaldynamical

- thermodynamicalthermodynamical

- electricelectric

- ……

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ObjectivesObjectives

Characterization of the populated microscopic states of molecules by Characterization of the populated microscopic states of molecules by molecular dynamics of spontaneous reversible motions in solution molecular dynamics of spontaneous reversible motions in solution

Investigate the effect of Investigate the effect of Thermodynamic conditionsThermodynamic conditionsSolvent environmentSolvent environmentAmino acid composition, chain lengthAmino acid composition, chain length

on the peptide folding behavioron the peptide folding behavior

Characterization of the unfolded state Characterization of the unfolded state

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Four ProblemsFour Problems4.4. The Experimental ProblemThe Experimental Problem

AA Any experiment involves Any experiment involves averaging averaging over over time time and and spacespace (molecules) (molecules)

So it determines the average of a distribution, So it determines the average of a distribution, notnot the distribution itself the distribution itself

However:However:

Very Very differentdifferent

distributions maydistributions may

yield yield samesame average average

Example: circular dichroism(CD)-spectra Example: circular dichroism(CD)-spectra -peptides -peptides

NOE’s + J-values of peptides inNOE’s + J-values of peptides in crystal crystal

solutionsolutionNOE: Nuclear Overhauser effect leads to changes in the intensity of signal(s) of a set of nuclei as a function of NOE: Nuclear Overhauser effect leads to changes in the intensity of signal(s) of a set of nuclei as a function of their respective distances. The use of NOE allows to obtain structural information on peptides and proteins in their respective distances. The use of NOE allows to obtain structural information on peptides and proteins in solution as well as the study of interactions between small ligands and biomolecules. solution as well as the study of interactions between small ligands and biomolecules.

probabilityP(Q)

quantity Q

(linear) average<Q>

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Four ProblemsFour Problems

NOE’s:NOE’s: are notoriously are notoriously insensitiveinsensitive to the (atom-atom-distance) to the (atom-atom-distance) distribution provided a small part satisfies the NOE boundsdistribution provided a small part satisfies the NOE bounds

J-values:J-values: may be sensitivemay be sensitive to dihedral angle distribution to dihedral angle distribution

X-ray:X-ray: crystalcrystal contains a much contains a much narrowernarrower distribution than a distribution than a (aqueous) (aqueous) solution solution

Experimental data cannot define a conformational ensembleExperimental data cannot define a conformational ensemble

BB Experimental data have Experimental data have insufficient accuracyinsufficient accuracy for force field calibration for force field calibration

and testingand testing

accuracy of NOE’s, J-values, structure factors, etc. is limited but may accuracy of NOE’s, J-values, structure factors, etc. is limited but may

improve with methodological and technical progressimprove with methodological and technical progress

Example: NMR data on beta-hexapeptide, alpha-octapeptideExample: NMR data on beta-hexapeptide, alpha-octapeptide

Experimental data may converge over time towards simulation results Experimental data may converge over time towards simulation results

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Molecular SimulationsMolecular Simulations

Molecular Mechanics: energy minimizationMolecular Mechanics: energy minimization

Molecular Dynamics: simulation of motionsMolecular Dynamics: simulation of motions

Monte Carlo methods: sampling techniquesMonte Carlo methods: sampling techniques

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What is molecular mechanics?What is molecular mechanics?

The term molecular mechanics refers to the use of Newtonian The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. mechanics to model molecular systems.

Molecular mechanics approaches are widely applied in Molecular mechanics approaches are widely applied in molecular structure refinement, molecular dynamics simulations, molecular structure refinement, molecular dynamics simulations, Monte Carlo simulations and ligand docking simulations. Monte Carlo simulations and ligand docking simulations.

Molecular mechanics can be used to study small molecules as Molecular mechanics can be used to study small molecules as well as large biological systems or material assemblies with well as large biological systems or material assemblies with many thousands to millions of atoms.many thousands to millions of atoms.

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What is molecular mechanics?What is molecular mechanics?

All-atomistic molecular mechanics methods have the All-atomistic molecular mechanics methods have the following properties:following properties:

– Each atom is simulated as a single hard spherical particle Each atom is simulated as a single hard spherical particle – Each such particle is assigned a radius (typically the van der Each such particle is assigned a radius (typically the van der

Waals radius) and a constant net charge (generally derived Waals radius) and a constant net charge (generally derived from high-level quantum calculations and/or experiment) from high-level quantum calculations and/or experiment)

– Bonded interactions are treated as "springs" with an Bonded interactions are treated as "springs" with an equilibrium distance equal to the experimental or calculated equilibrium distance equal to the experimental or calculated bond length bond length

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What is molecular mechanics?What is molecular mechanics?

Molecular Mechanics (MM) finds the geometry that Molecular Mechanics (MM) finds the geometry that corresponds to a minimum energy for the system - a corresponds to a minimum energy for the system - a process known as energy minimization. process known as energy minimization.

