uef // university of eastern finland

UEF // University of Eastern Finland

Part 1, Basics of molecular model

Integrate Summer School, Espoo, Finland, 7.6.2016Prof. Antti Poso

Virtual Screening and Molecular Modeling


What is molecular modeling ?o Visualization

o Graphical presentations o 3D glasses, virtual room

o Generation of realistic models of moleculeso Plastic modelso Electrostatic maps

o Prediction of propertieso Reactivityo Spectrum

o Simulationo Movements

o Comparison with experiment

Molecular modeling methods are the theoretical methods and computational techniques used to simulate the behavior of molecules and molecular systems


Why Use Molecular Modeling?(and not deal directly with the real world?)

• Visualization– Easier to understand

• Fast, safe, accurate and cheap way to– Study molecular properties– Make predictions for yet unstudied systems– Design new molecules– Interpret experimental results


Database of small molecules

Database of proteins

DOCKING/ QSAR/VIRTUAL SCREENING

HITS

Experimental evaluation in vitro/in vivo


Molecular Modeling experiment

•Build Structures and define charges•Perform Computations: Force-‐‑field and quantum mechanical models

offer sophisticated descriptions of molecules, both known and unknown, docking fits small molecule into proteins

•Visualize and Interpret Results: Results include structure, energies, molecular orbitals, electron densities, vibrationalmodes, dynamicssimulations, interactions, etc.

•Recycle: Each answer often will lead to more questions and new calculations


General concepts on Molecular Modeling•On “atomistic” modeling

– molecules are a collection of charged particles: electrons and nuclei

•Several properties of molecule can be studied theoretically :– Geometry– Energetic properties– Conformations, charges, dipole momentum,...– Structure and function as function of time– Interactions with protein(docking and scoring)– Correlate molecular structure to biological activity: QSAR

(CoMFA)


Define charges

•To study the properties of molecules•Usually point charges are used

– The term ‘point charge’ is a mathematical abstraction

•The dimension of a point charge is small compared with the distance between them


Partial charges

•Atom A and atom B have different electronegativity (like H-‐‑F)

•When forming covalent bond: Atom B is more positively charged and atom A is more negatively charged.

•The partial charge on an atom in a molecule depends on how this electron density is partitioned among the atoms

•crucial for:– hydrogen bonding– ionic bonding– dipole bonding

A B


Partial Charges


Partial charges

•Need for accurate determination of molecular electron distribution in 3D-‐‑space– often described using point charges, which are generated for atoms in the

system• Position at the atomic center

– are important when calculating molecular properties• electrostatic potentialmaps etc.

• two methodologically absolutely different approaches– topological procedures

• Gasteiger, Gasteiger-‐‑Hückel, MMFF94– quantum chemical wave function based methods

• ESP, Mulliken


Examples of charges


Computational Approaches

Atomistic Continuum

Finite Periodic

Quantum MechanicalMethods ClassicalMethods

Semi-‐‑Empirical Ab Initio

Quantum MC DFT Hartree-‐‑Fock QM/MM

Deterministic Stochastic

Monte-‐‑CarloMolecularDynamics

MolecularMechanisc


Level of theory

Computational methods Molecule sizeMolecular mechanics 1 000 000 atomsSemi-‐‑empiricalmethods up 1000 atomsAb initio Quantummechanics up 200 atomsCorrelated Quantummechanics

up 50 atoms

Correlated, relativisticQuantummechanics

Up 20 atoms

Decreas

ingtim

e

Increa

sing

accu

racy


Quantum Mechanics

– Most fundamental theoretical approach– Schrödinger equation: HΨ= EΨ

• H is Hamilton operator– Electrons and nuclei– Kinetic and potential energy

• Ψ is wave function– Position ( and momentum) of particles


Semi-‐‑empirical approach: Hartree-‐‑Fock equations are iteratively solved, consideringonly the valence electrons. Common methods: MNDO, AM1 and PM3.

DFT (Density Functional theory): The electron density is used in DFT as the fundamental property. Using the electron density significantly speeds up the calculation. One of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces.

