A biochemical oscillator explains several aspects ofMyxococcus xanthusbehavior during development

Abstract

During development, Myxococcus xanthus cells produce a series of spatial patterns by coordinating their motion through a contactdependent signal, the C-signal. C-signaling modulates the frequency at which cells reverse their gliding direction. It does this by interacting with the Frz system (a homolog of the Escherichia coli chemosensory system) via a cascade of covalent modifications. Here we show that introducing a negative feedback into this cascade results in oscillatory behavior of the signaling circuit. The model explains several aspects of M. xanthus behavior during development, including the nonrandom distribution of reversal times, and the differences in response of the reversal frequency to both moderate and high levels of C-signaling at different developmental stages. We also propose experiments to test the model.

Accordion waves inMyxococcus xanthus

“…In this study, we used the Frizilator model for the intracellular reversal clock, because it is based on the frz chemosensory system, which has been shown to control cell reversals (19,31). This model is built on interactions and covalent modifications involving FrzF (a methyltransferase that may also be involved in signal input), FrzCD (a chemoreceptor which is subject to methylation and demethylation), and FrzE (a kinase͞response regulator fusion protein).…”

“…This model is built on interactions and covalent modifications involving FrzF (a methyltransferase that may also be involved in signal input), FrzCD (a chemoreceptor which is subject to methylation and demethylation), and FrzE (a kinase͞response regulator fusion protein). Oscillations would require a feedback loop, and several possibilities were suggested, although none have been verified experimentally (19). However, the model we constructed does not depend on the detailed biochemistry of the regulatory system; it is based only on the first property: that the clock is a limit cycle oscillation with an asymmetric wave form for the component receiving the contact signal (FrzF in the Frizilator model) (19).…”

“…Oscillations would require a feedback loop, and several possibilities were suggested, although none have been verified experimentally (19). However, the model we constructed does not depend on the detailed biochemistry of the regulatory system; it is based only on the first property: that the clock is a limit cycle oscillation with an asymmetric wave form for the component receiving the contact signal (FrzF in the Frizilator model) (19). Cell contact has been shown to mediate intercell signaling and to effect the reversal cycle (9,30,31).…”

Quantifying Aggregation Dynamics during Myxococcus xanthus Development

“…These models have successfully uncovered sets of intercellular interactions that lead to patterns similar to those observed experimentally in M. xanthus. Models with various levels of complexity and with different formalisms have been used to describe development, and several of them are based on the traffic jam principle: cells tend to slow down or stop when entering regions of high cell density (5,8,19,20). This leads to a positive-feedback loop as more cells jam into the region, further increasing cell density so that aggregates are able to grow without any diffusible morphogens or chemoattractants.…”

Introduction to dynamical systems

“…Because mathematical models frequently employ the MichaelisMenten equation to describe such reactions, this equation is derived, and the assumptions underlying it, such as the assumption of excess substrate, are discussed (Slides 7 to 12). To illustrate how Michaelis-Menten assumptions are translated into ODEs, a model of a biochemical oscillator that uses Michaelis-Menten kinetics is described (Slides 13 to 15) (1,2). In certain cases, however, a diagram provided in a paper or textbook provides insufficient information for the relevant ODEs to be derived from the diagram (3).…”