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138
Some new directions in control theory inspired by systems biology
 IEE Systems Biology
, 2004
"... This paper, addressed primarily to engineers and mathematicians with an interest in control theory, argues that entirely new theoretical problems arise naturally when addressing questions in the field of systems biology. Examples from the author’s recent work are used to illustrate this point. 1 ..."
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Cited by 56 (19 self)
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This paper, addressed primarily to engineers and mathematicians with an interest in control theory, argues that entirely new theoretical problems arise naturally when addressing questions in the field of systems biology. Examples from the author’s recent work are used to illustrate this point. 1
A Petri net approach to the study of persistence in chemical reaction networks
 Mathematical Biosciences
, 2006
"... Persistence is the property, for differential equations in R n, that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the nonextinction property: provided that every species is present at the s ..."
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Cited by 54 (11 self)
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Persistence is the property, for differential equations in R n, that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the nonextinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.
Monotone chemical reaction networks
, 2004
"... We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis co ..."
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Cited by 43 (7 self)
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We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a selfcontained proof of a particular attractivity result which is used in
Molecular systems biology and control
 EUR. J. CONTROL 11:396–435
, 2005
"... This paper, prepared for a tutorial at the 2005 IEEE Conference on Decision and Control, presents an introduction to molecular systems biology and some associated problems in control theory. It provides an introduction to basic biological concepts, describes several questions in dynamics and control ..."
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Cited by 37 (9 self)
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This paper, prepared for a tutorial at the 2005 IEEE Conference on Decision and Control, presents an introduction to molecular systems biology and some associated problems in control theory. It provides an introduction to basic biological concepts, describes several questions in dynamics and control that arise in the field, and argues that new theoretical problems arise naturally in this context. A final section focuses on the combined use of graphtheoretic, qualitative knowledge about monotone buildingblocks and steadystate step responses for components.
Graphtheoretic characterizations of monotonicity of chemical networks in reaction coordinates
, 2009
"... This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence under the assumption that the rates of the reactions are monotone functions of the concentrations of their r ..."
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Cited by 28 (2 self)
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This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence under the assumption that the rates of the reactions are monotone functions of the concentrations of their reactants. This is satisfied for, yet not restricted to, the most common choices of the reaction kinetics such as mass action, MichaelisMenten and Hill kinetics. The key idea is to finding an alternative representation under which the resulting system is monotone. As a simple example, the paper shows that a phosphorylation/dephosphorylation process, which is involved in many signaling cascades, has a global stability property. We also provide a global stability result for a more complicated example that describes a regulatory pathway of a prevalent signal transduction module, the MAPK cascade.
Monotone Systems Under Positive Feedback: Multistability and a Reduction Theorem
, 2004
"... For feedback loops involving single input, single output monotone systems with welldefined I/O characteristics, a recent paper by Angeli and Sontag provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a c ..."
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Cited by 25 (11 self)
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For feedback loops involving single input, single output monotone systems with welldefined I/O characteristics, a recent paper by Angeli and Sontag provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a consequence of the technique. The present paper extends the approach to multiple inputs and outputs. A key idea is the introduction of a reduced system which preserves local stability properties.
Nonmonotone systems decomposable into monotone systems with negative feedback
 the Journal of Differential Equations
"... Motivated by the work of Angeli and Sontag [1] and Enciso and Sontag [7] in control theory, we show that certain finite and infinite dimensional semidynamical systems with “negative feedback ” can be decomposed into a monotone “open loop” system with “inputs ” and a decreasing “output ” function. T ..."
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Cited by 22 (10 self)
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Motivated by the work of Angeli and Sontag [1] and Enciso and Sontag [7] in control theory, we show that certain finite and infinite dimensional semidynamical systems with “negative feedback ” can be decomposed into a monotone “open loop” system with “inputs ” and a decreasing “output ” function. The original system is reconstituted by “plugging the output into the input”. Employing a technique of Gouzé [9] and Cosner [5] of imbedding the system into a larger symmetric monotone system, we are able to obtain information on the asymptotic behavior of solutions, including existence of positively invariant sets and global convergence. 1
Algorithmic and complexity results for decompositions of biological networks into monotone subsystems
 IN LECTURE NOTES IN COMPUTER SCIENCE: EXPERIMENTAL ALGORITHMS: 5TH INTERNATIONAL WORKSHOP, WEA 2006, SPRINGERVERLAG, 253–264. (CALA GALDANA, MENORCA
, 2006
"... A useful approach to the mathematical analysis of largescale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graphtheoretic la ..."
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Cited by 22 (6 self)
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A useful approach to the mathematical analysis of largescale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graphtheoretic language, the problems can be recast in terms of maximal signconsistent subgraphs. The theoretical results include polynomialtime approximation algorithms as well as constantratio inapproximability results. One of the algorithms, which has a worstcase guarantee of 87.9 % from optimality, is based on the semidefinite programming relaxation approach of GoemansWilliamson [23]. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model, and it was found to perform close to optimally.
On the Stability of a Model of Testosterone Dynamics
 Journal of Mathematical Biology
"... We prove the global asymptotic stability of a wellknown delayed negativefeedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability (and hence the impossibility of oscillations) even in the presence of delays of arbitrary length. ..."
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Cited by 21 (9 self)
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We prove the global asymptotic stability of a wellknown delayed negativefeedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability (and hence the impossibility of oscillations) even in the presence of delays of arbitrary length.