Publications by Eduardo D. Sontag in year 2015
Articles in journal or book chapters
  1. E.D. Sontag. Input-to-State Stability. In J. Baillieul and T. Samad, editors, Encyclopedia of Systems and Control. Springer-Verlag, 2015. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, input to output stability.
    The notion of input to state stability (ISS) qualitatively describes stability of the mapping from initial states and inputs to internal states (and more generally outputs). This entry focuses on the definition of ISS and a discussion of equivalent characterizations.

  2. P. Bastiaens, M. R. Birtwistle, N. Bluthgen, F. J. Bruggeman, K.-H. Cho, C. Cosentino, A. de la Fuente, J. B. Hoek, A. Kiyatkin, S. Klamt, W. Kolch, S. Legewie, P. Mendes, T. Naka, T. Santra, E.D. Sontag, H. V. Westerhoff, and B. N. Kholodenko. Silence on the relevant literature and errors in implementation. Nature Biotech, 33:336-339, 2015. [PDF] Keyword(s): modular response analysis, systems biology, biochemical networks, reverse engineering, gene and protein networks, protein networks, gene networks, systems identification.
    This letter discusses a paper in the same journal which reported a method for reconstructing network topologies. Here we show that the method is a variant of a previously published method, modular response analysis. We also demonstrate that the implementation of the algorithm in that paper using statistical similarity measures as a proxy for global network responses to perturbations is erroneous and its performance is overestimated.

  3. T. Kang, R. Moore, Y. Li, E.D. Sontag, and L. Bleris. Discriminating direct and indirect connectivities in biological networks. Proc Natl Acad Sci USA, 112:12893-12898, 2015. [PDF] Keyword(s): modular response analysis, stochastic systems, reverse engineering, gene networks, synthetic biology, feedforward, systems biology.
    Reverse engineering of biological pathways involves an iterative process between experiments, data processing, and theoretical analysis. In this work, we engineer synthetic circuits, subject them to perturbations, and then infer network connections using a combination of nonparametric single-cell data resampling and modular response analysis. Intriguingly, we discover that recovered weights of specific network edges undergo divergent shifts under differential perturbations, and that the particular behavior is markedly different between different topologies. Investigating topological changes under differential perturbations may address the longstanding problem of discriminating direct and indirect connectivities in biological networks.

  4. M. Skataric, E.V. Nikolaev, and E.D. Sontag. A fundamental limitation to fold-change detection by biological systems with multiple time scales. IET Systems Biology, 9:1-15, 2015. [PDF] Keyword(s): adaptation, biological adaptation, perfect adaptation, singular perturbations, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, incoherent feedforward loop, feedforward, IFFL.
    The phenomenon of fold-change detection, or scale invariance, is exhibited by a variety of sensory systems, in both bacterial and eukaryotic signaling pathways. It has been often remarked in the systems biology literature that certain systems whose output variables respond at a faster time scale than internal components give rise to an approximate scale-invariant behavior, allowing approximate fold-change detection in stimuli. This paper establishes a fundamental limitation of such a mechanism, showing that there is a minimal fold-change detection error that cannot be overcome, no matter how large the separation of time scales is. To illustrate this theoretically predicted limitation, we discuss two common biomolecular network motifs, an incoherent feedforward loop and a feedback system, as well as a published model of the chemotaxis signaling pathway of Dictyostelium discoideum.

  5. E.D. Sontag and A. Singh. Exact moment dynamics for feedforward nonlinear chemical reaction networks. IEEE Life Sciences Letters, 1:26-29, 2015. [PDF] Keyword(s): systems biology, biochemical networks, stochastic systems, chemical master equation, chemical reaction networks.
    Chemical systems are inherently stochastic, as reactions depend on random (thermal) motion. This motivates the study of stochastic models, and specifically the Chemical Master Equation (CME), a discrete-space continuous-time Markov process that describes stochastic chemical kinetics. Exact studies using the CME are difficult, and several moment closure tools related to "mass fluctuation kinetics" and "fluctuation-dissipation" formulas can be used to obtain approximations of moments. This paper, in contrast, introduces a class of nonlinear chemical reaction networks for which exact computation is possible, by means of finite-dimensional linear differential equations. This class allows second and higher order reactions, but only under special assumptions on structure and/or conservation laws.

  6. M. Marcondes de Freitas and E.D. Sontag. A small-gain theorem for random dynamical systems with inputs and outputs. SIAM J. Control and Optimization, 53:2657-2695, 2015. [PDF] Keyword(s): random dynamical systems, monotone systems, small-gain theorem, stochastic systems.
    A formalism for the study of random dynamical systems with inputs and outputs (RDSIO) is introduced. An axiomatic framework and basic properties of RDSIO are developed, and a theorem is shown that guarantees the stability of interconnected systems.

Conference articles
  1. A. O. Hamadeh, E.D. Sontag, and D. Del Vecchio. A contraction approach to output tracking via high-gain feedback. In Proc. IEEE Conf. Decision and Control, Dec. 2015, pages 7689-7694, 2015. [PDF]
    This paper adopts a contraction approach to the analysis of the tracking properties of dynamical systems under high gain feedback when subject to inputs with bounded derivatives. It is shown that if the tracking error dynamics are contracting, then the system is input to output stable with respect to the input signal derivatives and the output tracking error. As an application, it iss hown that the negative feedback connection of plants composed of two strictly positive real LTI subsystems in cascade can follow external inputs with tracking errors that can be made arbitrarily small by applying a sufficiently large feedback gain. We utilize this result to design a biomolecular feedback for a synthetic genetic sensor to make it robust to variations in the availability of a cellular resource required for protein production.

Internal reports
  1. E.D. Sontag. Incoherent feedforward motifs as immune change detectors. Technical report, bioRxiv, December 2015. [PDF] Keyword(s): scale invariance, fcd, fold change detection, T cells, incoherent feedforward loops, immunology, incoherent feedforward loop, feedforward, IFFL.
    We speculate that incoherent feedforward loops may be phenomenologically involved in self/nonself discrimination in immune-infection and immune-tumor interactions, acting as "change detectors". In turn, this may result in logarithmic sensing (Weber phenomenon) and even scale invariance (fold-change detection).



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