Internal Models in Control, Biology and Neuroscience

Huang, Jie; Isidori, Alberto; Marconi, Lorenzo; Mischiati, Matteo; Sontag, Eduardo D.; Wonham, W. M.

doi:10.1109/cdc.2018.8619624

Cited by 29 publications

(29 citation statements)

References 80 publications

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“…[30]). We conclude that the eigenvactors satisfy (12). Note that since A is also symmetric, the u i s are orthogonal, so u i ||u i || , i = 1, .…”

Section: Oscillatory Matricesmentioning

confidence: 69%

“…the eigenvectors of an oscillatory matrix can be used to provide an explicit representation of a subspace W(k 1 , k 2 ) such that W(k 1 , k 2 ) \ {0} ⊆ P (k 1 , k 2 ). Note that (12) implies in particular that…”

Section: Oscillatory Matricesmentioning

confidence: 99%

“…Feedback attenuates the degradation of performance due to disturbances as well as uncertainties not accounted for when originally designing (or evolving) a controller. Integral feedback (and more generally an "internal model" of the possible "exosignals) is necessary for regulation, as is well known in linear systems theory as well as for certain classes of nonlinear systems, and plays a central role in biological processes, both at the organism and cellular level [12]. Recently, there has been a considerable effort directed at the construction of integral feedback controllers in synthetic biology.…”

Section: Introductionmentioning

confidence: 99%

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Compact attractors of an antithetic integral feedback system have a simple structure

Margaliot

Sontag²

2019

Preprint

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Since its introduction by Briat, Gupta and Khammash, the antithetic feedback controller design has attracted considerable attention in both theoretical and experimental systems biology. The case in which the plant is a twodimensional linear system (making the closed-loop system a nonlinear four-dimensional system) has been analyzed in much detail. This system has a unique equilibrium but, depending on parameters, it may exhibit periodic orbits. An interesting open question is whether other dynamical behaviors, such as chaotic attractors, might be possible for some parameter choices. This note shows that, for any parameter choices, every bounded trajectory satisfies a Poincaré-Bendixson property. The analysis is based on the recently introduced notion of k-cooperative dynamical systems. It is shown that the model is a strongly 2-cooperative system, implying that the dynamics in the omegalimit set of any precompact solution is conjugate to the dynamics in a compact invariant subset of a two-dimensional Lipschitz dynamical system, thus precluding chaotic and other strange attractors. Index TermsPoincaré-Bendixson property, k-cooperative dynamical systems, sign-regular matrices, synthetic biology, antithetic feedback, synthetic biology, nonlinear control theory.MM is with the School of EE-Systems, Tel Aviv University, Israel 69978.

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“…[30]). We conclude that the eigenvactors satisfy (12). Note that since A is also symmetric, the u i s are orthogonal, so u i ||u i || , i = 1, .…”

Section: Oscillatory Matricesmentioning

confidence: 69%

Section: Oscillatory Matricesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Compact attractors of an antithetic integral feedback system have a simple structure

Margaliot

Sontag²

2019

Preprint

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“…To achieve perfect adaptation, the adaptation loop must therefore include an oscillator capable of producing a signal having the same frequency as the external disturbance, an assertion supported by the Internal Model Principle ( 37 , 43 ). Remarkably, the idea of an internal model has been invoked also for MdDS and firstly mentioned by Hain and Helminski ( 44 ).…”

Section: The Hypothesismentioning

confidence: 99%

Mal de Debarquement Syndrome: A Matter of Loops?

et al. 2020

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“…The "internal model principle" in control theory states, in essence, that the existence of an integrator in the control loop is necessary for the tight regulation of the concentration of an output species in the presence of disturbances or stimuli. 12 Inspired by these ideas from engineering and control theory, there have been several recent designs [13][14][15][16] and implementations [17][18] of biomolecular integral feedback controllers. These implementations are not completely satisfactory in that it is very difficult to make quantitative predictive models of their behaviors, in large part due to the biological noise which is found in cellular systems, which makes it hard to achieve precise control over model parameters, thereby complicating the design and feasibility of the system.…”

Section: Introductionmentioning

confidence: 99%

In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller

Agrawal

Marshall

Noireaux

et al. 2019

Preprint

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Feedback mechanisms play a critical role in the maintenance of cell homeostasis in the presence of disturbances and uncertainties. Motivated by the need to tune the dynamics and improve the robustness of synthetic gene circuits, biological engineers have proposed various designs that 2 mimic natural molecular feedback control mechanisms. However, practical and predictable implementations have proved challenging because of the complexity of synthesis and analysis of complex biomolecular networks. Here, we analyze and experimentally validate a first synthetic biomolecular controller executed in vitro. The controller is based on the interaction between a sigma and an anti-sigma factor, which ensures that gene expression tracks an externally imposed reference level, and achieves this goal even in the presence of disturbances. Our design relies upon an analog of the well-known principle of integral feedback in control theory. We implement the controller in an Escherichia coli cell-free transcription-translation (TXTL) system, a platform that allows rapid prototyping and implementation. Modeling and theory guide experimental implementation of the controller with well-defined operational predictability.

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Internal Models in Control, Biology and Neuroscience

Cited by 29 publications

References 80 publications

Compact attractors of an antithetic integral feedback system have a simple structure

Compact attractors of an antithetic integral feedback system have a simple structure

Mal de Debarquement Syndrome: A Matter of Loops?

In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller

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