accelerated(Molecular(Dynamics...

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accelerated Molecular Dynamics (aMD) Tutorial Levi Pierce 2012 NBCR Summer InsAtute

Transcript of accelerated(Molecular(Dynamics...

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accelerated  Molecular  Dynamics(aMD)  Tutorial    

Levi  Pierce  2012  

NBCR  Summer  InsAtute  

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Time  Scales  Accessible  with    Molecular  Dynamics  

•  Pierce,  L.C.T.;  Salomon-­‐Ferrer,  R.;  de  Oliveira  C.A.;  McCammon,  J.A.;  Walker,  R.C.;  RouAne  Access  to  Millisecond  Timescales  with  Accelerated  Molecular  Dynamics.  in  press  

   

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Molecular  Dynamics    

3  

Δt ...  

Δt

Ensemble of structures

•  McCammon J. A., Gelin, B. R., Karplus M. Nature 267, 585 (1977)

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MoAvaAon  

•  Why  do  we  need  to  accelerate  molecular  dynamics?  

•  Can  we  just  increase  our  Ame  step  used  for  integraAon?  

•  Can  we  just  heat  our  system  up?    

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struction of a compensating function, known as the umbrella,which is added to the true potential energy function in orderto bias the sampling to a particular set of conformations.However, construction of the umbrella requires prior knowl-edge of the conformations of interest.

Alternatively, we sought to develop a molecular dynam-ics approach based on earlier work by Voter9,10 that simulatesinfrequent events of molecular systems without any advanceknowledge of the location of either the potential energy wellsor barriers. Voter9,10 recently proposed a hyperdynamicsmethod to speed up molecular dynamics simulations by al-tering the amount of computational time systems spend inpotential energy minima in order to be able to move overpotential barriers and study long-time behavior of systems.The scheme modifies the potential energy surface, V(r), byadding a bias potential, !V(r), to the true potential such thatthe potential surfaces near the minima are raised and thosenear the barrier or saddle point are left unaffected. Statisticssampled on the biased potential are then corrected to removethe effect of the bias. In Voter’s implementation of the biaspotential, the Hessian matrix is diagonalized at each step, sothat the transition state regions can be identified, thus limit-ing its use to small systems because of its computationalcost. Alternatively, a prescription for a simple bias potentialwas proposed by Steiner et al.16 and later used by Rahmanand Tully17 in which the bias potential is chosen such that theresulting modified potentials around the minima are constantif the unmodified potential falls below a certain value. There-fore, this simple definition of the bias potential does not re-quire the diagonalization of the Hessian matrix at each step,and hence made it possible for it to be applied to largersystems. In this paper, we present a robust way of alteringthe potential energy landscape that is straightforward, pre-serves the underlying shape of the potential energy surface,and allows for the simulation to be extended to larger mo-lecular systems, like proteins. We show that our approachaccurately and efficiently explores conformational spacewith improved sampling and converges to the correct canoni-cal probability distribution.

THEORY

The general idea behind the accelerated molecular dy-namics scheme is depicted in Fig. 1. A continuous non-negative bias boost potential function !V(r) is defined suchthat when the true potential V(r) is below a certain chosenvalue E, the boost energy, the simulation is performed on themodified potential V*(r)!V(r)"!V(r), represented usingdashed lines, and when V(r) is greater than E, the simulationis performed on the true potential V*(r)!V(r). This leadsto an enhanced escape rate for V*(r). The modified potentialV*(r) is related to the true potential, bias potential, andboost energy by

V*"r#!! V"r#, V"r#$E ,V"r#"!V"r#, V"r##E .

"1#

During normal molecular dynamics simulations of biologicalmolecules on the unmodified potential surface, the systemsextensively sample conformations around a local minimum

without adequately sampling conformations elsewhere on thepotential energy surface. Therefore, the primary goal of thiswork is to develop a method for large biological systems thatis capable of accelerating the state to state evolution of asystem relative to normal molecular dynamics. The bias po-tential increases the escape rate of the system from potentialbasins, and the subsequent state to state evolution of thesystem on the modified potential occurs at an accelerated ratewith a nonlinear time scale of !t*, where

