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Publications by Eduardo D. Sontag in year 2016
Articles in journal or book chapters
  1. Z. Aminzare and E.D. Sontag. Some remarks on spatial uniformity of solutions of reaction-diffusion PDEs. Nonlinear Analysis, 147:125-144, 2016. [PDF] Keyword(s): contractions, contractive systems, matrix measures, logarithmic norms, synchronization, consensus, reaction-diffusion PDEs, partial differential equations.
    Abstract:
    This paper presents a condition which guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction diffusion partial differential equation (PDE) with Neumann boundary conditions in one dimension, using the Jacobian matrix of the reaction term and the first Dirichlet eigenvalue of the Laplacian operator on the given spatial domain. The estimates are based on logarithmic norms in non-Hilbert spaces, which allow, in particular for a class of examples of interest in biology, tighter estimates than other previously proposed methods.


  2. J.A. Ascensao, P. Datta, B. Hancioglu, E.D. Sontag, M.L. Gennaro, and O.A. Igoshin. Non-monotonic response dynamics of glyoxylate shunt genes in Mycobacterium tuberculosis. PLoS Computational Biology, 12:e1004741, 2016. [PDF]
    Abstract:
    Understanding how dynamical responses of biological networks are constrained by underlying network topology is one of the fundamental goals of systems biology. Here we employ monotone systems theory to formulate a theorem stating necessary conditions for non-monotonic time-response of a biochemical network to a monotonic stimulus. We apply this theorem to analyze the non-monotonic dynamics of the sigmaB-regulated glyoxylate shunt gene expression in Mycobacterium tuberculosis cells exposed to hypoxia. We first demonstrate that the known network structure is inconsistent with observed dynamics. To resolve this inconsistency we employ the formulated theorem, modeling simulations and optimization along with follow-up dynamic experimental measurements. We show a requirement for post-translational modulation of sigmaB activity in order to reconcile the network dynamics with its topology. The results of this analysis make testable experimental predictions and demonstrate wider applicability of the developed methodology to a wide class of biological systems.


  3. M. Margaliot, E.D. Sontag, and T. Tuller. Contraction after small transients. Automatica, 67:178-184, 2016. [PDF] Keyword(s): entrainment, nonlinear systems, stability, contractions, contractive systems.
    Abstract:
    Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We introduce three new forms of generalized contraction (GC) that are motivated by allowing contraction to take place after small transients in time and/or amplitude. These forms of GC are useful for several reasons. First, allowing small transients does not destroy the asymptotic properties provided by standard contraction. Second, in some cases as we change the parameters in a contractive system it becomes a GC just before it looses contractivity. In this respect, GC is the analogue of marginal stability in Lyapunov stability theory. We provide checkable sufficient conditions for GC, and demonstrate their usefulness using several models from systems biology that are not contractive, with respect to any norm, yet are GC.


  4. E.V. Nikolaev and E.D. Sontag. Quorum-sensing synchronization of synthetic toggle switches: A design based on monotone dynamical systems theory. PLoS Computational Biology, 12:e1004881, 2016. [PDF] Keyword(s): quorum sensing, toggle switches, monotone systems.
    Abstract:
    Synthetic constructs in biotechnology, bio-computing, and proposed gene therapy interventions are often based on plasmids or transfected circuits which implement some form of on-off (toggle or flip-flop) switch. For example, the expression of a protein used for therapeutic purposes might be triggered by the recognition of a specific combination of inducers (e.g., antigens), and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off. The robustness of such a design is hampered by molecular (intrinsic) or environmental (extrinsic) noise, which may lead to spontaneous changes of state in a subset of the population and is reflected in the bimodality of protein expression, as measured for example using flow cytometry. In this context, a majority-vote correction circuit, which brings deviant cells back into the required state, is highly desirable. To address this concrete challenge, we have developed a new theoretical design for quorum-sensing (QS) synthetic toggles. QS provides a way for cells to broadcast their states to the population as a whole so as to facilitate consensus. Our design is endowed with strong theoretical guarantees, based on monotone dynamical systems theory, of global stability and no oscillations, and which leads to robust consensus states.


