Metabolic reaction networks

To recognize the different levels of representation of biochemical reactions To understand metabolic reaction networks To know the principles of retrosynthetic analysis To understand the disconnection approach To become familiar with synthesis design systems... 

Biochemical pathways and metabolic reaction networks have recently attracted much interest and are an active and rich field for research,... 

A particularly challenging problem is the understanding and modeling of biochemical and metabolic reactions, and even more so of metabolic reaction networks. Much work will go into this field in the next few years. 

Note that Eq. (6) includes thermodynamic equilibrium (v° = 0) as a special case. However, usually the steady-state condition refers to a stationary nonequilibrium state, with nonzero net flux and positive entropy production. We emphasize the distinction between network stoichiometry and reaction kinetics that is implicit in Eqs. (5) and (6). While kinetic rate functions and the associated parameter values are often not accessible, the stoichiometric matrix is usually (and excluding evolutionary time scales) an invariant property of metabolic reaction networks, that is, its entries are independent of temperature, pH values, and other physiological conditions. 

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. 

Currently there is much interest in the reaction network structure. For example, Jeong et al. [5] studied the metabolic reaction network, without going... 

The main problem in applying stoichiometric considerations to bioprocessing (beyond quantification in non-open-reactor systems) arises from the complex metabolic reaction network. In simple reactions stoichiometry is trivial, and complex reactions can only be handled with the aid of a formal mathematical approach analogous to the approach for complex chemical reactions (Schubert and Hofmann, 1975). In such a situation, an elementary balance equation must be set up. Due to complexity, it is not surprising that the approach first used in the quantification of bioprocesses was much simpler— the concept of yield factors Y. This macroscopic parameter Y cannot be considered a biological constant. 

Real-time monitoring of enzymatic reactions is also useful for fundamental studies in synthetic biology. Bujara et al. [56] implemented ESI-QqQ-MS in the monitoring of a multi-enzyme reaction chain (Figure 13.7). This method may enable optimization of complex metabolic reaction networks for chemical synthesis. The on-line sampling system encompassed sampling of the reaction mixture via membrane, reduction of flow, dilution, and ionization. 

Hatzimanikatis, V., Floudas, C.A., Bailey, J.E. (1996) Analysis and design of metabolic reaction networks via mixed integer linear optimisation. AIChE J., 42, 1277-1292. 

If enough fluxes are measured at a metabolic steady state, MFA [11,12] can be used to estimate the fluxes through the remainder of the metabolic reaction network (Figure 15.1). This analysis is powerful because only the stoichiometry of the biochemical reaction network is required, and no knowledge of the chemical reaction kinetics is needed. MFA is usually formulated as a matrix equation ... 

This is not the place to expose in detail the problems and the solutions already obtained in studying biochemical reaction networks. However, because of the importance of this problem and the great recent interest in understanding metabolic networks, we hope to throw a little light on this area. Figure 10.3-23 shows a model for the metabolic pathways involved in the central carbon metabolism of Escherichia coli through glycolysis and the pentose phosphate pathway [22]. 

Other habitats Surface metabolism and geothermal vents as habitats with selected reaction networks... 

Stoichiometric analysis goes beyond topological arguments and takes the specific physicochemical properties of metabolic networks into account. As noted above, based on the analysis of the nullspace of complex reaction networks, stoichiometric analysis has a long history in the chemical and biochemical sciences [59 62]. At the core of all stoichiometric approaches is the assumption of a stationary and time-invariant state of the metabolite concentrations S°. As already specified in Eq. (6), the steady-state condition... 

