MD SIMULATION

Molecular Modeling and Drug Design

Dr. Puneet Kacker

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MD Simulation: Introduction

One of the principal tools in the theoretical study of biological molecules

Calculates the time dependent behavior of a molecular system

Provides detailed information on the fluctuations and conformational changes of proteins and nucleic acids

Used to investigate the structure, dynamicsand thermodynamics of biological molecules and their complexes

Reading Material: CHARMM Theory of MD Simulation

Time Scales Vs. Biological Process

ApplicationsProtein stabilityConformational changesProtein foldingMolecular recognition: proteins, DNA,

membranes, complexesIon transport in biological systems

Drug Design & Structure determination (X-ray and NMR)

Thermodynamics and Kinetics

Historical Background

First introduced by Alder and Wainwright by study of hard sphere interactions (1957) Rahman carried out the first simulation

using a realistic potential for liquid argon (1964)First protein simulations by McCammon

appeared in 1977 with the simulation of the bovine pancreatic trypsin inhibitor (BPTI)

Statistical MechanicsThe conversion of microscopic information

(e.g. atomic positions and velocities) to macroscopic observables (e.g. pressure, energy, heat capacities) requires statistical mechanics

Statistical mechanics provides the rigorous mathematical expressions that relate macroscopic properties to the distribution and motion of the atoms and molecules

Cont…

Relation??

Statistical Mechanics

Some DefinitionsThermodynamic state: of a system is usually

defined by a small set of parameters, e.g. the temperature– T, the pressure– P, and the number of particles– N

Mechanical or microscopic state: of a system is defined by the atomic positions– q, and momenta–p; these can also be considered as coordinates in a multidimensional space called phase space

Ensemble: is a collection of points in phase space satisfying the conditions of a particular thermodynamic state

An EnsembleAn ensemble is a collection of all possible systems which have different microscopic states but have an identical macroscopic or thermodynamic state.

There exist different ensembles with different characteristics

Classical MechanicsMD simulation method is based on Newton’s

second law of motion

Fi is the force exerted on particle i, mi is the mass of particle i and ai is the acceleration of particle i

Integration AlgorithmsThere is no analytical solution to the

equations of motion; they must be solved numerically

Numerous numerical algorithms have been developed for integrating the equations of motion– Verlet algorithm– Leap-frog algorithm– Velocity Verlet– Beeman’s algorithm

Setting up and Running MD Simulations

Potential Energy Function

Potential Energy is the energy of the object or a system due to the position of the body or arrangements of particles of the system

Some Function

InputAtomic Positions

OutputEnergy

Force FieldsBiological systems involve many atomsQuantum Mechanics not a feasible

methodPEF* are less computationally demandingNumerous approximations are introduced

which lead to certain limitationsProvides a reasonably good compromise

between accuracy and computational efficiency

*Potential Energy Functions

Cont…Often calibrated to experimental results

and quantum mechanical calculations of small model compoundsTheir ability to reproduce physical

properties measurable by experiment is testedThe development of parameter sets is a

very laborious task, requiring extensive optimization

Most commonly used potential energy functions

AMBER (Assisted Model Building with Energy Refinement)

CHARMM (Chemistry at HARvard Macromolecular Mechanics)

GROMOS (Groningen Molecular Simulation)

OPLS (Optimized Potentials for Liquid Simulations)/AMBER force fields

Force Field LimitationNo drastic changes in electronic structure are

allowed, i.e., no events like bond making or breaking can be modeled

SolutionMixed quantum mechanical - molecular

mechanical (QM/MM) method

Molecular Mechanics (MM)

Quantum Mechanics (QM)

The CHARMM Potential Energy Function

The energy, E, is a function of the atomic positions, R, of all the atoms in the systemAtomic Positions are usually expressed in

terms of Cartesian coordinates

Describes the bonds, angles and bond rotations in a molecule Describes the interactions between

nonbonded atoms or atoms separated by 3 or more covalent bonds

Ebonded

The Ebonded term is a sum of three terms:

1 2 3

Ebond-stretch

A harmonic potential representing the interaction between atomic pairs where atoms are separated by one covalent bond

Force constants Kb are specific for each pair of bound atoms, i.e. depend on chemical type of atoms-constituents

Ideal bond lengthForce constants

Values of force constant: from infrared stretching frequencies or from QM calculations. Values of bond length: from high resolution crystal structures or microwave spectroscopy data.

Ebond-bend

Associated with alteration of bond angles θ from ideal values θo

Kθ depends on chemical type of atoms constituting the angle

Ideal angle

Erotate-along-bond

Models the presence of steric barriers between atoms separated by 3 covalent bonds (1,4 pairs)

The motion associated with this term is a rotation, described by a dihedral angle and coefficient of symmetry n=1,2,3), around the middle bond

Function is assumed to be periodic and is often expressed as a cosine function

Coefficient of symmetry n=1,2,3)

Enon-bonded

Non-bonded interactions has two componentsSome other potential functions also include an

additional term to account for hydrogen bonds

Eelectrostatic

The electrostatic interaction between a pair of atoms is represented by Coulomb Potential

Effective dielectric function for the medium Distance between two

atoms having charges qiand qk

Evan-der-Waals

One of the most important interactions for the stability of the biological macromolecules

Modelled using the Lennard-Jones 6-12 potentialExpresses the interaction energy using the atom-type

dependent constants A and C

Force Field Limitations Fixed set of atom types for parameterizationAliphatic carbon atom in an sp3 bonding situation has different

properties than a carbon atom found in the His ring An approximation introduced to decrease the computational

demand is the pair-wise additive approximationThe simultaneous interaction between three or more atoms is

not calculated, so certain polarization effects are not explicitlyincluded in the force field

Potential energy function does not include entropic effectsE calculated as a sum of potential functions does not

necessarily correspond to the equilibrium, or the mostprobable state

MD Simulation Movies

MD Simulation Output

MD Simulation

Atomic Coordinates and Velocities

Analysis

X-axis

Y-axis

Conformations

Prop

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f Int

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All

Atom

RM

SDPo

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nerg

yRa

dius

of G

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ion

MD Simulation Packages

AMBERhttp://ambermd.org/

GROMACShttp://www.gromacs.org/

NAMDhttp://www.ks.uiuc.edu/Research/namd/

MD Simulation Analysis Packages

XMGrace (Plotting Tool)http://plasma-gate.weizmann.ac.il/Grace/

VMD (Trajectory Visualization and Plotting Tool)http://www.ks.uiuc.edu/Research/vmd/

Thanks!!

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