Scientific

• 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

• Local Pulse Analysis for RD equations
• Actin Waves
• Matlab examples and exercises

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.

• Local Pulse Analysis for RD equations
• Actin Waves
• Matlab examples and exercises

Here I return the pattern-formation discussion to the context of symmetry breaking and chemical patterns of GTPases such as Cdc42, Rac and Rho in cell polarization. I explain the spatial context of GTPase distributions in a stimulated chemotactic cell and derive the system of partial differential equations (PDEs) for these. These examples motivate the usefulness of LPA as an additional tool in testing for pattern formation and polarizability.