Kinetic modeling cellular metabolism

These differences probably contribute to the fact that mathematical modeling is, as yet, not seen as a mainstream research tool in many areas of molecular biology. However, as will be described in the remainder of this chapter, many obstacles in the construction of kinetic models of cellular metabolism can be addressed using a combination of novel and established experimental and computational techniques, enabling the construction of metabolic models of increasing complexity and size. 

As demonstrated in the work of Grimbs et al. [296] using a model of the human erythrocyte, the ranking obtained by any of the measures above is i) consistent independent of the specific measure and ii) corresponds closely to a ranking obtained from an explicit kinetic model of the pathway, and it is in excellent agreement with prior knowledge of the metabolic system. Consequently, we expect that the methods described here and in [296] provide a suitable starting point to locate crucial parameters and reactions in cellular metabolism, as well as in cases where the construction of explicit kinetic models is not (yet) feasible. 

Metabolic flux analysis Cellular metabolites and metabolic fluxes can be combined into a series of balance equations, not unlike a series of (bio)chemical reactions in a kinetic model. Metabolic flux analysis is the description of the components and their connections in a metabolic network. 

A kinetic model consists of a set of mathematical expressions that relate the rates of cellular growth and metabolism to the composition of the medium. With... 

Thus, the kinetics of conversions In metabolic cellular sequences, and even in whole cell kinetics, at or near steady state may be expected to resemble the kinetic rate form appropriate to one or a very small number of sequential enzyme catalyzed steps. The implications of this point in kinetic models of structured cell systems are reflected in later contributions in this conference. 

What goes by cellular metabolism is an immense class of chemical and physical rate processes within and without the cell marked most strikingly by their diversity and specificity. It forms the basis of the response of microorganisms to their environment, the modelling of which must of necessity suffer some oversimplification if it is to be of any value. In this context, kinetic models of microbial growth within the framework of interaction between lumped biochemical species and the environment have had considerable appeal in the past. However, the subtle facilities which derive from the elaborate Internal machinery of the cells pose a challenge that no meager expansion of the kinetic framework will ever meet. 

Due to lack of kinetic parameters, structural metabolic network modeling has been widely applied for analyzing cellular metabolism under steady-state. Depending on what assumptions are made and whether experimental data are required, different techniques have been developed to analyze the invariant of metabohc networks such as metabolic flux analysis (MFA), flux balance analysis (FBA), and metabolic pathway analysis (MPA) including elementary mode and extreme pathway analyses (Lewis et al. 2012 Stephanopoulos et al. 1998 Trinh et al. 2(X)9). 

The addition of new biochemical pathways, or the modification of existing pathways, is likely to affect the rest of the cellular metabolism. The new or altered pathways may compete with other reactions for intermediates or cofactors. To precisely predict the impact of the manipulation of a metabolic network is virtually impossible since it would require a perfect model of all enzyme kinetics and of the control of gene expression. Flowever, attempts have been made to develop modeling techniques to predict the behavior of altered organisms [29]. 

Kinetic models define the metabolic system by combining kinetics information about specific cellular process with known stoichiometry. Thus in principle kinetic models capture the dynamic properties of the metabolic network. However, a major problem associated with setting up these models is the lack of kinetic dafa and the difference between in vivo and in vitro kinetic parameters (Gombert and Nielsen, 2000). 

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. 

The model proposed for mammalian cell cultures provides a description of the possible influence of four of the main medium components - glucose, glutamine, lactate and ammonia - on the rates of cellular growth, death and metabolism. It contains kinetic terms that quantify the influence of each of the components either in reducing the rate of cellular growth or in increasing the rate of cell death. 

---