Rafael S. Costa

Modeling formalisms in Systems Biology

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future.

Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis–Menten and approximate kinetic equations

The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.

Exploring the gap between dynamic and constraint-based models of metabolism

Systems biology provides new approaches for metabolic engineering through the development of models and methods for simulation and optimization of microbial metabolism. Here we explore the relationship between two modeling frameworks in common use namely, dynamic models with kinetic rate laws and constraint-based flux models. We compare and analyze dynamic and constraint-based formulations of the same model of the central carbon metabolism of Escherichia coli. Our results show that, if unconstrained, the space of steady states described by both formulations is the same. However, the imposition of parameter-range constraints can be mapped into kinetically feasible regions of the solution space for the dynamic formulation that is not readily transferable to the constraint-based formulation. Therefore, with partial kinetic parameter knowledge, dynamic models can be used to generate constraints that reduce the solution space below that identified by constraint-based models, eliminating infeasible solutions and increasing the accuracy of simulation and optimization methods.

Critical perspective on the consequences of the limited availability of kinetic data in metabolic dynamic modelling

Detailed kinetic models at the network reaction level are usually constructed using enzymatic mechanistic rate equations and the associated kinetic parameters. However, during the cellular life cycle thousands of different reactions occur, which makes it very difficult to build a detailed large-scale ldnetic model. In this work, we provide a critical overview of specific limitations found during the reconstruction of the central carbon metabolism dynamic model from E. coli (based on kinetic data available). In addition, we provide clues that will hopefully allow the systems biology community to more accurately construct metabolic dynamic models in the future. The difficulties faced during the construction of dynamic models are due not only to the lack of kinetic information but also to the fact that some data are still not curated. We hope that in the future, with the standardization of the in vitro enzyme protocols the approximation of in vitro conditions to the in vivo ones, it will be possible to integrate the available kinetic data into a complete large scale model. We also expect that collaborative projects between modellers and biologists will provide valuable kinetic data and permit the exchange of important information to solve most of these issues.

Implementation of a specific rate controller in a fed-batch E. coli fermentation

Abstract The specific growth rate is one of the most important process variables characterizing the state of microorganisms during fermentations mainly because the biosynthesis of many products of interest is often related with the values assumed by this parameter. In the particular case of the fed-batch operation of Escherichia coli for the production of recombinant proteins, it is important to maintain the specific growth rate below a certain threshold in order to avoid the accumulation of acetic acid throughout the fermentation and, additionally, it is often argued that both pre- and the post-induction specific growth rates should be closely controlled in order to achieve maximum productivities of the desired recombinant protein. In a previous work the authors have developed and validated by simulations a strategy for the automatic control of the specific growth rate in E. coli fed-batch fermentations based on an asymptotic observer for biomass and on developed estimators for the specific growth rates. The main purpose of the present work was to implement experimentally the developed observer, estimator and controller in a real fed-batch fermentation process. For that purpose a data acquisition and control program was developed in LabVIEW that allows the acquisition of the necessary on line data (off gas and dissolved oxygen concentration and culture weight) and the calculation of the feeding rates using the developed equations. The feedforward-feedback controller developed was able to keep the culture growing in an exponential phase throughout the fermentation without accumulation of glucose and acetate.

A Critical Review on Modelling Formalisms and Simulation Tools in Computational Biosystems

Integration of different kinds of biological processes is an ultimate goal for whole-cell modelling. We briefly review modelling formalisms that have been used in Systems Biology and identify the criteria that must be addressed by an integrating framework capable of modelling, analysing and simulating different biological networks. Aware that no formalism can fit all purposes we realize Petri nets as a suitable model for Metabolic Engineering and take a deeper perspective on the role of this formalism as an integrating framework for regulatory and metabolic networks.

MULTI-LEVEL DYNAMIC MODELING IN BIOLOGICAL SYSTEMS - Application of Hybrid Petri Nets to Network Simulation

This work was partially supported by post-doctoral grant by Fundacao para a Ciencia e a Tecnologia (FCT) (SFRH/BPD/80784/2011), project PneumoSyS - A Systems Biology approach to the role of pneumococcal carbon metabolism in colonization and invasive disease (FCT contract: PTDC/SAU-MII/100964/2008) and by FCT (INESC-ID multiannual funding) through the PIDDAC program funds.

Evaluating the Integration of Proteomic Data for the Prediction of Intracellular Fluxes after Knockout Experiments

Abstract So far, few large scale kinetic models of metabolic networks have been successfully constructed. The main reasons for this are not only the associated mathematical complexity, but also the large number of unknown kinetic parameters required in the rate equations to define the system. In contrast to kinetic models, the constraint-based modelling approach bypasses these difficulties by using basically only stoichiometric information with certain physicochemical constraints to delimit the solution space without large fitted parameter sets. Although these constraint-based models are highly relevant to predict feasible steady-state fluxes under a diverse range of genetic and environmental conditions, the steady-state assumption may oversimplify cellular behaviour and cannot predict time-course profiles. To overcome these problems, combining these two approaches appears as a reasonable alternative to modelling large-scale metabolic networks. On the other hand, several of the experimental data required for model construction are often rare and in this way it is usually assumed that the enzyme concentrations are constant. In this work, we used a central carbon metabolic network of E. coli to investigate whether including high throughput enzyme concentration data into a kinetic model allows improved predictions of metabolic flux distributions in response to single knockouts perturbations. For this purpose, an E. coli model, based on results obtained from flux balance analysis (FBA) and approximate lin-log kinetics was constructed. The intracellular fluxes distributions, obtained using this model, were compared with published in vivo measurements.