Symmetry invariance for adapting biological systems

SIAM Journal on Applied Dynamical Systems

Volumn 10, Issue 3, 2011, Pages 857-886

  Shoval, Oren ^a   Alon, Uri ^a   Sontag, Eduardo ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Fold detection; Input transformations; Scale invariance

Indexed keywords

BACTERIAL CHEMOTAXIS; EQUIVARIANCE; FOLD-DETECTION; GENERAL CLASS; INPUT TRANSFORMATION; SCALE INVARIANCE; SENSORY SYSTEM; SIGNAL TRANSDUCTION MECHANISM; SIMPLE SYSTEM;

BIOCHEMISTRY; DYNAMICAL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS;

SIGNAL TRANSDUCTION;

EID: 80054991400     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/100818078     Document Type: Article

References (49)

1. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman & Hall, Boca Raton, FL, 2006.
2. L. Bleris, Z. Xie, D. Glass, A. Adadey, E. D. Sontag, and Y. Benenson, Synthetic incoherent feed-forward circuits show adaptation to the amount of their genetic template, Molecular Syst. Biol., 7 (2011).
3. C. Cohen-Saidon, A. A. Cohen, A. Sigal, Y. Liron, and U. Alon, Dynamics and variability of ERK2 response to EGF in individual living cells, Molecular Cell, 36 (2009), pp. 885-893.
4. A. Cournac and J. A. Sepulchre, Simple molecular networks that respond optimally to time-periodic stimulation, BMC Syst. Biol., 3 (2009), p. 29.
5. H. El-Samad, J. P. Goff, and M. Khammash, Calcium homeostasis and parturient hypocalcemia: An integral feedback perspective, J. Theoret. Biol., 214 (2002), pp. 17-29.
6. L. Evans, Partial Differential Equations, AMS, Providence, RI, 1998.
7. B. A. Francis and W. M. Wonham, The internal model principle for linear multivariable regulators, Appl. Math. Optim., 2 (1975), pp. 170-194.
8. L. Goentoro and M. W. Kirschner, Evidence that fold-change, and not absolute level, of β-catenin dictates Wnt signaling, Molecular Cell, 36 (2009), pp. 872-884.
9. L. Goentoro, O. Shoval, M. W. Kirschner, and U. Alon, The incoherent feedforward loop can provide fold-change detection in gene regulation, Molecular Cell, 36 (2009), pp. 894-899.
10. M. Golubitsky and I. Stewart, The Symmetry Perspective, Birkḧauser Verlag, Basel, 2002.
11. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
12. G. Hornung and N. Barkai, Noise propagation and signaling sensitivity in biological networks: A role for positive feedback, PLoS Comput. Biol., 4 (2008), p. e8.
13. P. Iglesias, Personal communication, 2010.
14. A. Isidori, Nonlinear Control Systems, 3rd ed., Springer, London, 1995.
15. D. Kim, Y. K. Kwon, and K. H. Cho, The biphasic behavior of incoherent feed-forward loops in biomolecular regulatory networks, Bioessays, 30 (2008), pp. 1204-1211.
16. A. Kremling, K. Bettenbrock, and E. D. Gilles, A feed-forward loop guarantees robust behavior in escherichia coli carbohydrate uptake, Bioinformatics, 24 (2008), pp. 704-710. (Pubitemid 351321215)
17. M. D. Lazova, T. Ahmed, D. Bellomo, R. Stocker, and T. S. Shimizu, Response-rescaling in bacterial chemotaxis, Proc. Natl. Acad. Sci. USA, in press.
18. A. Levchenko and P. A. Iglesias, Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils, Biophys J., 82 (2002), pp. 50-63. (Pubitemid 34289781)
19. D. Liberzon, A. S. Morse, and E. D. Sontag, Output-input stability and minimum-phase nonlinear systems, IEEE Trans. Automat. Control, 47 (2002), pp. 422-436. (Pubitemid 34531046)
20. A. Ma'ayan, S. L. Jenkins, S. Neves, A. Hasseldine, E. Grace, B. Dubin-Thaler, N. J. Eu-ngdamrong, G. Weng, P. T. Ram, J. J. Rice, A. Kershenbaum, G. A. Stolovitzky, R. D. Blitzer, and R. Iyengar, Formation of regulatory patterns during signal propagation in a Mammalian cellular network, Science, 309 (2005), pp. 1078-1083. (Pubitemid 41134466)
21. M. P. Mahaut-Smith, S. J. Ennion, M. G. Rol f, and R. J. Evans, ADP is not an agonist at P2X(1) receptors: Evidence for separate receptors sti mulated by ATP and ADP on human platelets, Br. J. Pharmacol., 131 (2000), pp. 108-114.
22. S. Mangan, S. Itzkovitz, A. Zaslaver, and U. Alon, The incoherent feed-forward loop accelerates the response-time of the gal system of Escherichia coli, J. Mol. Biol., 356 (2006), pp. 1073-1081. (Pubitemid 43199913)
23. S. Marsigliante, M. G. Elia, B. Di Jeso, S. Greco, A. Muscella, and C. Storelli, Increase of [Ca(2+)](i) via activation of ATP receptors in PC-Cl3 rat thyroid cel l line, Cell. Signal., 14 (2002), pp. 61-67. (Pubitemid 34020830)
24. P. Meǹe, G. Pugliese, F. Pricci, U. Di Mario, G. A. Cinotti, and F. Pugliese, High glucose level inhibits capacitative Ca2+ influx in cultured rat mesangial cells by a protein kinase C-dependent mechanism, Diabetologia, 40 (1997), pp. 521-527. (Pubitemid 27186787)
