# Mathematical Cell Biology Summer Course

This graduate course, taught May 1-31, 2012, was partially sponsored by the PIMS

International Graduate Training Center (IGTC) in Math-Biology, and by independent

funding held by Leah Keshet. Large parts of this course are available online at the

course Home Page,

where relevant biological topics and mathematical background needed to understand

current research in mathematical cell biology were taught. Some background in

(undergraduate) differential equations (ODEs, PDEs) is assumed. This course was

taught for credit at UBC (Math 563) or at the affiliated western universities under

the Western Dean's agreement. Lectures were held at the UBC campus of the Pacific

Institute for the Mathematical Sciences (PIMS), and were available via live links

online. This archive preserves most of the lectures in video format.

## Special Seminars

A number of special seminars were scheduled to coincide with the course.

- Week 1: James Feng - A Particle Based Model for Healthy and Malaria Infected Red Blood Cells
- Week 2: Daniel Coombs - Models of T cell activation based on TCR-pMHC bond kinetics
- Week 3: Adriana Dawes - Spatial Segregation Polarity Determinants of the Nematode Worm C. elegans
- Week 3: Eric Cytrynbaum - Self Organization in Cells, How to use Protiens to Solve a Geometry Problem
- Week 5: Francois Faure - From Computer Graphics to Computational Biology

## Tentative Schedule

The actual schedule may be amended slightly.

- May 1-4:
- Leah Keshet - Introduction: Cell motility and its regulation
- Leah Keshet - Simple Biochemcial Motifs (1, 2, & 3)
- linear, Michaelian, and sigmoidal kinetics
- Bistability, biochemical and genetic switches
- Bifurcation analysis with XPP

- Leah Keshet - Switches, Oscillators (and the Cell Cycle)
- Leah Keshet - Signalling, Small GTPasses and Cell Polarization
- Cory Simon - Pattern Formation of Proteins on the Surface of a Biological Cell
- 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 - Lecture 1****Raibatak (Dodo) Das - Lecture 2****Raibatak (Dodo) Das - Lecture 3****Raibatak (Dodo) Das - Lecture 4**- 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

- 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of

- May 7-11:
- Leah Keshet
**Leah Keshet - An Excitable Contractile Cell****Leah Keshet - Introduction to Polymerization Kinetics****Leah Keshet - Microtubules, - polymer size distribution - and other balance equation models****Leah Keshet - Polymer Size Distributions (continued)****Leah Keshet - Three Short Stories About Molecular Motors**- 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)
- Bicoid gradients

**Jun Allard****Lecture 1**Bonds, springs, dashpots and motors.

Wobbling keratocytes [Barnhart et al 2010 Biophys J]; Slip-clutch in

nerve growth cones and fixed-timestep stochastic simulation [Chan and

Odde 2008 Science]**Lecture 2**Biopolymer mechanics. The energy

functional, Young~Rs modulus, Euler-Lagrange equations; Microtubules

buckling in vesicles [Elbaum et al 1996 Phys Rev Lett] and in cells

[Brangwynne et al 2006 J Cell Sci].**Lecture 3**Thermal forces. Z-rings in a liposome

[Cytrynbaum et al 2012 Phys Rev E]; Fokker-Planck equations, the

Einstein relation and the principle of detailed balance;

Diffusion-limited attachment, Kramer rate theory, Bell~Rs Law;

Dimer-level microtubule assembly and Gillespie stochastic simulation

[vanBuren et al 2002 Proc Natl Acad Sci].**Lecture 4**Applications of thermal forces. Elastic

Brownian ratchet [Mogilner and Oster 1996 Biophys J]; Pulling by a

depolymerizing microtubule, master equations in discrete state space

[Peskin and Oster 1995 Biophys J]; Gel symmetry breaking [van der

Gucht et al 2005 Proc Natl Acad Sci].**Lecture 5**Membranes. Canham-Helfrich energies, the

Monge representation, Metropolis-Hastings simulation for thermal

fluctuations. Antigen bonds in T cells [Allard et al 2012 Biophys J].

- May 14-17:
- Leah Keshet
**Leah Keshet - Diffusion, Reaction and Biological Pattern Formation****Leah Keshet - Diffusion, Reaction and Biological Pattern Formation (continued 2 of 3)****Leah Keshet - Diffusion, Reaction and Biological Pattern Formation (continued 3 of 3)**- Turing RD systems and pattern formation
- Chemotaxis and aggregation
- Cell polarization models
- Travelling waves and wavepinning

**Dodo Das****Bill Holmes****Bill Holmes - Lecture 1****Bill Holmes - Lecture 2****Bill Holmes - Lecture 3****Bill Holmes - Lecture 4**- Local Pulse Analysis for RD equations
- Actin Waves
- Matlab examples and exercises

- Leah Keshet
- May 21-25:
**Dimitrios Vavylonis****Dimitrios Vavylonis - Lecture 1****Dimitrios Vavylonis - Lecture 2****Dimitrios Vavylonis - Lecture 4****Dimitrios Vavylonis - Lecture 4a**

- Regulatory circuits in Bacterial Chemotaxis and motility
- Introduction to molecular motors, porters vs rowers and cooperativity of myosin in muscle
- Microtubule dynamics
- Cytokinesis
- FRAP studies of microtubule dynamics in the mitotic spindle

- Leah Keshet
**Leah Keshet - Models for Cell Shape and Actin Filament Distributions****Leah Keshet - Cell Polarity Models & Simulating Cell Motility Using the Cellular Potts Model****Leah Keshet - Mechanical Simulations of Cell Motility**

- Signaling to actin in cell motility
- Crosstalk, feedback, and assembling signaling networks
- Cell motility models and simulations: a survey
- Hamiltonian-based models (Cellular Potts)
- Level set and mechanical cell motility models
- Keratocyte shape models

- May 28-31:
- Conclusions
- Student projects
- Rebecca Hiller - Spindle Assembly checkpoint
- Meghan Dutot - Local Pulse Analysis applied to polarization models
- Laura Liao - Positional information and gradients
- May Ann Mata - Glucose, Insulin, and beta cell dynamics
- Tenghu Wu - Reaction diffusion patterns
- Jia Guo - Transport of early endosomes on microtubules
- Naghmeh Rezai - Mechanics of invadopods
- Brendan Thrasher - Size regulation in cell organelles
- Amanda Swan - Diffusion of receptors on a cell membrane
- Hildur Knutsdottir - Cell-cell signaling between macrophages and mammory Tumor Cells

- Leah Keshet

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