Models for oscillation and bend propagation by flagella.

A computer program for simulating the movement of model flagella containing a four-state cross-bridge cycle provides a powerful tool for examining hypotheses about the control mechanisms involved in producing particular patterns of propagated bending. As learned previously with simpler models, a simple control of cross-bridge activity by curvature is sufficient to generate spontaneous oscillation and bend propagation, but fails to reproduce many important features of the behaviour of real flagella. The process of bend initiation can be isolated by studying the movement of demembranated sea urchin sperm flagella broken to lengths of 3-4 microns, and by studying the movement of the distal end of a flagellum when most of the length of the flagellum becomes stuck to a surface. In order to simulate the movement seen in these situations, at least one major modification of the control of cross-bridge activity appears to be necessary. When a new bend is forming, the active sliding of cross-bridges causing the bend to form can be turned off when the curvature of the bend reaches a critical value, as in the earlier models. However, the active sliding of cross-bridges in the opposite direction, which will cause propagation of the bend, does not appear to be turned on at the same time. The mechanisms which trigger this delayed activation of cross-bridges almost simultaneously throughout the length of a newly formed bend have not yet been identified. They are presumably the same as those involved in activating sliding throughout most of the length of a flagellum at the beginning of its effective stroke.