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41
The Effect of Negative Feedback Loops on the Dynamics of Boolean Networks
, 2008
"... Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, captures the number of independent negative feedback loops in the network, a ..."
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Cited by 15 (2 self)
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Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distancetopositivefeedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distancetopositivefeedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.
Analysis of lactose metabolism in E.coli using reachability analysis of hybrid systems
 IEE PROCEEDINGS  SYSTEMS BIOLOGY
, 2007
"... We propose an abstraction method for medium scale biomolecular networks, based on hybrid dynamical systems with continuous multiaffine dynamics. This abstraction method follows naturally from the notion of approximating nonlinear rate laws with continuous piecewise linear functions and can be easil ..."
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Cited by 14 (3 self)
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We propose an abstraction method for medium scale biomolecular networks, based on hybrid dynamical systems with continuous multiaffine dynamics. This abstraction method follows naturally from the notion of approximating nonlinear rate laws with continuous piecewise linear functions and can be easily automated. An efficient reachability algorithm is possible for the resulting class of hybrid systems. We construct an approximation for an ordinary differential equation model of the lac operon, and show that our abstraction passes the same experimental tests that were used to validate the original model. The wellstudied biological system exhibits bistability and switching behavior, arising from positive feedback in the expression mechanism of the lac operon. The switching property of the lac system is an example of the major qualitative features that are the building blocks of higher level, more coarsegrained descriptions. Our approach is useful in helping correctly identify such properties and in connecting them to the underlying molecular dynamical details. We use reachability analysis together with the knowledge of the steady state structure to identify ranges of parameter values for which the system maintains the bistable switching property.
A hybrid bounding method for computing an overapproximation for the reachable set of uncertain nonlinear systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2009
"... In this paper, we show how to compute an overapproximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relie ..."
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Cited by 10 (2 self)
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In this paper, we show how to compute an overapproximation for the reachable set of uncertain nonlinear continuous dynamical systems by using guaranteed set integration. We introduce two ways to do so. The first one is a full interval method which handles whole domains for set computation and relies on stateoftheart validated numerical integration methods. The second one relies on comparison theorems for differential inequalities in order to bracket the uncertain dynamics between two dynamical systems where there is no uncertainty. Since the derived bracketing systems are piecewisedifferentiable functions, validated numerical integration methods cannot be used directly. Hence, our contribution resides in the use of hybrid automata to model the bounding systems. We give a rule for building these automata and we show how to run them and address mode switching in a guaranteed way in order to compute the over approximation for the reachable set. The computational cost of our method is also analyzed and shown to be smaller that the one of classical interval techniques. Sufficient conditions are given which ensure thepractical stability of the enclosures given by our hybrid bounding method. Two examples are also given which show that the performance of our method is very promising.
Computing reachable sets for uncertain nonlinear monotone systems
, 2009
"... We address nonlinear reachability computation for uncertain monotone systems, those for which flows preserve a suitable partial orderings on initial conditions. In a previous work [1], we introduced a nonlinear hybridization approach to nonlinear continuous reachability computation. By analysing the ..."
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Cited by 10 (1 self)
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We address nonlinear reachability computation for uncertain monotone systems, those for which flows preserve a suitable partial orderings on initial conditions. In a previous work [1], we introduced a nonlinear hybridization approach to nonlinear continuous reachability computation. By analysing the signs of offdiagonal elements of system’s Jacobian matrix, a hybrid automaton can be obtained, which yields componentwise bounds for the reachable sets. One shortcoming of the method is induced by the need to use whole sets for addressing mode switching. In this paper, we improve this method and show that for the broad class of monotone dynamical systems, componentwise bounds can be obtained for the reachable set in a separate manner. As a consequence, mode switching no longer needs to use whole solution sets. We give examples which show the potentials of the new approach.
The Rôle of Control and System Theory in Systems Biology ∗ Preamble
, 2007
"... The use of new technology and mathematics to study the systems of nature is one of the most significant scientific trends of the century. Driven by the need for more precise scientific understand, advances in automated measurement are providing rich new sources of biological and physiological data. ..."
