A particle based computational model for eukaryotic flagella

The structure of the eukaryotic flagella is very complex and the exact mechanisms responsible for flagellar beating are not clearly understood. Here we present a minimal model to study flagellar beating in two dimensions, which demonstrates that regular beating with a well defined characteristic frequency can arise spontaneously in the absence of external control. In this model, the flagella is represented by two stiff filaments clamped on a surface, on which model ``molecular motors'' take directed steps on one of the filaments and thereby apply a local force. The fluid medium is simulated using Multiparticle Collision dynamics (MPC), which is a particle based method for hydrodynamic simulations. Within a certain range of motor concentrations, large amplitude periodic oscillations with a well defined frequency are observed; other qualitatively different beating patterns arise outside of this range. We present a phase diagram that characterizes the beating behaviour as a function of relevant parameters such as filament length, motor density on the filament and motor velocity.