Computational Biology Introduction to Biomolecular Modeling

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Computational BiologyIntroduction to
Biomolecular Modeling
Instructor Prof. Jesús A. Izaguirre Textbook
Tamar Schlick, Molecular Modeling and Simulation
An Interdisciplinary Guide, Springer-Verlag,
Berlin-New York, 2002 Reference C. Brooks, M.
Karplus, B. Pettitt, Proteins A Theoretical
Perspective of Dynamics, Structure, and
Thermodynamics, Wiley, 1988
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Outline

• What is biomolecular modeling?
• Historical perspective
• Theory and experiments
• Protein characterization
• Computational successes
• Remaining challenges

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What is biomolecular modeling?

• Application of computational models to understand
  the structure, dynamics, and thermodynamics of
  biological molecules
• The models must be tailored to the question at
  hand Schrodinger equation is not the answer to
  everything! Reductionist view bound to fail!
• This implies that biomolecular modeling must be
  both multidisciplinary and multiscale

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Historical Perspective

• 1946 MD calculation
• 1960 force fields
• 1969 Levinthals paradox on protein folding
• 1970 MD of biological molecules
• 1971 protein data bank
• 1998 ion channel protein crystal structure
• 1999 IBM announces blue gene project

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Theoretical Foundations

• Born-Oppenheimer approximation (fixed nuclei)
• Force field parameters for families of chemical
  compounds
• System modeled using Newtons equations of motion
• Examples hard spheres simulations (alder and
  Wainwright, 1959) Liquid water (Rahman and
  Stillinger, 1970) BPTI (McCammon and Karplus)
  Villin headpiece (Duan and Kollman, 1998)

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Experimental Foundations I

• X-ray crystallography
• Analysis of the X-ray diffraction pattern
  produced when a beam of X-rays is directed onto a
  well-ordered crystal. The phase has to be
  reconstructed.
• Phase problem solved by direct method for small
  molecules
• For larger molecules, sophisticated Multiple
  Isomorphous Replacement (MIR) technique used
• Current resolution below 2 \AA
• Protein crystallography
• Difficult to grow well-ordered crystals
• Early success in predicting alpha helices and
  beta sheets (Pauling, 1950s)

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Experimental Foundations II

• NMR Spectroscopy
• Nuclear Magnetic Resonance provides structural
  and dynamic information about molecules. It is
  not as detailed as X-ray, limited to masses of 35
  kDa
• Distances between neighboring hydrogens are used
  to reconstruct the 3D structure using global
  optimization

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Proteins I

• Polypeptide chains made up of amino acids or
  residues linked by peptide bonds
• 20 aminoacids
• 50-500 residues, 1000-10000 atoms
• Native structure believed to correspond to energy
  minimum, since proteins unfold when temperature
  is increased

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Protein Function in Cell

• Enzymes
• Catalyze biological reactions
• Structural role
• Cell wall
• Cell membrane
• Cytoplasm

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Protein The Machinery of Life
NH2-Val-His-Leu-Thr-Pro-Glu-Glu- Lys-Ser-Ala-Val-T
hr-Ala-Leu-Trp- Gly-Lys-Val-Asn-Val-Asp-Glu-Val- G
ly-Gly-Glu-..
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Proteins II

• Secondary structure alpha helices, beta sheets,
  turns
• Tertiary structure proteins are tightly packed,
  with hydrophobic groups in the core and charged
  sidechains in the surface
• Quaternary structure protein domains may
  assemble into so called quaternary structures

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Protein Structure
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Protein Structure
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Model Molecule Hemoglobin
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Hemoglobin Background

• Protein in red blood cells

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Red Blood Cell (Erythrocyte)
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Hemoglobin Background

• Protein in red blood cells
• Composed of four subunits, each containing a heme
  group a ring-like structure with a central iron
  atom that binds oxygen

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Heme Groups in Hemoglobin
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Hemoglobin Background

• Protein in red blood cells
• Composed of four subunits, each containing a heme
  group a ring-like structure with a central iron
  atom that binds oxygen
• Picks up oxygen in lungs, releases it in
  peripheral tissues (e.g. muscles)

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Hemoglobin Quaternary Structure
Two alpha subunits and two beta subunits (141 AA
per alpha, 146 AA per beta)
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Hemoglobin Tertiary Structure
One beta subunit (8 alpha helices)
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Hemoglobin Secondary Structure
alpha helix
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Proteins III

• Protein motions of importance are torsional
  oscillations about the bonds that link groups
  together
• Substantial displacements of groups occur over
  long time intervals
• Collective motions either local (cage structure)
  or rigid-body (displacement of different regions)
• What is the importance of these fluctuations for
  biological function?

