On the contribution of moment-bearing links to bending and twisting in a three-dimensional sliding filament model.

Previously (Hines, M., and J.J. Blum 1983, Biophys. J., 41:67-79), a method was developed that allowed one to compute curvature and twist for a three-dimensional sliding filament model. In that formalism it was difficult to specify the shear and bending moments arising from moment-bearing interfilament links such as fixed 5-6 bridges or dyneins. Euler's equation offers a straightforward method for computing these bending and shear moments when the potential energy stored in the links as a function of axonemal shape is specified. We used this approach to examine the effect of 5-6 bridges on curvature and twist for several distributions of internal shear moments. Twist changes the angle that a link makes with a doublet and thus in some circumstances may reduce the potential energy stored in those links. Twist is a second-order effect proportional to the square of the distance between an outer doublet and the neutral axis. Fixed links will not generate twist if they are symmetrically located around the axoneme.