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Publications by Eduardo D. Sontag in year 2007
Articles in journal or book chapters
  1. R. Albert, B. DasGupta, R. Dondi, S. Kachalo, E.D. Sontag, A. Zelikovsky, and K. Westbrooks. A novel method for signal transduction network inference from indirect experimental evidence. In R. Giancarlo and S. Hannenhalli, editors, 7th Workshop on Algorithms in Bioinformatics (WABI), volume 14, pages 407-419. Springer-Verlag, Berlin, 2007. Note: Conference version of journal paper with same title. Keyword(s): systems biology, biochemical networks, algorithms, signal transduction networks, graph algorithms.


  2. D. Angeli, P. De Leenheer, and E.D. Sontag. A Petri net approach to persistence analysis in chemical reaction networks. In I. Queinnec, S. Tarbouriech, G. Garcia, and S-I. Niculescu, editors, Biology and Control Theory: Current Challenges (Lecture Notes in Control and Information Sciences Volume 357), pages 181-216. Springer-Verlag, Berlin, 2007. Note: See abstract for A Petri net approach to the study of persistence in chemical reaction networks.[PDF]


  3. E.D. Sontag. Input to state stability: Basic concepts and results. In P. Nistri and G. Stefani, editors, Nonlinear and Optimal Control Theory, pages 163-220. Springer-Verlag, Berlin, 2007. [PDF] Keyword(s): input to state stability, stability, input to state stability, nonlinear systems, detectability, nonlinear regulation.
    Abstract:
    This expository presentation, prepared for a summer course, addresses the precise formulation of questions of robustness with respect to disturbances, using the paradigm of input to state stability. It provides an intuitive and informal presentation of the main concepts.


  4. E.D. Sontag. Monotone and near-monotone systems. In I. Queinnec, S. Tarbouriech, G. Garcia, and S-I. Niculescu, editors, Biology and Control Theory: Current Challenges (Lecture Notes in Control and Information Sciences Volume 357), pages 79-122. Springer-Verlag, Berlin, 2007. Note: Conference version of ``Monotone and near-monotone biochemical networks,'' basically the same paper.Keyword(s): systems biology, biochemical networks, monotone systems, Ising spin models, nonlinear stability, dynamical systems, consistent graphs, gene networks.
    Abstract:
    See abstract and pdf for ``Monotone and near-monotone biochemical networks''.


  5. E.D. Sontag. Stability and Feedback Stabilization. In Robert Meyers, editor, Encyclopedia of Complexity and Systems Science. Springer-Verlag, Berlin, 2007. Keyword(s): stability, nonlinear control, feedback stabilization.
    Abstract:
    The problem of stabilization of equilibria is one of the central issues in control. In addition to its intrinsic interest, it represents a first step towards the solution of more complicated problems, such as the stabilization of periodic orbits or general invariant sets, or the attainment of other control objectives, such as tracking, disturbance rejection, or output feedback, all of which may be interpreted as requiring the stabilization of some quantity (typically, some sort of ``error'' signal). A very special case, when there are no inputs, is that of stability. This short and informal article provides an introduction to the subject.


  6. E.D. Sontag and Y. Wang. Uniformly Universal Inputs. In Alessandro Astolfi, editor, Analysis and Design of Nonlinear Control Systems, volume 224, pages 9-24. Springer-Verlag, London, 2007. [PDF] Keyword(s): observability, identification.
    Abstract:
    A result is presented showing the existence of inputs universal for observability, uniformly with respect to the class of all continuous-time analytic systems. This represents an ultimate generalization of a 1977 theorem, for bilinear systems, due to Alberto Isidori and Osvaldo Grasselli.


  7. R. Albert, B. DasGupta, R. Dondi, S. Kachalo, E.D. Sontag, A. Zelikovsky, and K. Westbrooks. A novel method for signal transduction network inference from indirect experimental evidence. Journal of Computational Biology, 14:927-949, 2007. [PDF] Keyword(s): systems biology, biochemical networks, algorithms, signal transduction networks, graph algorithms.
    Abstract:
    This paper introduces a new method of combined synthesis and inference of biological signal transduction networks. The main idea lies in representing observed causal relationships as network paths, and using techniques from combinatorial optimization to find the sparsest graph consistent with all experimental observations. The paper formalizes the approach, studies its computational complexity, proves new results for exact and approximate solutions of the computationally hard transitive reduction substep of the approach, validates the biological applicability by applying it to a previously published signal transduction network by Li et al., and shows that the algorithm for the transitive reduction substep performs well on graphs with a structure similar to those observed in transcriptional regulatory and signal transduction networks.


  8. D. Angeli, P. de Leenheer, and E.D. Sontag. A Petri net approach to the study of persistence in chemical reaction networks. Mathematical Biosciences, 210:598-618, 2007. Note: Please look at the paper ``A Petri net approach to persistence analysis in chemical reaction networks'' for additional results, not included in the journal paper due to lack of space. See also the preprint: arXiv q-bio.MN/068019v2, 10 Aug 2006. [PDF] Keyword(s): Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles.
    Abstract:
    Persistency is the property, for differential equations in Rn, that solutions starting in the positive orthant do not approach the boundary. For chemical reactions and population models, this translates into the non-extinction 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.


