NMR Guided Biomolecular Conformation Sampling via GEMS

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NMR Guided BiomolecularConformation Sampling via
GEMS
Paul R. Brenner

• Advisor Dr. Jesús A. Izaguirre
• Department of Computer Science and Engineering
• University of Notre Dame

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Motivation

• Discovery of atomic scale biophysical mechanisms
  via computational simulation presents the
  potential to accelerate the understanding and
  treatment of disease.

• Flexible protein docking
• Aids exploratory drug design
• Incorporation of flexibility is dependent on
  comprehensive molecular knowledge of the protein
  and ligands.

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Flexible Protein Docking

• Modeling a fully flexible protein during docking
  is computationally impractical.
• Large structural changes are key to binding
  mechanisms

• Simplified representations rely on multiple
  protein structures (MPS)
• Molecular models provide transition path and
  structural information.

Movie Ref Kraut Research Group UCSD
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Challenge

• Systematic analysis is intractable because of the
  3N configuration space and 6N phase space.

• Molecular dynamics methods are limited by
• Step size instabilities (fs)
• Computational complexity of non-bonded forces
• Rough energy landscape localizes sampling over
  practical simulation times.

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Research Plan

• Two key areas of research responsibility and
  three interdisciplinary collaborations

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Coarse Path Identification
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Stochastic Difference Equation

• Boundary Value Formalization
• S is a path action, L is the Lagrangian, and U is
  the potential energy
• As a result of discretization errors the solution
  to the trajectory is not exact
• The error e can be considered noise which varies
  with the time step size (filtering fast motion
  instabilities!)

Ref Olender and Elber, 1996
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SDE Optimize Path Action

• To determine the most probable approximate path
  for a given timestep, minimize the
  Onsager-Machlup Action SOM.
• DX is a path integral summation
• ? 2 is the error distribution standard deviation

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SDE - Limitations

• Identification of timescale is critical
• SDE is computationally competitive only when
  using a large time step
• Large time steps may delegate significant fast
  motions to the error approximation
• Determination of order parameters ? required to
  specify initial and final states

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My Contribution

• Integrate NMR data into SDE order parameter and
  time step selection
• Recent NMR technological developments provide
  insight into flexible biomolecular residues over
  a wide range of timescales
• Fast motion (ps,ns) data is available in terms of
  an ordering parameter S2
• Slow motion (?s,ms) data is available in terms of
  excess transverse relaxation rates Rex

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Sample NMR Guidance
J(0)ex(ns)
Residue Number
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Transition Path Sampling

• Generate an ensemble of paths from an initial
  trajectory with the Shooting Algorithm
• Example for two coordinates

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TPS Ensemble Acceptance

• Accept trial paths with probability
• hA and HB represent the population and trajectory
  operators
• ?(X(0)) represents the distribution of initial
  phase space points. For the canonical ensemble
  (NVT)

Ref Dellago et al. 1998
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TPS Limitations

• Acceptance rate and path accuracy are highly
  dependent on determination of order parameters to
  uniquely specify
  initial and final states
• Example

• TPS is suited for rare event transitions over one
  predominant transition state barrier.
• Harvesting trajectories of slow transitions or
  multiple barrier transitions is highly improbable

?
?'
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My Contribution

• Integrate experimental NMR data to guide TPS
  order parameter selection
• Similar to NMR/SDE explanation
• TPS more sensitive to the selection
• Integrate current order parameter refinement
  methods with NMR recommendations
• Investigate computer learning methods

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My Contribution

• Exploit Grid Storage to extend TPS range
• Path ensemble accuracy improves with the ensemble
  size and trajectory resolution.
• As molecule size increases the storage capacity
  and communication requirements for centralized
  storage become impractical for an individual
  researcher.
• Execution on distributed computation and storage
  resources removes the hardware impediment to
  accurate TPS.

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Preliminary Work - GEMS

• Designed and implemented a grid toolkit for
  dynamic management of data over autonomous
  distributed storage resources
• Published multiple performance tests in support
  of the novel framework design

Ref Wozniak et al. 2005
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Extracting ConformationsFrom a Refined Path
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Replica Exchange Method (REM)

• Random walk in temperature space
• A set of independent simulations (replicas) with
  temperatures Thigh to Tlow run simultaneously
• At regular intervals exchange positions between
  neighboring replicas with probability
• U(X) is the potential energy and ? 1/(kBT)

Ref Hukushima and Nemoto, 1996
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REM Limitations

• A uniform probability of exchange is required
  between the replicas.
• The number of temperatures T required for this
  uniform switch scales with system size N as
• A random walk in temperature space requires O(T2)
  exchange attempts to transfer a conformation from
  Thigh to Tlow

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My Contribution

• Accelerate the random walk in REM
• Utilize insight from non-equilibrium methods
• Jarzynski Equality
• Equilibrium Process (t??)
• Non-Equilibrium (t is finite)
• Accelerate TH?TL
• Bias walk such that O(T2) is reduced to O(T)
• Use relation similar to Jarzynskis to compute
  unbiased observable from ensemble of size K
• K required for convergence such that KT lt T2

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Preliminary Work - REM

• REM method has been implemented through parallel
  execution of the ProtoMol framework
• Demonstrated superior sampling of United Atom
  Butane in recent publication

Ref Hampton et al. 2005
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Research Timeline

• Fall 2005
• Enhance REM sampling
• Test SDE using MOIL and implement TPS via GEMS
• Utilize published NMR data for BPTI in SDE and
  TPS
• Spring 2006
• Formal analysis of REM enhancement TPS-GEMS
  capabilities
• Incorporate NMR data for HIV1 and DHFR into SDE
  and TPS
• Summer 2006
• MPS generation procedure for HIV1 and DHFR
• Determine suitable MPS ensembles for flexible
  docking
• Fall 2006
• MPS ensembles to docking collaborators
• Paper revisions, final submissions, writing
  dissertation

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Summary of My Contributions

• Integrate experimental NMR data into SDE and TPS
  path identification methods
• Exploit Grid Storage to extend TPS range
• Enhance REM for acquisition of refined
  conformations along the transition path
• Introduce an efficient MPS generation process to
  aid Flexible Protein Docking

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Acknowledgements

• Collaborators
• NMR Dr. Peng, Mr. Namaja
• Distributed Systems Dr. Striegel, Dr. Thain,
• and Mr.
  Wozniak
• Advisor
• Dr. Jesús Izaguirre
• Funding Agency
• NSF Grant DBI-0450067
• Protomol Development Team
• Dr. Matthey, Mr. Hampton, Mr. Chatterjee

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• Questions