Bend propagation by a sliding filament model for flagella.

The important electron-microscope studies by Satir (1965,1968) have demonstrated that the bending of a cilium is accompanied by longitudinal sliding of its peripheral microtubular filaments relative to one another. These observations imply that the bending of the cilium is not generated by active contraction or extension of the filaments, since they appear to retain constant lengths throughout the bending cycle. More probably, bending is generated by an active sliding process involving filament interactions analogous to those occurring in the active sliding process which is believed to be the basis for muscular contraction. Support for Satir's conclusions can also be drawn from the manner in which filaments are interconnected in an unusual compound cilium (Horridge, 1965) and from some observations on the form of the movement of spermatozoa in the presence of an inhibitor, thiourea (Brokaw, 1965). Satir (1967, 1968) and others (Sleigh, 1968; Brokaw, 1968) have discussed some aspects of sliding-filament models for ciliary and flagellar movement. On the other hand, most attempts to deal quantitatively with the mechanics of wave propagation by flagella have been based on a 'local bending' type of model, in which the active moment and the bending of the flagellum at a particular point are considered to be generated by active processes at that point within the flagellum (Machin, 1958; Brokaw, 1966 a). These discussions of wave propagation have attempted to explain the ability of flagella to propagate bending waves by making simple assumptions about the local characteristics of the active process, so that no higher-level system for co-ordinating bending is required. These proposals for wave propagation have encountered some serious difficulties, which have been discussed in previous papers (Brokaw, 1962, 1968, 1970). In this paper I have attempted to define some of the quantitative properties of a sliding filament model for flagellar movement, with particular reference to the generation of the bending moments required to balance the viscous moments imposed on the flagellum by its movement in a viscous medium. It will be shown that the difficulties which have hindered previous attempts to understand the control of bend propagation in flagella can be resolved by consideration of a sliding filament model, and that this model suggests how a relatively simple mechanism for the control of the active process can explain the generation of propagated bending waves by flagella.