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Proteins IV

• Effect of fluctuations
• Thermodynamics equilibrium behavior important
  examples, energy of ligand binding
• Dynamics displacements from average structure
  important example, local sidechain motions that
  act as conformational gates in oxygen transport
  myoglobin, enzymes, ion channels

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Proteins V Local Motions

• 0.01-5 AA, 1 fs -0.1s
• Atomic fluctuations
• Small displacements for substrate binding in
  enzymes
• Energy source for barrier crossing and other
  activated processes (e.g., ring flips)
• Sidechain motions
• Opening pathways for ligand (myoglobin)
• Closing active site
• Loop motions
• Disorder-to-order transition as part of virus
  formation

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Proteins VI Rigid-Body Motions

• 1-10 AA, 1 ns 1 s
• Helix motions
• Transitions between substrates (myoglobin)
• Hinge-bending motions
• Gating of active-site region (liver alcohol
  dehydroginase)
• Increasing binding range of antigens (antibodies)

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Proteins VII Large Scale Motion

• gt 5 AA, 1 microsecond 10000 s
• Helix-coil transition
• Activation of hormones
• Protein folding transition
• Dissociation
• Formation of viruses
• Folding and unfolding transition
• Synthesis and degradation of proteins
• Role of motions sometimes only inferred from two
  or more conformations in structural studies

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Study of Dynamics I

• The computational study of atomic fluctuations in
  BPTI and other proteins has shown that
• Directional character of active-site fluctuations
  in enzymes contributes to catalysis
• Small amplitude fluctuations are lubricant
• It may be possible to extrapolate from short time
  fluctuations to larger-scale protein motions

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Study of Dynamics II

• Collective motions particularly important for
  biological function, e.g., displacements for
  transition from inactive to active
• Extended nature of these motions makes them
  sensitive to environment great difference
  between vacuum and solution simulations
• Collective motions transmit external solvent
  effects to protein interior

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Study of Dynamics III

• For the related storage protein, myoglobin
• Fluctuations in the globin are essential to
  binding the protein matrix in X-ray is so
  tightly packed that there is no low energy path
  for the ligand to enter or leave the heme pocket
• Only through structural fluctuations can the
  barriers be lowered sufficiently
• Demonstrated through energy minimization and
  molecular dynamics

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Study of Dynamics IV

• For the transport protein hemoglobin there are
  several important motions
• Oxygen binding produces tertiary structural
  change
• A quaternary structural change from deoxy (low
  oxygen affinity) to oxy configuration takes
  place. This transmits information over a long
  distance
• From the X-ray deoxy and oxy structures, a
  stochastic reaction path has been found. Detailed
  ligand binding has been performed using MD. A
  statistical mechanical model has provided
  coupling between these two processes

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Study of Dynamics VI

• Three open problems are the following
• Ion channel gating highly correlated
  fluctuations are likely to be of great
  importance. Long time dynamics problem
• Flexible docking for MMP, enzymes, etc.,
  fluctuations enter into thermodynamics and
  kinetic of reactions. Sampling problem
• Protein folding too complicated for full
  treatment but for smallest proteins, beyond
  current methodology. Coarsening problem

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Possible topics for final projects

• Applications
• Virtual screening
• Extend recommender for MD protocols
• Algorithms
• Multiscale integrators or sampling methods
• Cellular automata solvers for diffusion,
  reaction, advection, etc.
• Software
• 3D Visualization
• Extend simulation engines

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How to create hierarchical, multiscale,
multilevel algorithms?

• Examples
• Algorithms for N-body problem (linear complexity,
  multiple grids) e.g., Matthey and Izaguirre
  (2004) J. Par. Dist. Comp.
• Multiscale integration (15 order of magnitude gap
  on timescales) e.g. Ma and Izaguirre (2003),
  Multisc. Model. Simul.
• Coarse approximations (use averaging or
  stochastic or ensemble) solutions, e.g. Izaguirre
  and Hampton (2004), J. Comp. Phys.

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Lengthening scales DPD

• Dissipative Particle Dynamics combines coarsening
  of atoms into fluid packages with dissipative
  pair interactions, and a stochastic pair
  interaction
• Total momentum conserved

• Self-organization of lipid bilayer,
  self-assembled aggregates formed by amphiphilic
  lipid molecules in water.

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Lengthening Scales SRP

• Enzyme simulation of a ms using stochastic
  reaction path disadvantage need initial and
  final configuration
• Finds a trajectory where global energy is
  minimized

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How to predict protein interaction networks?

• Goal
• Predict proteins in a genome that are likely to
  interact, thus giving clue as to their function.
• Our current solution starts from experimental
  interaction data and uses clustering and a set
  cover approach to predict novel interactions.
• This is documented in Huang et al. (2004),
  IEEE/ACM TCBB, submitted

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How to create high-performance software that is
easy to use?
ProtoMol, CompuCell3D, Biologo

• Goals
• Encapsulate optimizations like parallelism and
  cluster/grid computing so that these can be used
  easily. MATLAB and Mathematica are examples of
  easy to use scientific software
• Allow easy prototyping of algorithms, extensions
  of the software by computational scientists (not
  expert computer scientists)
• Our current solutions use
• Generic and object-oriented programming
• Design patterns
• XML-based domain specific languages

• Related publications
• Matthey et al. (2004) ACM Trans. Math. Software,
  20(3)
• Cickovski et al. (2004) IEEE/ACM Trans. Comput.
  Biol. and Bioinformatics
• Cickovski and Izaguirre (2004) ACM Trans. Prog.
  Lang. and Systems, in preparation

ProtoMol is open source and available at
http//protomol.sourceforge.net
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How to help user select software, algorithms, and
parameters to solve their problems?
Simulation Requirements
Optimal parameters via XML
ProtoMol/MDSimAid Server
Our solution uses performance models and machine
learning to generate rules, run-time optimization
to fine tune suggestions. We want to use agents
and machine learning to update the rules. This is
documented in Ko (2002) and Crocker et al.
(2004), J. Comp. Chem.
Goal Recommend optimal software and
architectural parameters to solve particular
problems Make this easily available as web portals