BITS Embryo Lecture Multi-scale modeling and molecular simulations of materials and biological systems Arthi Jayaraman Post Doc, University of Illinois Urbana Champaign Ph.D. North Carolina State University 2006 B.E. Hons (Chemical Engineering) BITS Pilani 2000

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

What is molecular simulation? 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? (contd.) Example: A gaseous mixture of monoatomic molecules A-B B-B A-A A-C B-C C-C Components of the system atom A atom B atom C interaction between species i and j i-j

What is multiscale modeling and molecular simulation? 100 nm pico sec 1 μm nano sec micro sec Milli sec length time Kremer and Delle Site, Development of methods

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

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

Types of models Atomistic Coarse grained Explicitly represent every atom in the molecule C H Coarse grained Group of atoms combined together

Intermolecular forces and potential Contributions to potential energy (U) of a system with N molecules Intramolecular only Intra- and Inter- molecular only (between atoms within a molecule) Repulsion UvdW - van der Waals Uel - electrostatic Upol - polarization Ustr - stretch Ubend - bend Utors - torsion Ucross - cross Attraction - + - + - + - + Dr. D. A. Kofke’s lectures on Molecular Simulation, SUNY Buffalo http://www.eng.buffalo.edu/~kofke/ce530/index.html

Brief overview of simulation methods Monte Carlo Molecular Dynamics Specify the initial positions ri(0), and velocities vi(0) of all molecules Specify the initial positions of all molecules Solve Newton’s equations Fi = mi ai Generate random moves for the molecules Calculate ri(t), vi(t) Sample with probability  exp(-U/kT) Take averages Obtain equilibrium properties Obtain equilibrium and non-equilibrium properties Take averages Dr. Keith Gubbins lectures, NCSU

Monte Carlo (MC) versus Molecular Dynamics (MD) 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) Dr. Keith Gubbins lectures, NCSU

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)

Challenges pick the right model pick the right simulation method 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)

Modeling and simulation of confined polymers A bulk of copolymers confined between surfaces A-sA B-sB Attractive interaction A12B12 copolymer A12B12 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) Q. Wang et al. Macromolecules, 33, 4512 (2000);

Modeling and simulation of confined polymers Similar structures found in experiments and simulations Experiment2 Simulation1 polystyrene-b-polymethylmethacrylate copolymer A12B12 copolymer Simulation is able to predict other structures depending on pattern spacing LS 1) Q. Wang et al. Macromolecules, 33, 4512 (2000); 2) L. Rockford et al. Phys. Rev. Lett. 82, 2602(1999)

Protein folding Proteins 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.

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: c H N O United atom Atomistic side group Coarse-grained backbone Carol Hall’s group, NCSU

Modeling and simulation of proteins Two most commonly found motifs in folded proteins a-helix b-hairpin b-turn 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

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