טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentAvni Ronen
SubjectCell Motility Powered by Active Gel
DepartmentDepartment of Applied Mathematics
Supervisor Professor Nadav Liron


Abstract

Cell crawling is a highly complex integrated process, dependent on the actin-rich cortex beneath the plasma membrane. Three distinct activities are involved: protrusion, in which actin-rich structures are pushed out at the front of the cell; attachment, in which the actin cytoskeleton connects across the plasma membrane to the substratum; and traction, in which the bulk of the trailing cytoplasm is drawn forward. In some crawling cells these activities are closely coordinated, and the cells seem to glide forward smoothly without changing shape. Also three players are involved: the plasma membrane, the actin network and the adhesion points. The actin network consists of actin polymers and many other types of molecules which dynamically attach to and detach from the network, making it a biological gel. Furthermore, energy is consumed in the form of ATP due to both the activity of molecular motors and the polymerization at the filament tips; thus the system is far from thermodynamic equilibrium. This unique system is responsible for a wide range of phenomena (different force-velocity relationships) and behaviors (contraction, elongation, rotation, formation of dynamic structures)

In the first chapter we discuss the dynamics of polymerizing actin filaments, extending previous works, accounting for the unsteady state, proving that the previous result is incorrect and suggesting a new numerical solution .

As in the story of the elephant and the blind men where each one described the whole elephant according to a different part, many models have been derived in order to describe distinct processes of this complex phenomenon, not considering other crucial ones. In the recent years some works tried to cope with the entire motility phenomenon. However, these works used unrealistic assumptions, or still neglected some crucial processes; e.g. stochastic models which could not take into account the main body of the domain or hydrodynamic models which included unrealistic boundary conditions. In the second chapter we derive a mathematical model attempting to describe this phenomenon that accounts for all the major players and processes and where all processes fit together into a coherent mathematical description, with (almost) no arbitrary constraints .

Last, we describe a new numerical algorithm for the solution of the hydrodynamic model for free boundary fluid flow with surface tension, complex fluids and geometries, based on the Marker And Grid algorithm.