Coordination of the rhythm of beat in some ciliary systems

From representations to servomechanisms to oscillators: my journey in the study of cognition

The study of comparative cognition bloomed in the 1970s and 1980s with a focus on representations in the heads of animals that undergird what animals can achieve. Even in action-packed domains such as navigation and spatial cognition, a focus on representations prevailed. In the 1990s, I suggested a conception of navigation in terms of navigational servomechanisms. A servomechanism can be said to aim for a goal, with deviations from the goal-directed path registering as an error. The error drives action to reduce the error in a negative-feedback loop. This loop, with the action reducing the very signal that drove action in the first place, is key to defining a servomechanism. Even though actions are crucial components of servomechanisms, my focus was on the representational component that encodes signals and evaluates errors. Recently, I modified and amplified this view in claiming that, in navigation, servomechanisms operate by modulating the performance of oscillators, endogenous units that produce periodic action. The pattern is found from bacteria travelling micrometres to sea turtles travelling thousands of kilometres. This pattern of servomechanisms working with oscillators is found in other realms of cognition and of life. I think that oscillators provide an effective way to organise an organism's own activities while servomechanisms provide an effective means to adjust to the organism's environment, including that of its own body.

Oscillators and servomechanisms in orientation and navigation, and sometimes in cognition

Navigational mechanisms have been characterized as servomechanisms. A navigational servomechanism specifies a goal state to strive for. Discrepancies between the perceived current state and the goal state specify error. Servomechanisms adjust the course of travel to reduce the error. I now add that navigational servomechanisms work with oscillators, periodic movements of effectors that drive locomotion. I illustrate this concept selectively over a vast range of scales of travel from micrometres in bacteria to thousands of kilometres in sea turtles. The servomechanisms differ in sophistication, with some interrupting forward motion occasionally or changing travel speed in kineses and others adjusting the direction of travel in taxes. I suggest that in other realms of life as well, especially in cognition, servomechanisms work with oscillators.

Finding the ciliary beating pattern with optimal efficiency

We introduce a measure for energetic efficiency of biological cilia acting individually or collectively and numerically determine the optimal beating patterns according to this criterion. Maximizing the efficiency of a single cilium leads to curly, often symmetric, and somewhat counterintuitive patterns. However, when looking at a densely ciliated surface, the optimal patterns become remarkably similar to what is observed in microorganisms like Paramecium. The optimal beating pattern then consists of a fast effective stroke and a slow sweeping recovery stroke. Metachronal coordination is essential for efficient pumping and the highest efficiency is achieved with antiplectic waves. Efficiency also increases with an increasing density of cilia up to the point where crowding becomes a problem. We finally relate the pumping efficiency of cilia to the swimming efficiency of a spherical microorganism and show that the experimentally estimated efficiency of Paramecium is surprisingly close to the theoretically possible optimum.

Cilia internal mechanism and metachronal coordination as the result of hydrodynamical coupling

We present a simple but realistic model for the internal bend-generating mechanism of cilia, using parameters obtained from the analysis of data of the beat of a single cilium, and incorporate it into a recently developed dynamical model. Comparing the results to experimental data for two-dimensional beats, we demonstrate that the model captures the essential features of the motion, including many properties that are not built in explicitly. The beat pattern and frequency change in response to increased viscosity and the presence of neighboring cilia in a realistic fashion. Using the model, we are able to investigate multicilia configurations such as rows of cilia and two-dimensional arrays of cilia. When two adjacent model cilia start beating at different phase, they synchronize within two cycles, as observed in experiments in which two flagella beating out of phase are brought close together. Examination of various multicilia configurations shows that metachronal patterns (i. e., beats with a constant phase difference between neighboring cilia) evolve autonomously. This provides modeling evidence in support of the conjecture that metachronism may occur as a self-organized phenomenon due to hydrodynamical interactions between the cilia.

Propulsive force of Paramecium as revealed by the video centrifuge microscope

Using the video centrifuge microscope we constructed, we observed the behavior of Paramecium cells in a solution of graded densities under centrifugal acceleration. Beyond 300g, they not only gather in the zone where the density is closest to theirs, but also orient themselves with their longitudinal axis parallel to the direction of centrifugation turning their anterior ends toward either centripetal or centrifugal direction. Since all of them retain still active swimming capacity, it is possible to calculate their propulsive force from the difference in density between theirs (1.04 g cm-3) and that of the upper or lower layer which they can reach. The propulsive force of single Paramecium cells thus obtained was calculated to be about 7 x 10(-4) dyn.

Flagellar coordination in Chlamydomonas reinhardtii: isolation and reactivation of the flagellar apparatus

The flagellar apparatus (both flagella with basal bodies and accessory structures) of Chlamydomonas reinhardtii was isolated from a wall-less mutant and induced to swim in the presence of adenosine triphosphate. The movement of the flagella of the isolated apparatus was largely synchronous and indistinguishable from the movement of flagella on living cells. These observations suggest that the mechanism of flagellar coordination in this biflagellate alga is largely intrinsic to the structure of the flagellar apparatus itself.

Studies on the gill of Mytilus edulis: the eu-latero-frontal cirri

Adjacent eu-latero-frontal cirri beat alternately and alternate cirri exhibit metachronous activity. Each cirrus consists of 22─26 pairs of cilia arranged in two parallel but alternating rows. Individual cilia leave the shaft of the cirrus at regular (0.6 μ m) intervals on each side to extend across the intercirrus space. Each cilium, where it bends to leave the cirrus shaft, contains a stiffening rod which extends 1.5 μ m distally as a tapering, hemispherical rod, lying between peripheral fibril 1 and the paired central fibrils. Distal to the bend, the peripheral fibrils are singlets and lack arms. It is concluded that the disposition of this region of the cilium to the cirrus shaft remains more or less constant during both the effective and recovery strokes of the cirrus and this disposition is such that interference between adjacent cirri is minimal while permitting effective filtering of the space between alternate cirri. The mesh of the filter is 0.6 μ m by either 2.4 μ m or 4.8 μ m, the latter depending on the relative positions of adjacent cirri. The pro-latero-frontal cilia may serve to transfer material from the eu-latero-frontal cirri to the frontal cilia of the gill filament.

Flagellar movement: a sliding filament model

A sliding filament mechanism appears to provide the most satisfactory basis for a simple feedback mechanism for the control of bend propagation and bend initiation by flagella, and is supported by strong experimental evidence. A computer simulation of the movements of a flagellar model based on the sliding filament mechanism demonstrates that this mechanism offers a sufficient explanation for the automatic generation of flagellar bending waves. Further computer simulation studies may provide insight into questions such as the applicability of the sliding filament mechanism to the generation of the more complicated asymmetrical bending patterns of cilia, and the control of the bending pattern by interaction between several sliding filament systems within a flagellum.

The metachronal wave of lateral cilia of Mytilus edulis

The form of beat of cilia and the structure of the metachronal wave on the lateral gill epithelium of Mytulus edulis have been studied on living material by interference-contrast microscopy and stroboscopic illumination, and compared with the same features in rapid-fixed preparations studied by light microscopy and with the scanning electron microscope. The most striking finding is that the beat of the cilia is not planar, as previously assumed, but involves a sideways movement in the recovery stroke Previous reports on nonplanar ciliary beating from protozoan examples describe a planar effective stroke and a counterclockwise rotation in the recovery stroke; in this molluscan example there is a clockwise rotation in the recovery stroke The lateral inclination of the cilia in the recovery stroke is in the same direction as the propagation of the waves, and the orientation of cilia in the recovery stroke is thought to determine whether the waves move to the left or right of the direction of the effective stroke