Natural Bilinear Control Processes

Mohler, R.R.

doi:10.1109/tssc.1970.300341

Cited by 228 publications

(146 citation statements)

References 8 publications

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“…The general description in terms of bilinear control and multiplicative feedback calls for further study of these special engineering design principles in the biological context (12,26). It suggests that the study of the signal-processing properties of the biological system should go beyond its frequency response relying on linear system analysis (27).…”

Section: Discussionmentioning

confidence: 99%

“…Our theoretical analysis allows a solution in the appropriate approximation and a precise mapping of the dynamic behavior onto a control circuit diagram. This enables us to identify the universal aspects of seemingly different biological systems and dynamic behaviors: the availability variable averages over past activity, obeys a bilinear control equation (12), and implements a multiplicative feedback circuit regardless of the details of its kinetics. On the other hand, the kinetics of recovery of unavailable molecules back to the available pool determines the averaging kernel within the feedback branch and is a crucial ingredient in determining the adaptive dynamics and timescales.…”

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confidence: 99%

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Adaptive response by state-dependent inactivation

Friedlander

Brenner

2009

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

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Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus. A key mechanism that underlies this response is the slow, activitydependent removal of responding molecules to a pool which is unavailable to respond immediately to the input. This mechanism is implemented in different ways in various biological systems and has traditionally been studied separately for each. Here we highlight the common aspects of this principle, shared by many biological systems, and suggest a unifying theoretical framework. We study theoretically a class of models which describes the general mechanism and allows us to distinguish its universal from systemspecific features. We show that under general conditions, regardless of the details of kinetics, molecule availability encodes an averaging over past activity and feeds back multiplicatively on the system output. The kinetics of recovery from unavailability determines the effective memory kernel inside the feedback branch, giving rise to a variety of system-specific forms of adaptive response-precise or input-dependent, exponential or power-law-as special cases of the same model. adaptation | feedback | signal-processing | biochemical networks M any sensing molecules, such as membrane channels and receptors, have mechanisms of activity attenuation following exposure to strong, persistent stimulation. Sometimes termed "adaptation" or "desensitization," the quantitative hallmark of these responses is that an abrupt change in stimulus elicits a strong rapid rise in activity followed by a slower relaxation to steady state. Such responses have been studied extensively in the context of sensory systems (1) as well as cellular signaling systems (2, 3). They are thought to reflect the continuous need of a sensory system to adjust to changing external conditions while coping with limited resources and suggest connections to such concepts as homeostasis (4) and feedback control (5).A widely encountered mechanism underlying adaptive response is the slow activity-dependent modulation in the total number of molecules available to respond. This is a well-known phenomenon that characterizes a large class of biological systems and can be implemented physically in many ways; Fig. 1 illustrates voltage-gated ion channels (6, 7), bacterial chemotactic (8, 9) and G protein-coupled receptors (10) as typical examples. These receptors and channels can all become temporarily unavailable to respond to the external signal via either a change of protein conformation that blocks the channel pore (ion channels), covalent modifications (chemotactic receptors), or their physical removal from the cell surface (internalization of GPCR or trafficking in some synaptic receptors)(11). In all these examples transitions to the unavailable state are strongly dependent on the activity state of the molecule (e.g., primarily through open channels or through ligand-bound receptors). Despite these apparent common principles, differences in morphology and context have tr...

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Adaptive response by state-dependent inactivation

Friedlander

Brenner

2009

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

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“…It consists of the selecting the first vectors of the set given in (17). The drawback with the approach is that which is common to all techniques that involve working directly with bilinear systems and is that the size of bilinear system is large i.e.…”

Section: Discussionmentioning

confidence: 99%

“…A bilinear system is one which is linear in state, linear in control but not linear jointly. Bilinear systems frequently arise naturally in engineering, for example, nuclear fission, chemical and biological models and ecological models [17]. However, even when the system itself is not naturally bilinear, the bilinear representation offers a superior representation to a linear model.…”

Section: Introductionmentioning

confidence: 99%

Krylov subspaces from bilinear representations of nonlinear systems

Condon

Ivanov

2007

COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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-For efficient simulation of state-of-the-art dynamical systems as arise in all aspects of engineering, the development of reduced-order models is of paramount importance.While linear reduction techniques have received considerable study, increasingly nonlinear model reduction is becoming a significant field of interest. From a circuits and systems viewpoint, systems involving micromachined devices or systems involving mixed technologies necessitate the development of reduced-order nonlinear models. From a control systems viewpoint, the design of controllers for nonlinear systems is greatly facilitated by nonlinear model reduction strategies. To this end, the paper proposes two novel model-reduction strategies for nonlinear systems. The first involves the development, in a novel manner as compared to previous approaches, of a reduced-order model from a bilinear representation of the system while the second involves a reducing a polynomial approximation using subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example.

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“…The problem of eigenvalue optimization has received recent attention in applied mathematics (Burke et al, 2001) and may be of use here. One potentially fruitful approach may be the application of bilinear optimal control theory (Mohler, 1970(Mohler, , 1973. Another direction of future work may include alternative forms of immigration that describe the population dynamics in a hospital more accurately.…”

Section: Discussionmentioning

confidence: 99%

Simple models of antibiotic cycling

Reluga

2005

Mathematical Medicine and Biology: A Journal of the IMA

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The use of environmental heterogeneity is an old but potentially powerful method for managing biological systems. Determining the optimal form of environmental heterogeneity is a difficult problem. One family of heterogeneous management strategies that has received attention in the medical community is the periodic cycling of antibiotic usage to control antibiotic resistance. This paper presents a theory for the optimization of antibiotic cycling based on a density independent model of transmission and immigration of evolutionarily static strains. In the case of two pathogen strains, I show that the population's asymptotic growth rate is a monotonically increasing function of the oscillation period under certain common assumptions. Monte Carlo simulations show that this result fails in more general settings, but suggest that antibiotic cycling seldom provides a significant improvement over alternative mixing practices. The results support the findings of other researchers that antibiotic cycling does not offer significant advantages over idealized conventional practice. However, cycling strategies may be preferable in some special cases.

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Natural Bilinear Control Processes

Cited by 228 publications

References 8 publications

Adaptive response by state-dependent inactivation

Adaptive response by state-dependent inactivation

Krylov subspaces from bilinear representations of nonlinear systems

Simple models of antibiotic cycling

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