Hybrid Modeling and Robustness Analysis of Cell Cycle Regulation

Caulobacter crescentus is a model organism for studying asymmetrical bacteria cell cycle division. During the cell cycle, a Caulobacter cell needs to accomplish molecular functions in the right sequence: It sheds its flagella, grows a stalk, replicates and segregates its chromosomes, and initiates cytokinesis to compartmentalize the two morphologically distinct daughter cells, all of which are coordinated by a genetic control circuit comprised of cascaded regulatory proteins that are expressed in an orderly and timely fashion to drive the cell cycle progression. Non-genetic mechanisms like methylation-based promoter control, phospho-signal pathways and regulated proteolysis couple the cyclic genetic circuit back to the progression of various cell cycle processes, closing the feedback control loops. With advances in experimental technology, the understanding of this cellular regulatory system has progressed to a level of complexity which is difficult for intuitive understanding, especially when dynamic behaviors resulting from feedback effects are concerned. To simulate the dynamic properties of the cell cycle feedback control, an in silico hybrid simulation model was constructed based on the concept of hybrid system from control theory. Mimicking the Caulobacter control structure in vivo, the hybrid model uses continuous ordinary differential equations (ODE) to model well-understood molecular reactions such as protein synthesis, but uses discrete event-driven finite state machines (FSM) to phenomenologically model complex cell processes and instantaneous reactions. This model provides a flexible and extensible architecture capable of handling different levels of abstraction and mechanistic details. The model was validated by the demonstrative consistency between simulation results and experimental measurements including protein and mRNA concentration profiles. In addition, in silico mutants based on the model correctly predicted phenotypes of various in vivo mutants. Because biological systems have to survive under a variety of environmental, genetic, and stochastic perturbations, it has been postulated that their regulatory systems have to be quite robust, so a further analysis of the robustness property of the modeled cell cycle regulation can provide new biological insights. It is difficult to use traditional methods like parameter sensitivity analysis to fully explore the design space and intuitively interpret the result in terms of the robustness of a complex model. By creating an equivalent asynchronous digital circuit representation of the cell cycle model, which maintains properties of interest, formal model checking techniques were applied to exhaustively searching the entire state space to identify the potential scenarios which causes the cell cycle to fail to complete. The analysis revealed that the top level control of the Caulobacter cell cycle regulation is extremely robust with very few cases of potential failures. Furthermore, non-genetic mechanisms such as methylation-based control of promoter activation and its remaining basal expression have been shown to play an important role for robustness under special circumstances. Model checking also verified that the modeled cell cycle is able to robustly switch into growth arrest when facing stress or starvation.