  5. A. Raveh, M. Margaliot, E.D. Sontag, and T. Tuller. A model for competition for ribosomes in the cell. Proc. Royal Society Interface, 13:2015.1062, 2016. [PDF] Keyword(s): resource competition, ribosomes, entrainment, nonlinear systems, stability, contractions, contractive systems.
    Abstract:
    We develop and analyze a general model for large-scale simultaneous mRNA translation and competition for ribosomes. Such models are especially important when dealing with highly expressed genes, as these consume more resources. For our model, we prove that the compound system always converges to a steady-state and that it always entrains or phase locks to periodically time-varying transition rates in any of the mRNA molecules. We use this model to explore the interactions between the various mRNA molecules and ribosomes at steady-state. We show that increasing the length of an mRNA molecule decreases the production rate of all the mRNAs. Increasing any of the codon translation rates in a specific mRNA molecule yields a local effect: an increase in the translation rate of this mRNA, and also a global effect: the translation rates in the other mRNA molecules all increase or all decrease. These results suggest that the effect of codon decoding rates of endogenous and heterologous mRNAs on protein production might be more complicated than previously thought.


Conference articles
  1. M. Lang and E.D. Sontag. Scale-invariant systems realize nonlinear differential operators. In 2016 American Control Conference (ACC), pages 6676 - 6682, 2016. [PDF] Keyword(s): scale invariance, fold change detection, nonlinear systems, realization theory, internal model principle.
    Abstract:
    In this article, we show that scale-invariant systems, as well as systems invariant with respect to other input transformations, can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.


  2. F. Menolascina, R. Stocker, and E.D. Sontag. In-vivo identification and control of aerotaxis in Bacillus subtilis. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 764-769, 2016. [PDF] Keyword(s): identification, systems biology, aerotaxis, B. subtilis.
    Abstract:
    Combining in-vivo experiments with system identification methods, we determine a simple model of aerotaxis in B. subtilis, and we subsequently employ this model in order to compute the sequence of oxygen gradients needed in order to achieve set-point regulation with respect to a signal tracking the center of mass of the bacterial population. We then successfully validate both the model and the control scheme, by showing that in-vivo positioning control can be achieved via the application of the precomputed inputs in-vivo in an open-loop configuration.


  3. E.D. Sontag. Some remarks on immune control of infections and tumors. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 2476-2480, 2016. Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology, cancer.


  4. Q. Tyles, T. Kang, E.D. Sontag, and L. Bleris. Exploring the impact of resource limitations on gene network reconstruction. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 3350-3355, 2016. [PDF] Keyword(s): Biological systems, Genetic regulatory systems, Systems biology.
    Abstract:
    Applying Modular Response Analysis to a synthetic gene circuit, which was introduced in a recent paper by the authors, leads to the inference of a nontrivial "ghost" regulation edge which was not explicitly engineered into the network and which is, in fact, not immediately apparent from experimental measurements. One may thus hypothesize that this ghost regulatory effect is due to competition for resources. A mathematical model is proposed, and analyzed in closed form, that lends validation to this hypothesis.


  5. Y. Zarai, M. Margaliot, E.D. Sontag, and T. Tuller. Controlling the ribosomal density profile in mRNA translation. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 4184-4189, 2016. Keyword(s): ribosomes, translation.


Internal reports
  1. E.D. Sontag. A remark on incoherent feedforward circuits as change detectors and feedback controllers. Technical report, arXiv:1602.00162, 2016. [PDF] Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology.
    Abstract:
    This note analyzes incoherent feedforward loops in signal processing and control. It studies the response properties of IFFL's to exponentially growing inputs, both for a standard version of the IFFL and for a variation in which the output variable has a positive self-feedback term. It also considers a negative feedback configuration, using such a device as a controller. It uncovers a somewhat surprising phenomenon in which stabilization is only possible in disconnected regions of parameter space, as the controlled system's growth rate is varied.


  2. E.D. Sontag. Examples of computation of exact moment dynamics for chemical reaction networks. Technical report, arXiv:1612.02393, 2016. [PDF] Keyword(s): systems biology, biochemical networks, stochastic systems, Chemical Master Equation, chemical reaction networks, moments, molecular networks, complex-balanced networks.
    Abstract:
    We review in a unified way results for two types of stochastic chemical reaction systems for which moments can be effectively computed: feedforward networks and complex-balanced networks.


  3. E.D. Sontag. Two-zone tumor tolerance can arise from a simple immunological feedforward motif that estimates tumor growth rates. Technical report, bioRxiv https://doi.org/10.1101/095455, 2016. [PDF] Keyword(s): scale invariance, fold change detection, T cells, incoherent feedforward loops, immunology, cancer.
    Abstract:
    Preprint version of "A dynamical model of immune responses to antigen presentation predicts different regions of tumor or pathogen elimination", to appear in Cell Systems 2017. However, the journal version does not include Section 9 on degradation-based IFFL's from this preprint.



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