25. P. Miller and X. J. Wang, Inhibitory control by an integral feedback signal in prefrontal cortex: A model of discrimination between sequential stimuli, P roc. Natl. Acad. Sci. USA, 103 (2006), pp. 201-206. (Pubitemid 43078507)
26. T. Nagano, Linear differential systems with singularities and an application to transitive lie algebras, J. Math. Soc. Japan, 18 (1966), pp. 398-404.
27. T. Nagashima, H. Shimodaira, K. Ide, T. Nakakuki, Y. Tani, K. Takahashi, N. Yumoto, and M. Hatakeyama, Quantitative transcriptional control of ErbB receptor signaling undergoes graded to biphasic response for cell differentiation, J. Biol. Chem., 282 (2007), pp. 4045-4056. (Pubitemid 47084498)
28. R. Nesher and E. Cerasi, Modeling phasic insulin release: Immediate and time-dependent effects of glucose, Diabetes, 51 (Suppl 1) (2002), pp. S53-59. (Pubitemid 34761495)
29. L. A. Ridnour, A. N. Windhausen, J. S. Isenberg, N. Yeung, D. D. Thomas, M. P. Vitek, D. D. Roberts, and D. A. Wink, Nitric oxide reg ulates matrix metalloproteinase-9 activity by guanylyl-cyclase-dependent and-independent pathways, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 16898-16903. (Pubitemid 350210962)
30. S. Sasagawa, Y. Ozaki, K. Fujita, and S. Kuroda, Prediction and validation of the distinct dynamics of transient and sustained ERK activation, Nat. Cell Biol., 7 (2005), pp. 365-373. (Pubitemid 40533125)
31. S. Semsey, S. Krishna, K. Sneppen, and S. Adhya, Signal integration in the galactose network of Escherichia coli, Mol. Microbiol., 65 (2007), pp. 465-476. (Pubitemid 47052727)
32. O. Shoval, L. Goentoro, Y. Hart, A. Mayo, E. D. Sontag, and U. Alon, Fold change detection and scalar symmetry of sensory input fields, Proc. Natl. Acad. Sci. USA, 107 (2010), pp. 15995-16000.
33. M. Skataric and E. D. Sontag, Fold change detection in 3-node enzymatic networks, in preparation.
34. E. D. Sontag, Polynomial Response Maps, Lect ure Notes in Control Inform. Sci. 13, Springer-Verlag, Berlin, 1979.
35. E. D. Sontag, Spaces of observables in nonlinear control, in Proceedings of the International Congress of Mathematicians, Vol. 1-2 (Zürich, 1994), B irkḧauser, Basel, 1995, pp. 1532-1545.
36. E. D. Sontag, Mathematical Control Theory. De terministic Finite-Dimensional Systems, 2nd ed., Texts Appl. Math. 6, Springer-Verlag, New York, 1998.
37. E. D. Sontag, Adaptation and regulation with signal detection implies internal model, Systems Control Lett., 50 (2003), pp. 119-126.
38. E. D. Sontag, Remarks on feedforward circuits, adaptation, and pulse memory, IET Systems Biology, 4 (2010), pp. 39-51.
39. H. J. Sussmann, Existence and uniqueness of minimal realizations of nonlinear systems, Math. Systems Theory, 10 (1977), pp. 263-284.
40. J. Tsang, J. Zhu, and A. van Oudenaarden, M icroRNA-mediated feedback and feedforward loops are recurrent network motifs in mammals, Mol. C ell, 26 (2007), pp. 753-767. (Pubitemid 46856248)
41. Y. Tu, T. S. Shimizu, and H. C. Berg, Modeling the chemotactic response of Escherichia coli to time-varying stimuli, Proc. Natl. Acad. Sci. USA, 105 (2008), pp. 14855-14860.
42. J. J. Tyson, K. Chen, and B. Novak, Sniffers, buzzers, toggles, and blinkers: Dynamics of regulatory and signaling pathways in the cell, Curr. Opin. Cell. Biol., 15 (2003), pp. 221-231. (Pubitemid 36332198)
43. K. V. Venkatesh, S. Bhartiya, and A. Ruhela, Mulitple feedback loops are key to a robust dynamic performance of tryptophan regulation in Escherichia coli, FEBS Letters, 563 (2004), pp. 234-240. (Pubitemid 38471605)
44. E. Voit, A. R. Neves, and H. Santos, The intricate side of systems biology, Proc. Natl. Acad. Sci. USA, 103 (2006), pp. 9452-9457.
45. M. E. Wall, M. J. Dunlop, and W. S. Hla vacek, Multiple functions of a feed-forward-loop gene circuit, J. Mol. Biol., 349 (2005), pp. 501-514. (Pubitemid 40724561)
46. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, 3rd ed., Springer-Verlag, New York, 1985.
47. F.-D. Xu, Z.-R. Liu, Z.-Y. Zhang, and J.-W. Shen, Robust and adaptive microRNA-mediated incoherent feedforward motifs, Chinese Physics Letters, 26 (2009), 028701.
48. L. Yang and P. A. Iglesias, Positive feedback may cause the biphasic response observed in the chemoattractant-induced response of dictyostelium cells, Systems Control Lett., 55 (2006), pp. 329-337. (Pubitemid 43242962)
49. T. M. Yi, Y. Huang, M. I. Simon, and J. Doyle, Robust perfect adaptation in bacterial chemotaxis through integral feedback control, Proc. Natl. A cad. Sci. USA, 97 (2000), pp. 4649-4653. (Pubitemid 30238612)