|Research Area:||Biological modeling|
The hybrid simulation model revealed that the cell cycle is quite insensitive to parameter variations and single gene mutations. The robustness of the regulatory circuitry that our model displayed is not surprising, because Caulobacter bacteria cells have to withstand all kinds of perturbations and changing environment in the wild. To further investigate the robustness of the regulatory circuit, we wanted to identify the hazardous conditions under which the cell cycle model was unable to divide. Replicating these conditions in the laboratory would help biologists discover robustness mechanisms that are not expressed under typical laboratory environments. At first, the sheer number of parameters in the model made manual enumeration hard. Fortunately this problem has an electrical analogy - in digital circuits, there exist formal verification tools for identifying timing hazards in asynchronous designs. These tools are used by electrical circuit designers to determine if a circuit will still function correctly in the event of anomalous delays and we could apply them to analyze the robustness of the bacterial cell cycle control system to arbitrary delays of its biological functions. NuSMV is one of these validation tools that symbolically analyzes the branching graph of all possible paths using computational tree logic (CTL). We collaborated with Professor David Dill in the computer science department to build an equivalent circuit model of the cell cycle control using gates and state machines, with which NuSMV exhaustively checked and reported the failure cases in a format that was intuitive and replicable in in-vivo experiments. By checking these cases experimentally, we were able to find that the bacterial cell cycle control is extremely robust with extra cellular mechanisms previously undetected that further contribute to its robustness. For example, the leaky expression of promoters controlled by methylation, somewhat similar to leakage current of transistors, had always been considered as a non-ideality and something that had negligible effect on cell cycle operation. The validation tool showed that the slow accumulation of this leaky expression is actually leveraged by Caulobacter to revive the cell cycle progression when it falls into one of those hazardous conditions. Other mechanisms which were not included in the original model such as a normally inactive promoter and the inactivity of certain proteins were also shown to contribute to the robustness of the cell cycle. The existence of such robustness mechanisms illustrates why single-gene mutation rarely generate mutant phenotypes.