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

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

doi:10.1016/j.mbs.2023.108984

Cited by 5 publications

(4 citation statements)

References 41 publications

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“…Recently, mathematical methods has been put forward based on either linear [ 32 , 33 ] or nonlinear [ 34 ] generic models to describe and analyze physiological control systems. These more mathematically inclined methods differ from the approach taken here, which is based on mass action kinetics.…”

Section: Methodsmentioning

confidence: 99%

Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats

Nygård,

Ruoff

2023

PLoS ONE

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When in a reaction kinetic integral controller a step perturbation is applied besides a constant background, the concentration of a controlled variable (described as A) will generally respond with decreased response amplitudes ΔA as backgrounds increase. The controller variable E will at the same time provide the necessary compensatory flux to move A back to its set-point. A typical example of decreased response amplitudes at increased backgrounds is found in retinal light adaptation. Due to remarks in the literature that retinal light adaptation would also involve a compensation of backgrounds we became interested in conditions how background compensation could occur. In this paper we describe novel findings how background influences can be robustly eliminated. When such a background compensation is active, oscillatory controllers will respond to a defined perturbation with always the same (damped or undamped) frequency profile, or in the non-oscillatory case, with the same response amplitude ΔA, irrespective of the background level. To achieve background compensation we found that two conditions need to apply: (i) an additional set of integral controllers (here described as I1 and I2) have to be employed to keep the manipulated variable E at a defined set-point, and (ii), I1 and I2 need to feed back to the A-E signaling axis directly through the controlled variable A. In analogy to a similar feedback applied in quantum control theory, we term these feedback conditions as ‘coherent feedback’. When analyzing retinal light adaptations in more detail, we find no evidence of the presence of background compensation mechanisms. Although robust background compensation, as described theoretically here, appears to be an interesting regulatory property, relevant biological or biochemical examples still need to be identified.

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Section: Methodsmentioning

confidence: 99%

Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats

Nygård,

Ruoff

2023

PLoS ONE

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“…It can be observed that for (18) and ( 19) to be consistent if and only if the external disturbance level v is kept constant, which defies the entire purpose of adaptation. Therefore, this has to be treated as a contradiction.…”

Section: General Structural Requirements For Perfect Non-infinitesima...mentioning

confidence: 95%

“…In subsequent work, we also provided a method inspired by linear systems theory to provide a qualitative comparison of robustness to both the parametric disturbances and overall uncertainties across the structural possibilities. Additionally, we also provided a set of strong necessary conditions that constrict the search space for imperfect adaptation-capable topologies along with a relevant, sufficient condition for the same— This helped us provide structural refinements to improve the robustness of adaptation-capable networks in the presence of parametric and infinitesimal external disturbances [18].…”

Section: Introductionmentioning

confidence: 99%

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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“…Other contributions on near-perfect homeostasis include (Bhattacharya et al. 2023 ; Blanchini et al. 2022 ; Gross et al.…”

Section: Introductionmentioning

confidence: 99%

Homeostasis in networks with multiple inputs

de Oliveira Madeira,

Antoneli

2024

J. Math. Biol.

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Homeostasis, also known as adaptation, refers to the ability of a system to counteract persistent external disturbances and tightly control the output of a key observable. Existing studies on homeostasis in network dynamics have mainly focused on ‘perfect adaptation’ in deterministic single-input single-output networks where the disturbances are scalar and affect the network dynamics via a pre-specified input node. In this paper we provide a full classification of all possible network topologies capable of generating infinitesimal homeostasis in arbitrarily large and complex multiple inputs networks. Working in the framework of ‘infinitesimal homeostasis’ allows us to make no assumption about how the components are interconnected and the functional form of the associated differential equations, apart from being compatible with the network architecture. Remarkably, we show that there are just three distinct ‘mechanisms’ that generate infinitesimal homeostasis. Each of these three mechanisms generates a rich class of well-defined network topologies—called homeostasis subnetworks. More importantly, we show that these classes of homeostasis subnetworks provides a topological basis for the classification of ‘homeostasis types’: the full set of all possible multiple inputs networks can be uniquely decomposed into these special homeostasis subnetworks. We illustrate our results with some simple abstract examples and a biologically realistic model for the co-regulation of calcium ($$\textrm{Ca}$$ Ca ) and phosphate ($$\textrm{PO}_4$$ PO 4 ) in the rat. Furthermore, we identify a new phenomenon that occurs in the multiple input setting, that we call homeostasis mode interaction, in analogy with the well-known characteristic of multiparameter bifurcation theory.

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

Cited by 5 publications

References 41 publications

Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats

Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats

Design principles for perfect adaptation in biological networks with nonlinear dynamics

Homeostasis in networks with multiple inputs

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