Systems-Theoretic Approaches to Design Biological Networks with Desired Functionalities.

The deduction of design principles for complex biological functionalities has been a source of constant interest in the fields of systems and synthetic biology. A number of approaches have been adopted, to identify the space of network structures or topologies that can demonstrate a specific desired functionality, ranging from brute force to systems theory-based methodologies. The former approach involves performing a search among all possible combinations of network structures, as well as the parameters underlying the rate kinetics for a given form of network. In contrast to the search-oriented approach in brute force studies, the present chapter introduces a generic approach inspired by systems theory to deduce the network structures for a particular biological functionality. As a first step, depending on the functionality and the type of network in consideration, a measure of goodness of attainment is deduced by defining performance parameters. These parameters are computed for the most ideal case to obtain the necessary condition for the given functionality. The necessary conditions are then mapped as specific requirements on the parameters of the dynamical system underlying the network. Following this, admissible minimal structures are deduced. The proposed methodology does not assume any particular rate kinetics in this case for deducing the admissible network structures notwithstanding a minimum set of assumptions on the rate kinetics. The problem of computing the ideal set of parameter/s or rate constants, unlike the problem of topology identification, depends on the particular rate kinetics assumed for the given network. In this case, instead of a computationally exhaustive brute force search of the parameter space, a topology-functionality specific optimization problem can be solved. The objective function along with the feasible region bounded by the motif specific constraints amounts to solving a non-convex optimization program leading to non-unique parameter sets. To exemplify our approach, we adopt the functionality of adaptation, and demonstrate how network topologies that can achieve adaptation can be identified using such a systems-theoretic approach. The outcomes, in this case, i.e., minimum network structures for adaptation, are in agreement with the brute force results and other studies in literature.