Total enzyme activity constraint and homeostatic constraint impact on the optimization potential of a kinetic model

Abstract

The application of biologically and biochemically relevant constraints during the optimization of kinetic models reduces the impact of suggested changes in processes not included in the scope of the model. This increases the probability that the design suggested by model optimization can be carried out by an organism after implementation of design in vivo. A case study was carried out to determine the impact of total enzyme activity and homeostatic constraints on the objective function values and the following ranking of adjustable parameter combinations. The application of constraints on the model of sugar cane metabolism revealed that a homeostatic constraint caused heavier limitations of the objective function than a total enzyme activity constraint. Both constraints changed the ranking of adjustable parameter combinations: no "universal" constraint-independent top-ranked combinations were found. Therefore, when searching for the best subset of adjustable parameters, a full scan of their combinations is suggested for a small number of adjustable parameters, and evolutionary search strategies are suggested for a large number. Simultaneous application of both constraints is suggested.

Model-based metabolism design: constraints for kinetic and stoichiometric models

“…The homeostatic constraint limits optimized steady-state concentrations of metabolites within some range around the steady-state concentrations of the initial model. It can be applied for (1) a pool of internal metabolites [ 15 , 21 , 24 , 32 ], (2) each metabolite separately [ 23 , 29 , 33 ], or (3) a combination of both [ 22 ]. Heavy reduction in objective function values by the homeostatic constraint can take place [ 23 ].…”

“…It can be applied for (1) a pool of internal metabolites [ 15 , 21 , 24 , 32 ], (2) each metabolite separately [ 23 , 29 , 33 ], or (3) a combination of both [ 22 ]. Heavy reduction in objective function values by the homeostatic constraint can take place [ 23 ]. It might be useful to choose an acceptable concentration range for each metabolite separately taking into account their degree of involvement in other cellular processes outside of the model's scope [ 23 ].…”

“…Heavy reduction in objective function values by the homeostatic constraint can take place [ 23 ]. It might be useful to choose an acceptable concentration range for each metabolite separately taking into account their degree of involvement in other cellular processes outside of the model's scope [ 23 ]. A variety of homeostatic constraints is used by Magnus et al [ 15 ] applying metabolite concentration-dependent Gibbs-free energy calculations to assure feasibility of reactions.…”

“…The impact of the total enzyme activity constraint and the homeostatic constraint looking for minimal set of adjustable parameters (total optimization potential (TOP) approach) is demonstrated in detail [ 23 ] ( Figure 2 ), optimizing the model to increase sucrose accumulation in sugarcane culm [ 37 ]. The aim is to maximize objective function: proportion of sucrose accumulation in the vacuole relative to sucrose hydrolysis by invertase [ 23 ]. The best objective function value for a combination of all five adjustable parameters without constraints was 2.6 × 10 6 ( Figure 2B ), requesting an unrealistic 1500-fold increase in glucose concentration and a 5-fold increase in enzyme concentrations that are used as adjustable parameters.…”

“…Despite that it brings an 34% increase in the objective function value of the original model. Implementation of both the total enzyme activity and homeostatic constraints ( Figure 2D ) did not reduce further the objective function value of the full set of five adjustable parameters (concentrations of five enzymes) [ 23 ]. This illustrates how highly promising but unrealistic designs are made less promising by the value of objective function but are improved in terms of biological viability by implementing additional constraints.…”