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Publications of Eduardo D. Sontag jointly with D. Del Vecchio
Articles in journal or book chapters
  1. M. A. Al-Radhawi, D. Del Vecchio, and E. D. Sontag. Multi-modality in gene regulatory networks with slow gene binding. 2017. Note: Submitted. Preprint in arXiv:1705.02330, May 2017 rev Nov 2017. [PDF] Keyword(s): multistability, gene networks, Markov Chains, Master Equation, cancer heterogeneity, phenotypic variation, nonlinear systems, stochastic models, epigenetics.
    Abstract:
    In biological processes such as embryonic development, hematopoietic cell differentiation, and the arising of tumor heterogeneity and consequent resistance to therapy, mechanisms of gene activation and deactivation may play a role in the emergence of phenotypically heterogeneous yet genetically identical (clonal) cellular populations. Mathematically, the variability in phenotypes in the absence of genetic variation can be modeled through the existence of multiple metastable attractors in nonlinear systems subject with stochastic switching, each one of them associated to an alternative epigenetic state. An important theoretical and practical question is that of estimating the number and location of these states, as well as their relative probabilities of occurrence. This paper focuses on a rigorous analytic characterization of multiple modes under slow promoter kinetics, which is a feature of epigenetic regulation. It characterizes the stationary distributions of Chemical Master Equations for gene regulatory networks as a mixture of Poisson distributions. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations and a trans-differentiation network.


  2. A.C. Jiang, A. C. Ventura, E. D. Sontag, S. D. Merajver, A. J. Ninfa, and D. Del Vecchio. Load-induced modulation of signal transduction networks. Science Signaling, 4, issue 194:ra67, 2011. [PDF] Keyword(s): systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity.
    Abstract:
    Biological signal transduction networks are commonly viewed as circuits that pass along in the process amplifying signals, enhancing sensitivity, or performing other signal-processing to transcriptional and other components. Here, we report on a "reverse-causality" phenomenon, which we call load-induced modulation. Through a combination of analytical and experimental tools, we discovered that signaling was modulated, in a surprising way, by downstream targets that receive the signal and, in doing so, apply what in physics is called a load. Specifically, we found that non-intuitive changes in response dynamics occurred for a covalent modification cycle when load was present. Loading altered the response time of a system, depending on whether the activity of one of the enzymes was maximal and the other was operating at its minimal rate or whether both enzymes were operating at submaximal rates. These two conditions, which we call "limit regime" and "intermediate regime," were associated with increased or decreased response times, respectively. The bandwidth, the range of frequency in which the system can process information, decreased in the presence of load, suggesting that downstream targets participate in establishing a balance between noise-filtering capabilities and a s ability to process high-frequency stimulation. Nodes in a signaling network are not independent relay devices, but rather are modulated by their downstream targets


  3. D. Del Vecchio and E.D. Sontag. Synthetic Biology: A Systems Engineering Perspective. In B.P. Ingalls and P. Iglesias, editors, Control Theory in Systems Biology, pages 101-123. MIT Press, 2009.
    Abstract:
    This is an expository paper about certain aspects of Synthetic Biology, including a discussion of the issue of modularity (load effects from downstream components).


  4. D. Del Vecchio and E.D. Sontag. Engineering Principles in Bio-Molecular Systems: From Retroactivity to Modularity. European Journal of Control, 15:389-397, 2009. Note: Preliminary version appeared as paper MoB2.2 in Proceedings of the European Control Conference 2009, August 23-26, 2009, Budapest. [PDF] Keyword(s): systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity.


  5. D. Del Vecchio, A.J. Ninfa, and E.D. Sontag. Modular Cell Biology: Retroactivity and Insulation. Molecular Systems Biology, 4:161, 2008. [PDF] Keyword(s): retroactivity, systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity.
    Abstract:
    Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon interconnection. Just as electrical, hydraulic, and other physical systems often do not display modularity, nor do many biochemical systems, and specifically, genetic networks. Here, we study the effect of interconnections on the input/output dynamic characteristics of transcriptional components, focusing on a property, which we call "retroactivity," that plays a role analogous to non-zero output impedance in electrical systems. In transcriptional networks, retroactivity is large when the amount of transcription factor is comparable to, or smaller than, the amount of promoter binding sites, or when the affinity of such binding sites is high. In order to attenuate the effect of retroactivity, we propose a feedback mechanism inspired by the design of amplifiers in electronics. We introduce, in particular, a mechanism based on a phosphorylation/dephosphorylation cycle. This mechanism enjoys a remarkable insulation property, due to the fast time scales of the phosphorylation and dephosphorylation reactions. Such a mechanism, when viewed as a signal transduction system, has thus an inherent capacity to provide insulation and hence to increase the modularity of the system in which it is placed.


Conference articles
  1. N.S. Kumar, M. A. Al-Radhawi, D. Del Vecchio, and E. D. Sontag. Stochasticity is necessary for multiple attractors in a class of differentiation networks. In 2017 American Control Conference (ACC), pages submitted, 2017. Keyword(s): systems biology, genetic regulatory, multistability, gene networks.
    Abstract:
    Deterministic models remain the most common option for modeling gene regulatory networks even when the underlying assumptions of high copy numbers and fast promoter kinetics are unsatisfied. Here, we analyze a widely studied differentiation network motif known as the PU.1-GATA-1 circuit and we show that an ODE model of the biomolecular reactions consistent with known biology is incapable of exhibiting multistability, a defining behaviour for such a network. Thus, we consider the chemical master equation model of the same biomolecular reactions and using results recently developed by the authors, we analytically construct the stationary distribution. We show that this distribution is indeed capable of admitting a multitude of modes. We illustrate the results with a numerical example.


  2. 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]
    Abstract:
    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.


  3. D. Del Vecchio, A.J. Ninfa, and E.D. Sontag. A Systems Theory with Retroactivity: Application to Transcriptional Modules. In Proceedings of the 2008 American Control Conference, Seattle, June 2008, pages Paper WeC04.1, 2008. [PDF] Keyword(s): retroactivity, systems biology, biochemical networks, synthetic biology, futile cycles, singular perturbations, modularity.


  4. 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.



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Last modified: Thu Nov 23 10:40:56 2017
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