Existence of Limit Cycles in the Repressilator Equations

Buse, Olguta; Kuznetsov, Alexey; Pérez, Rodrigo A.

doi:10.1142/s0218127409025237

Cited by 38 publications

(36 citation statements)

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“…2C). This finding is consistent with our theoretical understanding of the corresponding well-mixed repressilator system, which is known to exhibit oscillations when p max exceeds a critical value (dependent on other parameters) (14). Increasing the number density of capsules should similarly favor oscillations, because chemicals can be produced at a higher rate per unit volume of the colony.…”

Section: Resultssupporting

confidence: 88%

“…With the repressilator (12)(13)(14) modulating the production of signaling species in the capsule, species j, with concentration denoted by c j , acts as an inhibitor for the production of the next chemical j + 1 in the cycle, and, conversely, the production of species j is inhibited by the presence of chemical j − 1 (Fig. 1B).…”

Section: Resultsmentioning

confidence: 99%

“…As in previous theoretical studies of repressilator systems (12)(13)(14), we model inhibition using the Hill function (20). Expressed in dimensionless form (see SI Text for details of nondimensionalization), the Hill function reads f ðcÞ = p max =ð1 + c n Þ, where p max is the maximum production rate per unit volume; for brevity, we also refer to p max as the "production capacity."…”

Section: Resultsmentioning

confidence: 99%

“…Mathematical models for chemical production regulated by the repressilator network have shown that the long-term behavior of the network is either stationary or oscillatory, depending on system parameters (12)(13)(14)(15). Associating the stationary behavior with an off state and oscillatory behavior with an on state, the repressilator network could support QS ability if the emergent state depended on the population density.…”

mentioning

confidence: 99%

“…Associating the stationary behavior with an off state and oscillatory behavior with an on state, the repressilator network could support QS ability if the emergent state depended on the population density. Prior models (12)(13)(14)(15), however, described the dynamics of small systems in which spatial variations in concentrations are unimportant, such as within a single cell or tightly packed cluster of a few cells. Hence, these models cannot reveal how changes in colony size and number density could lead to oscillations and, ultimately, QS.…”

mentioning

confidence: 99%

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Synthetic quorum sensing in model microcapsule colonies

Shum

Balazs

2017

Proc. Natl. Acad. Sci. U.S.A.

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Biological quorum sensing refers to the ability of cells to gauge their population density and collectively initiate a new behavior once a critical density is reached. Designing synthetic materials systems that exhibit quorum sensing-like behavior could enable the fabrication of devices with both self-recognition and selfregulating functionality. Herein, we develop models for a colony of synthetic microcapsules that communicate by producing and releasing signaling molecules. Production of the chemicals is regulated by a biomimetic negative feedback loop, the "repressilator" network. Through theory and simulation, we show that the chemical behavior of such capsules is sensitive to both the density and number of capsules in the colony. For example, decreasing the spacing between a fixed number of capsules can trigger a transition in chemical activity from the steady, repressed state to largeamplitude oscillations in chemical production. Alternatively, for a fixed density, an increase in the number of capsules in the colony can also promote a transition into the oscillatory state. This configuration-dependent behavior of the capsule colony exemplifies quorum-sensing behavior. Using our theoretical model, we predict the transitions from the steady state to oscillatory behavior as a function of the colony size and capsule density.quorum sensing | repressilator | microcapsules Q uorum sensing (QS) refers to the ability of organisms in a population to assess the number and density of individuals present, allowing a specific behavior to be initiated only when a critical threshold in the population size and density is reached. QS plays a vital role in the life cycle of bacteria (1, 2), yeast (3, 4), and slime molds (5, 6), as well as social insects (7). In microorganisms, QS is based on chemical signaling among individuals in a colony. Bacteria (1, 8), for example, produce and secrete signaling molecules, which diffuse into the surrounding medium where they can be detected by other cells in the population. Through regulatory networks, the signaling molecule acts as an autoinducer; the rate of production of the autoinducer increases with its concentration. When the cell density is low, the concentration of the signaling molecule is low, and production is maintained at a low, basal rate. The cells are considered to be in the "off" QS state. When the population density is high, each cell detects a high concentration of the signaling molecule resulting from the collective production of many nearby neighbors. The cells are switched "on," increasing production of the signaling molecule and activating further metabolic pathways that are triggered by QS. Hence, spatially separated cells interact through regulatory networks, which coordinate the collective behavior of the colony.An intriguing challenge in both synthetic biology and materials science is to design man-made systems that exhibit behavior analogous to QS, i.e., sensing and responding to the system size and density. Such synthetic QS abilities could provide a route to ...

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Section: Resultssupporting

confidence: 88%

Section: Resultsmentioning

confidence: 99%