Publications by Eduardo D. Sontag in year 2018
Articles in journal or book chapters
  1. E.D. Sontag. Examples of computation of exact moment dynamics for chemical reaction networks. In R. Tempo, S. Yurkovich, and P. Misra, editors, Emerging Applications of Control and Systems Theory, volume 473 of Lecture Notes in Control and Inform. Sci., pages 295-312. Springer-Verlag, Berlin, 2018. [PDF] Keyword(s): chemical master equations, stochastics, moments, chemical reaction networks, incoherent feedforward loop, feedforward, IFFL.
    The study of stochastic biomolecular networks is a key part of systems biology, as such networks play a central role in engineered synthetic biology constructs as well as in naturally occurring cells. This expository paper reviews in a unified way a pair of recent approaches to the finite computation of statistics for chemical reaction networks.

  2. D. Del Vecchio, Y. Qian, R.M Murray, and E.D. Sontag. Future systems and control research in synthetic biology. Annual Reviews in Control, 45:5-17, 2018. [PDF] Keyword(s): synthetic biology, systems biology.
    This paper is a review of systems and control problems in synthetic biology, focusing on past accomplishments and open problems. It is partially a report on the workshop "The Compositionality Problem in Synthetic Biology: New Directions for Control Theory" held on June 26–27, 2017 at MIT, and organized by D. Del Vecchio, R. M. Murray, and E. D. Sontag

  3. E.V. Nikolaev, S.J. Rahi, and E.D. Sontag. Chaos in simple periodically-forced biological models. Biophysical Journal, 114:1232-1240, 2018. [PDF] Keyword(s): chaos, entrainment, systems biology, periodic inputs, subharmonic responses, biochemical systems, forced oscillations.
    What complicated dynamics can arise in the simplest biochemical systems, in response to a periodic input? This paper discusses two models that commonly appear as components of larger sensing and signal transduction pathways in systems biology: a simple two-species negative feedback loop, and a prototype nonlinear integral feedback. These systems have globally attracting steady states when unforced, yet, when subject to a periodic excitation, subharmonic responses and strange attractors can arise via period-doubling cascades. These behaviors are similar to those exhibited by classical forced nonlinear oscillators such as those described by van der Pol or Duffing equations. The lack of entrainment to external oscillations, in even the simplest biochemical networks, represents a level of additional complexity in molecular biology.

  4. T.H. Segall-Shapiro, E. D. Sontag, and C. A. Voigt. Engineered promoters enable constant gene expression at any copy number in bacteria. Nature Biotechnology, 36:352-358, 2018. [PDF] Keyword(s): synthetic biology, systems biology, genetic circuits, gene copy number, incoherent feedforward loop, feedforward, IFFL.
    This paper deals with the design of promoters that maintain constant levels of expression, whether they are carried at single copy in the genome or on high-copy plasmids. The design is based on an incoherent feedforward loop (iFFL) with a perfectly non-cooperative repression. The circuits are implemented in E. coli using Transcription Activator Like Effectors (TALEs). The resulting stabilized promoters generate near identical expression across different genome locations and plasmid backbones (pSC101, p15a, ColE1, pUC), and also provide robustness to strain mutations and growth media. Further, their strength is tunable and can be used to maintain constant ratios between proteins.

  5. Y. Zarai, M. Margaliot, E.D. Sontag, and T. Tuller. Controllability analysis and control synthesis for the ribosome flow model. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 15:1351-1364, 2018. [PDF] Keyword(s): systems biology, ribosomes, controllability, RFM.
    The ribosomal density along the coding region of the mRNA molecule affects various fundamental intracellular phenomena including: protein production rates, organismal fitness, ribosomal drop off, and co-translational protein folding. Thus, regulating translation in order to obtain a desired ribosomal profile along the mRNA molecule is an important biological problem. This paper studies this problem formulated in the context of the ribosome flow model (RFM) in which one views the transition rates between site as controls.

