The University of Texas Health Science Center

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The University of Texas Health Science Center at
San Antonio, Department of Biochemistry Borries
Demeler, Ph.D.
Computational Challenges in Biophysics Two
Applications in Hydrodynamics
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Hydrodynamic Studies of Biological Macromolecules

• Using hydrodynamic approaches, we can model
  transport processes Sedimentation and Diffusion
• Analytical Ultracentrifugation
• Experimental Background
• Models and Parameterization
• Optimization
• Bead Modeling
• Examples

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Hydrodynamic Studies of Biological Macromolecules

• Why study the structure and function of
  macromolecules and macro-molecular assemblies
  with analytical ultracentrifugation (AUC)?
• Molecules can be studied in a physiological
  environment (pH,
  concentration, ionic strength, oxidation state,
  ligands, etc.)?
• Molecules are not fixed to a microscope grid
• Molecules are not distorted by crystal packing
  forces
• Very large size range (102 108 Dalton,
  complements cryo-EM and NMR)?
• Several detectors available (Rayleigh
  Interference, UV/VIS, Fluorescence Emission,
  Schlieren, Turbidity, MWL, Raman, SALS)?
• Dynamic processes can be studied
• Conformational changes, reversible
  self-association, binding strengths, slow
  kinetics
• Composition analysis
• Partial concentration, molecular weight, shape
• First Principles approach

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Hydrodynamic Studies of Biological Macromolecules

• Why study the structure and function of
  macromolecules and macro-molecular assemblies
  with analytical ultracentrifugation (AUC)?
• Molecules can be studied in a physiological
  environment (pH,
  concentration, ionic strength, oxidation state,
  ligands, etc.)?
• Molecules are not fixed to a microscope grid
• Molecules are not distorted by crystal packing
  forces
• Very large size range (102 108 Dalton,
  complements cryo-EM and NMR)?
• Several detectors available (Rayleigh
  Interference, UV/VIS, Fluorescence Emission,
  Schlieren, Turbidity, MWL, Raman, SALS)?
• Dynamic processes can be studied
• Conformational changes, reversible
  self-association, binding strengths, slow
  kinetics
• Composition analysis
• Partial concentration, molecular weight, shape
• First Principles approach

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AUC Experimental Setup
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AUC Background Experiment at Rest
At Rest rotor speed 0
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AUC Background Sedimentation Velocity
Sedimentation Velocity Duration is
hours high rotorspeed
At Rest rotor speed 0
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AUC Background Sedimentation Equilibrium
Sedimentation Velocity Duration is
hours high rotorspeed
Sedimentation Equilibrium Duration
is gt 1 day low rotorspeed
At Rest rotor speed 0
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Sedimentation Velocity
Sedimentation velocity profile of a mixture of
macromolecules over time
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Sedimentation Velocity
Composition Analysis We need to answer these
questions

• How many components?

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Sedimentation Velocity
Composition Analysis We need to answer these
questions

• How many components?
• What are their molecular weights?

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Sedimentation Velocity
Composition Analysis We need to answer these
questions

• How many components?
• What are their molecular weights?
• What are their shapes?

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Sedimentation Velocity
Composition Analysis We need to answer these
questions

• How many components?
• What are their molecular weights?
• What are their shapes?
• What is the partial concentration of each
  component?

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Sedimentation Velocity
Composition Analysis We need to answer these
questions

• How many components?
• What are their molecular weights?
• What are their shapes?
• What is the partial concentration of each
  component?
• What is the reliability of our measurement?

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Initialization of Genetic Algorithms
Diffusion coefficients are randomly assigned
based on a reasonable range from the frictional
ratio k f/f0 parameterization
k 1.0
1.0 k 4.0 for most proteins, higher for
rod-shaped and unfolded proteins, DNA, fibrils
and aggregates or linear molecules
k 1.2 - 2.5
k gt 3
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Optimization Approach 1
Solving the inverse problem of finding the
parameters for the finite element solution of the
Lamm equation that best reconstructs the
experimental data Solution Use a stochastic
optimization approach Example Genetic
Algorithms
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Genetic Algorithms (GA)