Ab initio (means from the beginning) : all results are calculated from computational analysis of Schrödinger equation ( no exact solvation). No parametrization.

Quantum Mechanics

Semi-‐‑empirical Ab initioDFT


Ab initio• Ab initio latin for “ from the beginning”• Based on Schrödinger equation• Common type Hartree Fock

– Coulombic electron-‐‑electron repulsion is not specifically included, only it’s net effect

– The energy is in Hartrees ( 1H = 27.2214 eV)– Because of approximation, the energy is always greater than the exact energy.

• Wavefunction is described by functional form:– Slater type orbitals– Gaussia type orbitals

• Basis set:– Basis set is a collection of functions that describe spatial position of an electron.– The basis set needs to be able to approximate the actual wave function sufficiently

well to give chemically meaningful results.

• The simplest of these basis sets is that designated STO-‐‑3G, an acronym for Slater-‐‑Type-‐‑Orbitals simulated by 3 Gaussians added together

– reproduce well geometries of simple organic molecules– Not well on energies– fail in carbocations and carbanions


Basis set• To improve the description of molecular geometry and properties split

valence basis sets are normally used – the AOs are split into two parts: an inner, compact orbital and an outer, more

diffuse one.– For simple molecules, the simplest split valence basis set is sufficient– 3-‐‑21G: 3 Gaussian functions are used for the core orbitals

2 for the inner shell and1 for the outer one

– 6-‐‑31G is good for geometry optimization

• Based on the accuracy– Basis set: 3-‐‑21G< 6-‐‑31G<MP2<MP4<CCSD<CCSD(T)

• For complex molecules polarization and diffuse functions areneed to add into basis functions, like

– 6-‐‑31 G*: polarization basis set• All non-‐‑hydrogen atoms additionally are represented with a set of five D-‐‑orbitals• Must be employed to obtain good electron densities if delocalization, polarization

or hyperconjugative effects play a role


DFT Density Functional Theory• The electron density of any system determines all ground-‐‑state properties of the

system– The exact form of the universal energy density functional is unknown. The

functional form is APPROXIMATED by various models including LDA (LocalDensity Approximation), WDA (weighted density approximations), and GEA/GGA (Gradient expansion approximation)

– Extension to excited states is no obvious

• DFT is less expensive than ab initio and more accurate especially for solids– The wavefunction of an N-‐‑electron system includes 3N variables, while the

density has only three variables x, y, and z.

• Nowadays widely used in modeling– DFT provides some chemically important concepts, such as electronegativity

(chemical potential), hardness (softness), Fukui function, response function

• The most popular functional in DFT is B3LYP which is used to produce reliablemolecular geometry.


Semiempirical methods• Less computationally intensive than solving the Hartree-‐‑Fock equation• These methods are not necessarily less accurate than some ab initio methods

• MNDO (Modified Neglect of Differential Overlap) can be primarily applied to molecules composed of atoms that have s and p orbitals

– Not good at modeling systems with hydrogen bonds– Not good for 4-‐‑membered rings– Energies are too positive for sterically crowded molecules

• AM1 (Austin Method 1)– Generally functions much better than MNDO– Still limited primarily to atoms that have s-‐‑ and p-‐‑orbitals– Many parameters obtained via chemical ‘intuition’

• PM3 (ParameterizedMethod 3)– Has parameters for a larger set of atoms than MNDO or AM1 (many transition

elements included in PM3)– Performs very well for molecules similar to those used in the parameterization.– Performance for other molecules can be better or worse than MNDO or AM1


When to use QM ?• Typical applications:

– Chemical reactions– Spectra– Transition states

• Molecular Structure– QC (ab initio, DFT) more universal than MM– Ab initio methods relatively reliable– Semi-‐‑empirical methods sometimes fail

• Electronic properties– electron density distribution– dipole moment– electrostatic potentials

• Molecular Orbitals– Frontier Molecular Orbitals: what are the mostfavorable orbital interactions(donor-‐‑HOMO – acceptor-‐‑LUMO)– rationalization and generalization of chemical reactivity


Molecular Mechanics/Force field method

Based on the following simplifications:• A molecule is a collection of spherical particles held together by simple

spring

• The motions of the nuclei are studied (electrons are ignored)

• Limited flexibility due to lack of electron treatment

• The potential energies are calculatedwith HOOKE‘s LAW: Force needed to extend or compress a spring by some distance is proportional to that distance.

