Stability of Systems with Stochastic Delays and Applications to Genetic Regulatory Networks.

The dynamics of systems with stochastically varying time delays are investigated in this paper. It is shown that the mean dynamics can be used to derive necessary conditions for the stability of equilibria of the stochastic system. Moreover, the second moment dynamics can be used to derive sufficient conditions for almost sure stability of equilibria. The results are summarized using stability charts that are obtained via semi-discretization. The theoretical methods are applied to simple gene regulatory networks where it is demonstrated that stochasticity in the delay can improve the stability of steady protein production.

Tunable Dynamics in a Multistrain Transcriptional Pulse Generator.

One challenge in synthetic biology is the tuning of regulatory components within gene circuits to elicit a specific behavior. This challenge becomes more difficult in synthetic microbial consortia since each strain's circuit must function at the intracellular level and their combination must operate at the population level. Here we demonstrate that circuit dynamics can be tuned in synthetic consortia through the manipulation of strain fractions within the community. To do this, we construct a microbial consortium comprised of three strains of engineered Escherichia coli that, when cocultured, use homoserine lactone-mediated intercellular signaling to create a multistrain incoherent type-1 feedforward loop (I1-FFL). Like naturally occurring I1-FFL motifs in gene networks, this engineered microbial consortium acts as a pulse generator of gene expression. We demonstrate that the amplitude of the pulse can be easily tuned by adjusting the relative population fractions of the strains. We also develop a mathematical model for the temporal dynamics of the microbial consortium. This model allows us to identify population fractions that produced desired pulse characteristics, predictions that were confirmed for all but extreme fractions. Our work demonstrates that intercellular gene circuits can be effectively tuned simply by adjusting the starting fractions of each strain in the consortium.

Majority sensing in synthetic microbial consortia.

As synthetic biocircuits become more complex, distributing computations within multi-strain microbial consortia becomes increasingly beneficial. However, designing distributed circuits that respond predictably to variation in consortium composition remains a challenge. Here we develop a two-strain gene circuit that senses and responds to which strain is in the majority. This involves a co-repressive system in which each strain produces a signaling molecule that signals the other strain to down-regulate production of its own, orthogonal signaling molecule. This co-repressive consortium links gene expression to ratio of the strains rather than population size. Further, we control the cross-over point for majority via external induction. We elucidate the mechanisms driving these dynamics by developing a mathematical model that captures consortia response as strain fractions and external induction are varied. These results show that simple gene circuits can be used within multicellular synthetic systems to sense and respond to the state of the population.

Bistability and oscillations in co-repressive synthetic microbial consortia.

Synthetic microbial consortia are conglomerations of multiple strains of genetically engineered microbes programmed to cooperatively bring about population-level phenotypes. By coordinating their activity, the constituent strains can display emergent behaviors that are difficult to engineer into isogenic populations. To do so, strains are engineered to communicate with one another through intercellular signaling pathways. As a result, the regulatory networks that control gene transcription throughout the population are sensitive to the extracellular concentration of the signaling molecules, and hence the relative densities of constituent strains. Here, we use computational modeling to examine how the behavior of a synthetic microbial consortium results from the interplay between the population dynamics governed by cell growth and the internal transcriptional dynamics governed by cell-to-cell signaling. Specifically, we examine a synthetic microbial consortium in which two strains each produce signals that down-regulate transcription in the other. Within a single strain this regulatory topology is called a "co-repressive toggle switch" and can lead to bistability. We find that in a two-strain synthetic microbial consortium the existence and stability of different states depends on the population-level dynamics of the interacting strains. As the two strains passively compete for space within the colony, their relative fractions can fluctuate and thus alter the strengths of intercellular signals. These fluctuations can drive the consortium to alternative equilibria. Additionally, if the growth rates of the strains depend on their transcriptional states, an additional feedback loop is created that can generate relaxation oscillations. These findings demonstrate that the dynamics of microbial consortia cannot be predicted from their regulatory topologies alone, but also is determined by interactions between the strains.