• Genetic algorithms (GA) provide a
• stochastic optimization method
• Evolutionary paradigm for adjusting parameters
• Mutation, recombination, deletion, insertion,
  crossover operators
• Random number generators are used to manipulate
  operators
• Generational Model survival of the fittest
  (...fitting function)?
• Generation ? iterations, genes ? parameter
  strings, bases ? s, D
• J.H. Holland, Adaption in Natural and Artificial
  Systems, 1975, U. of Michigan Press
• J.R. Koza, Genetic Programming On the
  Programming of Computers by Means of Natural
  Selection, 1992, MIT Press

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GA genes
Genes are strings of parameters, each gene
consists of a pair of corresponding
sedimentation and diffusion coefficients.
S1 S2 S3 ... Sn
Gene
D1 D2 D3 ... Dn
Component n
Component 3
Component 2
Component 1
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Mutation
Generation 1
Generation 2
S1a S2a S3a ... Sna
S1a S2a S3a ... Snc
Gene A
D1a D2a D3a ... Dna
D1a D2a D3a ... Dna
Mutation
S1b S2b S3b ... Snb
S1b S2b S3b ... Snb
Gene B
D1b D2b D3b ... Dnb
D1b D2c D3b ... Dnb
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Genetic Algorithm Implementation

• Concentration values of components j in each gene
  G are determined with NNLS (a linear fitting
  approach)
• Mutation/Crossover/Recombination operators are
  applied
• Progeny is calculated and this process is
  iterated
• Deme migration and regularization rates are
  applied
• Typically 100 individuals/deme
• 30-50 generations leads to convergence
• Lawson, C. L. and Hanson, R. J. 1974. Solving
  Least Squares Problems. Prentice-Hall, Inc.
  Englewood Cliffs, New Jersey

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Optimization Approach 2
Solving the inverse problem of finding the
parameters for the finite element solution of the
Lamm equation that best reconstructs the
experimental data Solution Linearize the
problem Example 2-dimensional Spectrum Analysis
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2-D Spectrum Analysis
Blue initial grid points. Perform NNLS and
save non-zero coefficients.
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2-D Spectrum Analysis
NNLS result Blue zero Red positive value
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2-D Spectrum Analysis
1. Filter nonzero results 2. Refine grid 3.
Perform Monte Carlo 4. Initialize GA parameter
space 5. Use GA analysis to increase
parsimony 6. Use Monte Carlo to reduce signal
from noise
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Final Result is used to initialize GA
Idea Build probability surfaces around each
non-zero entry and use the surface to initialize
the GA. Surfaces can be circular, elliptical, or
rectangular Probabilities from neighboring
points add up.
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2-D Spectrum Analysis refinement - Example

• Simulate a 5-component system with heterogeneity
  in shape and mass
• Add stochastic noise equivalent to instrument

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2-D Spectrum Analysis refinement - Example

• Final result is not parsimonious doesn't
  satisfy Occam's razor
• Solution is over-determined
• Noise contributes to false positives

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Implementation of Monte Carlo Method

• The Monte Carlo method is a stochastic approach
  that can be used to identify the effect noise has
  on the reliability of determined parameters. With
  the Monte Carlo approach the statistical
  confidence limits of each measured parameter can
  be determined.
• Recipe for Monte Carlo
• Obtain a best-fit solution from regularized GA
  fit and confirm that the residuals are random and
  without systematic deviation
• Generate new synthetic Gaussian noise with the
  same quality as was observed in the original
  experiment and add it to the best-fit solution
• Re-fit the solution
• Repeat (2-4) at least 100 times and collect all
  parameter values
• Calculate statistics from Monte Carlo
  distribution for each parameter

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2-D Spectrum Analysis refinement - Example

• Perform 2DSA Monte Carlo analysis to amplify
  signal linearly
• Stochastic noise only amplifies with

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2-D Spectrum Analysis - Refinement

• Stochastic noise signals disappear when frequency
  is plotted
• Sample signal is amplified

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Genetic Algorithm Analysis - Refinement

• Genetic Algorithm produces parsimonious solution
• Still affected by stochastic noise

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Global Genetic Algorithm Monte Carlo Analysis

• Add low-speed data to emphasize diffusion signal
• Perform global GA Monte Carlo analysis

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High-Performance Computing Implementation
The 2 dimensional Spectrum Analysis and the
Genetic Algorithms present several
parallelization targets

