Publications by Eduardo D. Sontag in year 2019
Articles in journal or book chapters
  1. D.K. Agrawal, R. Marshall, V. Noireaux, and E.D. Sontag. In vitro implementation of robust gene regulation in a synthetic biomolecular integral controller. 2019. Note: Submitted.Keyword(s): tracking, synthetic biology, integral feedback, TX/TL, systems biology, dynamical systems, adaptation, internal model principle.
    Cells respond to biochemical and physical internal as well as external signals. These signals can be broadly classified into two categories: (a) ``actionable'' or ``reference'' inputs that should elicit appropriate biological or physical responses such as gene expression or motility, and (b) ``disturbances'' or ``perturbations'' that should be ignored or actively filtered-out. These disturbances might be exogenous, such as binding of nonspecific ligands, or endogenous, such as variations in enzyme concentrations or gene copy numbers. In this context, the term robustness describes the capability to produce appropriate responses to reference inputs while at the same time being insensitive to disturbances. These two objectives often conflict with each other and require delicate design trade-offs. Indeed, natural biological systems use complicated and still poorly understood control strategies in order to finely balance the goals of responsiveness and robustness. A better understanding of such natural strategies remains an important scientific goal in itself and will play a role in the construction of synthetic circuits for therapeutic and biosensing applications. A prototype problem in robustly responding to inputs is that of ``robust tracking'', defined by the requirement that some designated internal quantity (for example, the level of expression of a reporter protein) should faithfully follow an input signal while being insensitive to an appropriate class of perturbations. Control theory predicts that a certain type of motif, called integral feedback, will help achieve this goal, and this motif is, in fact, a necessary feature of any system that exhibits robust tracking. Indeed, integral feedback has always been a key component of electrical and mechanical control systems, at least since the 18th century when James Watt employed the centrifugal governor to regulate steam engines. Motivated by this knowledge, biological engineers have proposed various designs for biomolecular integral feedback control mechanisms. However, practical and quantitatively predictable implementations have proved challenging, in part due to the difficulty in obtaining accurate models of transcription, translation, and resource competition in living cells, and the stochasticity inherent in cellular reactions. These challenges prevent first-principles rational design and parameter optimization. In this work, we exploit the versatility of an Escherichia coli cell-free transcription-translation (TXTL) to accurately design, model and then build, a synthetic biomolecular integral controller that precisely controls the expression of a target gene. To our knowledge, this is the first design of a functioning gene network that achieves the goal of making gene expression track an externally imposed reference level, achieves this goal even in the presence of disturbances, and whose performance quantitatively agrees with mathematical predictions.

  2. M. A. Al-Radhawi, D. Del Vecchio, and E. D. Sontag. Multi-modality in gene regulatory networks with slow gene binding. PLoS Computational Biology, 2019. Note: To appear. 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.
    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.

  3. J.M. Greene, J.L. Gevertz, and E. D. Sontag. A mathematical approach to distinguish spontaneous from induced evolution of drug resistance during cancer treatment. JCO Clinical Cancer Informatics, 2019. Note: To appear.Keyword(s): cancer heterogeneity, phenotypic variation, nonlinear systems, epigenetics.
    Resistance to chemotherapy is a major impediment to the successful treatment of cancer. Classically, resistance has been thought to arise primarily through random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that the progression to resistance need not occur randomly, but instead may be induced by the therapeutic agent itself.This process of resistance induction can be a result of genetic changes, or can occur through epigenetic alterations that cause otherwise drug-sensitive cancer cells to undergo ``phenotype switching''. This relatively novel notion of resistance further complicates the already challenging task of designing treatment protocols that minimize the risk of evolving resistance. In an effort to better understand treatment resistance, we have developed a mathematical modeling framework that incorporates both random and drug-induced resistance. Our model demonstrates that the ability (or lack thereof) of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. The importance of induced resistance in treatment response led us to ask if, in our model, one can determine the resistance induction rate of a drug for a given treatment protocol. Not only could we prove that the induction parameter in our model is theoretically identifiable, we have also proposed a possible in vitro experiment which could practically be used to determine a treatment's propensity to induce resistance.

  4. M. Margaliot and E.D. Sontag. Revisiting totally positive differential systems: A tutorial and new results. Automatica, 101:1-14, 2019. [PDF] Keyword(s): tridiagonal systems, cooperative systems, monotone systems.
    A matrix is totally nonnegative (resp., totally positive) if all its minors are nonnegative (resp., positive). This paper draws connections between B. Schwarz's 1970 work on TN and TP matrices to Smillie's 1984 and Smith's 1991 work on stability of nonlinear tridiagonal cooperative systems, simplifying proofs in the later paper and suggesting new research questions.

  5. E.V. Nikolaev, A. Zloza, and E.D. Sontag. Immunobiochemical reconstruction of influenza lung infection - melanoma skin cancer interactions. Frontiers in Immunology, 2019. Note: To appear.Keyword(s): cancer, tumors, infections, immunology, checkpoint inhibition, systems biology.
    Recent experimental results from the Zloza lab combined a mouse model of influenza A virus (IAV) infection (A/H1N1/PR8) and a highly aggressive model of infection-unrelated cancer, B16-F10 skin melanoma. This paper showed that acute influenza infection of the lung promotes distal melanoma growth in the dermis of the flank and leads to decreased host survival. Here, we proceed to ground the experimental observations in a mechanistic immunobiochemical model that incorporates the T cell receptor signaling pathway, various transcription factors, and a gene regulatory network (GRN). A core component of our model is a biochemical motif, which we call a Triple Incoherent Feed-Forward Loop (TIFFL), and which reflects known interactions between IRF4, Blimp-1, and Bcl-6. The different activity levels of the TIFFL components, as a function of the cognate antigen levels and the given inflammation context, manifest themselves in phenotypically distinct outcomes. Specifically, both the TIFFL reconstruction and quantitative estimates obtained from the model allowed us to formulate a hypothesis that it is the loss of the fundamental TIFFL-induced adaptation of the expression of PD-1 receptors on anti-melanoma CD8+ T cells that constitutes the essence of the previously unrecognized immunologic factor that promotes the experimentally observed distal tumor growth in the presence of acute non-ocogenic infection. We therefore hope that this work can further highlight the importance of adaptive mechanisms by which immune functions contribute to the balance between self and non-self immune tolerance, adaptive resistance, and the strength of TCR-induced activation, thus contributing to the understanding of a broader complexity of fundamental interactions between pathogens and tumors.



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Last modified: Fri Jan 18 11:44:37 2019
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