Analysis of the forces acting on beating cilia

Detailed analysis of the forces acting on a uniform-diameter beating cilium is carried out to determine the moment generated by the inter-doublet forces acting along the length of a cilium and the results are compared with the sliding-control theory according to which the moment is a function of the interdoublet sliding. In the central part of the cilium the inter-doublet forces are found to be proportional to the inter-doublet sliding. However, in spite of the uniformity of the diameter of the cilium, the proportionality constant, known as the dynamic stiffness, is not constant along its entire length. Significant variations are observed in the regions both near the tip of the cilium and proximal to the cell body. In the tip region the magnitude of the dynamic stiffness is found to decrease. This decrease is probably due to decrease in the number density of the molecular motors in that region and in the number of doublet microtubules. The behavior in the proximal region, on the other hand, does not appear to be well described by the sliding control theory. Our analysis therefore suggests that the dynamics of ciliary beating cannot be adequately described by a simple sliding-control theory with constant dynamic stiffness. Our analysis suggests that the cilium is differentiated into a basal region optimized for the creation of a wave and a central region optimized to support a traveling wave that provides the thrust for the cell. (paper)