Karthik Raman

Network architecture plays a crucial role in governing the dynamics of any biological network. Further, network structures have been shown to remain conserved across organisms for a given phenotype. Therefore, the mapping between network structures and the output functionality not only aids in understanding of biological systems but also finds application in synthetic biology and therapeutics. Based on the approaches involved, most of the efforts hitherto invested in this field can be classified into three broad categories, namely, computational efforts, rule-based methods and systems-theoretic approaches. The present review provides a qualitative and quantitative study of all three approaches in the light of three well-researched biological phenotypes, namely, oscillation, toggle switching, and adaptation. We also discuss the advantages, limitations, and future research scope for all three approaches along with their possible applications to other emergent properties of biological relevance.

Designing biological networks that are capable of achieving specific functionality has been of sustained interest in the field of synthetic biology for nearly a decade. Adaptation is one such important functionality that is observed in bacterial chemotaxis, cell signalling and homoeostasis. It refers to the ability of a cell to cope with environmental perturbations. All of these adaptation networks, involve negative feedback loops or open loop control strategies. A typical enzymatic network is a circuit of enzymes whose connections are characterized by enzymatic reactions that exhibit non-linear dynamics. Previous approaches to design of enzymatic networks capable of perfect adaptation have used brute force searches encompassing the complete set of possibilities to identify suitable circuit designs. In contrast, this work presents a systematic algorithm for circuit design, using a linear systems-theoretic approach. The key idea is to set up a design-oriented problem formulation as against employing a brute force search in the space of possible circuits. To this effect, we first linearize the non-linear dynamical circuit, subsequently, we translate the requirements for adaptation to design specifications for a linear time-invariant system and imposing these design specifications on the linearized system, we obtain the minimal topologies or motifs that can perform perfect adaptation, with an optimal set of rate constants. The optimal set of rate constants is obtained by solving a structure-specific constrained optimisation problem. In effect, we demonstrate that the proposed approach identifies the key motifs of the biological network that were identified by the existing brute force approach, albeit in a systematic manner and with very little computational effort.

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.