• Calculation of finite element models for
  noninteracting solutes
• Calculation of individual genes
• Parallelization of NNLS
• Calculation of each subgrid
• Calculation of individual demes

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Bioinformatics Core Facility (BCF) Cluster Master
Node
UltraScan LIMS DB
Webserver
Local Supercomputer
TIGRE HPC Grid
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CuZn Superoxide Dismutase mutant - freshly
purified hSOD mutant protein (Data kindly
provided by P.J. Hart and Sai Venkatesh
Seetharaman, UTHSCSA/Biochemistry)?
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CuZn Superoxide Dismutase mutant - After 7 days
showing clear signs of degradation (monomer
species is visible) and aggregation and
unfolding. Aggregation is proceeding in an
end-to-end fashion forming a fibril-like
conformation. Dimer peak is showing several
conformations. (Data kindly provided by P.J. Hart
and Sai Venkatesh Seetharaman, UTHSCSA/Biochemistr
y)?
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Mo30Fe72 (Keplerate)?
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A
B
B
D
C
Example Clathrin baskets assembling from
clathrin triskelia (A). The sample also displays
several nonglobular species which represent the
building block subunits required for assembly of
intact baskets (B, D). Sample shows a large
heterogeneity of different sized baskets that
assume a mostly globular form with a unity
frictional ratio (B,C). (Data kindly provided by
E. Lafer, UTHSCSA, Dept. of Biochemistry)?
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eNOS-NOSIP Binding Experiment GA/MC analysis
ENOS-NOSIP 10
ENOS-NOSIP 11
ENOS-NOSIP 10
ENOS-NOSIP 15
ENOS-NOSIP 110
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UltraScan Software

• Open Projects
• Analysis Software
• Add interacting models to GA, 2DSA for
  hetero-associating systems and reversibly
  self-associating systems, develop new
  optimization methods
• Implement Monte Carlo methods for accurate
  confidence limits
• Enhance Web-based application interfaces
• Global analysis
• Additional parallelizations
• Software Developments for new Detectors
• Multiwavelength UV/Visible detectors (project is
  in collaboration with Dr. Helmut Cölfen, Max
  Planck Institute, Berlin, Germany)?

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Project 2 Bead Modeling
Use Bead Modeling to represent atomic structures
from NMR and X-ray Crystallography and calculate
hydrodynamic parameters for the model from an
assembly of beads (Project in Collaboration with
Dr. Mattia Rocco, Italian Cancer Research
Institute, Genova, Italy)?
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Program SOMO (SOlution MOdeller) generating
medium-resolution bead models from atomic
coordinates
Main features 1 bead/side chain 1 bead/peptide
bond. Water of hydration included in each bead.
A?B Exposed side -chains beads are placed.
B?C Beads overlapping by more than a preset
threshold can be fused together. Overlaps are
then removed hierarchically, reducing the radii
and outward translating the centers of exposed
beads.
C?D Exposed peptide bond beads are placed and
overlaps removed.
D?E Buried beads are placed and overlaps removed.
They should be excluded from the computations of
the hydrodynamic parameters.
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Program UltraScan SOMO (SOlution MOdeller)
Front-end GUI Used to enter new residues and to
define beads
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Program UltraScan SOMO (SOlution MOdeller)

• Open Projects
• Introduce flexibility between beads consistent
  with bond constraints and model conformational
  heterogeneity and Brownian motion.
• This will provide translational diffusion
  coefficients, and rotational diffusion
  coefficients from trajectories.
• Software needs to be developed to implement
  parallel Monte Carlo approaches for simulation

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Acknowledgements

• Department of
• Applied Mathematics
• Dr. Weiming Cao

• Department of
• Computer Science
• Dr. Raj Boppana
• Emre Brookes

UTSA
Warren Smith, Ashok Adiga the rest of the good
folks at TACC, the TIGRE Team from HIPCAT, and
all the TIGRE sites that spent time to provide us
with access help to get the software working.
Max-Planck Institute for Colloids and Interfaces

• Dr. Helmut Cölfen

• Department of Biochemistry
• Virgil Schirf
• Jeremy Mann
• Yu Ning
• Bruce Dubbs
• Dan Zollars

• Funding
• National Science Foundation
• NSF Teragrid
• San Antonio Life Science Institute
• Howard Hughes Medical Institute
• UT Permanent University Fund