Model of flagellar waves

Abstract

A previously developed model of flagellar bend propagation is extended to allow active contraction to occur in both top and bottom fibers, in periodic alternation. The extension permits computation of the complete wave shape from first principles. Calculated wave shape parameters are compared with the experimental measurements of Brokaw. Good agreement is obtained for living sperm of Lytechinus and for glycerinated sperm of Lytechinus reactivated in 2.0 m m-ATP over the entire range of viscosities studied. The calculated wavelengths for the sperm of Ciona closely match the experimental values throughout the viscosity range studied, but the calculated values for wave amplitude and radius of curvature deviate from the experimental values at high viscosities. For these sperm better estimates of the mechanochemical parameters than in the previous study are obtained and the significance of these parameters for wave generation is assessed. The theoretical treatment did not fit the data for the sperm of Chaetopterus or of glycerinated Lytechinus at 0.2 m m-ATP. Some implications of these findings are discussed.