Analysis metabolic control

Let us first consider the case where the concentration of a species, species n, is changed x —x + Sxn. Since the state x is asymptotically stable, the system will return to the original steady state if xn is a dynamic variable. However, if x is a clamped concentration, then the system will achieve a new steady state. Locally 

The coefficient is distinguished from the coefficient which characterizes the steady state response [208]. When a new steady state is established following a change of x - x + Sxn in clamping the species n, the remaining (N - 1) concentrations satisfy the system of linear equations  

Solving Equation (6.74) for Sxt, we have Sxt/x = BinSxn/Bnnx where Bin is the nth column vector of the matrix A-1. The new steady state established near x is x + Sx,. 2 

We now consider the case where enzyme activity for the mth reaction Em is changed Em — Em + 8Em. Assuming that the flux through the reaction is linearly proportional to the activity of the enzyme catalyzing the reaction, Em, when Em - Em + SEm, the new steady state satisfies 

There exist several important theorems related to sums of these control coefficients [209, 53], From Equation (6.79) it is apparent that 

---

Fell, D.A. (1992). Metabolic control analysis A survey of its theoretical and experimental development. Biochem. J. 286,313-330. 

Metabolic control analysis (MCA) assigns a flux control coefficient (FCC) to each step in the pathway and considers the sum of the coefficients. Competing pathway components may have negative FCCs. To measure FCCs, a variety of experimental techniques including radio isotopomers and pulse chase experiments are necessary in a tissue culture system. Perturbation of the system, for example, with over-expression of various genes can be applied iteratively to understand and optimize product accumulation. 

Metabolic Flux Analysis and Metabolic Control Analysis... 

After measuring the fluxes through the metabolic network, it is necessary to determine the extent to which each pathway or enzyme controls the net fluxes. Metabolic control analysis (MCA) is a technique used to elucidate how flux control is distributed in a metabolic network, thereby providing the information for identification of potential targets for metabolic engineering [8],... 

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],... 

The utility and success of Metabolic Control Analysis is mostly due to a number of simple relationships that interconnect the various coefficients and that bridge between local and global properties of the network. First, the summation theorems relate to the structural properties of the network and are independent of kinetic parameters [96]. Using Eq. (90) and (91), it is straightforward to verify that... 

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. 

To reconcile the nomenclature with Metabolic Control Analysis, we note that the kinetic orders corresponds to the (scaled) elasticities of the reaction... 

The interpretation of the elements of the matrix 0 is slightly more subtle, as they represent the derivatives of unknown functions fi(x) with respect to the variables x at the point x° = 1. Nevertheless, an interpretation of these parameters is possible and does not rely on the explicit knowledge of the detailed functional form of the rate equations. Note that the definition corresponds to the scaled elasticity coefficients of Metabolic Control Analysis, and the interpretation is reminiscent to the interpretation of the power-law coefficients of Section VII.C Each element 6% of the matrix measures the normalized degree of saturation, or likewise, the effective kinetic order, of a reaction v, with respect to a substrate Si at the metabolic state S°. Importantly, the interpretation of the elements of does again not hinge upon any specific mathematical representation of specific... 

To highlight the relationship of the matrices A and to the quantities discussed in Section VILA (Dynamics of Metabolic Systems) and Section VII.B (Metabolic Control Analysis), we briefly outline an alternative approach to the parameterization of the Jacobian matrix. Note the correspondence between the saturation parameter and the scaled elasticity ... 

S. Schuster, Use and limitations of modular metabolic control analysis in medicine and biotechnology. Metab. Eng. 1, 232 242 (1999). 

P. J. Mulquiney and P. W. Kuchel, Model of 2,3 bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations Computer simulation and metabolic control analysis. Biochem. J. 342 (3), 597 604 (1999). 

J. H. S. Hofmeyr, Metabolic control analysis in a nutshell. Online Proceedings ICSB 2001, http //www.icsb 2001.org (2001). 

M. A. Savageau, Dominance according to metabolic control analysis Major achievement or house of cards (letter to the editor). J. Theor. Biol. 154, 131 136 (1992). 

J. Nielsen, Metabolic control analysis of biochemical pathways based on a thermokinetic description of reaction rates. Biochem. J. 321(1), 133 138 (1997). 

The formalized application of metabolic control analysis deals with several parameters (a) The flux control coefficient is defined as the fractional change in pathway flux... 

METABOLIC CONTROL ANALYSIS METABOLONS META-MODEL FMN,... 

METABOLIC CONTROL ANALYSIS TOP-DOWN CONTROL ANALYSIS Metabolic flux,... 

---