This thesis consists of five projects in three topics with a shared theme of understanding cellular
decision-making processes with mathematical modeling. In the first topic, we address the
possible interaction between bacterial Toxin-Antitoxin (TA) systems and stringent response
alarmone guanosine tetra- and pentaphosphate [(p)ppGpp] and examine how this interaction
contributes to bacterial persistence. We show that TA systems mediate a negative feedback to
early stringent response by reducing the available mRNA. We also show that the redundancy
of TA systems can be realized if bacterial growth-dormancy transition is primarily mediated
by (p)ppGpp fluctuation.
In the second topic, we discuss the transition paths between two stable steady states. We
construct a simple model of coupled bistable gene circuits and demonstrate the possibility
of bifurcation of transition path in biology. We then construct a theory to predict whether a
general coupled bistable system exhibits bifurcated path or not and verify the theory through
numerical simulation. We also show that a primary function of bifurcated paths is to facilitate
transition by lowering the associated action.
In the third topic, we discuss the function of extrinsic noises in digital signaling using
mammalian NF-kB pathway. We show that when cells are stimulated by one ligand, digital
signaling allows one to independently control the fraction of responding cells (population-level
response) and temporal profiles of NF-kB activity (individual-level response). We also show
that under co-stimulation of two ligands, cells respond to only one input rather than both.
We term this behavior "non-integrative processing" and we propose a possible mechanism by
introducing an ultrasensitive negative feedback, allowing cells to block signaling pathways
upon activation by one ligand.