Nutrition and metabolism are fundamental to cellular function. Metabolic activity (i.e. rates of flow, most commonly referred to as flux) is constrained by thermodynamics and regulated by the activity of enzymes. The general principles that relate biological and physical variables to metabolic control are incompletely understood. Using metabolic control analysis and computer simulations in several models of simplified metabolic pathways, we derive analytical expressions that define relationships between thermodynamics, enzyme activity, and flux control. The relationships are further analyzed in a mathematical model of glycolysis as an example of a complex biochemical pathway. We show that metabolic pathways that are very far from equilibrium are controlled by the activity of upstream enzymes. However, in general, regulation of metabolic fluxes by an enzyme has a more adaptable pattern, which relies more on distribution of free energy among reaction steps in the pathway than on the thermodynamic properties of the given enzyme. These findings show how the control of metabolic pathways is shaped by thermodynamic constraints of the given pathway. 3 The abbreviations used are: MCA, metabolic control analysis; FCC, flux control coefficient; TDF, thermodynamic driving force. Figure 4. Thermodynamics and flux regulation in a pathway with a branch point and two downstream fluxes. A, diagram of the pathway and related parameters.S in is the input substrate, S out,1 and S out,2 are the two final products, S BP is the intermediary metabolite at branch point, k i is the rate constant of the ith reaction, K i is the equilibrium constant of the ith reaction, J 2 and J 3 are two downstream fluxes, and J 1 ϭ J 2 ϩ J 3 is the upstream flux. B, distribution of the flux control coefficients for the network in A with randomly sampled parameters. FCC(i,j) ϭ C vj J is the flux control coefficient of the ith flux with respect to the jth reaction. Limits of the boxes are the 25th and 75th percentiles, central lines are median values, and whiskers indicate minimal and maximal values. C, scatter plots comparing flux control coefficients and reaction free energy changes in the network in A with randomly sampled parameters. C vi J is the ith flux control coefficient, and g i ϭ ⌬G i /RT quantifies the ith free energy change. D, scatter plots comparing flux control coefficients and the thermodynamic driving force (max{g i }) in the network in A with randomly sampled parameters. Variables are the same as in C.
Thermodynamics in control of metabolism