Conference articles
  1. M.A. Al-Radhawi, N.S. Kumar, E.D. Sontag, and D. Del Vecchio. Stochastic multistationarity in a model of the hematopoietic stem cell differentiation network. In Proc. 2018 IEEE Conf. Decision and Control, pages 1886-1892, 2018. [PDF] Keyword(s): multistability, biochemical networks, systems biology, stochastic systems, cell differentiation, multistationarity.
    In the mathematical modeling of cell differentiation, it is common to think of internal states of cells (quanfitied by activation levels of certain genes) as determining different cell types. We study here the "PU.1/GATA-1 circuit" that controls the development of mature blood cells from hematopoietic stem cells (HSCs). We introduce a rigorous chemical reaction network model of the PU.1/GATA-1 circuit, which incorporates current biological knowledge and find that the resulting ODE model of these biomolecular reactions is incapable of exhibiting multistability, contradicting the fact that differentiation networks have, by definition, alternative stable steady states. When considering instead the stochastic version of this chemical network, we analytically construct the stationary distribution, and are able to show that this distribution is indeed capable of admitting a multiplicity of modes. Finally, we study how a judicious choice of system parameters serves to bias the probabilities towards different stationary states. We remark that certain changes in system parameters can be physically implemented by a biological feedback mechanism; tuning this feedback gives extra degrees of freedom that allow one to assign higher likelihood to some cell types over others.

  2. F. Blanchini, H. El-Samad, G. Giordano, and E. D. Sontag. Control-theoretic methods for biological networks. In Proc. 2018 IEEE Conf. Decision and Control, pages 466-483, 2018. [PDF] Keyword(s): systems biology, dynamic response phenotypes, multi-stability, oscillations, feedback, nonlinear systems, incoherent feedforward loop, feedforward, IFFL.
    This is a tutorial paper on control-theoretic methods for the analysis of biological systems.

  3. J.M. Greene, C. Sanchez-Tapia, and E.D. Sontag. Control structures of drug resistance in cancer chemotherapy. In Proc. 2018 IEEE Conf. Decision and Control, pages 5195-5200, 2018. [PDF]
    The primary factor limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. This work extends the work reported in "A mathematical approach to distinguish spontaneous from induced evolution of drug resistance during cancer treatment" by introducing a time-optimal control problem that is analyzed utilizing differential-geometric techniques: we seek a treatment protocol which maximizes the time of treatment until a critical tumor size is reached. The general optimal control structure is determined as a combination of both bang-bang and path-constrained arcs. Numerical results are presented which demonstrate decreasing treatment efficacy as a function of the ability of the drug to induce resistance. Thus, drug-induced resistance may dramatically effect the outcome of chemotherapy, implying that factors besides cytotoxicity should be considered when designing treatment regimens.

  4. J. Huang, A. Isidori, L. Marconi, M. Mischiati, E. D. Sontag, and W. M. Wonham. Internal models in control, biology and neuroscience. In Proc. 2018 IEEE Conf. Decision and Control, pages 5370-5390, 2018. [PDF] Keyword(s): feeedback, internal model principle, nonlinear systems, incoherent feedforward loop, feedforward, IFFL.
    This tutorial paper deals with the Internal Model Principle (IMP) from different perspectives. The goal is to start from the principle as introduced and commonly used in the control theory and then enlarge the vision to other fields where "internal models" play a role. The biology and neuroscience fields are specifically targeted in the paper. The paper ends by presenting an "abstract" theory of IMP applicable to a large class of systems.

  5. M. Margaliot and E.D. Sontag. Analysis of nonlinear tridiagonal cooperative systems using totally positive linear differential systems. In Proc. 2018 IEEE Conf. Decision and Control, pages 3104-3109, 2018. [PDF] Keyword(s): tridiagonal systems, cooperative systems, monotone systems.
    This is a conference version of "Revisiting totally positive differential systems: A tutorial and new results".

Internal reports
  1. J.M. Greene, C. Sanchez-Tapia, and E.D. Sontag. Mathematical details on a cancer resistance model. Technical report, bioRxiv 2018/475533, 2018. [PDF] Keyword(s): drug resistance, chemotherapy, optimal control theory, singular controls.
    The primary factor limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy . In this work, the control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie techniques. A structural identfiability analysis is also presented, demonstrating that patient-specfic parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy.

  2. M. Sadeghi, M.A. Al-Radhawi, M. Margaliot, and E.D. Sontag. On the periodic gain of the Ribosome Flow Model. Technical report, bioRxiv 2018/507988, 2018. [PDF] Keyword(s): systems biology, biochemical networks, ribosomes, RFM.
    We consider a compartmental model for ribosome flow during RNA translation, the Ribosome Flow Model (RFM). This model includes a set of positive transition rates that control the flow from every site to the consecutive site. It has been shown that when these rates are time-varying and jointly T-periodic, the protein production rate converges to a unique T-periodic pattern. Here, we study a problem that can be roughly stated as: can periodic rates yield a higher average production rate than constant rates? We rigorously formulate this question and show via simulations, and rigorous analysis in one simple case, that the answer is no.



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