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

Abstract

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.

A Hemispherical Motor Oscillator for Experiments on Swimming and Flying of Small Animals

“…The sequence of turning the electromagnets on and off is calculated for the required mechanical oscillator, such as penguin pectoral fins [2,7] or the pectoral fins of Clione antarctica [19][20][21] or fly wings [22] or the cilia of a paramecium [23,24]. Then, the power supply to the electromagnets is sequenced by using relays ( Fig.…”

“…1(a)) of a paramecium whose axial temporal posture is shown in Fig. 7(c) [23]. Next, the single ball was replaced by a three-ball mass.…”

“…It has been possible to accurately model the position and velocity of the cilia of the paramecium, which remains self-similar along its length [23]. This uses the slow ionic oscillator (Ca 2 -dependent) part of the FitzHugh-Nagumo (FN) model of the inferior-olive neurons of motion control of animals.…”

“…Note that, in Ref. [23] as summarized earlier, the actual deflection of the propulsive surface is not being directly modeled, but it is indirectly calculated by modeling the input ionic olivocerebellar control signal at the base (Fig. 1(a)).…”

Experiments on the Effects of Reynolds Number and Advance Ratio on the Unfolding of Disorganization in Low-Speed Underwater Propulsors With Vibrating Blades

“…It turns out that all animals, including swimming and flying animals also have motion controlling mechanisms that are self-regulating. For example, we have accurately calculated the motion of the cilia of a paramecium in water [16], and the planar motion of a bat in a room [10] using olivocerebellar control models, namely, the FitzHugh-Nagumo models. These wakes signify the similarity between temporal [10,17], or spatiotemporal [7] control and transitional turbulence mechanisms of hydrodynamics.…”