limitations of temperature replica exchange (t-remd) for
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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]
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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
1.0
0.8
0.6
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0.0
Sca
led
SV
D150100500
Time (µs)
Fl. data, 63 �C Fl. fit IR data, 63 �C IR fit
Ma & Gruebele, PNAS 2005
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IBM Research
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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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IBM Research
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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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IBM Research
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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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IBM Research
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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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ln k
MD
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MD
aggregate transitions in 2.5x10^7 steps vs MD (4.5k /4.5k)
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IBM Research
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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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IBM Research
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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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IBM Research
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trpzip2 thermodynamics – CαRMSD PMF vs. T
� Measure of the backbone deviation from the NMR structure
from folded from unfoldedtemperature (K)
Cαα αα
RM
SD
(Å
)
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trpzip2 thermodynamics – heavy atom RMSD PMF vs. T
� Spurious absence of a barrier
from folded from unfoldedtemperature (K)
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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IBM Research
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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