8.592J | Spring 2011 | Graduate

Statistical Physics in Biology

Lecture Notes

Introduction; Master Equation

Outline

TOPICS DESCRIPTION CATEGORY
I. Sequence nucleic acids in DNA/RNA; amino-acids in proteins information
II. Structure DNA double helix; RNA secondary form; protein folding interactions
III. Function building blocks, force and motion: membranes, tubules, motors… mechanisms
IV. Assembly networks: modules, patterns, collective dynamics… complexity

Evolving Probabilities

  1. Mutating Sequence:
    • Mutations & Classical genetics
    • Binary sequence of independent elements
    • Transition matrix and time dependent evolution
  2. Population Perspective:
    • Master equation for evolving population
    • Steady state (binary distribution)
    • Enzymatic analog

(Detailed Lecture Notes (PDF))

  1. Introduction to polymers:
    • Entropy and elasticity
    • Interactions and the coil-globule transition
    • Ionic interactions
  2. DNA double helix:
    • Watson-Crick pairs; symmetries
    • Energy/entropy considerations, and melting
    • Elasticity; bend, twist, and topology
    • Unzipping; translocation, packing, …
  3. RNA strands:
    • Varieties: mRNA, tRNA, ribosomal RNA, …
    • Hartree equation for obtaining secondary structures without pseudo-knots
    • Kinetics folding (local minimum) vs thermodynamics hypothesis (global minimum)
  4. Sequence to Structure maps
  5. Protein folding:
    • Role of hydrophobicity and other interactions
    • Secondary structure elements: alpha-helices & beta-sheets
    • Classification of protein structures, and their evolution
    • Simple lattice models of protein folding, solvation model
    • Random Energy Model for freezing
    • Dynamics of fast folding
    • Folding in the cell: chaperones, co-translational, agregation and fibrils
    • Hemoglobin: evolution, polymorphism, folding and fibrilation, function, regulation, …
  6. Protein-Nucleic acid composites:
    • Electrostatic interactions
    • Specific and non-specific binding of factors to DNA regulatory elements
    • Borg-von Hippel, wight matrices (profiles), information content
    • Large scale packaging of DNA; histones, heterochromatin, …

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  1. Networks:
    • Simple biological modules:
      • Transcription regulation; lac operon
      • Genetic switches
      • Signal transduction
      • Repressilator: a simple clock
    • Statistics of complex networks:
      • Random (Erdös-Rényi) networks
      • Percolation, diameter, degree distribution
      • Scale free networks, construction and properties
  2. Dynamics on networks:
  3. Biological patterns:
    • Turing instability
    • Cortical patterns

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  1. Biological information:
  2. Molecular evolution and Population genetics:
    • Mutations
      • Transition probability matrix; approach to steady state
    • Population size
      • Master equation
    • Genetic drift
    • Selection
      • Forward and backward Kolmogorov equations
  3. Gene annotation and similarity detection:

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Spring 2011
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