1

BITS Embryo Lecture

Multi-scale modeling and molecular simulations of materials and

biological systems

Arthi Jayaraman

Post Doc, University of Illinois Urbana ChampaignPh.D. North Carolina State University 2006

B.E. Hons (Chemical Engineering) BITS Pilani 2000

2

Outline

• What is molecular simulation?• Why do we need multi-scale modeling and

simulations?• Steps involved in modeling and simulations• Types of models • Brief overview of simulation methods • Examples of systems from

– material science– biological science

3

• Molecular simulations use computer models to describe chemical systems at an atomic level of detail

• In a computer simulation

– Provide individual positions and orientations of every atom or molecule

– Place atoms and molecules in a simulation cell

– Let them interact with each other through a potential

– Let the system evolve according to some simulation algorithm.

What is molecular simulation?

4

What is molecular simulation? (contd.)

i-j interaction between species i and j

atom Batom A

Example: A gaseous mixture of monoatomic molecules

atom C

A-BB-B

A-A

A-CB-C

C-C

Components of the system

5

What is multiscale modeling and molecular simulation?

Kremer and Delle Site, Development of methods

1 A 100 nm

pico sec

1 μm

nano sec

micro sec

Milli sec

length

time

6

Why do we need modeling and simulation?

• Experiments– cannot study systems at some length scales and time

scales

– require very expensive equipments to study systems at certain conditions

• Modeling and Simulations – allow us to study systems at varying length scales and

time scales

– are cheaper (computers!)

– give us the ability to isolate the effect of each and every parameter involved in the system

7

Steps involved in modeling and simulations

• 1: What is the system and what do we want to investigate?

– How to model the different components of the system

– What length scale to use

• 2: What are interactions between the different components

of the system?

– What force fields and potentials to use

• 3: Do we want to study system dynamics or equilibrium

thermodynamics?

– What simulation method to use

– What time scale to use

• 4: Analysis of the results

8

Types of models• Atomistic

– Explicitly represent every atom in the molecule

C

H

• Coarse grained– Group of atoms combined together

9

• Contributions to potential energy (U) of a system with N molecules

(between atoms within a molecule)

Intramolecular only

• Ustr - stretch

• Ubend - bend

• Utors - torsion

• Ucross - cross

• UvdW - van der Waals

• Uel - electrostatic

• Upol - polarization

Dr. D. A. Kofke’s lectures on Molecular Simulation, SUNY Buffalohttp://www.eng.buffalo.edu/~kofke/ce530/index.html

Repulsion

- +-+

-+ -+

Intermolecular forces and potential

Intra- and Inter- molecular only

Attraction

( )N str bend tors cross vdW el polU U U U U U U U r

10

Monte Carlo

Specify the initial positions of all molecules

Generate random moves for the molecules

Sample with probability exp(-U/kT)

Take averages

Obtain equilibrium properties

Molecular Dynamics

Specify the initial positions ri(0), and velocities vi(0) of all

molecules

Solve Newton’s equations Fi = mi ai

Calculate ri(t), vi(t)

Obtain equilibrium and non-equilibrium

properties

Take averages

Brief overview of simulation methods

Dr. Keith Gubbins lectures, NCSU

11

• MD gives information about dynamical behavior and equilibrium, thermodynamic properties

so transport properties can be calculated.

MC can only give static, equilibrium properties

• In MD the motions of the molecules are natural (follow newton’s law)

In MC the motions are artificial (random moves)

Monte Carlo (MC) versus Molecular Dynamics (MD)

Dr. Keith Gubbins lectures, NCSU

12

Brief Overview of Simulation Methods (contd.)

• Other simulation methods– Brownian dynamics simulation– Quantum Mechanics-Molecular Mechanics

(QM/MM)– Dissipative Particle Dynamics Simulation

• Suggested Reading: – A. R. Leach, Molecular Modelling, Longman, London (1996) – D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed., Academic Press (2002) – M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford (1987)

13

Challenges• pick the right model

– How much detail is required to represent the system

accurately and yet have reasonable simulation time ?

(note: too much detail in the model will slow down the

simulations tremendously)

• pick the right simulation method– Which method would be able to simulate the complete

phenomena we are interested in ?

(note: often in some simulation methods the system

simply will not equilibrate)

14

Modeling and simulation of confined polymers

Q. Wang et al. Macromolecules, 33, 4512 (2000);

A bulk of copolymers confined between surfaces

A12B12 copolymer A-sAB-sB

Attractive interaction

Attractive interaction

Using experiments difficult to make these patterned surfaces (nanometer size patterns) difficult to study how the polymer organize on these patterned surfaces

(observe the organized at the molecular level)

A12B12

15

• Simulation is able to predict other structures depending on pattern spacing LS

Modeling and simulation of confined polymers

A12B12 copolymer

• Similar structures found in experiments and simulations

Simulation1Experiment2

polystyrene-b-polymethylmethacrylate

copolymer

1) Q. Wang et al. Macromolecules, 33, 4512 (2000);2) L. Rockford et al. Phys. Rev. Lett. 82, 2602(1999)

16

Protein foldingProteins are large organic compounds made of a sequence of amino acids.

sidechain

amine group

carboxyl group

Before proteins can carry out their important functions, they assemble themselves, or fold

When proteins do not fold correctly (i.e. "misfold"), there can be serious consequences, including many well known diseases, such as Alzheimer's, Mad Cow (BSE), Huntington's, Parkinson's disease, etc.

17

Modeling and simulation of protein folding

Experimental determination of the folded structure is a lengthy and complicated process, involving methods like X-ray crystallography and NMR. Simulations are trying to predict structures based on the amino acid sequence

There are many ways to model proteins:

United atomc

c

c HH

H

H

N

OH

Atomistic

side group

backbone

Coarse-grained

Carol Hall’s group, NCSU

18

-hairpin

-turn

-helix

Modeling and simulation of proteinsTwo most commonly found motifs in folded proteins

Structure of the protein is very complex

Modeling and simulations can be very useful in predicting these complex structures

Dr. Stefan Franzen’s lectures NCSU

19

Summary• Modeling and simulation are a useful tool in

understanding the molecular phenomena underlying complex processes in– Material science

• Confined polymers, pattern recognition in polymers* micelle formation, phase transitions in materials, colloidal systems, etc.

– Biological science • Structure of proteins, DNA and other biopolymers;

assembly of proteins; recognition in DNA microarrays* DNA-protein binding, drug design, etc.

• Modeling and simulations complement experiments by predicting phenomena that are difficult to study experimentally.

* My PhD thesis http://turbo.che.ncsu.edu/arthi