• GOAL: to reproduce molecular geometries and RELATIVE energies


Molecular Mechanics/Force field methods

• Fit experimental data from a small set of molecules to bunch of molecules

• Fast method, can be utilized systems containing >106 atoms

• Predict the energy associated with a given conformation of a molecule• Numerical value of Force Field energy has no meaning as absolute

quantities• Only differences in energy between two or more conformations

have meaning

• Typical applications:– Geometry optimization– Conformational search– Simulation


Why molecular mechanics /force fieldmethod?

Advantages:

Ø The greatest advantages: computational simplicity and speedØ In some case it gives same level accuracy as high-level quantum mechanicsØ Transferablity ( force field developed for one set of molecule can be used for other)Ø Can be applied for largemolecules /systems ( proteins, biomolecules, polymers)Ø Molecules can be studied in vacuum, implicit or explicit solvent environmentsØThermodynamic and kinetic propertiesØ Geometry optimization

ØDisadvantages:

ü In general less accurate than quantum mechanics or semi-empirical methodsü No electronic transitionsü No electron transportü No proton transferüBond breaking/forming is not possible =>chemical reactions or reactivity of molecules cannot be studiedü The lack of available parameters for some compound types


Force field

•Force field is a simple mathematical equation withparameterswhich describe the energy cost of deviating fromideal geometry

•E is energywhich is defined as the difference in energybetween a real molecule and ideal molecule, and r0 is theideal bond lenght etc. derived from experimental values orab initio calculations.

•The force constants kb , kƟ , etc. are experimentally derivedusually from x-‐‑ray, NMR, IR and Raman spectoscopy


A general form of force field

Epot =SSEstr +SSEbend +SSEtors+SSEEoop+ SSEvdw+SSEelecThere can be also cross-terms


Force Field(1): Bond streching Estr

•This is the approximation to the energy of a bond as a function of displacement from the ideal bond length, r0. The force constant, Kb, determines the strength of the bond. Both ideal bond lengths r0 and force constants Kb are specific for each pair of bound atoms, i.e. depend on chemical type of atoms-constituents.

• Bond streching can be described more accurant Morse equation (blue) or simple quadratic potential (black).

E=1/2kb(r-ro)2

quadratic


Force field (2): Bond angle Ebend

• Ebend represents with a harmonic potential the alteration of bond angles theta from ideal values qo Values of qo and Kq depend on chemical type of atoms constituting the angle

• If parabel is broad (k is small), more energy is needed to bend bond angle away from ideal geometry.

E= 1/2kq(q-qo)2

ideal geometry


Force Field (3) :Torsion angle function Ebend

• Models the presence of steric barriers between atoms separated by 3 covalent bonds A-‐‑B-‐‑C-‐‑D (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. This potential is assumed to be periodic and is often expressed as a cosine function.

E= 1/2k [1+cos(nt-f)]


Force Field (4): Torsion out of the plane (out-‐‑of plane)

Eoop= 1/2k(c-co)2

H R'

RO


Force Field (5): Non-‐‑bonded interactions ( van der waals :

Ø The repulsive force arises at short distances where the electron-‐‑electron interaction is strong (red))

Ø The attractive force arises from fluctuations in the charge distribution in the electron clouds, atoms are at average distance

Ø Each of these two effects is equal to zero as atoms are at infinite separationØ Van der Waals interactions are one of the most important for the stability of the

biological macromolecules.

EvdW =S[(-A)/r6 + (B)/r12]

Lennard-Jones 12-6 equation


Time saving trick

•Usually cut-‐‑off value 8-‐‑10 Å for Lennard-‐‑Jones is used to speed calculation.

