Mathematics

Cell Polarity Models & Simulating Cell Motility Using the Cellular Potts Model (CPM)

Speaker: 
Leah Edelstein-Keshet
Date: 
Wed, May 23, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
First, the universal features of polarizing cells are listed, and details of the Mori-Jilkine wave-pinning model are assembled and discussed biologically and mathematically. A short review of thelocal pulse analysis is provided to indicate the usefulness of this method of analysis. Then, I discuss the survey of polarizing cells from a paper by Jilkine and LEK (2011) that appeared in PLoS Comput Biol 7(4): e1001121. Here, common and distinct attributes of different cell types and of several models for cell polarization are compared. The responses of models to a set of computational perturbations mimicking stimuli protocols are described. This lecture introduces the topic of 2D cell motility simulations, but focuses on one specific method, the CPM (as implemented by Maree et al in Bull Math Biol (2006), 68(5):1169-1211 and PLoS Comput Biol (2012) 8(3): e1002402). I explain the details of the method, the biological facts that were included (signaling from GTPases and phosphoinositides to actin assembly and myosin contraction). I illustrate typical results, and then discuss some of the technical aspects of the method, emphasizing its link to the (previously discussed) Metropolis-Hastings algorithm. I also show how Stan Maree was able to chose CPM parameters to phenomenologically mimic the known relationship between actin filament ends and cell protrusion speed.

Mathematical Cell Biology Summer Course Lecture 33

Speaker: 
Dimitrios Vavylonis
Date: 
Wed, May 23, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
Introduction to molecular motors, porters vs rowers and cooperativity of myosin in muscle

Models for Cell Shape and Actin Filament Distributions

Speaker: 
Leah Edelstein-Keshet
Date: 
Tue, May 22, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
In this lecture I describe a model by Grimm et al (2003) Eur Biophys J 32: 563-577. The authors ask what processes might account for a parabolic density profile of actin seen across the front edge of a keratocyte. In an elegant coupled PDE model, they show that right and left growing actin filaments, competing for the actin branching complex Arp2/3 have solutions with the appropriate profile. I here consider one of the cases, that of local competition and slow capping of filaments, where the equations are fully analytically solvable in closed form.

Mathematical Cell Biology Summer Course Lecture 31

Speaker: 
Dimitrios Vavylonis
Date: 
Tue, May 22, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
  • 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

Mathematical Cell Biology Summer Course Lecture 30

Speaker: 
Hildor
Date: 
Fri, May 18, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
TBA

Mathematical Cell Biology Summer Course Lecture 29

Speaker: 
William Holmes
Date: 
Fri, May 18, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
  • Local Pulse Analysis for RD equations
  • Actin Waves
  • Matlab examples and exercises

Mathematical Cell Biology Summer Course Lecture 28

Speaker: 
Raibatak (Dodo) Das
Date: 
Fri, May 18, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
Data Analysis Methods

Self Organization in Cells - How to Use Proteins to Solve a Geometry Problem

Speaker: 
Eric Cytrynbaum
Date: 
Thu, May 17, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
Fragments of fish pigment cells can form and center aggregates of pigment granules by dynein-motor-driven transport along a self-organized radial array of microtubules (MTs). I will present a quantitative model that describes pigment aggregation and MT-aster self-organization and the subsequent centering of both structures. The model is based on the observations that MTs are immobile and treadmill, while dynein-motor-covered granules have the ability to nucleate MTs. From assumptions based on experimental observations, I'll derive partial integro-differential equations describing the coupled granule-MT interaction. Analysis explains the mechanism of aster self-organization as a positive feedback loop between motor aggregation at the MT minus ends and MT nucleation by motors. Furthermore, the centering mechanism is explained as a global geometric bias in the cell established by spontaneously-nucleated microtubules. Numerical simulations lend additional support to the analysis. The model sheds light on role of polymer dynamics and polymer-motor interactions in cytoskeletal organization.

Spatial Segregation of Polarity Determinants in Embryos of the Nematode Worm C. elegans

Speaker: 
Adriana Dawes
Date: 
Thu, May 17, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
Polarization, where cells segregate specific factors to distinct domains, is a fundamental and evolutionarily conserved biological process. Polarizing cells often rely on the same toolkit of proteins and lipids, including actin, myosin, microtubules and the Par and Rho protein families. In this talk, I will present experimental and theoretical work demonstrating the importance of Par protein oligomerization for stable spatial segregation in early embryos of C. elegans. I will discuss some current research directions in my lab, including the incorporation of Rho proteins into our theoretical and experimental frameworks.

Mathematical Cell Biology Summer Course Lecture 27

Speaker: 
William Holmes
Date: 
Thu, May 17, 2012
Location: 
PIMS, University of British Columbia
Conference: 
Mathematical Cell Biology Summer Course
Abstract: 
  • Local Pulse Analysis for RD equations
  • Actin Waves
  • Matlab examples and exercises
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