Analytical study for swimmers in a channel

There is an overabundance of microswimmers in nature, including bacteria, algae, mammalian cells and so on. They use flagellum, cilia or global shape changes (amoeboid motion) to move forward. In the presence of confining channels, these swimmers exhibit often non-trivial behaviours, such as accumulation at the wall, navigation and so on, and their swimming speed may be strongly influenced by the geometric confinement. Several numerical studies have reported that the presence of walls either enhances or reduces the swimming speed depending on the nature of the swimmer, and also on the confinement. The purpose of this paper is to provide an analytical explanation of several previously obtained numerical results. We treat the case of amoeboid swimmers and the case of squirmers having either a tangential (the classical situation) or normal velocity prescribed at the swimmer surface (pumper). For amoeboid motion we consider a quasi-circular swimmer which allows us to tackle the problem analytically and to extract the equations of the motion of the swimmer, with several explicit analytical or semi-analytical solutions. It is found that the deformation of the amoeboid swimmer as well as a high enough order effect due to confinement are necessary in order to account for previous numerical results. The analytical theory accounts for several features obtained numerically also for non-deformable swimmers.

A Mathematical Model for Cellular Locomotion Exhibiting Chemotaxis

A fundamental problem of cellular biology is to understand the mechanisms underlying cellular locomotion. Bacterial organisms may use appendages such as flagellae or cilia to facilitate motion. Amoeboid motion [6], exhibited by eucaryotic cells are seen to flatten onto surfaces and extend thin sheets of cytosol called lamellipodia. These in turn make attachments to the surface and by the initiation of internal contractions within the cell, a forward motion is achieved. The processes which govern this behaviour are extremely complex, however, key ingredients have been identified which may provide a sufficient basis for persistent cellular motion. These factors are osmotichydrostatic expansion and cellular contraction mediated by intracellular calcium ca2+. In this paper, we develop a simple two dimensional model for a non-muscle motile cell based on these two key factors. We show it is capable of producing persistent cellular motion and chemotactic behaviour.

Induction of either contractile or structural actin-based gels in sea urchin egg cytoplasmic extract.

The gel formed by warming the 100,000 g supernate of isotonic extracts of sea urchin eggs to 40 degrees C is made up of actin and two additional proteins of mol wt of 58,000 and 220,000. Actin and 58,000 form a characteristic structural unit which has now been identified in the microvilli of the urchin egg and in the filopods of urchin coelomocytes. However, egg extract gels did not contract as those from other cell types do, and the aim of these experiments was to determine the reason for this lack of contraction. Although the extracts are dialyzed to a low ionic strength, myosin is present in soluble form and makes up approximately 1% of the protein of the extract. It becomes insoluble in the presence of high ATP concentrations at 0 degrees C, and the precipitate formed under these conditions consists almost entirely of myosin. This procedure provides a simple method of isolating relatively pure myosin without affecting other extract components and functions. Contraction will follow gelation in these extracts if the temperature and time of incubation used to induce actin polymerization are reduced to minimize myosin inactivation. At the optimal ATP and KCl concentration for contraction, the contracted material has an additional 250,000 component and contains very little 58,000. The conditions found to provide maximum gel yields favor the formation of the actin-58,000-220,000 structural gel, while reduced temperature and increase in KCl concentration results in a contractile gel whose composition is similar to those reported from amoeboid cell types. Both the structural protein cores found in the egg microvilli and a gel contraction related to the amoeboid motion which is seen in later urchin embryonic development can thus be induced in vitro in the same extract.