Biological objective functions and optimization

Mathematical optimization deals with determining values for a set of unknown variables x, X2, , x , which best satisfy (optimize) some mathematical objective quantified by a scalar function of the unknown variables, F(xi, X2, , xn). The function F is termed the objective function bounds on the variables, along with mathematical dependencies between them, are termed constraints. Constraint-based analysis of metabolic systems requires definition of the constraints acting on biochemical variables (fluxes, concentrations, enzyme activities) and determining appropriate objective functions useful in determining the behavior of metabolic systems. 

That a cell functions precisely following some rule of optimality is, of course, highly suspect. There may be an evolutionary argument in favor of certain objective functions, but the ultimate justification lies in the correctness of its predictions. 

In this sense, the constraint-based optimization approach provides a convenient way to efficiently generate quantitative predictions of biological hypotheses formulated in terms of objective functions.5 The value of this approach is in facilitating the systematic prediction-experimental verification-hypothesis modification cycle, ideally leading to new discoveries. 

5 Objectives that have proved useful include optimal energetic efficiency or optimal cell growth rate [48, 204]. 

---