Maria  Fyta  

Ins,tut  für  Computerphysik,  Universität  Stu<gart  Stu<gart,  Germany  

Nuggets  on  mul,scale  computa,onal  schemes  

Computa,onal  Physics  

Systems/proper,es  

Methodology/accuracy  

Time/length  scales  

Hierarchy  of  scales  

length

cm

mm

μm

nm

ps ns μs ms time

electron

ic  

structure  

atom

ic    

structure  

mesoscopic  

processes  

con/nuum:  connec/on  to  experiments  

Coarse-­‐graining  (CG)  •  Reduce  degrees  of  freedom  •  Computa,onal  efficiency  

Yethiraj group, U. Wisconsin-Madison

CG:  more  examples  

Effect of glycosylation on protein folding

D. Shental-Bechor and Y. Levy, PNAS 105, 8256 (2008)

Knots in protein folding

E. Shakhnovich, Nat. Mater. 10, 84 (2011)

Modeling  the  nucleosome  

C.W. Hsu, AM 250b, Harvard University (2011)

Hsu, et al, JCP 2012 model

DNA

Histone Core

Initial and relaxed configuration of a histone

The Scientist, March 1, 2011

Modeling  the  nucleosome  

C.W. Hsu, AM 250b, Harvard University (2011)

Hsu, et al, JCP 2012 model

DNA

Histone Core

Initial and relaxed configuration of a histone

Mul,scale  Computa,onal  Schemes  ➪   Single-­‐scale  

 Quantum-­‐mechanical/electronic  structure  (different  levels  of  accuracy:  CI,  DFT)  

 Classical  (Molecular  Dynamics)   Semi-­‐empirical  (Tight  binding)   Stochas,c  (Monte-­‐Carlo)   Discre,zed  schemes  (FEM,LB)  

➪ Mul/-­‐scale    ✽ Sequen,al  

✽ Concurrent  

I   II   III  

I  

II  

III  

Sophis/cated  schemes  and    

powerful  resources  

Concurrent  Mul/scale  Schemes  

Coupling  different  regions  

Computational Chemistry Group, University of Amsterdam

Coupling  different  regions  

M. Praprotnik, U. Ljubljana

3 scales:atomistic, mesoscopic, continuum

changing the number of molecular degrees of freedom on-the-fly thermodynamic equilibrium of all-atom with far simpler coarse-grained system

Crack  propaga,on  in  Si  

A   concurrent   computa,onal  approach  to  the  simula,on  of  crack     propaga,on   in   silicon  seamlessly   unites   quantum,  atomis,c,   and   con,nuum  descrip,ons  of  ma<er  

Abraham,  Broughton,  Bernstein,  Kaxiras,  Computers  in  Physics  (1998)  

Metal  contacts:  Joule  hea,ng  

D. I. Irving et al, Model. Sim. Mater. Sci. Engin. 17, 015004 (2009)

Co-Al contacts

Molecular Dynamics coupled to heat-transport equation

Asperity contact geometry

Temperature contours

25ps MD simulations

"bo<om-­‐up"  design  of  novel  molecular  nano-­‐electronic  structures  

Hexagonal phase found in NaCl

ab initio quantum mechanical calculations, molecular dynamics simulations with classical and reactive force fields, monte carlo simulations and mesoscale simulations

MSE, U. Michigan

QM/MM  

Sierka Lab, FS U. Jena

J.B.Rommel and J. Kaestner, JACS 133, 10195 (2011)

Fragmentation–Recombination mechanism of the enzyme glutamate mutase

Biomolecular  Simula,ons  

Parallel  mul,scale  simula,ons  of  a  brain  aneurysm  

L. Grinberg et al, J. Comput. Phys 244, 131 (2013)

Large scale flow features: Navier Stokes solver Blood rheology inside aneurysm: coarse-grained stochastic MD

brain vasculature

Multiscale approach for molecules moving in a fluid solvent:

– Molecular Dynamics (MD) (atomistic) for molecules

– Lattice Boltzmann (LB) (mesosopic) method for solvent

Coupling of LB to MD:

Ahlrichs and B. Duenweg, Int. J. Mod. Phys C, 9, 1429, (1998). MF, Melchionna, Kaxiras, Succi, Multisc. Model. & Sim.(2006)

u fluid velocity v bead velocity

€

Fpf = γ up −υ p( )

LB  -­‐  MD  coupling  scheme  

particle (P) → grid (G)

time exchange dtMD=M·ΔtLB (M=5-10)

transfer of spatial information

grid (G) → particle (P)

1.  G→ P interpolation of velocity

2.  For m=1,M : advance molecular state (t → t+dt)

3.  P → G extrapolation of forces

4.  t → t+Δt : advance Boltzmann populations

Hemodynamics  Model  blood  flow  in  human  arterioles  

Rybicki  et  al,  Int.  J.  Cardiovasc.  Imaging  (2009)  h<p://hemo.seas.harvard.edu  

A  concurrent  coupling  of  Lacce-­‐Boltzmann  and  Molecular  Dynamics  

DNA  transloca,on  through  nanopores  

a bead ~ 100-150 base-pairs

a bead ~ 1base

MF, S. Melchionna, E. Kaxiras, S. Succi

Sequen/al  Mul/scale  Schemes  

Adsorp/ve  processes  for  energy  gas  storage  and  CO2  capture  in  porous  networks  

Z. Xiang et al, Energy. Envir. Sci. 3, 1469 (2010)

Polymer-­‐clay  nanocomposites  

A. Danani, SUPCI, CH

MD: obtain interaction energies among components (polymer, clay, surface modifier) DPD: interaction parameters between beads FEM: calculate properties (exfoliation, etc.)

Thermoelectric  Materials  

T. Gruhn, U. Bayreuth

Microphase separations in thermoelectric materials like Co(Ti,Mn)Sb occurs as the system is quenched in to the coexisting region (b). Dynamics and 3D structures are studied numerically with multiscale simulations.

DFT

Monte-Carlo Phase-field theory

Connect  molecular  scale  to  cellular  processes  

CMTS, U. Chicago

Barnett et al, J. Mater. Sci. (2007)

(a):  Electronic  states  of  bases/base  pairs  at  various  distances  and  angles  

(c):  Construc/on  of  effec/ve  Hamiltonian  for  electron  localiza/on  along  DNA  

(b):  Fron/er  orbitals  of  stretched  poly-­‐CG   Stretching  

         0%  

       30%  

       60%  

       90%  

(a) (b) (c)  

Electronic  structure  of  stretched  B-­‐DNA  

(a)   (b)