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Publications about 'Biological systems'
Articles in journal or book chapters
  1. 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.


  2. 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): singular perturbations, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection.
    Abstract:
    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.


  3. O. Shoval, U. Alon, and E.D. Sontag. Symmetry invariance for adapting biological systems. SIAM Journal on Applied Dynamical Systems, 10:857-886, 2011. Note: See here for a small typo: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/shoval.alon.sontag.erratum.pdf.[PDF] Keyword(s): adaptation, feedforward loops, integral feedback, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection.
    Abstract:
    Often, the ultimate goal of regulation is to maintain a narrow range of concentration levels of vital quantities (homeostasis, adaptation) while at the same time appropriately reacting to changes in the environment (signal detection or sensitivity). Much theoretical, modeling, and analysis effort has been devoted to the understanding of these questions, traditionally in the context of steady-state responses to constant or step-changing stimuli. In this paper, we present a new theorem that provides a necessary and sufficient characterization of invariance of transient responses to symmetries in inputs. A particular example of this property, scale invariance (a.k.a. "fold change detection"), appears to be exhibited by biological sensory systems ranging from bacterial chemotaxis pathways to signal transduction mechanisms in eukaryotes. The new characterization amounts to the solvability of an associated partial differential equation. It is framed in terms of a notion which considerably extends equivariant actions of compact Lie groups. For several simple system motifs that are recurrent in biology, the solvability criterion may be checked explicitly.


  4. E.D. Sontag. Remarks on Feedforward Circuits, Adaptation, and Pulse Memory. IET Systems Biology, 4:39-51, 2010. [PDF] Keyword(s): adaptation, feedforward loops, integral feedback, systems biology, transient behavior.
    Abstract:
    This note studies feedforward circuits as models for perfect adaptation to step signals in biological systems. A global convergence theorem is proved in a general framework, which includes examples from the literature as particular cases. A notable aspect of these circuits is that they do not adapt to pulse signals, because they display a memory phenomenon. Estimates are given of the magnitude of this effect.


  5. E.D. Sontag. Monotone and near-monotone biochemical networks. Systems and Synthetic Biology, 1:59-87, 2007. [PDF] [doi:10.1007/s11693-007-9005-9] Keyword(s): systems biology, biochemical networks, monotone systems, Ising spin models, nonlinear stability, dynamical systems, consistent graphs, gene networks.
    Abstract:
    This paper provides an expository introduction to monotone and near-monotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone. In addition, interconnections of monotone systems may be fruitfully analyzed using tools from control theory.


  6. D. Angeli, J. E. Ferrell, and E.D. Sontag. Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems.. Proc Natl Acad Sci USA, 101(7):1822-1827, 2004. Note: A revision of Suppl. Fig. 7(b) is here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/nullclines-f-g-REV.jpg; and typos can be found here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/angeli-ferrell-sontag-pnas04-errata.txt. [WWW] [PDF] [doi:10.1073/pnas.0308265100] Keyword(s): multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    Multistability is an important recurring theme in cell signaling, of particular relevance to biological systems that switch between discrete states, generate oscillatory responses, or "remember" transitory stimuli. Standard mathematical methods allow the detection of bistability in some very simple feedback systems (systems with one or two proteins or genes that either activate each other or inhibit each other), but realistic depictions of signal transduction networks are invariably much more complex than this. Here we show that for a class of feedback systems of arbitrary order, the stability properties of the system can be deduced mathematically from how the system behaves when feedback is blocked. Provided that this "open loop," feedback-blocked system is monotone and possesses a sigmoidal characteristic, the system is guaranteed to be bistable for some range of feedback strengths. We present a simple graphical method for deducing the stability behavior and bifurcation diagrams for such systems, and illustrate the method with two examples taken from recent experimental studies of bistable systems: a two-variable Cdc2/Wee1 system and a more complicated five-variable MAPK cascade.


  7. L. Moreau and E.D. Sontag. Balancing at the border of instability. Phys. Rev. E (3), 68(2):020901, 4, 2003. [PDF] Keyword(s): bifurcations, adaptive control.
    Abstract:
    Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the nervous system and hair cell oscillations in the auditory system. In both examples the question arises as to how the required fine-tuning may be achieved and maintained in a robust and reliable way. We study this question using tools from nonlinear and adaptive control theory. We illustrate our approach on a simple model which captures some of the essential features of neural integration. As a result, we propose a large class of feedback adaptation rules that may be responsible for the experimentally observed robustness of neural integration. We mention extensions of our approach to the case of hair cell oscillations in the ear.