!t i*!!te%!V&r" t i#'. "2#

This allows us to advance the clock at each step dependingon the strength of !V(r), where !t is the actual time step ofthe simulation on the unmodified potential. Hence, the totalestimated simulation time becomes a statistical property andis given by Eqs. "3# and "4#,

t*!(i

N

!t i*!!t(i

N

e%!V&r" t i#', "3#

t*!t)e%!V&r" t i#'*, "4#

where N is the total number of molecular dynamics stepscarried out during the whole simulation, and )e%!V&r(t i)'* istermed the boost factor. The boost factor is a measure of theextent to which the simulation has been accelerated. At eachstep, the time step, !t*, is nonlinearly dependent on thevalue of the bias potential, !V(r). It follows from Eq. "2#that !t*!!t when the system is on the true potential, V(r),that is when !V(r)!0. If the choice of the boost energy E isvery high, then the boost factor will be very large, leading tonoisy statistics because the wells would not be sampled suf-ficiently. However, correct statistics will be obtained aftermany transitions and adequate sampling of the potential en-ergy wells.

Furthermore, it is important that this method yields cor-rect canonical averages of an observable A(r), so that ther-modynamics and other equilibrium properties can be accu-rately determined from accelerated MD simulations. Theequilibrium ensemble average value of any observable A(r)on the normal potential V(r) is given by

FIG. 1. Schematic representation of the normal potential, the biased poten-tial, and the threshold boost energy, E.

11920 J. Chem. Phys., Vol. 120, No. 24, 22 June 2004 Hamelberg, Mongan, and McCammon

Downloaded 24 Jan 2005 to 128.54.56.45. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp

Accelerated  Molecular  Dynamics  •  Add  a  bias  to  our  potenAal  energy  surface  to  promote  escape  from  energeAc  

traps.  •  EquaAon  as  applied  to  total  potenAal  energy  

 

 

•  The  corrected  canonical  ensemble  average    of  a  given  property,  <A>c  can  be  obtained  by  reweighAng  each  point  in  the  configuraAon  space  on  the  modified  potenAal  by  the  strength  of  the  Boltzmann  factor  of  the  bias  energy,  exp(ΒΔV(r,  ti))  

!! ! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! !! !!! ! ! ! !!

!!! !! ! ! ! ! !!!!!!!!! ! ! ! !

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LimitaAons  of  aMD  

•  In  2008  code  was  not  efficiently  parallelized  – Sander  aMD  implementaAon  is  slow  

•  How  can  we  accelerate  aMD?  – Port  method  to  faster  codes  (pmemd,NAMD)  – Use  Graphics  Processing  Units  (GPUs)  

0  0.5  1  

1.5  2  

2.5  3  

1   12   24   36   48   60   72   84   96  

ns/day  

Number  of  Processors  

BPTI  Simula<on  17,758  Atoms  

sander  aMD  

6  

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ComputaAon  on  the  GPU  •  Why  are  they  so  fast?    –  Lots  of  relaAvely  fast  workers  vs  a  few  fast  workers  –  Cluster  (48  processors  operaAng  at  2.6GHz)  30ns/day  –  1GTX  580  (512  processors  operaAng  at  770MHz)  40ns/day  

•  Why  are  they  so  popular  now?      –  Compute  Unified  Design  Architecture  (CUDA)  

•  GPU  molecular  dynamics  codes  –  ACEMD  hkp://mulAscalelab.org/acemd  –  OPENMM  hkps://simtk.org/home/openmm  –  AMBER  (pmemd.cuda)  hkp://ambermd.org/gpus/  –  NAMD  hkp://www.ks.uiuc.edu/Research/gpu/  

 

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ImplemenAng  aMD  on  the  GPU  

•  First  ported  sander  aMD  to  pmemd  •  Next  ported  aMD  to  pmemd.cuda    

–  1  GTX  580  43.2  ns/day  cMD  –  1  GTX  580  41.3  ns/day  aMD  

•  How  fast  can  we  run  aMD?  –  2  GTX580  53.2  ns/day  aMD  

•  How  can  we  validate  our  implementaAon?  

