Systems-Theoretic Approaches to Design Biological Networks with Desired Functionalities

Bhattacharya, Priyan; Raman, Karthik; Tangirala, Arun K.

doi:10.1007/978-1-0716-0822-7_11

Cited by 8 publications

(7 citation statements)

References 22 publications

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“…Using Eq 6 , the condition for zero final value can be obtained as It is to be noted that the zero final value condition may not be achieved in several practical scenarios, leading to imperfect adaptation [ 40 ]. However, we shall limit this discussion to perfect adaptation.…”

Section: Methodsmentioning

confidence: 99%

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

2022

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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.

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Section: Methodsmentioning

confidence: 99%

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

2022

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“…It is to be noted that for any matrix A ∈ ℝ n×n to be Hurwitz, it is required to satisfy exactly N number of conditions. The condition mentioned in (33) is one of them which is concerned with the product of the eigenvalues.…”

Section: Resultsmentioning

confidence: 99%

“…It is to be noted that the zero final value condition may not be achieved in several practical scenarios, leading to imperfect adaptation [33]. However, we shall limit this discussion to perfect adaptation.…”

Section: Conditions For Perfect Adaptationmentioning

confidence: 99%

A generic systems-theoretic approach to identify biological networks capable of adaptation

Bhattacharya

Raman

Tangirala

2021

Preprint

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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. Interestingly, the design principles obtained by the proposed method remain the same for a network of arbitrary size and connectivity. Finally, we prove that the motifs discovered for adaptation are non-retroactive for a canonical downstream connection. 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.

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“…Further, Drenstig et al (2008) translated the condition for imperfect adaptation as a requirement of at least one zero in the underlying dynamical system of the network [20]. Later, Bhattacharya et al (2021) proved that a three-node network performs imperfect adaptation as long as there exists one zero (with negative real part) that is placed before all three stable poles in the left half of the s—plane [28].…”

Section: Introductionmentioning

confidence: 99%

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

Bhattacharya

Raman

Tangirala

2022

Preprint

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Biological adaptation, the tendency of every living organism to regulate its essential activities in environmental fluctuations, is a well-studied functionality in systems and synthetic biology. In this work, we present a generic methodology inspired by systems theory to discover the design principles for robust adaptation, perfect and imperfect, in two different contexts: (1) in the presence of deterministic external disturbance and (2) in a stochastic setting. In all the cases, firstly, 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. Thus, contrary to the existing approaches, the proposed methodologies provide an exhaustive set of admissible network structures without resorting to computationally burdensome brute-force techniques. Further, the proposed frameworks do not assume prior knowledge about the particular rate kinetics, thereby validating the conclusions for a large class of biological networks. In the deterministic setting, we show that, unlike the incoherent feed-forward network structures (IFFLP), the modules containing negative feedback with buffer action (NFBLB) are robust to parametric fluctuations when a specific part of the network is assumed to remain unaffected. To this end, we propose a sufficient condition for imperfect adaptation and show that adding negative feedback in an IFFLP topology improves the robustness concerning parametric fluctuations. Further, we propose a stricter set of necessary conditions for imperfect adaptation. Turning to the stochastic scenario, we adopt a Wiener-Kolmogorov filter strategy to tune the parameters of a given network structure towards minimum output variance. We show that both NFBLB and IFFLP can be used as a reduced-order W-K filter. Further, we define the notion of nearest neighboring motifs to compare the output variances across different network structures. We argue that the NFBLB achieves adaptation at the cost of a variance higher than its nearest neighboring motifs, whereas the IFFLP topology produces locally minimum variance when compared with its nearest neighboring motifs. We present numerical simulations to support the theoretical results. Overall, our results present a generic, systematic, and robust framework for advancing the understanding of complex biological networks.

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Systems-Theoretic Approaches to Design Biological Networks with Desired Functionalities

Cited by 8 publications

References 22 publications

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

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

A generic systems-theoretic approach to identify biological networks capable of adaptation

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

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