Mathematical Cell Biology Graduate Summer Course
Instructor: Leah Edelstein-Keshet
May 1-31, 2012
Tentative Schedule
The actual schedule may be amended slightly.
- 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
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