0  5  10  15  20  25  30  35  

1   12  

24  

36  

48  

60  

72  

84  

96  

ns/day  

Number  of  Processors  

BPTI  TIP4PEW  NVT  18226  atoms  

PMEaMD  

sander  aMD  

GTX  580  PMEaMD  

0  

10  

20  

30  

40  

50  

1   12  

24  

36  

48  

60  

72  

84  

96  

108  

120  

132  

144  

ns/day  

Number  of  Processors  

BPTI  TIP3P  NVT  18226  atoms  

PMEaMD  

sander  aMD  

NAMD  aMD  

GTX580  aMD  

Wang,  Y.,  et.  al.,  ImplementaAon  of  Accelerated  Molecular  Dynamics  in  NAMD.  Computa,onal  Science  &  Discovery,  2011.  

 

0  

5  

10  

15  

20  

25  

30  

1   12   24   36   48   60   72   84   96  

ns/day  

Number  of  Processors  

PKA  72277  atoms  

PMEaMD  

NAMD  aMD  

GTX  580  PMEaMD  

0  5  

10  15  20  25  30  

1   12   24   36   48   60   72   84   96  

ns/day  

Number  of  Processors  

BPTI  17,758  atoms  NVT  

PMEaMD  

sander  aMD  0  

10  20  30  40  50  

1   12   24   36   48   60   72   84   96  

ns/day  

Number  of  Processors  

BPTI  17,758  atoms  NVT  

PMEaMD  

sander  aMD  

GTX580  aMD  

0  

10  

20  

30  

40  

50  

1   12  

24  

36  

48  

60  

72  

84  

96  

108  

120  

132  

144  

ns/day  

Number  of  Processors  

BPTI  17,758  atoms  NVT  

PMEaMD  

sander  aMD  

NAMD  aMD  

GTX580  aMD  

Lindert,  S.;  Kekenes-­‐Huskey,  P.;  Huber,  G.;  Pierce,  L.C.T.;  McCammon,  J.A.;  Dynamics  and  Calcium  AssociaAon  to  the    N-­‐Terminal  Regulatory  Domain  of  Human  Cardiac  Troponin  C:  A  MulA-­‐Scale  ComputaAonal  Study.  J.  Chem.  Phys.  B.  2012  

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Protocol  Outline    

•  Run  convenAonal  molecular  dynamics  unAl  dihedral  and  total  potenAal  energy  are  converged  usually  10-­‐50ns  is  all  that  is  needed  

•  Compute  the  Ecut  and  alpha  needed  for  boosAng  dihedral  potenAal  

•  Compute  Ecut  and  alpha  needed  for  boosAng  total  potenAal  

•  Fire  off  aMD  simulaAon!  

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Amber12  BPTI  Example    Step  1  Running  ConvenAonal  Molecular  Dynamics  (cMD)  

•  I  generally  run  10ns  of  NVT  dynamics  and  then  look  at  the  output  log  for  the  average  total  potenAal  energy  and  dihedral  energy    

•  You  can  also  grep  EPtot  and  DIHED  out  from  your  log  file  and  compute  the  averages    

 A  V  E  R  A  G  E  S      O  V  E  R      25000  S  T  E  P  S        NSTEP  =  25000000      TIME(PS)  =      56000.000    TEMP(K)  =      300.02    PRESS  =          0.0    Etot      =        -­‐39246.4544    EKtot      =            7882.3144          EPtot            =        -­‐47128.7688    BOND      =              179.6315    ANGLE      =              430.3040      DIHED            =              595.3485    1-­‐4  NB  =              203.3891    1-­‐4  EEL  =            1779.4670    VDWAALS        =            7637.5034    EELEC    =        -­‐57954.4124    EHBOND    =                  0.0000    RESTRAINT    =                  0.0000    -­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐  

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Amber12  BPTI  Example  Step  2  Compute  EthreshP  and  alphaP    

