UCLA

As global oil demand approaches unsustainable levels, people have turned to living organisms as a possible alternative source for many petroleum-derived products. Great advances in the fields of synthetic biology and metabolic engineering have enabled microbial production of fuels and other chemical feedstock. Nevertheless, the production cost of many of these processes makes it hard to compete with their petroleum derived counterparts.

Due to their complexity, living organisms present a particular challenge to their use as chemical catalysts. Although metabolic engineering has greatly enhanced the catalytic capabilities of microbes, the minor alterations that have yielded such improvements seem to be unable to take the catalytic activity to the levels necessary to compete with petroleum. Novel efforts are trying to use major changes in bacterial metabolism in order to bypass the current limitations of biological systems. Although very promising, engineered pathways do not have the chance to be tuned through years of evolution; as such their incorporation into metabolism can lead to metabolic imbalances, which will ultimately hamper production. Due to the complexity of these metabolic systems, mathematical tools would be instrumental to assessing such problems.

Currently, there are no metabolic modeling methods that can both consider metabolite concentrations explicitly and account for all annotated reactions for the particular organism. There are two main difficulties impeding the development of such method: (1) Kinetic parameter values are unavailable for most reactions (the parameter space grows exponentially with the number of reactions); and (2) computation time increases exponentially as the system becomes larger, making difficult the use of random sampling. Through the use Ensemble Modeling and parameter continuation we were able to overcome these hurdles and develop some specific tools for the mathematical analysis of metabolic systems.

If a system is not robust, small changes in expression levels may lead to system failure due to the disappearance of a stable steady state. Given a lack of regulatory mechanisms, this problem becomes especially important when designing synthetic pathways. Nevertheless, it is often difficult to identify flaws in the design which might lower robustness using intuition alone. To address this issue, we developed a method termed Ensemble Modeling for Robustness Analysis (EMRA), which combines parameter continuation with the EM approach for investigating the robustness issue of metabolic pathways. Using a large ensemble of reference models with different parameters, we can determine the effects of parameter drifting until a bifurcation point. This method gives us an unbiased analysis of the robustness issues of a particular pathway structure.

Similarly, in order to be able to maintain a viable phenotype under small changes in internal or external conditions (e.g. variations in enzyme levels or nutrient concentrations) cells must possess a robust metabolic network. Through evolution, native metabolic pathways have seemingly solved the robustness problem by selecting a robust network structure and regulatory mechanisms such that the feasible range of each parameter is sufficiently large. Although this fact is well accepted, it has never been used during the creation of kinetic models of native metabolism. By developing a quantitative and scalar index based on EMRA, we can add robustness as an objective during parameter-fitting. As kinetic models have a large number of parameters and the number of available data points is relatively low, we hypothesize that the additional robustness criterion will greatly improve the quality of fitted models.

By utilizing robustness, a cell-wide model of Escherichia coli was constructed. Cell-wide metabolic models incorporate many of the intrinsic complexities of living organisms. Although the utility of encompassing such a large portion of cellular metabolism is undeniable, the computational difficulties regarding such models have hampered their use. The use of entropy allowed for more intelligent model curation, eased the computational difficulties un-robust models present. Additionally, a novel application of parameter continuation was developed and used to successfully predict in vivo isobutanol production.