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Publications by Eduardo D. Sontag in year 2005
Articles in journal or book chapters
  1. M. Andrec, B.N. Kholodenko, R.M. Levy, and E.D. Sontag. Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy. J. Theoret. Biol., 232(3):427-441, 2005. Note: Supplementary materials are here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/andrec-kholodenko-levy-sontag-JTB04-supplementary.pdf. [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, systems identification, reverse engineering.
    Abstract:
    One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells, and knowledge of their properties is essential for the understanding of cellular behavior. This paper studies the effect of experimental uncertainty on the accuracy of the inferred structure of the networks determined using the method in "Untangling the wires: a novel strategy to trace functional interactions in signaling and gene networks".


  2. M. Chaves, R. Albert, and E.D. Sontag. Robustness and fragility of Boolean models for genetic regulatory networks. J. Theoret. Biol., 235(3):431-449, 2005. [PDF] Keyword(s): systems biology, biochemical networks, boolean systems, gene and protein networks.
    Abstract:
    Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. Here we propose a framework for gene regulatory networks that combines the intuitive appeal of a qualitative description of gene states with a high flexibility in incorporating stochasticity in the duration of cellular processes. We apply our methods to the regulatory network of the segment polarity genes, thus gaining novel insights into the development of gene expression patterns. For example, we show that very short synthesis and decay times can perturb the wild type pattern. On the other hand, separation of timescales between pre- and post-translational processes and a minimal prepattern ensure convergence to the wild type expression pattern regardless of fluctuations.


  3. G.A. Enciso and E.D. Sontag. Monotone systems under positive feedback: multistability and a reduction theorem. Systems Control Lett., 54(2):159-168, 2005. [PDF] Keyword(s): multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a previous paper 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. New results characterizing strong monotonicity of feedback loops involving cascades are also presented.


  4. J.P. Hespanha, D. Liberzon, D. Angeli, and E.D. Sontag. Nonlinear norm-observability notions and stability of switched systems. IEEE Trans. Automat. Control, 50(2):154-168, 2005. [PDF] Keyword(s): observability, input to state stability, observability, invariance principle.
    Abstract:
    This paper proposes several definitions of observability for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.


  5. J. L. Mancilla-Aguilar, R. Garcža, E.D. Sontag, and Y. Wang. On the representation of switched systems with inputs by perturbed control systems. Nonlinear Anal., 60(6):1111-1150, 2005. [PDF]
    Abstract:
    This paper provides representations of switched systems described by controlled differential inclusions, in terms of perturbed control systems. The control systems have dynamics given by differential equations, and their inputs consist of the original controls together with disturbances that evolve in compact sets; their sets of maximal trajectories contain, as a dense subset, the set of maximal trajectories of the original system. Several applications to control theory, dealing with properties of stability with respect to inputs and of detectability, are derived as a consequence of the representation theorem.


  6. J. L. Mancilla-Aguilar, R. Garcža, E.D. Sontag, and Y. Wang. Uniform stability properties of switched systems with switchings governed by digraphs. Nonlinear Anal., 63(3):472-490, 2005. [PDF]
    Abstract:
    This paper develops characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions.


  7. E.D. Sontag. Molecular systems biology and control. Eur. J. Control, 11(4-5):396-435, 2005. [PDF] Keyword(s): cell biology, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems, molecular biology, systems biology, cellular signaling.
    Abstract:
    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 graph-theoretic, qualitative knowledge about monotone building-blocks and steady-state step responses for components.


  8. P. de Leenheer, D. Angeli, and E.D. Sontag. On predator-prey systems and small-gain theorems. Math. Biosci. Eng., 2(1):25-42, 2005. [PDF] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    This paper deals with an almost global attractivity result for Lotka-Volterra systems with predator-prey interactions. These systems can be written as (negative) feedback systems. The subsystems of the feedback loop are monotone control systems, possessing particular input-output properties. We use a small-gain theorem, adapted to a context of systems with multiple equilibrium points to obtain the desired almost global attractivity result. It provides sufficient conditions to rule out oscillatory or more complicated behavior which is often observed in predator-prey systems.


Conference articles
  1. G.A. Enciso and E.D. Sontag. A remark on multistability for monotone systems II. In Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications, pages 2957-2962, 2005. Keyword(s): multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.


  2. E.D. Sontag. A notion of passivity gain and a generalization of the `secant condition' for stability. In Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications, pages 5645-5649, 2005. Keyword(s): nonlinear stability, dynamical systems.


  3. E.D. Sontag and M. Chaves. Computation of amplification for systems arising from cellular signaling pathways. In Proc. 16th IFAC World Congress, Prague, July 2005, 2005. Keyword(s): systems biology, biochemical networks, dynamical systems.



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