COBRA methods require the statement of an objective. Objective functions are used to perform a search over the space of possible solutions to find particular functional states. There are many types of objective functions that can be used to find different types of functional states that reconstructed networks can attain. Perhaps the most interesting group are the objective functions that are those used to represent expected physiological functions. From the early days of development of COBRA methods, the objective function has been the center of attention, and attempts were made to determine appropriate objective functions in a data-driven fashion [372]. Importantly, objective functions can be used to describe selection pressures and thus distal causation.

The Objective Function

Dual causality can be represented conceptually in a plane with two axes (Figure 21.1). Proximal causation is represented on the y-axis. It represents the response of an organism to environmental stimuli against a constant genetic background. For example, the diauxic shift in substrate uptake from glucose to acetate upon depletion of glucose when E. coli is grown an aerobically. Given a constant genetic background, this response is dominated by physicochemical factors.

Distal causation is represented on the x-axis. These changes take place over multiple generations where the genotype is changing, such as in a population of cells optimizing growth rate through acquisition of advantaged mutations. Applying the same environmental stimulus at each generation may lead to different proximal responses.

The processes of generation of diversity and selection drive phenotypic changes over generations. The selection process is hard to describe based on fundamental principles. However, an objective function can be used to describe the driving force for this change. Because we do not always know the driving force, we formulate the objective function based on intuition or guesses about the evolutionary history of the organism. Adaptive laboratory evolution (see Chapter 26) has risen over the past decades that allows us to begin to study the process of evolution experimentally [228, 316].