Fundamentals of Systems Analysis and Modeling of Biosystems and Metabolism

A brief overview is given for the current status of systems biology and modeling. Systems biology focuses on the profiling of the whole cellular metabolism using high-throughput data of different levels of information to understand and unraveling the underlying principles of the living organisms. The systems biology allows the development of mathematical models that can be computationally simulated. Various modeling approaches can be classified into two such as flux balance analysis (FBA) based on the stoichiometric constraints, and the kinetic modeling based on the enzymatic kinetic expressions. Although the former approach can be extended to large genome-scale, it is difficult to incorporate the metabolic regulation mechanism and to express the dynamics, while the latter approach can reasonable incorporate the metabolic regulation mechanism. The problem for the kinetic modeling is the increase in the model parameters as the system size becomes large. It is important for the modeling of a cell system to properly understand and express how the environmental stimuli are detected, how those are transduced, and how the cell metabolism is regulated. It is quite useful from science and metabolic engineering points of view to develop quantitative models toward whole cell modeling.

Basic notion and systems analysis method is briefly explained for the preparation to the understanding of the later chapters. Non-linear and linear systems equations are explained, where the standard formulation and its representation is useful for the basis of various types of modeling. Transfer function is explained for the linear system as the input-output representation. Basic graph theory is explained with its applications, where it is important to analyze large-scale metabolic reaction networks. Data analysis such as regression analysis and the principal component analysis (PCA) are also briefly explained, where it is important for analyzing the experimental data and experimental design in relation to modeling.

The transport phenomena such as mass balance, momentum balance, and heat balance are briefly explained for the basis of modeling, where all the appropriate models must be constructed based on the principles which govern the organisms and their living environment. The model reduction by singular perturbation is explained for the simple enzyme reaction. The basic modeling approaches such as flux balance analysis (FBA), metabolic flux analysis (MFA), kinetic model, and their integration are briefly explained. Unstructure models are explained for the batch, fed-batch, and continuous cultures. For the modeling of Eco-systems, some population dynamic models are explained. As the datadriven modeling, the structure and the algorithm of artificial neural networks (ANNs) are explained together with simple examples. These modeling approaches may cover a variety of modeling approaches to the variety of cell systems.

Kinetic models for the main metabolic pathways such as glycolysis, TCA cycle, pentose phosphate pathway together with anaplerotic pathways and gluconeogenic pathways are explained. Kinetic models for substrate uptake pathways such as glucose PTS, glycerol uptake pathways, and xylose assimilating pathways are then explained. Kinetic models for the fermentation pathways under anaerobic condition are also explained. Moreover, kinetic models for amino acid synthetic pathways such as glutamic acid/ glutamine synthetic pathways and lysine synthetic pathways are explained. Unlike flux balance analysis based on the stoichiometric constraints, kinetic modeling approach based on enzymatic reactions for the metabolic pathways can be easily extended for the inclusion of enzyme level and transcriptional regulations, and the kinetic models can reasonably express the dynamics.

Model identification method is briefly explained. Then the sensitivity analysis is explained in relation to model parameter identification. In view of sensitivity analysis, the metabolic control analysis (MCA) is explained, followed by its application to find the limiting pathways for lysine fermentation by Corynebacterium sp. In relation to flux balance analysis (FBA) and its extension to genome-scale as mentioned in Chapter 3, the linear programming method is explained for the optimization of a single objective function under the constraint of stoichiometric equations. A basic approach for the vector-valued objective function and non-inferior Pareto optimal set is briefly explained. In relation to model parameter identification, various types of direct and gradient-based optimum seeking methods are explained. A global search method such as genetic algorithm (GA) is also explained. Moreover, the optimal operation or optimal control strategies based on the Maximum principle is explained to find the time optimal trajectories with some application to ethanol fermentation.

Once the appropriate model was developed, the steady-state and dynamic characteristics such as multiple steady states and stability etc. can be analyzed. Multiple steady states are analyzed from the point of view of Catastrophy. The dynamic characteristics around the steady state are analyzed based on the perturbation of the state and the stability analysis with phase plane analysis. The bifurcation analysis is briefly explained for the limit cycle bifurcating from the steady state as Hopf-bifurcation. The dynamics of continuous stirred tank fermenter (CSTF) for the different expression of the cell growth rate is explained. The dynamics of the Lotka-Volterra population model is explained. The chaotic behavior is also explained for the simple logistic model.

It is quite important to understand the overall regulation mechanism of a cell system for the proper modeling. Namely, it is desirable to incorporate how the cell detect environmental signals, integrate such information, and how the cell system is regulated. In particular, carbon catabolite regulation (CCR) is of primal importance for the analysis of overflow metabolism and for the selective assimilation of multiple carbon sources. Metabolic regulation is made by enzyme level regulation and transcriptional regulation via the transcription factors. The effects of feed-forward and feed-back regulations on the metabolism is also explained based on the simple linear system. For CCR, proper understanding on the phosphotransferase system (PTS) and the transcriptional regulation by cAMP-Crp and Cra is important. The coordinated regulation between catabolic and anabolic (nitrogen source-assimilation) metabolism may be made by the keto acid such as αKG. The effect of oxygen level on the metabolism is explained in terms of global regulators such as ArcA/B and Fnr. Moreover, the nitrogen regulation in response to nitrogen limitation is explained. The modeling may be made by taking into account the metabolic regulation mechanisms of the central metabolism.

Modeling of the main metabolic pathways such as glycolysis, TCA cycle, pentose phosphate (PP) pathway, and anaplerotic pathways is considered, where the fluxes obtained by computer simulation can be used to compute the specific ATP production rate, the specific CO2 production rate, and the specific NAD(P)H production rate. The specific ATP production rate thus computed can be used for the estimation of the specific growth rate. The model can be further extended for catabolite regulation by incorporating the effects of transcription factors such as Cra and cAMP-Crp, where acetate overflow metabolism and co-consumption of multiple sugars can be clarified by this modeling approach. Modeling for anaerobic fermentation is also considered, where aerobic/ anaerobic switch can be made by incorporation of the roles of ArcA/B and Fnr. Modeling for NH3 assimilation pathways is then considered, where this may be combined with the main metabolism to simulate nitrogen regulation at various C/N ratios. Finally, amino acid synthetic pathways are considered for lysine production.