Breakup and then makeup: a predictive model of how cilia self-regulate hardness for posture control

Functioning as sensors and propulsors, cilia are evolutionarily conserved organelles having a highly organized internal structure. How a paramecium's cilium produces off-propulsion-plane curvature during its return stroke for symmetry breaking and drag reduction is not known. We explain these cilium deformations by developing a torsional pendulum model of beat frequency dependence on viscosity and an olivo-cerebellar model of self-regulation of posture control. The phase dependence of cilia torsion is determined, and a bio-physical model of hardness control with predictive features is offered. Crossbridge links between the central microtubule pair harden the cilium during the power stroke; this stroke's end is a critical phase during which ATP molecules soften the crossbridge-microtubule attachment at the cilium inflection point where torsion is at its maximum. A precipitous reduction in hardness ensues, signaling the start of ATP hydrolysis that re-hardens the cilium. The cilium attractor basin could be used as reference for perturbation sensing.