Abstract
This tutorial presents an introduction into continuum descriptions of cytoskeletal dynamics. In contrast to discrete models in which each molecule keeps its identity, such descriptions are given in terms of averaged quantities per unit volume like the number density of a certain molecule. Starting with a discrete description for the assembly dynamics of cytoskeletal filaments, we derive the continuity equation, which serves as the basis of many continuum theories. We illustrate the use of this approach with an investigation of spontaneous cytoskeletal polymerization waves. Such waves have by now been observed in various cell types and might help to orchestrate cytoskeletal dynamics during cell spreading and locomotion. Our analysis shows how processes at the scale of single molecules, namely, the nucleation of new filaments and filament treadmilling, can lead to the spontaneous appearance of coherent traveling waves on scales spanning many filament lengths. For readers less familiar with calculus, we include an informal introduction to the Taylor expansion.
Highlights
With the advancements in microscopy techniques it has become increasingly clear that a true understanding of many cellular phenomena requires to take spatial aspects into account
We show how continuum theories can be developed and used in a cellular context to describe cytoskeletal dynamics
We introduce the densities n+ and n- of nucleation promoting factors (NPFs) bound to plus- and minus-filaments, respectively, and the density nc of cytosolic NPFs
Summary
With the advancements in microscopy techniques it has become increasingly clear that a true understanding of many cellular phenomena requires to take spatial aspects into account. Most biological and medical curricula today lack, a thorough introduction into mathematical and physical tools, which often leads to discomfort on the part of biologists and physicians, when confronted with the results of a theoretical study. This holds in particular for continuum descriptions. This tutorial is meant to familiarize life scientists with the basic ideas underlying this approach
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