Hongguang Xi

Graduation Semester and Year




Document Type


Degree Name

Master of Science in Mathematics



First Advisor

Marc Turcotte


Bacillus subtilis is one of the very well-studied organisms in biology. Recent results show that an alternative competence regulation circuit for this bacterium, differing only in the order of the composite negative feedback loop onto the master competence regulator gene comK, despite presenting equivalent functionality, exhibits physiologically important differences.It is not clear why Nature only selects a specific gene regulation circuit other than a plethora of equivalent others. Here, we hope, from the point of view of reverse engineering, to discover the fundamental reasons for natural selection of a particular circuit structure over another. Based on the wild-type Bacillus subtilis circuit, we add a positive autoregulation feedback loop to the intermediate gene comS in the composite negative feedback loop onto ComK. Since positive feedback loops are most frequently observed in biology, this hypothetical modification of the original circuit is evolutionarily plausible.We use bifurcation theory to study the dynamical features of the hypothetical gene circuit vs. the feedback strength of the added positive autoregulation loop, and we rely on stochastic simulations to perform in silico experiments. We discover the existence of a bistable system: a stable limit cycle and a stable fixed point separated by an unstable limit cycle with a varying height of underlying stochastic potential. This structure is absent from the wild type. The coexistence of the unstable limit cycle and stochastic noise endows the circuit with an ability to trap, shield or switch between its two stable attractors. We study the implications for competence. By calculating the probability of entering competence, we conclude that the hypothetical circuit possesses less ability, compared to the wild-type circuit, to survive the severe environmental stresses. This provides some insight into the natural selection of a particular circuit structure by Evolution.


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons