Parallel methods for evaluating the electrostatics of cellular components

1
Parallel methods for evaluating the
electrostatics of cellular components

• Nathan A. Baker
• Department of Chemistry and Biochemistry
• University of California at San Diego
• NPACI All-Hands Meeting
• March 8, 2002

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Introduction to biomolecular electrostatics

• Highly relevant to biological function
  specificity, affinity, rates, etc.
• Important tools in interpretation of structure
  and function
• Implicit solvent methods reduce degrees of
  freedom
• Discrete solvent ? dielectric continuum
• Mobile counterions ? continuous charge
  distribution
• Useful for
• Qualitative analysis
• Static free energy calculations pKa, binding,
  mutagenesis
• Dynamics calculations flexibility, binding rate
  constants, dynamic properties

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Poisson-Boltzmann equation
Free energies and forces obtained from integrals
of u
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Poisson-Boltzmann equationsolution methods

• Variety of algorithms for solving the equation
• Cartesian mesh multigrid/finite difference
• Boundary element
• Finite element
• Typically suffer from
• Inefficient solvers
• Lack of adaptivity
• Poor parallelism
• Insufficient problem flexibility
• Developed new methods for very large biomolecular
  systems
• Parallel multilevel adaptive finite element
  techniques
• Parallel focusing methods

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Parallel focusing background

• Extension of existing Cartesian mesh solver
  technology
• Based on
• Highly efficient sequential solvers
• Solution of nonlinear equation through inexact
  damped Newtons methods
• Solution of linearized problems via multigrid
  solver
• Electrostatic focusing
• Uses coarse mesh calculation to provide fine mesh
  boundary conditions
• Popular for highly accurate local solutions at
  titratable and binding sites
• Sequential focusing is similar to new Bank-Holst
  parallel finite element methods
• Provably convergent
• Trivially parallel

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Parallel focusing algorithm

• Given the problem data and P processors of a
  parallel machine
• Each processor i 1, , P
• Obtains a coarse solution over the global domain
• Subdivides the global domain into P subdomains,
  each of which is assigned a processor
• Assigns boundary conditions to a fine
  discretization of its subdomain using the coarse
  global solution
• Solves the equation on its subdomain
• A master processor collects observable data from
  other processors and controls I/O

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Parallel focusing benefits

• Loosely coupled focusing calculations
• Trivially parallel algorithm
• No load balancing issues
• Simple implementation
• Leverage existing, highly optimized multigrid
  solvers
• Simple force and observable evaluation

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New electrostatics methodsAPBS software

• APBS Adaptive Poisson-Boltzmann Solver
• 23,000 lines of object-oriented, ANSI-compliant C
  code
• Extremely portable due to hardware abstraction
  through MALOC
• Provides biomolecule- and equation-specific
  routines with numerical work performed by Holst
  group libraries
• Public beta release planned for 2002
• Transparent processing of PDB files (Jens
  Nielsen, UCSD)
• Currently available as web portal (Jerry
  Greenberg, SDSC) https//gridport.npaci.edu/apbs
• Visit http//mccammon.ucsd.edu/apbs for more
  information

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Validation and proof of concept

• Smaller systems
• Analytic test cases
• pKa calculations
• Ligand affinities
• Solvation energies
• Protein-protein interactions
• Larger systems
• Polio virus
• Ribosome subunits
• Microtubules

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Ribosome calculationsintroduction

• Ribosome central to protein synthesis machinery
  target for several pharmaceuticals
• Composed of two subunits (large and small)
• 30S 88,000 atoms, roughly 200 Å cube
• 50S 95,000 atoms, roughly 200 Å cube
• Function involves several interesting features
• Protein-nucleic acid and protein-protein
  association
• Conformational changes
• Salt dependence (type and quantity)
• Investigated two scales
• Large-scale calculations for qualitative analysis
• Small-scale calculations to examine antibiotic
  binding

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Ribosomelarge-scale calculations

• Separate calculations on 30S and 50S subunits
• Parallel focusing
• 973 meshes
• 343 processors of Blue Horizon
• 0.41 Å (30S) and 0.43 Å (50S) resolution
• Lower resolution calculations demonstrate linear
  scaling of parallel algorithm

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Ribosomesmall-scale calculations

• Determine binding energies between 30S ribosomal
  subunit and aminoglycoside antibiotics
• Excellent fit to data 0.78 0.13 slope with
  small antibiotics, 0.95 0.19 slope without
• Suggests importance of basic functional groups on
  Ring IV

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Microtubule calculationsintroduction

• Important cytoskeletal components structure,
  transport, motility, division
• Target for variety of pharmaceuticals
• Typically 250-300 Å in diameter and up to
  millimeters in length
• Computationally difficult due to size (1,500
  atoms/Å ) and charge (-4.5 e/Å)
• Investigated microtubules on two scales
• Large-scale calculations for qualitative analysis
• Medium-scale calculations to elucidate role of
  electrostatics in stability

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Microtubuleslarge-scale calculations

• 15-protofilament microtubule assembled from dimer
  structure initially based on structure of Nogales
  et al.
• 1.2 million atoms
• 600 Å long and 300 Å wide
• Parallel focusing using 973 meshes on 686
  processors of Blue Horizon gives uniform
  resolution of 0.54 Å quantitative accuracy
• Linear scaling to 686 processors matches
  anticipated (trivial) parallel complexity

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Microtubulesmedium-scale calculations

• 30-processor calculations on complexes of 4
  tubulin dimers Meurer-Grob et al.)
• Explicit divalent ions
• Ca and all-atom descriptions
• LPBE energies
• Surface area-based apolar energy
• Examined differences between inter- and
  intra-protofilament energies
• Studied relative positioning of protofilaments
  (starting from 10.4 Å shift in original structure)

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Microtubulesprotofilament interactions
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Microtubulesprotofilament alignment
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Conclusions

• New methods and software enable large-scale
  electrostatics calculations
• Trivially parallel methods scale with computer
  technology
• Applied to several large biomolecular systems
• Microtubules
• Illustrate asymmetry of electrostatic potential
• Continuum calculations give stable binding
  energies
• Reproduce differing intra- and inter-protofilament
  affinities
• Examine protofilament alignment minimum near
  crystal structure position

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Future directions

• Trivially parallel nature makes ideal match for
  TeraGrid
• Make application TeraGrid-ready
• Enhance capabilities of Grid portal
• Work on increased user-friendliness
• Graphical front-end support (PMV)
• Large-scale visualization capabilities (PMV,
  QMView)
• Link to on-demand resource for interactive work
• Increase functionality and features of APBS

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Acknowledgements

• Thesis advisors Andy McCammon, Mike Holst
• Collaborators Art Olson, Michel Sanner,
  Chandrajit Bajaj, Phil Bourne, Kim Baldridge,
  Jerry Greenberg, David Sept, Chiansan Ma, Simpson
  Joseph, Peter Wolynes
• Computer time NPACI/SDSC, NBCR, W. M. Keck
  Foundation
• Fellowships Howard Hughes Medical Institute, La
  Jolla Interfaces in Science program

Animation by Jerry Greenberg