While genomics allows the blueprints of life to be read into static networks of thousands of interacting biomolecules that carry out essential cellular functions, a better understanding of the functioning of such networks is still required. Here we propose a dynamic modeling framework to integrate genomic detail and cellular physiology within functionally complete ‘hybrid’ bacterial cell models. An initial step in this approach is the development of a whole-cell coarse-grained model which explicitly links DNA replication, metabolism, and cell geometry with the external environment. A hybrid model can then be constructed from chemically-detailed and genome-specific subsystems, called modules, inserted into the original coarse-grained model. We use the sensitivity analysis of the original coarse-grained model to identify which pseudo-molecular processes should be de-lumped into molecularly-detailed mathematical modules to implement a particular biological function. To illustrate the modeling principles, the Cornell coarse-grained E.coli model, comprised of 36 ODEs, two algebraic equations, and 31 discrete events, is considered. In this approach, computational challenges immediately arise due to discrete events (e.g. cell division, etc.), resulting in non-continuous periodic solutions. However, the return map corresponding to the cell division cycle is smooth and, hence, the map can be used in the sensitivity analysis of the model. Due to scaling properties of the model, the objectives for the sensitivity analysis should be carefully chosen. The sensitivity analysis has correctly suggested which modules should be constructed to implement the corresponding biological functions (e.g. bacterial viability, protein overproduction, etc.). Interestingly, the stability analysis reveals the potential for autonomous quasi-periodic oscillations with ‘periods’ of 20-30 hours corresponding to the Hopf bifurcation of the cell-division return map. Given the primary cell division cycle of 45 minutes, the secondary long-term ‘oscillator’ has to be transmitted to the progeny cells. Further studies are needed to characterize the external medium, metabolic and genetic changes relevant to these intriguing ‘metabolic-genetic’ oscillations with periods much longer than the cell cycle. Thus, while the construction of large-scale ‘whole-cell’ kinetic models seems to be a daunting problem, moderate-sized hybrid cellular models provide a systematic way to relate genomic detail to physiologic response with a broad applicability in fundamental and applied research.
This project is supported by a DOE GTL grant. JCA gratefully acknowledges support from a DOE Computational Science Graduate Fellowship and MLS acknowledges support as an NYSTAR Professor (New York State Office of Science, Technology, and Academic Research).