Internal Models in Control, Bioengineering, and Neuroscience

Bin, Michelangelo; Huang, Jie; Isidori, Alberto; Marconi, Lorenzo; Mischiati, Matteo; Sontag, Eduardo D.

doi:10.1146/annurev-control-042920-102205

Cited by 17 publications

(14 citation statements)

References 102 publications

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“…However, a deep result from control theory, called the internal model principle (IMP) (see ref. 30 for a recent review), stipulates that every RPA network can, at least theoretically, be separated into two components - an internal model (IM) that dynamically evaluates the effect of disturbance by measuring the regulated output, and generates counteracting signals, that are then passed to the rest of the network (RoN) via the actuation mechanism to complete the feedback loop ( Fig. 2 A ).…”

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confidence: 99%

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Gupta

Khammash

2022

Proc. Natl. Acad. Sci. U.S.A.

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Adaptation is a running theme in biology. It allows a living system to survive and thrive in the face of unpredictable environments by maintaining key physiological variables at their desired levels through tight regulation. When one such variable is maintained at a certain value at the steady state despite perturbations to a single input, this property is called robust perfect adaptation (RPA). Here we address and solve the fundamental problem of maximal RPA (maxRPA), whereby, for a designated output variable, RPA is achieved with respect to perturbations in virtually all network parameters. In particular, we show that the maxRPA property imposes certain structural constraints on the network. We then prove that these constraints are fully characterized by simple linear algebraic stoichiometric conditions which differ between deterministic and stochastic descriptions of the dynamics. We use our results to derive a new internal model principle (IMP) for biomolecular maxRPA networks, akin to the celebrated IMP in control theory. We exemplify our results through several known biological examples of robustly adapting networks and construct examples of such networks with the aid of our linear algebraic characterization. Our results reveal the universal requirements for maxRPA in all biological systems, and establish a foundation for studying adaptation in general biomolecular networks, with important implications for both systems and synthetic biology.

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confidence: 99%

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Gupta

Khammash

2022

Proc. Natl. Acad. Sci. U.S.A.

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“…Moreover, this structural characterisation would enable us to develop novel controller motifs that can potentially be synthetically engineered to correct for the failure of natural controllers. In this context, the Internal Model Principle (IMP) [12] from control theory provides a clue on how RPA systems may be organised. This principle asserts that for a system to be robust to a class of dynamic disturbances, it must contain a subsystem, called the internal model (IM), that is able to generate these disturbances, and then pass counteracting signals to the rest of the network (RoN) in a feedback fashion (see Figure 1).…”

Section: A the Formalism Of Reaction Networkmentioning

confidence: 99%

“…where f and g are nonlinear functions of the state variable x, and u is the disturbance input which enters linearly into the dynamics. For a recent review on IMP, we refer the readers to [12]. Generally, biomolecular networks exhibiting RPA are nonlinear and even the disturbances can enter their dynamics nonlinearly, typically via perturbations of the reaction propensities.…”

Section: A the Formalism Of Reaction Networkmentioning

confidence: 99%

“…In this article we call for systematic development of novel and broadly applicable control-theoretic principles that are specifically tailored to understanding and designing biomolecular control systems. The aim of this note is to discuss one such control-theoretic concept, the Internal Model Principle (IMP) [9], [10], [11], [12], from the perspective of biomolecular networks.…”

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confidence: 99%

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The Internal Model Principle for Biomolecular Control Theory

Gupta¹,

Khammash²

2023

IEEE Open J. Control. Syst.

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The well-known Internal Model Principle (IMP) is a cornerstone of modern control theory. It stipulates the necessary conditions for asymptotic robustness of disturbance-prone dynamical systems by asserting that such a system must embed a subsystem in a feedback loop, and this subsystem must be able to reduplicate the dynamic disturbance using only the regulated variable as the input. The insights provided by IMP can help in both designing suitable controllers and also in analysing the regulatory mechanisms in complex systems. So far the application of IMP in biology has been case-specific and ad hoc, primarily due to the lack of generic versions of the IMP for biomolecular reaction networks that model biological processes. In this short article we highlight the need for an IMP in biology and discuss a recently developed version of it for biomolecular networks that exhibit maximal Robust Perfect Adaptation (maxRPA) by being robust to the maximum number of disturbance sources.

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“…A normal form for output robustness based on internal model representation is proposed in [15]. A contemporary review of internal models can be found in [16].…”

Section: Introductionmentioning

confidence: 99%

Foundations of static and dynamic absolute concentration robustness

Joshi

Crăciun

2022

J. Math. Biol.

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In a reaction network, the concentration of a species with the property of dynamic absolute concentration robustness (dynamic ACR) converges to the same value independent of the overall initial values. This property endows a biochemical network with output robustness and therefore is essential for its functioning in a highly variable environment. It is important to identify structure of the dynamical system as well as constraints required for dynamic ACR. We propose a normal form of dynamic ACR and obtain results regarding convergence to the ACR value based on this form. Furthermore, we study an archetypal model of dynamic ACR in the context of a chemostat, where the network is coupled with inflows and outflows of the species. We prove that dynamic ACR persists at the same value as the uncoupled system in a wide variety of situations.

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Internal Models in Control, Bioengineering, and Neuroscience

Cited by 17 publications

References 102 publications

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

Universal structural requirements for maximal robust perfect adaptation in biomolecular networks

The Internal Model Principle for Biomolecular Control Theory

Foundations of static and dynamic absolute concentration robustness

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