Modern Statistical Mechanics and Protein Research

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Modern Statistical Mechanics and Protein Research

• Introduction
• Statistical mechanics can be applied in the
  research of disordered condensed system
• Disordered
• Condensed
• System

Spin glass
Homo-
Polymer
Hetero-
Protein
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• Objective
• Given the nature of subunits, to investigate
• a. Proteins structures
• b. Proteins features
• c. Interactions with other biological
  systems
• Subunit amino acid

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• Research methods --- Computational methods
• HP lattice model
• - Consider hydrophobic(H) and polar(P)
• amino acid residues only
• - Exhaustive computer enumeration
• for short chain (Chan and Dill, 1991)
• - Maximum entropy chain SklnO
• (Fiebig and Dill, 1993)

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• Monte Carlo methods
• - Mechanism
• . Key Random number generator
• . Compute
• procedures
• pick a state (any state), call it k
• pick a new trial state n at random
• if p(n)/p(k) gt1, move to state n
• if p(n)/p(k) lt1, move to state n
• with possibility 0lt p(n)/p(k) lt1
• from this, walk then

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• Monte Carlo Methods (continue)
• Metropolis MC procedure for protein
• . Similar to Ising model a new
• conformation is randomly chosen and the
• new conformation accepted or rejected
• based on Boltzmann distribution
• . Selection of new conformation must
• involve major portion of chain to avoid
• glassy state

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• Monte Carlo Methods (continue)
• . Long-range interactions are necessary
• for protein folding to the native state,
• but not sufficient
• . Short-range interactions (secondary
• structure) be considered before long-
• range interactions (tietiary structure)
  
• take effect

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• Monte Carlo Methods (continue)
• Feature
• . Well suited to find the lowest energy
• conformation (protein folding)
• Drawback
• . Sample only a small part of configuration
• space near the initial conformation

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• Spin glass model
• - Key words
• freezing temperature, frustration
• - Simple model
• E energy of protein ei energy of i th
  residue
• Ji,i1 nearest neighbor interaction energy
• KiJ energy of short range interactions
  between residues

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• c. Spin Glass model (continue)
• - Similarities
• Spin Glass
  Protein
• 1. Freezing transition denatured state to
  
• 
  native or glass state
• 2. Frustration by local free energy minima
• 3. Magnetic state residues
  randomly
• randomly distributed distributed
• 4. Order parameter
• ltmgt2 fraction of
  residues
• in
  native states

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• Molecular dynamics method
• - Generate microscopic information
• - Convert to macroscopic observables
• - Ergodic hypothesis
• ensemble average time average
• - Newtons equation of motion
• - Simulation of solvated proteins
• calculated up to nanosec scale,
• millisec regime reported
• - CHARMM program by Harvard Univ.
• - First protein simulation of bovine
  pancreatic trypsin
• inhibitor (BPTI) (McCammon, et al, 1977)

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• Applications in study of
• Protein folding
• Protein stability
• Protein conformational changes
• Molecular motion
• Molecular recognition DNA, membranes, complexes
• Ion transport in biological systems
• Drug design

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• References
• D. Chandler, Introduction to Modern Statistical
  Mechanics (Oxford University Press, New York,
  1987)
• R. E. Wilde and S. singh, Statistical Mechanics,
  Fundamentals and Modern Applications (John Wiley
  Sons, Inc, new York, 1998)
• Theory of Molecular Dynamics Simulations,
  http//www.ch.embnet.org/MD_turorial/pages/MD.part
  1.html
• McCammon, J. A., Gelin, B. R., and Karplus, M.
  Nature (Lond.) 267, 585 (1977)