RESUMO
The modeling of dynamic systems is frequently hampered by a limited knowledge of the system to be modeled and by the difficulty of acquiring accurate data. This often results in a number of uncertain system parameters that are hard to incorporate into a mathematical model. Thus, there is a need for modeling formalisms that can accommodate all available data, even if uncertain, in order to employ them and build useful models. This paper shows how the Flexible Nets (FNs) formalism can be exploited to handle uncertain parameters while offering attractive analysis possibilities. FNs are composed of two nets, an event net and an intensity net, that model the relation between the state and the processes of the system. While the event net captures how the state of the system is updated by the processes in the system, the intensity net models how the speed of such processes is determined by the state of the system. Uncertain parameters are accounted for by sets of inequalities associated with both the event net and the intensity net. FNs are not only demonstrated to be a valuable formalism to cope with system uncertainties, but also to be capable of modeling different system features, such as resource allocation and control actions, in a facile manner.
RESUMO
The current production of a number of commodity chemicals relies on the exploitation of fossil fuels and hence has an irreversible impact on the environment. Biotechnological processes offer an attractive alternative by enabling the manufacturing of chemicals by genetically modified microorganisms. However, this alternative approach poses some important technical challenges that must be tackled to make it competitive. On the one hand, the design of biotechnological processes is based on trial-and-error approaches, which are not only costly in terms of time and money, but also result in suboptimal designs. On the other hand, the manufacturing of chemicals by biological processes is almost exclusively carried out by batch or fed-batch cultures. Given that batch cultures are expensive and not easy to scale, technical means must be developed to make continuous cultures feasible and efficient. In order to address these challenges, we have developed a mathematical model able to integrate in a single model both the genome-scale metabolic model for the organism synthesizing the chemical of interest and the dynamics of the bioreactor in which the organism is cultured. Such a model is based on the use of Flexible Nets, a modeling formalism for dynamical systems. The integration of a microscopic (organism) and a macroscopic (bioreactor) model in a single net provides an overall view of the whole system and opens the door to global optimizations. As a case study, the production of citramalate with respect to the substrate consumed by E. coli is modeled, simulated and optimized in order to find the maximum productivity in a steady-state continuous culture. The predicted computational results were consistent with the wet lab experiments.
RESUMO
Current research on systems and synthetic biology relies heavily on mathematical models of the systems under study. The usefulness of such models depends on the quantity and quality of biological data, and on the availability of appropriate modelling formalisms that can gather and accommodate such data so that they can be exploited properly. Given our incomplete knowledge of biological systems and the fact that they consist of many subsystems, biological data are usually uncertain and heterogeneous. These facts hinder the use of mathematical models and computational methods. In the scope of dynamic biological systems, e.g. metabolic networks, this difficulty can be overcome by the novel modelling formalism of flexible nets (FNs). We show that an FN can combine, in a natural way, a stoichiometric model and a kinetic model. Moreover, the resulting net admits nonlinear dynamics and can be analysed in both transient and steady states.