Simulation testing of mechanisms for inducing the formation of the contractile ring in cytokinesis

There is persuasive evidence that the role of the mitotic apparatus (MA) in cytokinesis is to control the location of the cleavage furrow. The geometric aspects of this interaction between the MA and the cortex are complex and, thus, computer simulation can be a useful means for testing hypotheses about the induction process. White and Borisy (1983. J. Theor. Biol. 101:289-316) used computer simulations to show that long-range signals from the asters, varying inversely as various powers of distance, produce summed effects that are minima at the equator of spherical cells. Their results have seemed to support the "polar relaxation" class of hypotheses, in which the effect of the asters is to weaken cortical contractility so that contraction becomes maximized at the equator because it is least inhibited there. However, the experimental studies of Rappaport and Rappaport (1988. J. Exp. Zool. 247:92-98) indicate that the asters actually strengthen cortical contractility. In this paper, we use computer simulation to determine how signals from the MA will need to vary in effect as functions of distance to cause cortical contractility to become maximized where the furrows are to be induced. Although we confirm that inverse power inhibitory signals could induce equatorial furrows in spherical cells, we also find that this ability is destroyed by flattening, constricting, or distorting cells into cylinders, geometries for which Rappaport's experiments show furrows form (1986. Int. Rev. Cytol. 105:245-281). We then show that stimulatory signals of the right kind would induce furrows at the locations observed, in spherical cells as well as cells distorted by experimental manipulation. These signals must be constant out to a threshold distance but decrease abruptly beyond that distance. We also show that this ability depends on having the "drop-off" threshold occur at just the right distance relative to the dimensions of the cell and separation of the asters.