Modeling Approachto Control of Carbohydrate Metabolism During Gitric Acid Accumulationby Aspergillus niger: ll. SensitivityAnalysis Néstor V. Torres Departamento de Bioquímica y Biología Molecular, Facultad de Biología, Universidad de La Laguna, 38206 La Laguna, Tenerife, lslas Canarías, Spain Received September 29, |994/Accepted January 7, 1994 Steady state sensitivity analysis of a model of carbo- hydrate metabol¡sm and anapleroticsynthesis of oxal- acetate were, in Aspergillus niger under conditions of citric acid accumulation, carried out. The flux and metabolite concentration control structure of the system obtained shows that the hexokinase/substrate transport step is the main controlling step of the pathway. The quantitative contribution of the other enzyme catalyzed or transport steps are also discussed. These results allow the design of a proper strategyof biotechnological manipulation aimed at improvement of the process. @ 1994 John Wiley& Sons, Inc. Key words: sensitivity analysis . carbohydrate metabo- fism . Aspergillus niger. citric acid . optimization INTRODUCTION In a previous article,lT we built up a metabolic model of the carbohydrate metabolism in Aspergillus niger under conditions of citric acid accumulation (seeFig. 1). Once the AspergíIlus niger culture, developed in a medium devised for the citric acid accumulation reaches idiophase, the citric acid-accumulating stage, the system attains a well- characterizedsteady state in which citric acid production is the only metabolic process of quantitative importance.T,r2 The above-mentioned model integrated most of the avail- able information on this part of the process, and the steady state was characterized in terms of its flux and metabolite concentration values. The mechanistic model was subsequently translatedin mathematical terms adopting the expression of an S-system representation within the framework of biochemical system theory (BST).13 This mathematical representationshowed that the steady state is stable, thus allowing sensitivity analysis,which is canied out in the present article. Sensitivity analysis refers here to the distribution of control of fluxes and metabolite concentrations among the enzymes and transport steps of the system and the influence of substrates and effectors on fluxes and metabolite concentrations. Within the BST, this analysis is given in terms of trvo distinct sensitivity coefficients, the flux and metabolite concentration logarith- mic gains,l3 which are conceptually equivalent to the flux and meiabolite control coefficients defined in the metabolic control analysis (MCA).5,6 Biotechnology and Bioengineering, Vol. 44, Pp. 112-118 (1994) O 1994 John Wiley& Sons, Inc. In our particular case, these studies are especially rele- vant becausethey constitute the basis of a design strategy for biotechnological optimization: How should we modify which enzymes in order to increasethe steady state flux of the citric acid? The answer to this question will eventually lead us to the best perfonnance of the process. In fact, our model has allowed us to explore the type and magnitude of enzymemodulations of the metabolic pathway necessary to obtain a maximal rate of citric acid production. THEORETICAL BACKGROUND Logarithmic Gains The theoretical basis for the mathematical representation of the system represented in Figure L has been outlined in the previous articlet7 and extensively reviewed and de- veloped elsewhere.l3'le However, it is pertinent here to recall the definition and meaning of logarithmic gains, the sort of sensitivity coefficients that will be used in this work. There are two main types: the metabolite concentration logarithmic gains, and the flux logarithmic gains. Both share the same meaning as the concentration and flux control coefficients defined within the frame- work of the MCA. The first ones are defined as: L(x¡,xr): cl:: l+ +) '\x \dxt Xi/o i:1,,..,fli k:n+ 1,...,n* m (1) where X¡ stands for a dependent variable (the metabo- lite concentration) and X¡ for an independent variable (usually an enzyme activity or carrier activity). In a sim- ilar fashion, one obtains the logarithmic gains in the dependent fluxes through the pools of the system: L(V¡,X*): CY,: l+ +) '\K \dX¿ V¡ lo i : 1 , . . . , f l i k: n+ 1,...,nt m (2) where V¡ represents a given flux and X¿ the same as above. In both cases, the subscript 0 refers to the steady state. These sensitivity coefficients represent the percent- age change in a dependent concentration X¡ or flux V¡, ccc 0006- 359219 4 |01 01 1 2-07