•  First  calculate  alphaP  from  the  total  number  of  atoms  

•  To  calculate  EthreshP  you  need  the  average  Eptot  and  the  total  number  of  atoms  in  your  system  EthreshP=  -­‐47128  kcal  mol-­‐1  +  alphaP  =  -­‐44212  kcal  mol-­‐1      

alphaP=  (0.16kcal  mol-­‐1  atom-­‐1  *  18,226  atoms)  =  2916  kcal  mol-­‐1    

Grant,  B.  J.;  Gorfe,  A.  A.;  McCammon,  J.  A.,  Ras  conformaAonal  switching:  simulaAng  nucleoAde-­‐dependent  conformaAonal  transiAons  with  accelerated  molecular  dynamics.  PLoS  Comput.  Biol.  2009,  5,  (3),  e1000325.  de  Oliveira,  C.  A.  F.;  Grant,  B.  J.;  Zhou,  M.;  McCammon,  J.  A.,  Large-­‐Scale  ConformaAonal  Changes  of  Trypanosoma  cruzi  Proline  Racemase  Predicted  by  Accelerated  Molecular  Dynamics  SimulaAon.  PLoS  Comput.  Biol.  2011,  7,  (10),  e1002178.  

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Amber12  BPTI  Example  Step  3  Compute  EthreshD  and  alphaD    

•  First  calculate  alphaP  from  the  total  number  of  solute  residues  

•  To  calculate  EthreshD  you  need  the  average  DIHED  and  the  total  number  of  solute  residues  in  your  system  EthreshD=  595  kcal  mol-­‐1  +  (4kcal  mol-­‐1  residue-­‐1  *  58  solute  residues)    =  46.4  kcal  mol-­‐1      

alphaD=  (1/5)*(4kcal  mol-­‐1  residue-­‐1  *  58  solute  residues)  =  827  kcal  mol-­‐1    

Grant,  B.  J.;  Gorfe,  A.  A.;  McCammon,  J.  A.,  Ras  conformaAonal  switching:  simulaAng  nucleoAde-­‐dependent  conformaAonal  transiAons  with  accelerated  molecular  dynamics.  PLoS  Comput.  Biol.  2009,  5,  (3),  e1000325.  de  Oliveira,  C.  A.  F.;  Grant,  B.  J.;  Zhou,  M.;  McCammon,  J.  A.,  Large-­‐Scale  ConformaAonal  Changes  of  Trypanosoma  cruzi  Proline  Racemase  Predicted  by  Accelerated  Molecular  Dynamics  SimulaAon.  PLoS  Comput.  Biol.  2011,  7,  (10),  e1002178.  

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Amber12  BPTI  Example  Step  4  Run  aMD  SimulaAon!    

•  For  the  GPU  version  simply  run  –  pmemd.cuda  -­‐O  -­‐i  amd.in  -­‐o  amd1.out  -­‐r  amd1.rst  -­‐x  amd1.nc  -­‐p  bpA.prmtop  -­‐c  eq.rst  

•  For  the  effeciently  parallelized  CPU  version  run  –  mpirun  -­‐np  NPROCS  pmemd.MPI  -­‐O  -­‐i  amd.in  -­‐o  amd1.out  -­‐r  amd1.rst  -­‐x  amd1.nc  -­‐p  bpA.prmtop  -­‐c  eq.rst  

•  For  the  inefficient  CPU  version  run  –  mpirun  -­‐np  NPROCS  sander.MPI  -­‐O  -­‐i  amd.in  -­‐o  amd1.out  -­‐r  amd1.rst  -­‐x  amd1.nc  -­‐p  bpA.prmtop  -­‐c  eq.rst  

amd.in  (NVT-­‐CONTINUE)    &cntrl      imin=0,irest=1,ntx=5,      nstlim=50000000,dt=0.002,      ntc=2,nv=2,ig=-­‐1,      cut=10.0,  ntb=1,  ntp=0,      ntpr=1000,  ntwx=1000,      nk=3,  gamma_ln=2.0,      temp0=300.0,iouvm=1,      iamd=3,iwrap=1,      EthreshD=827,      alphaD=46.4,EthresP=-­‐44212,      alphaP=2916,    /  

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Examining  Results  

•  How  do  we  observe  more  sampling  from  aMD  compared  to  MD?  

•  PhiPsi  plots  of  dihedral  angles  •  RMSD  •  Principal  Component  Analysis  

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ReweighAng  

•  Using  the  true  exponenAal    – Alanine  DipepAde  

•  Using  approximaAons  to  the  exponenAal  – BPTI  

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Useful  links    

•  hkp://ambermd.org/gpus/  

•  aMD  on  NAMD  •  hkp://www.ks.uiuc.edu/Research/namd/2.8/ug/node63.html