High-throughput molecular dynamics simulation and Markov modeling Frank Noé (FU Berlin) frank.noe@fu-berlin.de
Molecular dynamics • Molecular dynamics are stochastic • Single trajectories are usually not representative • Objective is to sample expectation values
Conformation Dynamics / Markov models Reconciliation with Sampling Problem Analysis Problem Experiment ms - s huge, complex datasets hugedata sets ns - µ s
50 K atom system (explicit solvent) 100 ns / day / GPU* Rate 10 µs / day / Anton I e.g. Amber, AceMD, OpenMM
50 K atom system (explicit solvent) 100 ns / day / GPU* Rate 10 µs / day / Anton I e.g. Amber, AceMD, OpenMM 100 GPUs 1 Anton I 1 traj. of 10 µs / day 100 traj. of 100 ns / day Throughput 10 µs / day 10 µs / day
50 K atom system (explicit solvent) 100 ns / day / GPU* Rate 10 µs / day / Anton I e.g. Amber, AceMD, OpenMM 100 GPUs 1 Anton I 1 traj. of 10 µs / day 100 traj. of 100 ns / day Throughput 10 µs / day 10 µs / day 10.000.000 USD Cost 100.000 USD
Example for ligand binding: Trypsin – Benzamidine System Size: 50 K atoms (100 ns/day/GTX780) Simulation lengths: 100 ns to 2 µ s Total sampling data: 200 µ s pyemma.org
Good situation: diffuse landscape with intermediate steps energy rare event unbound not-so rare events bound conformation
Markov State Models Early contributions Review book Schütte et al, J. Comput. Phys. 1999 de Groot et al, J. Mol. Biol. 2001 Swope, Pitera and Suits, JPCB 2004 Sriraman, Kevrikidis and Hummer, JPCB 2005 Schultheis et al, JCTC 2005 Singhal, Pande, JCP 2005 Chodera et al, JCP 2007 Noé et al, JCP 2007 Construction and Analysis Dimension reduction Perez-Hernandez et al, JCP 2013 Estimation and Validation Prinz et al, JCP 2011 Computing kinetic experimental observables Noé et al, PNAS 2011 Computing transition pathways Noé et al, PNAS 2009
PyEMMA: Software for construction of Markov state models www.pyemma.org
Trypsin apo conformation dynamics pyemma.org Plattner and Noé, Nature Comm. 6, 7653 (2015)
Trypsin bound-state conformation dynamics t unbind = 91 ±40 µs t unbind = 0.03 ±0.001 µs G = 3.6 ±0.6 kcal/mol G = 7.8 ±0.6 kcal/mol 1* 1* T unbind = 3.5 ±2 µs 1 G = 4.9 ±0.7 kcal/mol 1* t unbind = 1.1 ±2 µs G = 6.5 ±0.8 kcal/mol t unbind = 394 ±141 µs 1 G = 2.0 ±0.8 kcal/mol 1 or 1* p ij > 0.01 T unbind = 5.3 ±4 µs p ij > 0.001 G = 4.3 ±0.7 kcal/mol p ij > 0.0001 t unbind = 63 ±6 µs p ij < 0.0001 G = 0.03 ±0.2 kcal/mol 1* pyemma.org Plattner and Noé, Nature Comm. 6, 7653 (2015)
Overall binding / conformational kinetics pyemma.org Plattner and Noé, Nature Comm. 6, 7653 (2015)
Trypsin excited conformations found as ground-state conformations of other serine proteases pyemma.org Plattner and Noé, Nature Comm. 6, 7653 (2015)
MSM: examples Substrate binding to HIV protease Protein folding mechanisms 0.52 2.57 0.52 0.52 5.35 7.4 5.35 Sadiq, Noé, De Fabritiis, PNAS (2012) Relaxed state Noé et al, PNAS (2009) Scission +GTP Protein complexes Faelber, … ,Sadiq, Noé, Daumke Nature (2011) Constricted state Reubold et al, Nature (2015)
Current examples (in prep) Barnase-barstar (120K atoms) Protein-protein association 2 ms Rhodopsin (60 K atoms) Activation transition 1.5 ms
”High performance” computing Parallel nodes time
”High performance” computing Parallel nodes time
Ensemble MD client pilot jobs Parallel nodes time
Automatic / adaptive sampling machines copernicus-computing.org htmd.org https://radicalensemblemd.readthedocs.org
Transition-based reweighting analysis method (TRAM)
Example: binding and folding of PMI to MDM2 fast (microseconds) slow (10-100 milliseconds) nanomolar binder
Bad situation: single high barriers (e.g. salt bridge) energy rare event not-so unbound rare events bound conformation
Bad situation: single high barriers (e.g. salt bridge) energy biased or generalized ensemble simulation (e.g. Replica-exchange, Metadynamics,...) direct MD unbound bound conformation direct molecular dynamics biased or generalized joint optimal estimate? ensemble simulation Wu, Mey, Rosta, Noé, JCP 141, 214106 (2014)
Example for an enhanced sampling method: Umbrella sampling v(x) . . . + b i (x) Wu, Mey, Rosta, Noé, JCP 141, 214106 (2014)
Reweighting of equilibrium probabilities Reweighted probabilities: normalization reweighting equilibrium constant factor probabilites Wu, Mey, Rosta, Noé, JCP 141, 214106 (2014)
Transition-based Reweighting Analysis Method (dTRAM) Reweighted probabilities: Estimation problem Constraints Wu, Mey, Rosta, Noé, JCP 141, 214106 (2014) pyemma.org
Example: binding and folding of PMI to MDM2 System Size: 50 K atoms (100 ns/day/GTX780) Trajectories: 500 x 1000 ns Total sampling data: 500 µ s
Acknowledgements Funding Positions available frank.noe@fu-berlin.de Collaborations Funding Christof Schütte (FU Berlin) Vijay Pande (Stanford) Eric Vanden-Eijnden (Courant Institut NY) Katja, Faelber, Oliver Daumke (MDC) Thomas Weikl (MPI Potsdam) John Chodera (MSKCC NY) Marcus Sauer, Sören Doose (Uni Würzburg) Gianni de Fabritiis (Barcelona)
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