limitations of temperature replica exchange (t-remd) for

IBM Research

ACS 2006 REMD © 2006 IBM Corporation

Limitations of temperature replica exchange (T-REMD) for protein folding simulations

Jed W. Pitera, William C. SwopeIBM [email protected]

IBM Research

© 2006 IBM CorporationACS 2006 REMD

Anomalies in protein folding

� thermodynamic

� kinetic

Yang & Gruebele, Nature 2003

322K

~320K

305K

~325K

Garcia-Mira et al,Science 2002

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Sca

led

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D150100500

Time (µs)

Fl. data, 63 �C Fl. fit IR data, 63 �C IR fit

Ma & Gruebele, PNAS 2005

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Hunting anomalies – with a computational model

� Do we have the correct/converged answer for our model?

– How do we know?

� Do we have a model that reflects reality?

– How do we compare the model against experiment?

– What is missing from our model?

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Replica exchange molecular dynamics (REMD)

� Multiple simulations of the same system are run in parallel at different temperatures (T-REMD), state points or Hamiltonians

� Monte Carlo moves periodically exchange systems bet ween adjacenttemperatures

– Allows escape from local minima

� Ideal for cases where we want temperature-dependent properties

400K

350K

300K

350K ensemble

{ }

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T-REMD motivations

� Interested in a system at a temperature/state point where sampling is slow ( Tlow )– Long correlation times– Broken ergodicity

� Assume that sampling is fast at some other temperature/state point ( Thigh )

� Simulate as many intermediate state points as neces sary to bridge Tlow and Thigh

– Trajectories (MD) or Markov Chains (MC) decorrelate at Thigh, importance sample at Tlow

� In many cases T was an interesting variable anyway – Experiments often provide A(T) or perturb a system by ∆T– T-dependent phenomena of biological interest

Thigh – realm of perfect sampling

Tlow – broken ergodicity

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Model system T-REMD� 1-D double well potential, compare MD and T-REMD

� Energetic barrier; activated process with Arrheniuskinetics (ln( k) linear in 1/T)

Similar rates vs. 1/T All replicas undergo transitio ns

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aggregate transitions in 2.5x10^7 steps vs MD (4.5k /4.5k)

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“trpzip2” β-hairpin in explicit solvent� 12 amino acid peptide trpzip2 in explicit solvent

– TIP3P, AMBER parm96 or parm99SB

– 3605 waters, 11034 atoms

– Cubic box (equil.10ns NPT @ 310K, 1 atm) edge length 48.095 Å

– PME electrostatics

– 9Å Switch for vdW/direct; long range vdW correction

� Replica exchange molecular dynamics (80 replicas at a range of temperatures)

– Exchanges every 40 ps; Andersen collisions every 10 ps

� 2 independent calculations with different initial c onditions

– 80 representative conformations from implicit solvent“folded” (0.68 µs/replica, aggregate 54 µs)

– All 80 replicas started in the same fully extended conformation

“unfolded” (1.45 µs/replica, aggregate 116 µs)

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Effect of exchange period on relaxation from the folded state

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The hazards of non-thermalized initial conditions

� Rapid unfolding from folded initial conditions

� Exchange period shorter than the relaxation time of the potential energy

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Stability of “folded” initial conditions

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Convergence from “unfolded” initial conditions

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trpzip2 thermodynamics – SASA PMF vs. T

� Continuous, weak collapse transition

fr

from folded from unfoldedtemperature (K)

SA

SA

(Å

2 )

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trpzip2 thermodynamics – CαRMSD PMF vs. T

� Measure of the backbone deviation from the NMR structure


Cαα αα

RM

SD

(Å

)

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trpzip2 thermodynamics – heavy atom RMSD PMF vs. T

� Spurious absence of a barrier


hea

vy a

tom

RM

SD

(Å

)

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Comparison of cluster populations

� Approximate stochastic k-medoid clustering of merged & downsampled data set to produce a set of 40 clusters ; metric was distance matrix error of C αααα, trp C δδδδ and C ζζζζ3

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The energy landscape

� Markov model of 425K kinetics (N. Singhal)

� Compact states are isolated local minima connected by unfolded state

� Kinetics in/out of these minima are slow

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Apparent folding rates – RMSD criteria

� folded: < 2.5 Å Cαααα-RMSD from NMR

� unfolded: > 6 Å Cαααα-RMSD from NMR

� Track per-replica transitions, record T

� Exp’tl k f5x10-7, ku5x10-8 ps -1

@ 296 K (Snow et al PNAS 2004)

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Apparent folding rates – cluster membership

� Transitions to/from cluster #1

� Order of magnitude difference in rates

� Different T-dependence

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Apparent folding rates – nonequilibrium data

� Successive block averages of same data set

� Started folded, parm99SB

� Systematic ~2x change in unfolding rate

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Conclusions

� T-REMD is useful but not a panacea

– No increase in aggregate # of transitions

– Many interesting barriers entropic rather than energetic

– No T where sampling is infinitely fast

� Explicit solvent REMD of proteins has limitations

– Decoupling of D.O.F. of interest (protein) from extended variables (T, U, etc.)

– Large N → small ∆T, limiting replica motion in T

– Sampling limited by intra-replica correlation time

– Folding not a simple activated process

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Acknowledgements

� William Swope, Hans Horn, Julia Rice (ARC)

� Robert Germain (YKT), Blue Gene Science & Applicatio n Team

� Martin Gruebele & Wei Yang (UIUC)

� Vijay Pande, Nina Singhal, Michael Shirts (Stanford )

� John Chodera & Ken Dill (UCSF)

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Gordon Research Conference in Computational Chemistry, July 27 – Aug 1 2008

� Mount Holyoke, MA

� Chair: Dr. Jed W. Pitera, IBM Research

� Vice Chair: Prof. Dr. Walter Thiel, MPI-Kohlenforschung

� Force fields, electronic structure, quantum dynamics, chemical reactions, drug design, docking, coarse-grained simulation

� http://www.grc.org time and space

accu

racy

limitations of temperature replica exchange (t-remd) for

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