Mathematical Cell Biology Graduate Summer Course

Instructor: Leah Edelstein-Keshet

May 1-31, 2012

Tentative Schedule

• May 1-4:
  • Leah Keshet
    • Introduction to problems in Cell Biology - where chemistry, and physics meet life
    • Simulation software (XPP)
    • Chemical reactions, kinetics, and circuits
    • Signaling cascades
    • Introduction to non-dimensionalization and scaling
    • Simple polymerization reactions
  • Raibatak (Dodo) Das
    • Cell biology imaging techniques
      • 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
      • 2. Fluorescence microscopy: Fluorescent labelling biological samples | Epifluorescence microscopy |
        Confocal fluorescence microscopy
      • 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging (time permitting)
      • 4. FRAP data and modelling integrin dynamics
• May 7-11:
  • Leah Keshet
    • Combining mechanics and biochemistry
    • Application of scaling to deciphering a molecular mechanism
    • Actin and cytoskeleton assembly
    • Actin dynamics in the (1D) cell lamellipod
    • Continuity (Balance) eqs and Reaction-Diffusion eqs (PDEs)
  • Jun Allard
    • 1. Bonds, springs, dashpots and motors
      • Bipedal cells [Barnhart 2011 Biophys J]
      • Slip-clutch [Chan and Odde 2008 Science]
      • Fixed-timestep stochastic simulation (Matlab)
    • 2. Biopolymer mechanics
      • Solid mechanics, Young's modulus
      • Functional derivatives and Euler-Lagrange equations
      • Euler buckling
      • Microtubule buckling in a liposome [Elbaum et al 1996 Phys Rev Lett]
      • Microtubule buckling in a cell [Brangwynne et al 2006 J Cell Sci]
    • 3. Diffusion in a potential and thermal forces
      • Smoluchowski equation (diffusion-advection equation)
      • Huxley muscle model [Howard, Chapter 16]
      • Einstein relation
      • Kramar rate theory, diffusion-limited on-rates and Bell's Law
      • Dimer-level microtubule assembly [VanBuren 2002 Proc Natl Acad Sci] (Matlab)
      • Entropy
    • 4. Thermal forces on biopolymers
      • Brownian ratchet and Elastic Brownian ratchet [Mogilner and Oster 1996 Biophys J]
      • Pulling by a depolymerizing microtubule [Peskin and Oster 1995 Biophys J]
      • Master equation for discrete state space models
      • Polymerization in a bundle
    • 5. Mechanics of two- and three-dimensional structures
      • Breaking of actin gels [van der Gucht 2005 Proc Natl Acad Sci]
      • Membrane mechanics
      • Stochastic simulation using Metropolis-Hastings (Matlab)
      • T-cell receptor mechanics [Allard et al 2012 Biophys J]
    • 6. Extra stuff
      • Laplace pressure
      • Membrane tension instabilities [Sedzinski et al 2011 Nature]
      • Immune synapse [Qi and Chakraborty 2001 Proc Natl Acad Sci]
      • Shape of the golgi [Shibata et al 2010 Cell]
• May 14-18:
  • Leah Keshet
    • Morphogenesis and positional information
    • Bicoid gradients in Drosophilla development
    • Turing RD systems and pattern formation
    • Chemotaxis and aggregation (self-study material)
  • Dodo Das
    • Data Analysis methods:
      • 1: Motivation | The principle of maximum likelihood | Least squares regression | Linear regression
      • 2: Nonlinear regression | Levenberg-Marquardt algorithm | Other likelihood-maximization methods | Parameter confidence intervals
      • 3: Bootstrap confidence intervals | Assessing differences in parameter distributions using bootstrap
      • 4: Model selection | Bias variance trade-off | F-test | Akaike's information criterion
  • Bill Holmes
    • (1) Local Pulse Analysis for RD equations: Theory and Context
    • (2) LPA - Finer Points
    • (3) Matcont for Bifurcation Analysis (With associated matcont examples)
    • (4) Wave Pinning, Actin Waves, and LPA (With associated matcont examples)
• May 22-25:
  • Dimitrios Vavylonis
    • Diffusion-controlled processes in the cell and sensing in bacterial chemotaxis
      • Compact vs non-Compact Exploration [deGennes, Macromolecules 1982]
      • Bacterial Chemotaxis [Berg and Purcell Biophys J 1977]
      • Reduction of Dimensionality [Philips, Kondev and Theriot, Physical Biology of the Cell]
      • Formins and Tip-tracking
    • Robustness of protein circuits [from Alon, "Introduction to Systems Biology, Chapter 8].
      • precise adaptation in chemotaxis
      • fine tuned versus robust models
    • Molecular motors: porters vs rowers and cooperativity
      • Introduction to myosin, kinesin, and dynein
      • Thermal ratchet models
      • Duty ratio
      • Porters versus Rowers [Leibler and Huse, JCB 1993]
      • Muscle Contraction [Duke, PNAS 1999]
    • Cytokinesis
      • Assembly of the Contractile Ring
      • Search, capture, pull and release model [Vavylonis, Wu et al, 2008]
      • Role of actin filament cross-linkers
  • Leah Keshet
    • Cell motility models and simulations: a survey
    • Hamiltonian-based models (Cellular Potts)
    • Level set and mechanical cell motility models
    • Keratocyte shape models
    • Cell polarization models (self-study material)
    • Travelling waves and wavepinning (self-study material)
• May 28-31:
  • Conclusions
  • Student projects