Discovering adaptation-capable biological network structures using control-theoretic approaches

Abstract

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.

On biological networks capable of robust adaptation in the presence of uncertainties: A systems-theoretic approach

“…Further, Bhattacharya et al (2022) proved that in the case of buffer action (one or more diagonal elements of A C w is/are zero), the network has to contain at least one negative cycle to achieve stability. This concludes the first part of the proof [27].…”

“…Further, Araujo et al suggested that the balancer module must contain negative feedback for stability [24]. Recently, we (2022) proved that a balancer module of any size, without a single negative feedback loop, renders the system unstable, thereby proving Araujo's conjecture [27]. Further, we (2022) argued that adaptation-capable network structures are modular i.e.…”

“…It has been well-established in the literature that only the balancer and opposer modules can provide perfect adaptation. Recently, Bhattacharya et al (2022) also argued that the balancer module should contain at least one negative feedback engaging the buffer node to provide perfect adaptation [27]. Despite certain seminal contributions in this domain, the question of adaptation in the practical scenario i. e. imperfect adaptation has remained relatively unexplored.…”

“…It is well-known in the literature that perfect adaptation can be performed by two distinct classes of network structures [24, 27]: (i) negative feedback loop with buffer action or balancer modules, as termed by Araujo et al (2018), and (ii) multiple feed-forward paths from the input-receiving to the output node with mutually opposing effects or opposer modules as denoted by Araujo et al (2018). We here provide a theoretical evaluation of these network architectures vis-a-vis their performance in the presence of parametric disturbances.…”

“…Further, due to the instability of the positive feedback loops with buffer node [27], we start with the network structures containing negative feedback loop without buffer node. We first start with a 2–node balancer module and subsequently, extend the results to the N–node case.…”