Besides the two most well-known cases, the local bifurcations of the saddle-node and Hopf type, biochemical systems may show a variety of transitions between qualitatively different dynamic behavior [13, 17, 293, 294, 297 301]. Transitions between different regimes, induced by variation of kinetic parameters, are usually depicted in a bifurcation diagram. Within the chemical literature, a substantial number of articles seek to identify the possible bifurcation of a chemical system. Two prominent frameworks are Chemical Reaction Network Theory (CRNT), developed mainly by M. Feinberg [79, 80], and Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83]. An analysis of the (local) bifurcations of metabolic networks, as determinants of the dynamic behavior of metabolic states, constitutes the main topic of Section VIII. In addition to the scenarios discussed above, more complicated quasiperiodic or chaotic dynamics is sometimes reported for models of metabolic pathways [302 304]. However, apart from few special cases, the possible relevance of such complicated dynamics is, at best, unclear. Quite on the contrary, at least for central metabolism, we observe a striking absence of complicated dynamic phenomena. To what extent this might be an inherent feature of (bio)chemical systems, or brought about by evolutionary adaption, will be briefly discussed in Section IX. 

An early systematic approach to metabolism, developed in the late 1970s by Kacser and Burns [313], and Heinrich and Rapoport [314], is Metabolic Control Analysis (MCA). Anticipating systems biology, MCA is a quantitative framework to understand the systemic steady-state properties of a biochemical reaction network in terms of the properties of its component reactions. As emphasized by Kacser and Burns in their original work [313],... 

Although the importance of a systemic perspective on metabolism has only recently attained widespread attention, a formal frameworks for systemic analysis has already been developed since the late 1960s. Biochemical Systems Theory (BST), put forward by Savageau and others [142, 144 147], seeks to provide a unified framework for the analysis of cellular reaction networks. Predating Metabolic Control Analysis, BST emphasizes three main aspects in the analysis of metabolism [319] (i) the importance of the interconnections, rather than the components, for cellular function (ii) the nonlinearity of biochemical rate equations (iii) the need for a unified mathematical treatment. Similar to MCA, the achievements associated with BST would warrant a more elaborate treatment, here we will focus on BST solely as a tool for the approximation and numerical simulation of complex biochemical reaction networks. 

Any biochemical pathway intermediate that can proceed along more than one route in a network of metabolic reactions. 

The cytosol is the soluble part of the cytoplasm where a large number of metabolic reactions take place. Within the cytosol is the cytoskeleton, a network of libers (microtubules, intermediate filaments and microfilaments) that maintain the shape of the cell. 

Table 1 describes all the microbe-specific databases, and Table 2 lists databases for the microbial community. These databases provide genomic sequence data, gene and protein information, gene expression data, metabolic reactions and pathways, interaction network,... 

We constructed our network from the metabolic reaction database PlasmoCyc. The metabolites were taken as nodes. Two metabolites were connected by an edge if an enzymatic reaction existed that had them as an educt or product, respectively (23). We discarded highly connected metabolites such as water, C02, and adenosine triphosphate. These metabolites are needed in many reactions and are therefore unspecific in the metabolic network. 

In practice, a gray-box model is developed in steps. One early step is to decide which variables and interactions to include. This is often done by the sketching of an interaction-graph. It must then be decided if a variable should be a state or a dependent variable, and how the interactions should be formulated. In the case of metabolic reactions, the expression forms for the reactions have often been characterized in in-vitro experiments. If this has been done, there are also often in-vitro estimates of the kinetic parameters. For enzymatic networks, however, such in-vitro studies are much more rare, and it is hence typically less known which expression to choose for the reaction rates, and what a good estimate for the kinetic parameters is. In any case, the standard method of combining reaction rates, r,-, and an interaction graph into a set of differential equations is to use the stoichiometric coefficients, Sij... 

Many methods have been developed for model analysis for instance, bifurcation and stability analysis [88, 89], parameter sensitivity analysis [90], metabolic control analysis [16, 17, 91] and biochemical systems analysis [18]. One highly important method for model analysis and especially for large models, such as many silicon cell models, is model reduction. Model reduction has a long history in the analysis of biochemical reaction networks and in the analysis of nonlinear dynamics (slow and fast manifolds) [92-104]. In all cases, the aim of model reduction is to derive a simplified model from a larger ancestral model that satisfies a number of criteria. In the following sections we describe a relatively new form of model reduction for biochemical reaction networks, such as metabolic, signaling, or genetic networks. 

---