Biochemical reaction fluxes

Possible driving forces for solute flux can be enumerated as a linear combination of gradient contributions [Eq. (20)] to solute potential across the membrane barrier (see Part I of this volume). These transbarrier gradients include chemical potential (concentration gradient-driven diffusion), hydrostatic potential (pressure gradient-driven convection), electrical potential (ion gradient-driven cotransport), osmotic potential (osmotic pressure-driven convection), and chemical potential modified by chemical or biochemical reaction. 

One of the most distinguishing features of metabolic networks is that the flux through a biochemical reaction is controlled and regulated by a number of effectors other than its substrates and products. For example, as already discovered in the mid-1950s, the first enzyme in the pathway of isoleucine biosynthesis (threonine dehydratase) in E. coli is strongly inhibited by its end product, despite isoleucine having little structural resemblance to the substrate or product of the reaction [140,166,167]. Since then, a vast number of related... 

S. Schuster and C. Hilgetag, On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 2, 165 182 (1994). 

Net flux for nearly irreversible reactions is proportional to reverse flux In computational modeling of biochemical systems, the approximation that certain reactions are irreversible is often invoked. In this section, we explore the consequences of such an approximation, and show that the flux through nearly irreversible enzyme-mediated reactions is proportional to the reverse reaction flux. 

There is almost no biochemical reaction in a cell that is not catalyzed by an enzyme. (An enzyme is a specialized protein that increases the flux of a biochemical reaction by facilitating a mechanism [or mechanisms] for the reaction to proceed more rapidly than it would without the enzyme.) While the concept of an enzyme-mediated kinetic mechanism for a biochemical reaction was introduced in the previous chapter, this chapter explores the action of enzymes in greater detail than we have seen so far. Specifically, catalytic cycles associated with enzyme mechanisms are examined non-equilibrium steady state and transient kinetics of enzyme-mediated reactions are studied an asymptotic analysis of the fast and slow timescales of the Michaelis-Menten mechanism is presented and the concepts of cooperativity and hysteresis in enzyme kinetics are introduced. 

The data and associated model fits used to obtain these kinetic constants are shown in Figures 4.10 through 4.12. These data on quasi-steady reaction flux as functions of reactant and inhibitor concentrations are obtained from a number of independent sources, as described in the figure legends. Note that the data sets were obtained under different biochemical states. In fact, it is typical that data on biochemical kinetics are obtained under non-physiological pH and ionic conditions. Therefore the reported kinetic constants are not necessarily representative of the biochemical states obtained in physiological systems. 

Appropriate expressions for the fluxes of each of the reactions in the system must be determined. Typically, biochemical reactions proceed through multiple-step catalytic mechanisms, as described in Chapter 4, and simulations are based on the quasi-steady state approximations for the fluxes through enzyme-catalyzed reactions. (See Section 3.1.3.2 and Chapter 4 for treatments on the kinetics of enzyme catalyzed reactions.)... 

Analysis of biochemical systems, with their behaviors constrained by the known system stoichiometry, falls under the broad heading constraint-based analysis, a methodology that allows us to explore computationally metabolic fluxes and concentrations constrained by the physical chemical laws of mass conservation and thermodynamics. This chapter introduces the mathematical formulation of the constraints on reaction fluxes and reactant concentrations that arise from the stoichiometry of an integrated network and are the basis of constraint-based analysis. 

In addition to the stoichiometric mass-balance constraint, constraints on reaction fluxes and species concentration arise from non-equilibrium steady state biochemical thermodynamics [91]. Some constraints on reaction directions are... 

One can view biochemical systems as represented at the most basic level as networks of given stoichiometry. Whether the steady state or the kinetic behavior is explored, the stoichiometry constrains the feasible behavior according to mass balance and the laws of thermodynamics. As we have seen in this chapter, some analysis is possible based solely on the stoichiometric structure of a given system. Mass balance provides linear constraints on reaction fluxes non-linear thermodynamic constraints provide information about feasible flux directions and reactant concentrations. 

Elaborate models have been developed to account for the behavior of cellular biochemical networks. Boolean network models use a set of logical rules to illustrate the progress of the network reactions [10]. These models do not take into explicit account the participation of specific biochemical reactions. Models that account for the details of biochemical reactions have been proposed [11,12]. The behavior of these models depends on the rate constants of the chemical reactions and the concentrations of the reactants. Measurements like those described below of reaction fluxes and reactant concentrations will be able to test such network models. In the following sections, we will use simple examples to illustrate the characteristic steady-state behavior and propose an approach to measure fluxes and concentrations. 

Another two key concepts in metabolic engineering are metabolic pathway analysis and metabolic pathway modeling. The former is used for assessing inherent network properties in the complete biochemical reaction networks. It involves identification of the metabolic network structure (or pathway topology), quantification of the fluxes through the branches of the metabolic network, and identification of the control structures within the metabolic network. 

The biosynthesis pathways of the vitamins thiamine (Bl), pyridoxine (B6), and biotin (B7) have been elucidated during the last 10 years to some detail. It became clear that in all cases enzymes catalyzing unusual or complex biochemical reaction mechanisms are involved, which perform at least in vitro with very low catalytic efficiency. Previous attempts to breed B. suhtilis production strains for these vitamins as a base for the development of superior processes to supersede the decades old chemical processes are reviewed here briefly. These efforts followed the blueprints that were successful for other metabolites like amino acids, nucleotides, the vitamins mentioned above, and others. However, the metabolic fluxes toward the vitamins Bl, B6, and B7 have proven to be particularly adamant to engineering. The strains that were obtained overproduced these value compounds only at marginal levels. 

The dissipated heat is not the enthalpy differences, since the system is cyclic heat of reaction in forward and backward directions are balanced. As Eqn (e) shows that for an open biochemical network, fluxes and concentrations are important observable variables. Spectroscopic measurements show that concentrations of biochemical species in living cells are fluctuating. Concentrations and the standard state chemical potentials fi° yield the nonequilibrium chemical potentials. 

Behre J, Wilhelm T, von Kamp A, Ruppin E, Schuster S (2008) Stmctuial robustness of metabolic networks with respect to multiple knockouts. J Theor Biol 252 433M41 Bell SL, Palsson BO (2005) Expa a program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 21 1739-1740 Beurton-Aimar M, Beauvoit B, Monier A, Vallee F Dieuaide-Noubhani M, Colombie S (2011) Comparison between elementary flux modes analysis and 13c-metabolic fluxes measured in bacterial and plant cells. BMC Syst Biol 5 95... 

Schuster R, Schuster S (1993) Refined algorithm and computer program calculating All Nonnegative fluxes admissible in steady states of biochemical reaction systems with and without some fluxes rates fixed. CABIOS 9 79-85... 

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 ... 

The timescales of biochemical reactions and the preservation conditions applied to the organism play crucial roles in determining the success of preservation. For example, the ratio of the timescale of water diffusion, td, across the ceU membrane (td = r/SIpAIl, where r. Ip, and AO are the cell radius, membrane permeability, and osmotic pressure differential, respectively) to the timescale of cooling the ceU experiences, xq xq = (2cp/or A T)where Cp, p, q", and A T are the specific heat, mass density, heat flux, and temperature differential, respectively) determines the fate of a cell during freezing such that (Figure 41.1) ... 

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