Recent experiments have provided new quantitative measurements of the rippling phenomenon in fields of developing myxobacteria cells. These measurements have enabled us to develop a mathematical model for the ripple phenomenon on the basis of the biochemistry of the C-signaling system, whereby individuals signal by direct cell contact. The model quantitatively reproduces all of the experimental observations and illustrates how intracellular dynamics, contact-mediated intercellular communication, and cell motility can coordinate to produce collective behavior. This pattern of waves is qualitatively different from that observed in other social organisms, especially Dictyostelium discoideum, which depend on diffusible morphogens.
Myxobacteria are common components of soil, but their life cycle is far from common. Although they are prokaryotes, their life, in some respects, is similar to that of multicellular organisms (1, 2). Under starvation conditions, a population of myxobacterial cells aggregates by streaming into a number of central foci, eventually forming at the focus a multicellular fruiting body. During this aggregation phase, the cells may pass through a period where the surface is swept by a complex pattern of waves, called the ''ripple phase.'' These waves are composed of bacteria moving in concert in such a way that colliding waves appear to pass through one another (3). This is quite unlike the seemingly similar phenomenon observed in Dictyostelium discoideum and in chemical waves where colliding wave fronts annihilate one another (4, 5). Here we present a quantitative model for the ripple phase in Myxococcus xanthus that reproduces most of the observed phenomena. A distinguishing feature of this model is that it depends only on intercellular communication by direct cell contact, without any diffusible morphogen signaling.We shall base our model on the following consequences of experimental observations on Myxobacteria.(i) Contact Signaling. Myxobacteria signal via the C-signaling system, which operates only when two cells contact one another nearly end to end (3, 6, 7). The ripple patterns can be altered significantly, or even abolished, by manipulation of external C-signal protein concentration or dilution of wild-type cells by mutants that can receive, but not send, C-signal (3). Therefore, we shall base the model on signaling that depends entirely on direct cell contacts, with no diffusible signaling molecule.(ii) Reversal Cycle. Experiments on individual prerippling bacteria under various conditions show that they glide back and forth, reversing their direction spontaneously about every 5-10 min with a variance much smaller than the mean (see table 1 of ref. 8 and table 2 of ref. 9). Thus the times between reversals are not exponentially distributed, i.e., not Markovian. We interpret this to mean that the internal biochemical circuit controlling reversals contains a delay or cycle time for completion.(iii) Density Dependence. Measurements show that reversal frequencies depend on the amount of C...