Optimality principles in the regulation of metabolic networks

Abstract

One of the challenging tasks in systems biology is to understand how molecular networks give rise to emergent functionality and whether universal design principles apply to molecular networks. To achieve this, the biophysical, evolutionary and physiological constraints that act on those networks need to be identified in addition to the characterisation of the molecular components and interactions. Then, the cellular "task" of the network-its function-should be identified. A network contributes to organismal fitness through its function. The premise is that the same functions are often implemented in different organisms by the same type of network; hence, the concept of design principles. In biology, due to the strong forces of selective pressure and natural selection, network functions can often be understood as the outcome of fitness optimisation. The hypothesis of fitness optimisation to understand the design of a network has proven to be a powerful strategy. Here, we outline the use of several optimisation principles applied to biological networks, with an emphasis on metabolic regulatory networks. We discuss the different objective functions and constraints that are considered and the kind of understanding that they provide.

Figure 1

Overview of regulatory interactions involved in metabolic regulatory networks. The function of metabolic networks are governed by constraints. The regulation of a metabolic network involves a tight interplay between different cellular networks such as signalling and gene networks and by interactions with its environment. The enzyme capacity is the net result of the amount of enzyme expressed and its activity as dictated by post-translational modification and allosteric regulation. Metabolite pools and fluxes are considered as the outputs of metabolic reaction networks and can be involved in various regulatory feedback loops to other networks within the metabolic reaction networks as indicated by the dashed arrows.

Figure 2

Schematic overview of the interactions involved in the process of evolutionary optimization of metabolic regulatory networks. Constraints limit the functionality of a metabolic reaction network (MRN), which for a given environmental condition can be analysed with respect to (a) certain objective function(s), giving rise to some fitness. Depending on selective pressures (which in turn are also dependent on the environment), natural selection acts on the fitness of a metabolic reaction network.

Figure 3

Different approaches to study metabolic regulatory networks classified according to the level of detail. Depending on the level of detail of analysis, different objective functions can be addressed. Pathway analysis refers to the analysis of (detailed) reactions that might be embedded into a pathway. With this type of analysis why questions can be addressed. Semi-autonomous modules function independently of the rest of the network, and have a discrete function. Concepts from control and information theory have been applied to understand how functionality emerges from the molecular components of these modules. Genome scale models uses the information content from the entire genome to figure out what flux distribution may lead to an optimal behaviour.

Figure 4

Illustration of network motifs to study molecular networks. In the left column the molecular interactions underlying the networks are shown, the middle column shows the network motif and corresponding characteristics are plotted in the right column. The examples shown here, are discussed in detail in the main text. A Chemotaxis signalling network in E. coli. (Figures adapted from [26,46]). B Catabolite repression of the gal operon in E. coli. (Figures adapted from [31]). C Competence in Bacillus subtilllis. (Figures adapted from [47,48]).