•Cut-‐‑off value is also usedfor calculations of electrostatic interactions. The electrostaticinteractions decreasesmoreslowly so cut-‐‑off value is larger


Force Field (6): Non-‐‑bonding interactions (Electrostatic

interactions)

Eelec= q1q2/r12

• The electrostatic interaction between a pair of atoms is represented by Coulomb potential; D is the effective dielectric function for the medium and r is the distance between two atoms having charges q1 and q2.

• Other non-‐‑bonding intercations : hydrogen-‐‑bonding interactions.


Components of a force field : •Any force field contains the necessary building blocks for calculating energy :

1. A list of atom types2. A list of atomic charges3. Rules for atom-‐‑types4. Functional forms of the components of the energy expression5. Parameters for function terms

• What is atom type ?• Atom type is a unique description of an element and itsenvironment ( such as C=O vs C-‐‑O) and its hybridization (for Carbon, sp, sp2, sp3)

• If atom type is not correct, molecular geometry is not correct!


Molecular geometry

•carbonhave different geometry– sp3 (tetrahedral)

– sp2 (plane)

– sp1 (linear)


Atom types•Different force field have usually different atom types

•Each atom type declaration must be unique

•Atom types must be correct to get correct geometry

•Crystal structures may have “different” atom types and bonds– Check when using structures from

different databases• Atom types correct?• Bond lengths, bond angles reasonable?

• Bond orders correct?• Correct enantiomer?

Tripos atom types


Create force field terms for propane ?

What atom types ? How many different bonds ?How many different angles?How many torsion angles ?What about non-bonded interactions ?

H

HHHH

H

HH


Where to get parameters for force fields:

– Emperical force field• calibrated by experimental data (including structural data obtained from x-‐‑ray crystallography and NMR, dynamic data obtained from spectroscopy and inelastic neutron scattering and thermodynamic ) of small molecules (cvff)

– Ab initio force field• ab initio calculations (QM) are used to produce data to calibrate the functional form and parameters(cff)


Force fields

They differ:– in parameters and cross terms– methods of parameterization


Force fields

•The usage of the force field depends on purposes they aredesigned:

– MMFF94 optimized for small organic compounds-‐‑wide structuralvariety

– Tripos: general purpose-‐‑ reasonable ( but not excellent( parameters for wide varietyof atom enivironments

– Amber94:optimized for proteins-‐‑oftenmissing parameters for otherorganics

– CFF95 for polymers– UFF: universal forcefiels, contains parameters even for metal– PEFSA95 optimized for carbohydrates

•Force field is usually a compromise between speed and accuracy


Energy minimization = Geometry optimization

• After sketching or download from database, a molecule has usually bond lengths and angles etc far from ideal.

• Energy mimimization is an approach that findsstable, low energy conformations by changingthe geometry of a structure.

• During minimization Cartesian coordinates (X,Y,Z position) for each atom are moved to obtain the optimal geometry and minimal energy.

• Energy E is minimized by assuming the entropy effect can be neglect.

• Typically, only small movements in atom position are made.

E


Potential energy surface PESo Geometry optimization/Energy minimization is done usingminimization algorithms.

o Minimization algorithm is used to locate minumum points in potential energy surface (PES).

o Most minimization algorithms go only downhill on the PES - Important to have several starting structures- Several local minimum


Minimizing process :

I. Check the starting geometry ( remove bad van der Waals contacts, minimum energy geometry depends on starting geometry)

II. Select suitable force fieldIII. Select minimizing algorithm (Steepest

descent, Conjugate Gradient, Powell, Newton-‐‑Raphson etc.)

