Modelling of the duplication of cortical units along a kinety of Paramecium using reaction-diffusion equations

Nuclear and cortical regulation in doublets of Paramecium: II. When and how do two cortical domains reorganize to one?

Homopolar doublets with twofold rotational symmetry were generated in Paramecium tetraurelia and in P. undecaurelia by electrofusion or by arrested conjugation. These doublets underwent a complex cortical reorganization over time, which led to their reversion to singlets. This reorganization involved a reduction in number of ciliary rows, a progressive inactivation and loss of one oral meridian, and a reduction and eventual disappearance of one cortical surface (semicell) situated between the two oral meridians. The intermediate steps of this reorganization included some processes that resemble those previously described in regulating doublets of other ciliates, and others that are peculiar to members of the "P. aurelia" species-group and some of its close relatives. The former included a disappearance of one cortical landmark (a contractile vacuole meridian) and transient appearance of another (a third cytoproct) within the narrower semicell. The latter included a reorganization of the paratene zone and the associated invariant (non-duplicating) region to occupy the entire narrower semicell and a redistribution of zones of most active basal-body proliferation within the opposite, wider semicell. The final steps of reorganization involved anterior displacement, invagination, and resorption of one of the two oral apparatuses and eventual disappearance of the associated oral meridian. An oral meridian deprived of its oral apparatus, either by spontaneous resorption or microsurgical removal, could persist for some time in "incomplete doublets" before regulating to the singlet condition. The phylogenetically widespread events encountered in the regulation of doublets to singlets suggest that Paramecium shares some of the global regulatory properties that are likely to be ancestral in ciliates. The more specific events are probably associated with the complex cytoskeletal architecture of this organism and with the frequent occurrence of autogamy that was described in the preceding study (Prajer et al. 1999).

Periodic activity of the cortical cytoskeleton of the lymphoblast: modelling by a reaction-diffusion system

The cytoplasm of cultured human lymphoblasts has a particular organization. A ring formed by actin and myosin delimits a region of the cell where an active membrane veil forms. Depolymerization of the microtubular cytoskeleton releases this ring, which then oscillates between the two poles of the cell. This periodic movement has been studied and described with great precision. We have used these experimental results to model the oscillation of the ring. We have constructed a system of reaction-diffusion equations designed to stimulate the behaviour of the actin and have considered three variables representing, respectively, the proteins involved in actin nucleation, F-actin bound to the plasma membrane and free F-actin, part of which is assumed to constitute the ring, together with myosin. There are two types of results. First, from a theoretical point of view, we have succeeded in simulating a perfect back-and-forth movement of a wave. Second, this model suggests that actin alone, by virtue of its intrinsic properties, can generate an oscillatory movement within the cell, without the need for other oscillators.