Seminar Details:

**LANS Informal Seminar***"Multiscale Approach to Self-Organization of Microtubules and Actin Filaments"*

DATE: June 13, 2007

TIME: -

SPEAKER: Dmitry Karpeev, *MCS*

LOCATION: Building 221, A-261, Argonne National Laboratory

**Description:**

Recent experiments have shown that a system of microtubules and molecular

motors is capable of sustaining a variety of large-scale two-dimensional

structures (asters, vortices, and other topological defects). Underlying

this phenomenon is a multiscale process, where nonlinear interactions on a

microscopic scale result in the emergence of coherent structures on the

macroscopic scale. For the study of this process, we propose a mathematical

framework based on a master equation on the mesoscopic scale. The equation

describes the evolution of the density of microtubules as a function of

position and angular orientation. The interaction kernel is determined by

the molecular interactions on the microscopic scale. Macroscopic

spatiotemporal structures are identified through dimension reduction from

the mesoscopic scale. All three scales interact strongly, resulting in

macroscopically observable patterns of self-organization.

Recently we have developed mathematical analysis and simulations to address

different aspects of the problem. At the mesoscopic level we have developed

an approach at analytically solving the master equation in the homogeneous

2D case.

At the microscopic case we have investigated the effects of flexibility of

filaments on their collision properties that control the kernel of the

master equation at the mesoscopic level. We have shown that flexibility

enhances the inelasticity of interaction and that motor dwelling may be

responsible for complete alignment of tubules. Furthermore, we have

investigated interaction of much softer filaments, such as actin, which is

responsible for the cytoskeleton formation. Interacting actin pairs

exhibited an Euler-type buckling instability for sufficient motor stengths.

It is conjectured that the buckled states are responsible for cross-linking

of actin into cytoskeletal networks and, thereby, for the rheological

properties of these networks.

Please send questions or suggestions to Charlotte Haley: haley at anl dot gov.