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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: [email protected]@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
22
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
33
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
44
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
55
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
66
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.
77
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
88
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
99
How can an enzyme metabolite escape?How can an enzyme metabolite escape?
Metabolite unlikely escape from the entrance
How can it escape?
1010
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
1111
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
1212
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
1313
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
1414
Processes: Thermodynamic EquilibriumProcesses: Thermodynamic EquilibriumFolding Micelle Formation
Complexation Partitioning
folded/native denatured micelle mixture
bound unbound in membrane in water in mixtures
1515
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
1717
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
1818
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
1919
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
2020
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
2121
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
2222
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
- ……
2323
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
2424
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>
2525
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
2626
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
2727
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.
2828
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
2929
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.
3030
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.
3131
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.
3232
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.
3333
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,…)
3434
Molecular Dynamics SimulationsMolecular Dynamics Simulations
Schrödinger equation
Born-Oppenheimer approximation
Nucleic motion described classically
Empirical force field
3535
Molecular Dynamics Simulations
Interatomic interactions
3636
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
3737
Computational task:
Solve the Newtonian equations of motion:
3838
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)
3939
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)
4040
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
4141
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