  9. P. Berman, B. Dasgupta, and E.D. Sontag. Algorithmic issues in reverse engineering of protein and gene networks via the modular response analysis method. Annals of the NY Academy of Sciences, 1115:132-141, 2007. [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification, graph algorithms.
    Abstract:
    This paper studies a computational problem motivated by the modular response analysis method for reverse engineering of protein and gene networks. This set-cover problem is hard to solve exactly for large networks, but efficient approximation algorithms are given and their complexity is analyzed.


  10. P. Berman, B. Dasgupta, and E.D. Sontag. Randomized approximation algorithms for set multicover problems with applications to reverse engineering of protein and gene networks. Discrete Applied Mathematics Special Series on Computational Molecular Biology, 155:733-749, 2007. [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, systems identification, reverse engineering.
    Abstract:
    This paper investigates computational complexity aspects of a combinatorial problem that arises in the reverse engineering of protein and gene networks, showing relations to an appropriate set multicover problem with large "coverage" factor, and providing a non-trivial analysis of a simple randomized polynomial-time approximation algorithm for the problem.


  11. B. DasGupta, G.A. Enciso, E.D. Sontag, and Y. Zhang. Algorithmic and complexity aspects of decompositions of biological networks into monotone subsystems. BioSystems, 90:161-178, 2007. [PDF] [doi:http://dx.doi.org/10.1016/j.biosystems.2006.08.001] Keyword(s): monotone systems, systems biology, biochemical networks.
    Abstract:
    A useful approach to the mathematical analysis of large-scale 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 graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximability results. One of the algorithms, which has a worst-case guarantee of 87.9% from optimality, is based on the semidefinite programming relaxation approach of Goemans-Williamson. The algorithm was implemented and tested on a Drosophila segmentation network and an Epidermal Growth Factor Receptor pathway model.


  12. T. Gedeon and E.D. Sontag. Oscillations in multi-stable monotone systems with slowly varying feedback. J. of Differential Equations, 239:273-295, 2007. [PDF] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    This paper gives a theorem showing that a slow feedback adaptation, acting entirely analogously to the role of negative feedback for ordinary relaxation oscillations, leads to periodic orbits for bistable monotone systems. The proof is based upon a combination of i/o monotone systems theory and Conley Index theory.


  13. W. Maass, P. Joshi, and E.D. Sontag. Computational aspects of feedback in neural circuits. PLoS Computational Biology, 3:e165 1-20, 2007. [PDF] Keyword(s): neural networks, feedback linearization, computation by cortical microcircuits.
    Abstract:
    It had previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate in this article the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise the resulting computational model can perform a large class of biologically relevant real-time computations that require a non-fading memory.


  14. E.D. Sontag. Monotone and near-monotone biochemical networks. Systems and Synthetic Biology, 1:59-87, 2007. [PDF] [doi:10.1007/s11693-007-9005-9] Keyword(s): systems biology, biochemical networks, monotone systems, Ising spin models, nonlinear stability, dynamical systems, consistent graphs, gene networks.
    Abstract:
    This paper provides an expository introduction to monotone and near-monotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone. In addition, interconnections of monotone systems may be fruitfully analyzed using tools from control theory.


  15. P. de Leenheer, D. Angeli, and E.D. Sontag. Monotone chemical reaction networks. J. Math Chemistry, 41:295-314, 2007. [PDF] [doi:10.1007/s10910-006-9075-z] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    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 self-contained proof of a particular attractivity result which is used in proving our main result.


Conference articles
  1. D. Angeli, P. de Leenheer, and E.D. Sontag. Petri nets tools for the analysis of persistence in chemical networks. In Proc. 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), Pretoria, South Africa, 22-24 August, 2007, 2007. Keyword(s): Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles.


  2. M. Arcak and E.D. Sontag. A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007, pages 4477-4482, 2007. Note: Conference version of journal paper with same title. Keyword(s): systems biology, biochemical networks, cyclic feedback systems, secant condition, nonlinear stability, dynamical systems.


  3. D. Del Vecchio and E.D. Sontag. Dynamics and control of synthetic bio-molecular networks. In Proceedings American Control Conf., New York, July 2007, pages 1577-1588, 2007. Keyword(s): systems biology, biochemical networks, synthetic biology.
    Abstract:
    This tutorial paper presents an introduction to systems and synthetic molecular biology. It provides an introduction to basic biological concepts, and describes some of the techniques as well as challenges in the analysis and design of biomolecular networks.


  4. M.R. Jovanovic, M. Arcak, and E.D. Sontag. Remarks on the stability of spatially distributed systems with a cyclic interconnection structure. In Proceedings American Control Conf., New York, July 2007, pages 2696-2701, 2007. Keyword(s): systems biology, biochemical networks, cyclic feedback systems, spatially distributed systems, secant condition.
    Abstract:
    For distributed systems with a cyclic interconnection structure, a global stability result is shown to hold if the secant criterion is satisfied.


  5. E.D. Sontag, Y. Wang, and A. Megretski. Remarks on Input Classes for Identification of Bilinear Systems. In Proceedings American Control Conf., New York, July 2007, pages 4345-4350, 2007. Keyword(s): realization theory, observability, identifiability, bilinear systems.


  6. L. Wang and E.D. Sontag. Further results on singularly perturbed monotone systems, with an application to double phosphorylation cycles. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007, pages 627-632, 2007. Note: Conference version of Singularly perturbed monotone systems and an application to double phosphorylation cycles.Keyword(s): singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, multistability, monotone systems.



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