IV. Choose parameters for minimization ( convergence criteria,maximum gradient etc)


Minimization algorithms

Minimization algorithms can be divided:I. Non derivative algorithms (No functional form for E)

o Simplex

II. Derivate-based algorithms1. First derivative methods

o Steepest descento Conjugate gradient/Powello Broyden-Fletcher-Goldfarb-Shannon (BFGS) (Quasi-newton)

2. Second derivative methodso Newton-‐‑Raphson (NR)o Truncated Newton (TN)

III. Multidimensional methodso Monte Carloo Molecular Dynamicso Simulated Annealingo Genetic Algorithm

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rdrVd

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I. Non-‐‑derivate minimization algorithms:oOptimization algorithms that do not usederivatives of the energy function

SIMPLEX ( In Sybyl):Three basic strategies

Ø ReflectionØ ExpansionØ Contraction

ØEffective for bad geometries,very slow near minima, very crude,

ØMay invert chiralities !Ø Do not use for proteins!


II. Derivative-‐‑based minimization algorithm• Requires derivatives to be calculates (can be obtained eitheranalytically or numerically)

• Energy function is in a form that allows the first(also if wanted the second) derivatives to be calculated.

I. First derivativeo indicates slope of energy surface=gradiento Gradient=0 indicates minima and saddle points

II. Second derivativeo differentiates type of points in energy surface,Positive curvature = minimaNegative curvature = maximaZero curvature =saddle points


I. First derivative minimization algorithms

Steepest Descent

• Numerically calculated deritivatives• Proceeds along the direction of the forces. • Inefficient after a few iterations ( use only if the gradient is extremely high)•Working best when molecule is far from a minimum,have poor convergence close minimum because the gradient becomes

smaller as minimum is approached (oscillates close to minimum)


I. First derivative minimization algorithms continues..

ConjugateGradients/Powell•Uses gradients from two successivepoints to determine direction after first step

- Have a less oscillation•Powell is similar to conjugate gradients ( sometimes torsion angles are modifiedtoo much)• Powell is not suitable algorithm after conformational analysis• Efficient near the minimum ( finds usually a minimum in fewer step thanSteepest Descent)•May have problems if the initial conformation is far from a minimum•A good choice for small molecules (Powell method also for proteins as it ismost efficient minimization method (~3X faster )


II Second derivative minimization algorithms:

o Newton-Raphson (NR)•Calculate the second derivatives of energy function• Predicts the location of a minimum and heads in that direction• Fast convergence, but requires a lot of memory• Unstable if far from minimum• For small molecules

o Truncated Newton (TN)• similar to NR ( the iterative linear equation solver is terminated after smallnumber of iterations.• efficient when gradient is reasonable

o Broyden-Fletcher-Goldfarb-Shannon (BFGS, Quasi-NR method)•Approximates the second derivatives by iteration•Predicts the location of a minimum and goes in that direction• Slow method


Multidimensionalmethods

•Uphillsmovements allowed !!!!•Applications macromolecules, like proteins•These methods are described in next lession.


How to end minimization?1. Number of minimization step

- Define how many minimization steps are taken

2. Gradient method

o Minimization stop if gradient is less than a selectedvalueo Gradient can be RMSD / energyo A rough minimization gradient :0.1 kcal/mol/Åo Fine minimization for small molecule: 0.001 kcal/mol/Å

3. Delta Energyo Minimization is ended as the change in energybetween current step and previous step is less than set criteria ( for example 0.05 kcal/mol/Å)

4. Step size criteria- The size of the change in coordinates is

monitored and when this change is smaller than set parameter, minimization ends.


Local vs global minimum

o Minimization algorithm finds only local minimum !

o A deep narrow minimum may be less populated than broad minimum with higher energy

o Also local minimum can be inaccurate, because the methods slow done as approaching a minimum.

o The initial structure determines the results of the minimization!

Global minimum

local minimum


How to find global minimum ?

Ø Do minimization with several starting conformationsØ Starting conformation effects on the minimum energy structure

Ø Use MD or Simulated Annealing approach to overcome barriers

Ø Systematic scanning of the molecular potential energy surface (PES)


Comparing steric energies ?• Be careful!• Compare only steric energies directly for conformationalisomers or geometric isomers which have same number and types of bonds

• In case of hexane compared to pentane, the difference of stericenergy is larger due to fact that hexane has more atoms.

• Enthalpy of formation or bond enthalpy can be used reliablyfor comparing molecules of different atom numbers.