Conference articles
  1. 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.


  2. M. Skataric, E.V. Nikolaev, and E.D. Sontag. Scale-invariance in singularly perturbed systems. In Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014, pages 3035-3040, 2014. [PDF] Keyword(s): singular perturbations, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection.
    Abstract:
    This conference paper (a) summarizes material from "A fundamental limitation to fold-change detection by biological systems with multiple time scales" (IET Systems Biology 2014) and presents additional remarks regarding (b) expansion techniques to compute FCD error and (c) stochastic adaptation and FCD


  3. M. Skataric and E.D. Sontag. Remarks on model-based estimation of nonhomogeneous Poisson processes and applications to biological systems. In Proc. European Control Conference, Strasbourg, France, June 2014, pages 2052-2057, 2014. [PDF] Keyword(s): systems biology, random dynamical systems.
    Abstract:
    This paper studies model-based estimation methods of a rate of a nonhomogeneous Poisson processes that describes events arising from modeling biological phenomena in which discrete events are measured. We describe an approach based on observers and Kalman filters as well as preliminary simulation results, and compare these to other methods (not model-based) in the literature. The problem is motivated by the question of identification of internal states from neural spikes and bacterial tumbling behavior.


  4. A. O. Hamadeh, E.D. Sontag, and B.P. Ingalls. Response time re-scaling and Weber's law in adapting biological systems. In Proc. American Control Conference, pages 4564-4569, 2013. [PDF] Keyword(s): scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, chemotaxis.
    Abstract:
    Recent experimental work has shown that transient E. coli chemotactic response is unchanged by a scaling of its ligand input signal (fold change detection, or FCD), and this is in agreement with earlier mathematical predictions. However, this prediction was based on certain particular assumptions on the structure of the chemotaxis pathway. In this work, we begin by showing that behavior similar to FCD can be obtained under weaker conditions on the system structure. Namely, we show that under relaxed conditions, a scaling of the chemotaxis system's inputs leads to a time scaling of the output response. We propose that this may be a contributing factor to the robustness of the experimentally observed FCD. We further show that FCD is a special case of this time scaling behavior for which the time scaling factor is unity. We then proceed to extend the conditions for output time scaling to more general adapting systems, and demonstrate this time scaling behavior on a published model of the chemotaxis pathway of the bacterium Rhodobacter sphaeroides. This work therefore provides examples of how robust biological behavior can arise from simple yet realistic conditions on the underlying system structure.


  5. O. Shoval, U. Alon, and E.D. Sontag. Input symmetry invariance, and applications to biological systems. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2011, pages TuA02.5, 2011. Keyword(s): adaptation, feedforward loops, integral feedback, scale invariance, systems biology, transient behavior, symmetries, fcd, fold-change detection, jump Markov processes.
    Abstract:
    This paper studies invariance with respect to symmetries in sensory fields, a particular case of which, scale invariance, has recently been found in certain eukaryotic as well as bacterial cell signaling systems. We describe a necessary and sufficient characterization of symmetry invariance in terms of equivariant transformations, show how this characterization helps find all possible symmetries in standard models of biological adaptation, and discuss symmetry-invariant searches.


  6. B. Andrews, E.D. Sontag, and P. Iglesias. An approximate internal model principle: Applications to nonlinear models of biological systems. In Proc. 17th IFAC World Congress, Seoul, pages Paper FrB25.3, 6 pages, 2008. [PDF] Keyword(s): biological adaptation, internal model principle.
    Abstract:
    The proper function of many biological systems requires that external perturbations be detected, allowing the system to adapt to these environmental changes. It is now well established that this dual detection and adaptation requires that the system have an internal model in the feedback loop. In this paper we relax the requirement that the response of the system adapt perfectly, but instead allow regulation to within a neighborhood of zero. We show, in a nonlinear setting, that systems with the ability to detect input signals and approximately adapt require an approximate model of the input. We illustrate our results by analyzing a well-studied biological system. These results generalize previous work which treats the perfectly adapting case.



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