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Publications about 'futile cycles'
Articles in journal or book chapters
  1. J. Barton and E.D. Sontag. The energy costs of insulators in biochemical networks. Biophysical Journal, 104:1390-1380, 2013. [PDF]
    Abstract:
    Complex networks of biochemical reactions, such as intracellular protein signaling pathways and genetic networks, are often conceptualized in terms of ``modules,'' semi-independent collections of components that perform a well-defined function and which may be incorporated in multiple pathways. However, due to sequestration of molecular messengers during interactions and other effects, collectively referred to as retroactivity, real biochemical systems do not exhibit perfect modularity. Biochemical signaling pathways can be insulated from impedance and competition effects, which inhibit modularity, through enzymatic ``futile cycles'' which consume energy, typically in the form of ATP. We hypothesize that better insulation necessarily requires higher energy consumption. We test this hypothesis through a combined theoretical and computational analysis of a simplified physical model of covalent cycles, using two innovative measures of insulation, as well as a new way to characterize optimal insulation through the balancing of these two measures in a Pareto sense. Our results indicate that indeed better insulation requires more energy. While insulation may facilitate evolution by enabling a modular ``plug and play'' interconnection architecture, allowing for the creation of new behaviors by adding targets to existing pathways, our work suggests that this potential benefit must be balanced against the metabolic costs of insulation necessarily incurred in not affecting the behavior of existing processes.


  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. Angeli, P. de Leenheer, and E.D. Sontag. Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates. J. Mathematical Biology, 61:581-616, 2010. [PDF] Keyword(s): biochemical networks, fluxes, monotone systems, reaction cordinates, Petri nets, persistence, futile cycles.
    Abstract:
    This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it investigates their monotonicity and convergence without making assumptions on the form of the kinetics (e.g., mass-action) of the dynamical equations involved, and relying only on stoichiometric constraints. The key idea is to find an alternative representation under which the resulting system is monotone. As a simple example, the paper shows that a phosphorylation/dephosphorylation process, which is involved in many signaling cascades, has a global stability property.


  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. Angeli and E.D. Sontag. Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles. Nonlinear Analysis Series B: Real World Applications, 9:128-140, 2008. [PDF] [doi:10.1016/j.nonrwa.2006.09.006] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    Strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a global convergence property.


  6. 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.


  7. L. Wang and E.D. Sontag. On the number of steady states in a multiple futile cycle. Journal of Mathematical Biology, 57:29-52, 2008. [PDF] Keyword(s): singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, multistability.
    Abstract:
    This note studies the number of positive steady states in biomolecular reactions consisting of activation/deactivation futile cycles, such as those arising from phosphorylations and dephosphorylations at each level of a MAPK cascade. It is shown that: (1) for some parameter ranges, there are at least n+1 (if n is even) or n (if n is odd) steady states; (2) there never are more than 2n-1 steady states (so, for n=2, there are no more than 3 steady states); (3) for parameters near the standard Michaelis-Menten quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten quasi-steady state conditions, there is at most one steady state.


  8. L. Wang and E.D. Sontag. Singularly perturbed monotone systems and an application to double phosphorylation cycles. J. Nonlinear Science, 18:527-550, 2008. [PDF] Keyword(s): singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, multistability, monotone systems.
    Abstract:
    The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation "futile cycle" motif which plays a central role in eukaryotic cell signaling.


  9. D. Angeli, P. de Leenheer, and E.D. Sontag. A Petri net approach to the study of persistence in chemical reaction networks. Mathematical Biosciences, 210:598-618, 2007. Note: Please look at the paper ``A Petri net approach to persistence analysis in chemical reaction networks'' for additional results, not included in the journal paper due to lack of space. See also the preprint: arXiv q-bio.MN/068019v2, 10 Aug 2006. [PDF] Keyword(s): Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles.
    Abstract:
    Persistency is the property, for differential equations in Rn, that solutions starting in the positive orthant do not approach the boundary. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.


Conference articles
  1. 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.


  2. D. Angeli, P. de Leenheer, and E.D. Sontag. Petri nets tools for the analysis of persistence in chemical networks. In Proc. 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), Pretoria, South Africa, 22-24 August, 2007, 2007. Keyword(s): Petri nets, systems biology, biochemical networks, nonlinear stability, dynamical systems, futile cycles.


  3. L. Wang and E.D. Sontag. Further results on singularly perturbed monotone systems, with an application to double phosphorylation cycles. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007, pages 627-632, 2007. Note: Conference version of Singularly perturbed monotone systems and an application to double phosphorylation cycles.Keyword(s): singular perturbations, futile cycles, MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, multistability, monotone systems.


  4. D. Angeli and E.D. Sontag. A note on monotone systems with positive translation invariance. In Control and Automation, 2006. MED '06. 14th Mediterranean Conference on, 28-30 June 2006, pages 1-6, 2006. IEEE. Note: Available from ieeexplore.ieee.org. [PDF] [doi:10.1109/MED.2006.3287822B2B2B2B2B2B] Keyword(s): systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems.
    Abstract:
    Strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a global convergence property.


Internal reports
  1. J. Barton and E.D. Sontag. Remarks on the energy costs of insulators in enzymatic cascades. Technical report, http://arxiv.org/abs/1412.8065, December 2014. [PDF] Keyword(s): retroactivity, systems biology, biochemical networks, futile cycles, singular perturbations, modularity.
    Abstract:
    The connection between optimal biological function and energy use, measured for example by the rate of metabolite consumption, is a current topic of interest in the systems biology literature which has been explored in several different contexts. In [J. P. Barton and E. D. Sontag, Biophys. J. 104, 6 (2013)], we related the metabolic cost of enzymatic futile cycles with their capacity to act as insulators which facilitate modular interconnections in biochemical networks. There we analyzed a simple model system in which a signal molecule regulates the transcription of one or more target proteins by interacting with their promoters. In this note, we consider the case of a protein with an active and an inactive form, and whose activation is controlled by the signal molecule. As in the original case, higher rates of energy consumption are required for better insulator performance.


  2. J. Barton and E.D. Sontag. The energy costs of biological insulators. Technical report, http://arxiv.org/abs/1210.3809, October 2012. Keyword(s): retroactivity, systems biology, biochemical networks, futile cycles, singular perturbations, modularity.
    Abstract:
    Biochemical signaling pathways can be insulated from impedance and competition effects through enzymatic "futile cycles" which consume energy, typically in the form of ATP. We hypothesize that better insulation necessarily requires higher energy consumption, and provide evidence, through the computational analysis of a simplified physical model, to support this hypothesis.



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