Discovering design principles for biological functionalities: Perspectives from systems biology

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

doi:10.1007/s12038-022-00293-4

Cited by 7 publications

(7 citation statements)

References 78 publications

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“…Therefore, in the case where one of the diagonal elements (A z ) of the closed-loop system matrix A C w is zero, all the terms in the determinant expression of A C w contain at least one loop. 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].…”

Section: Supporting Informationmentioning

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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Section: Supporting Informationmentioning

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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Section: Introductionmentioning

confidence: 99%

“…Further, using algebraic graph theoretic strategies, these abstract conditions are translated into structural requirements for adaptation. 3,9 Previously, it has been shown in several works that perfect adaptation -infinite precision and non-zero finite sensitivity translates to a zero-gain system condition in the linear, time-invariant dynamical system. [10][11][12][13] Bhattacharya et al (2018) used these systems-theoretic conditions to provide the network structures for perfect adaption for disturbance of small magnitude in three node networks.…”

Section: Introductionmentioning

confidence: 99%

“…Identifying network structures capable of adaptation has attracted a lot of multi-disciplinary attention ranging from computational sciences to mathematical systems theory, thereby giving rise to broadly three different categories of approaches. 3 As the name suggests, the computational screening approach involves scanning through the entire topology parameter sets. Previously, Ma et al (2008) adopted a three-protein network and scanned through every possible topology-parameter combination with an assumption of Michaelis-Menten rate kinetics.…”

Section: Introductionmentioning

confidence: 99%

“…), these performance parameters give rise to a number of abstract mathematical conditions for adaptation. Further, using algebraic graph theoretic strategies, these abstract conditions are translated into structural requirements for adaptation [3, 9]. Previously, it has been shown in several works that perfect adaptation – infinite precision and non-zero finite sensitivity translates to a condition of zero-gain system in the domain of linear, time-invariant dynamical system [10, 11, 12, 13].…”

Section: Introductionmentioning

confidence: 99%

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Design principles for perfect adaptation in biological networks with nonlinear dynamics

Bhattacharya

Raman

Tangirala

2022

Preprint

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Establishing a mapping between the emergent biological properties and network structure has always been of great relevance in systems and synthetic biology. Adaptation is one such biological property of paramount importance, which aids in regulation in the face of environmental disturbances. In this paper, we present a nonlinear systems theory-driven framework to identify the design principles for perfect adaptation in the presence of large disturbances. Based on the input-output configuration of the network, we use invariant manifold methods to deduce the condition for perfect adaptation to constant input disturbances. Subsequently, we translate these conditions into necessary structural requirements for adaptation in networks of small size. We then extend these results to argue that only two classes of architectures exist for a network of any size that can provide local adaptation in the entire state space---namely, incoherent feed-forward structure and negative feedback loop with buffer node. The additional positiveness constraints further restrict the admissible set of network structures---this also aids in establishing the global asymptotic stability for the steady state given a constant input disturbance. The entire method does not assume any explicit knowledge of the underlying rate kinetics barring some minimal assumptions. Finally, we also discuss the infeasibility of the incoherent feed-forward structure to provide adaptation in the presence of downstream connections. Our theoretical findings are corroborated by detailed and extensive simulation studies. Overall, we propose a generic and novel algorithm based on a nonlinear systems theory to unravel the design principles for global adaptation.

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Design Principles for Biological Adaptation: A Systems and Control-Theoretic Treatment

Bhattacharya,

Raman,

Tangirala

2023

Methods in Molecular Biology

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Discovering design principles for biological functionalities: Perspectives from systems biology

Cited by 7 publications

References 78 publications

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

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

Design principles for perfect adaptation in biological networks with nonlinear dynamics

Design Principles for Biological Adaptation: A Systems and Control-Theoretic Treatment

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