Table: MM2/ MM3 energies of alkanes


Fair structure comparisons ?• Use enthalpy if possible (usually not available)• Use reference structure and study difference with that• Reference structure helpl to cancel out effects of having differentnumbers of atoms and bonds.– For example:Incorrect comparison :Cyclopentane ó Cyclohexane óCycloheptaneBetter choice:(cyclopentane-‐‑pentane) ó(cyclohexane-‐‑hexane)ó(cycloheptane-‐‑

heptane)

Comparison Steric Energy Directly

Difference withReference

ConformationalIsomers

yes yes

Geometric Isomers If sameenvironment

yes

Different Formulas never yes

Table: Molecular mechanics steric energy comparisons


Utilizing minimization methods:

SteepestDescent

ConjugateGradient orPowell

Newton-Raphson orBFGS

Small molecule (<200 atoms)Far from a minimum 1. 2.Close to a minimum 1. 2.Large molecule(>200 atoms)Far from a minimum 1. 2.Close to a minimum 1.

The choice of the minimization method depends on 1) the size of system 2) the current state of optimization


Example. Minimization of Netropsin with Stepest descent and conjugate gradients :

pre minimization minimizationmethod < 1 kcal/Å <0.1 kcal/Å

cpu-time (s) number of itera cpu- time(s) num iterat

Steepest descents 67 98 1405 1893

Conjugate gradients 149 213 257 367

Leach, A. R. Molecular Modelling: Principles and applications.


Minimizing a part of a molecule :

o Only a part of the structure is minimized or certain atom types are minimized.

o Usage:•The added hydrogens for the crystal structure

• avoid bumps with other atoms

• Point mutated amino acids and their close environment• Generated loops in protein


Conformational search and analysis


CCoonnffoorrmmaattiioonnaall sseeaarrcchh::

•Definition: The purpose of conformational search is to find all different conformers that are possible.

•In practise: Search a set of energetically accessible minima

AIM: make a representative sampling of conformational space with the smallest number of conformers that contains the bio-‐‑active conformation within the required accuracy


Conformational search outline

Energy minimizing

Duplicates elimination

Representative structures for each potential minimum

Randomly or systematically generated conformations


Conformational analysis in modeling is needed for:• pharmacophore modeling•rigid docking•shape fitting•3D QSAR•virtual screening•Any in silico 3D drug discovery approach which depends on the accurate representation of low-‐‑energy conformations


Conformational search strategies :

1. Deterministic methods– Systematic search– Molecular dynamics

• Simulated annealing

2. Stochastic– Random search– Monte Carlo– Genetic algorithm– Distance geometry


Number of conformations= Pin [360/Qi]

Rotatable bonds: 3increment: 30°conformations: 1728minimization: 1 conf/sTotal time: 29 minutes

Rotatable bonds: 5increment: 30°conformations: 248832minimization.:conf /sTotal time: 69 h

If there is 7 rotatable bonds, so over 36 milj. conformations are generated which takes415 days to minimize !

Combinatorial explosion:


Restricted systematic search method:

•Uses energy cut-‐‑off value to decrease the number of conformations – Conformations with severe intra-‐‑molecular clashes are removed– High energy conformations are ignored

•Can be used to study even 10-‐‑15 rotatable bonds

Starting gometry

Acceptable conformation minimum

High energy conformations


Advantages and disadvantages of systematic search methodAdvantages:ØExplore whole conformational space systematically. All possible mimimal conformers can be found.

Disadvantages:ØTime consuming: the number of conformations is huge ØCannot be used for large systems anda great limitation for the ring systems

Partial solution:Resctricted systematic search ( energy cut-‐‑off)


Random search:• Generates conformers by random perturbation of Cartesian

coordinates or the torsion angles of rotatable bonds and then structure is minimized. Conformation is compared with others and registered if it is different than others. This cycle is repeated several times.

• The perturbation of Cartesian coordinates relys heavily on minimization step as conformations generated can be very distorted with high energy.

• In random search conformation can move from one region of the energy surface to completely unconnected region in a single step.