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Cited by 7 (1 self)
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The use of new technology and mathematics to study the systems of nature is one of the most significant scientific trends of the century. Driven by the need for more precise scientific understand, advances in automated measurement are providing rich new sources of biological and physiological data. This data provides information with which to create mathematical models of increasing sophistication and realism models that can emulate the performance of biological and physiological systems with sufficient accuracy to advance our understanding of living systems and disease mechanisms. New measurement and modelling methods set the stage for control and systems theory to play their rôle in seeking out the mechanisms and principles that regulate life. It is of inestimable importance for the future of control as a discipline that this rôle is performed in the correct manner. If we handle the area wisely then living systems will present a seemly boundless range of important new problems just as physical and engineering systems have done in previous centuries. But there is a crucial difficulty. Faced with a bewildering array of
Oscillations in I/O monotone systems under negative feedback
 IEEE Trans. Automat. Control
, 2008
"... Oscillatory behavior is a key property of many biological systems. The SmallGain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a necessary condition for the existence of periodic solutions ..."
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Cited by 7 (0 self)
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Oscillatory behavior is a key property of many biological systems. The SmallGain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a necessary condition for the existence of periodic solutions. One advantage of the use of the monotone SGT technique is its robustness with respect to all perturbations that preserve monotonicity and stability properties of a very lowdimensional (in many interesting examples, just onedimensional) model reduction. This robustness makes the technique useful in the analysis of molecular biological models in which there is large uncertainty regarding the values of kinetic and other parameters. However, verifying the conditions needed in order to apply the SGT is not always easy. This paper provides an approach to the verification of the needed properties, and illustrates the approach through an application to a classical model of circadian oscillations, as a nontrivial “case study, ” and also provides a theorem in the converse direction of predicting oscillations when the SGT conditions fail. Keywords:. Circadian rhythms, monotone systems, negative feedback, periodic behaviors 1
Feedforward control of a piezoelectric flexure stage for AFM
 In: Proc American control conference
, 2008
"... Abstract—We review basic issues in the control of scanning probe microscopes. To improve the performance of the present generation of instruments, we have developed a simple feedforward technique that nonetheless increases the effective bandwidth of the positioning stage by a factor of 15 over its ..."
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Abstract—We review basic issues in the control of scanning probe microscopes. To improve the performance of the present generation of instruments, we have developed a simple feedforward technique that nonetheless increases the effective bandwidth of the positioning stage by a factor of 15 over its standard operation. If the desired control signal is known in advance (as it is for a periodic scan signal), the feedforward filter can be noncausal: information about the future can be used to cancel the phase lag produced by the stage response. We compare our design with other control techniques. We show that modelbased iterative control algorithms can lead to a substantial performance boost, at the cost of more measurements of the system transfer function. We then introduce a modelfree variant that is simpler to set up, performs better, and is more robust to system changes. I.
Parveen “A New Approach for Modelling Gene Regulatory Networks Using Fuzzy Petri Nets
 Journal of Integrative Bioinformatics
"... Gene Regulatory Networks are models of genes and gene interactions at the expression level. The advent of microarray technology has challenged computer scientists to develop better algorithms for modeling the underlying regulatory relationship in between the genes. Fuzzy system has an ability to sea ..."
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Cited by 5 (0 self)
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Gene Regulatory Networks are models of genes and gene interactions at the expression level. The advent of microarray technology has challenged computer scientists to develop better algorithms for modeling the underlying regulatory relationship in between the genes. Fuzzy system has an ability to search microarray datasets for activator/repressor regulatory relationship. In this paper, we present a fuzzy reasoning model based on the Fuzzy Petri Net. The model considers the regulatory triplets by means of predicting changes in expression level of the target based on input expression level. This method eliminates possible false predictions from the classical fuzzy model thereby allowing a wider search space for inferring regulatory relationship. Through formalization of fuzzy reasoning, we propose an approach to construct a rulebased reasoning system. The experimental results show the proposed approach is feasible and acceptable to predict changes in expression level of the target gene. 1
Qualitative control of periodic solutions in piecewise affine systems; application to genetic networks
, 2009
"... ..."
Almost global convergence in singular perturbations of strongly monotone systems. In: Positive Systems
 Berlin/Heidelberg, (Lecture Notes in Control and Information Sciences Volume 341, Proceedings of the second Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 06
, 2006
"... Abstract. This paper deals with global convergence to equilibria, and in particular Hirsch’s generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems. 1 ..."
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Abstract. This paper deals with global convergence to equilibria, and in particular Hirsch’s generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems. 1