A molecular system will generally exhibit numerous A molecular system will generally exhibit numerous minima, each corresponding to a feasible conformation. minima, each corresponding to a feasible conformation. Each minimum will have a characteristic energy, which Each minimum will have a characteristic energy, which can be computed. The lowest energy, or global minimum, can be computed. The lowest energy, or global minimum, will correspond to the most likely conformation. will correspond to the most likely conformation.

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What is molecular dynamics simulation?What is molecular dynamics simulation?

Simulation that shows how the atoms in the Simulation that shows how the atoms in the system move with timesystem move with time

Typically on the nanosecond timescaleTypically on the nanosecond timescale

Atoms are treated like hard balls, and their Atoms are treated like hard balls, and their motions are described by Newton’s laws.motions are described by Newton’s laws.

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What is molecular dynamics simulation?What is molecular dynamics simulation?

Beginning in theoretical physics, the method of MD gained Beginning in theoretical physics, the method of MD gained popularity in material science and since the 1970s also in popularity in material science and since the 1970s also in biochemistry and biophysics. biochemistry and biophysics.

In chemistry, MD serves as an important tool in protein In chemistry, MD serves as an important tool in protein structure determination and refinement (see also structure determination and refinement (see also crystallography, NMR)crystallography, NMR)

In physics, MD is used to examine the dynamics of atomic-In physics, MD is used to examine the dynamics of atomic-level phenomena that cannot be observed directly, such as level phenomena that cannot be observed directly, such as thin film growth. It is also used to examine the physical thin film growth. It is also used to examine the physical properties of nanotechnology devices that have not or properties of nanotechnology devices that have not or cannot yet be created.cannot yet be created.

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What is molecular dynamics simulation?What is molecular dynamics simulation?Note that there is a large difference between the focus and Note that there is a large difference between the focus and methods used by chemists and physicists, and this is methods used by chemists and physicists, and this is reflected in differences in the jargon used by the different reflected in differences in the jargon used by the different fields.fields.

In Chemistry, the interaction between the objects is either In Chemistry, the interaction between the objects is either described by a force field (chemistry) (classical MD), a described by a force field (chemistry) (classical MD), a quantum chemical model, or a mix between the two. These quantum chemical model, or a mix between the two. These terms are not used in Physics, where the interactions are terms are not used in Physics, where the interactions are usually described by the name of the theory or usually described by the name of the theory or approximation being used.approximation being used.

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Why MD simulations?Why MD simulations?

Link physics, chemistry and biologyLink physics, chemistry and biology

Model phenomena that cannot be observed Model phenomena that cannot be observed experimentallyexperimentally

Understand protein folding…Understand protein folding…

Access to thermodynamics quantities (free Access to thermodynamics quantities (free energies, binding energies,…)energies, binding energies,…)

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Molecular Dynamics SimulationsMolecular Dynamics Simulations

Schrödinger equation

Born-Oppenheimer approximation

Nucleic motion described classically

Empirical force field

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Molecular Dynamics Simulations

Interatomic interactions

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Molecular dynamics Simulations of Biopolymers

• Motions of nuclei are described classically, .N,...,),,...,(Edt

dm)( Nela 112

2

RRR

• Potential function Eel describes the electronic influence on motions of the nuclei and is approximated empirically „classical MD“:

...,)EEE(EEEE vdW,

.rep,

.Coul,

kwinkelDihedral

dihek

iBindungen

jwinkelBindungs

anglej

bondiel

approximated

exact

Eibond

|R|0

KBT {

Covalent bonds Non-bonded interactions

==R

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Computational task:

Solve the Newtonian equations of motion:

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Molecular dynamics is very expensive ... Example: F1-ATPase in water (183 674 atoms), 1 nanosecond:

106 integration steps

8.4 * 1011 flop per step [n(n-1)/2 interactions]

total: 8.4 * 1017 flop

on a 100 MFLOPS workstation: 250 years

...but performance has been improved by use of:

multiple time stepping 25 years

+ structure adapted multipole methods 6 years

+ FAMUSAMM 2 years

+ parallel computers 55 days

• FLOPS : Floating Point Operations Per Second on a standard benchmark such as LINPACK benchmark

• Many other factors affect computation speed: I/O, inter-processor communication, cache coherence, memory hierarchy.

• Typical systems: 2GHz Pentium 4 (few GFLOPS); IBM Blue Gene/L 131,072 processors (207.3 TFLOPS); SETI@home (100 TFLOPS); Pocket calculator (10 FLOPS); Human (milliFLOPS)

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Limits of MD-Simulations

• Classical description: Chemical reactions not described Poor description of H-atoms (proton-transfer) Poor description of low-T (quantum) effects Simplified electrostatic model Simplified force field

• Only small systems accessible (104 ... 106 atoms)

• Only short time spans accessible (ps ... μs)

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MD as a tool for minimizationMD as a tool for minimization

Energy

positionEnergy minimizationstops at local minima

Molecular dynamicsuses thermal energyto explore the energysurface

State A

State B

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Crossing energy barriers

A

B

I

G

Position

En

erg

y

time

Po

siti

on

State A

State B

The actual transition time from A to B is very quick (a few pico seconds).

What takes time is waiting. The average waiting time for going from A to B can beexpressed as:

kT

G

BA Ce