Random search advantages and disadvantages:

Advantages:ØExplore conformations of the ring systemsØChiral centers can be preserved to their original geometry or inverted during generation

ØFast and powerful method for large flexible with many chiral centers.

Disadvantages:ØNo real end point of search.ØOne can never be sure that all of minimum conformations have been found!


What is molecular dynamics?

•Molecular dynamics (MD) is a computer simulation technique that allows one to predict the time evolution of a system of interacting particles (atoms, molecules, granules, etc.)

•Model the motion of some group of particles (e.g., atoms) by solving the classical equations of motion


MD basics1. Specify the system

o a set of initial conditions initial positions & velocities of particles in the system

o the interaction potential for deriving the forces = Suitable force field

2. Follow the evolution of the system in timeo Solve a set of classical equations of motion for all particles

in the system

Typically MD simulations feature 102 -‐‑108 atoms, over times of 10 ps – 100 ns.


•MD Total energy Etot= Epot + Ekin

-‐‑ Epot is from force field ( Amber, Charmm, Gromos)

Epot =SEstr (1) +SEbend(2) +SEtors(3)+SEoop(4)+ SEvdw(5)+SEelec(6)

-‐‑ Ekin is kinetic part of energy ( from Newton'ʹs law)


Why Molecular dynamics (MD) ?•To explore the conformational space where a molecule could visit

•To get detailed information on the fluctuations and conformational changes of molecules ( also proteins and nucleic acids)– Molecules are not static or rigid structures in room temperature– If temperature is 0 K molecule does not move

•To study of complex, dynamic processes like (protein stability, conformational changes, protein folding, molecular recognition, ion transport in biological systems)


MD simulation

• An initial configuration of the system, a starting point, or t=0 is selected

– It can be an x-‐‑ray crystal structure or an NMR structure.

• Initial configuration can influence the quality of the simulation => choose carefully. It is often good to choose a configuration close to the state that you wish to simulate.

• Minimize the energy of the structure to remove any strong van der Waals interactions, which might otherwise lead to local structural distortion and result in an unstable simulation

• Add solvent (explicit water molecules) • Use Periodic Boundary Conditions (PBC)• Simulate your system over tine with specific conditions (Pressure, Volume and Temparature)

• Run time 1ns-‐‑ 500 ns ( can take weeks /months)


Choosing a time step

•Too small: covering small conformation space

•Too large: instability

•Suggested time steps– Translation, 10 fs– Flexible molecules and rigid bonds, 2fs– Flexible molecules and bonds, 1fs


Periodic boundary conditions (PBC) :• With PBC we can use small number of

molecules to present bulk system with less surface effects

• When using PBC, particles are enclosed in a box, and we can imagine that this box is replicated to infinity by rigid translation in all the three cartesian directions, completely filling the space.

• When particle is leaving the box, the image of the particle will enter from the opposite direction.


Analyzing results

• MD simulation, coordinates and velocities of the system are saved; these are then used for the analysis. Time dependent properties (energy, rmsd etc) can be displayed graphically.

• Average structures can be calculated and compared to experimental structures

Potential Energy as a Function of Time

-250

-200

-150

-100

-50

0

0 20 40 60 80 100time (ps)

Potential Energy (kcal/mol)


MD can be used for :

•Visualize movement of the system•Study dynamic behavior of system•Conformational analysis•Simulated Annealing•Refinement of protein structure like side chains in homology modeling

•Predict folding of protein


Conformational analysis using MD

•MD can provide information about the conformational properties of molecular system as well as the way in which conformation changes with time in certain temperature.

Energy

Simulation time


Advangaes and Disadvantages of MD conformation analysisAdvantages:ØFor large molecules (proteins)ØRing systems can be studiedØHigher temperatures can be used and energy barriers can be overcome

Ø”Movie” of molecular motions

Disadvantages:Ø Slow method. For large systems, a long simulation times are needed ( usually nanoseconds).

ØLarge structural rearrangements happens in 1 miliseconds timescale

Thank you!

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