Abstract
Multisite modifications are widely recognized as an essential feature of many switch-like responses in signal transduction. It is usually assumed that the modification of one site directly or indirectly increases the rate of modification of neighboring sites. In this paper we provide a new set of assumptions for a multisite system to become highly ultrasensitive even in the absence of cooperativity or allostery. We assume that the individual sites are modified independently of each other, and that protein activity is an ultrasensitive function of the fraction of modified sites. These assumptions are particularly useful in the context of multisite systems with a large (8+) number of sites. We estimate the apparent Hill coefficient of the dose responses in the sequential and nonsequential cases, highlight their different qualitative properties, and discuss a formula to approximate dose responses in the nonsequential case. As an example we describe a model of bacterial chemotaxis that features robust ultrasensitivity and perfect adaptation over a wide range of ligand concentrations, based on non-allosteric multisite behavior at the level of receptors and flagella. We also include a model of the inactivation of the yeast pheromone protein Ste5 by cell cycle proteins.
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References
Baker M, Wolanin P, Stock J (2006) Signal transduction in bacterial chemotaxis. Bioessays 28:9–22
Bardwell L (2004) A walk-through of the yeast mating pheromone response pathway. Peptides 25(9):1465–1476
Beard D, Qian H (2008) Chemical biophysics: quantitative analysis of cellular systems. Cambridge University Press, Cambridge
Bernstein S (1912–1913) Demonstration du théorème de Weierstrass, fondée sur le calcul des probabilités. Comm Kharkov Math Soc 13:1–2
Chan C, Liu X, Wang L, Bardwell L, Nie Q, Enciso G (2012) Protein scaffolds can enhance the bistability of multisite phosphorylation. PLoS Comp Biol 8:1–9
Cornish-Bowden A (1979) Fundamentals of enzyme kinetics, chapter 8. Butterworth & Co. Ltd., London
Danos V, Feret J, Fontana W, Harmer R, Krivine J (2010) Abstracting the differential semantics of rule-based models: exact and automated model reduction. Annual IEEE Symp Logic Comp Sci
Dohlman H (2002) G proteins and pheromone signaling. Annu Rev Physiol 64:129–152
Duke T, Novère NL, Bray D (2001) Conformational spread in a ring of proteins: a stochastic approach to allostery. J Mol Biol 308:541–553
Enciso G (2013) Multisite mechanisms for ultrasensitivity in signal transduction. In: Poetsche C, Kloeden P (eds) Nonautonomous and random dynamical systems in life sciences. Lecture notes in mathematical biology. Springer, Berlin
Ferrell J (1996) Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem Sci 21(12):460–466
Ferrell J (2009) Q &A: Cooperativity. J Biol 8:53.1-53.6
Ghaemmaghami S, Huh W, Bower K, Howson R, Belle A, Dephoure N, O’Shea E, Weissman J (2003) Global analysis of protein expression in yeast. Nature 425:737–741
Goldbeter A, Koshland D (1981) An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci USA 78(11):6840–6844
Goldbeter A, Koshland D (1984) Ultrasensitivity in biochemical systems controlled by covalent modification: interplay between zero-order and multistep effects. J Biol Chem 259(14):441–447
Gunawardena J (2005) Multisite protein phosphorylation makes a good threshold but can be a poor switch. Proc Natl Acad Sci USA 102(41):14,617–14,622
Hansen C, Sourjik V, Wingreen N (2010) A dynamic signaling-team model for chemotaxis receptors in Escherichia coli. Proc Natl Acad Sci USA 107:17,170–17,175
Harmer R, Danos V, Feret J, Krivine J, Fontana W (2010) Intrinsic information carriers in combinatorial dynamical systems. Chaos 20(037):108
Herzog F, Hill J (1946) The Bernstein polynomials for discontinuous functions. Am J Math 68(1):109–124
Huang C, Ferrell J (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc Natl Acad Sci USA 93:10,078–10,083
Iakoucheva L, Radivojac P, Brown C, O’Connor T, Sikes J, Obradovic Z, Dunker A (2004) The importance of intrinsic disorder for protein phosphorylation. Nucl Acids Res 32:1037–1049
Keener J, Sneyd J (2008) Mathematical physiology. Cellular physiology, vol I. Springer, Berlin
Koshland D, Nemethy G, Filmer D (1966) Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry 5:365–385
Lenz P, Swain P (2006) An entropic mechanism to generate highly cooperative and specific binding from protein phosphorylations. Curr Biol 16:2150–2155
Levchenko A (2003) Allovalency: A case of molecular entanglement. Curr Biol 13:R876–R878
Liu X, Bardwell L, Nie Q (2010) A combination of multisite phosphorylation and substrate sequestration produces switch-like responses. Biophys J 98(8):1396–1407
Malleshaiah MK, Shahrezaei V, Swain PS, Michnick SW (2010) The scaffold protein ste5 directly controls a switch-like mating decision in yeast. Nature 465(7294):101–105
McLaughlin S, Aderem A (1995) The myristoyl-electrostatic switch: a modulator of reversible protein-membrane interactions. Trends Biochem Sci 20:272–276
Monod J, Wyman J, Changeux J (1965) On the nature of allosteric transitions: a plausible model. J Mol Biol 12:88–118
Murray D, Hermida-Matsumoto L, Buser C, Tsang J (1998) Electrostatics and the membrane association of Src: theory and experiment. Biochemistry 37:2145–2159
Ogawa S, McConnell H (1967) Spin-label study of hemoglobin conformations in solution. Proc Natl Acad Sci USA 58:19–26
O’Shaughnessy E, Palani S, Collins J, Sarkar C (2011) Tunable signal processing in synthetic map kinase cascades. Cell 144:119–131
Pryciak P, Huntress F (1998) Membrane recruitment of the kinase cascade scaffold protein Ste5 by the Gbeta gamma complex underlies activation of the yeast pheromone response pathway. Genes Dev 12(17):2684–2697
Rivlin T (2003) An introduction to the approximation of functions, chapter 1. Dover Phoenix Editions. Dover Publications, Dover
Ryerson S, Enciso G (2013) Site variability in a multisite, signal transduction system (to appear)
Serber Z, Ferrell J (2007) Tuning bulk electrostatics to regulate protein function. Cell 128(3):441–444
Sourjik V, Berg H (2004) Functional interactions between receptors in bacterial chemotaxis. Nature 428:437–441
Spiro P, Parkinson J, Othmer H (1997) A model of excitation and adaptation in bacterial chemotaxis. Proc Natl Acad Sci USA 94(14):7263–7268
Strickfaden S, Winters M, Ben-Ari G, Lamson R, Tyers M, Pryciak P (2007) A mechanism for cell-cycle regulation of MAP kinase signaling in a yeast differentiation pathway. Cell 128(3):519–531
Tindall M, Porter S, Maini P, Gaglia G, Armitage J (2008) Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell. Bull Math Biol 70:1525–1569
Wadhams G, Armitage J (2004) Making sense of it all: bacterial chemotaxis. Nat Rev Mol Cell Biol 5(12):1024–1037
Wang L, Nie Q, Enciso G (2010) Nonessential sites improve phosphorylation switch. Biophys J 99(6):L41–L43
Yi TM, Huang Y, Simon M, Doyle J (2000) Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proc Natl Acad Sci USA 97(9):4649–4653
Acknowledgments
We would like to thank Ned Wingreen for discussions and criticism, and Uri Alon for useful comments and advice. This material is based upon work supported by the National Science Foundation under Grants Nos. DMS-1122478 and 1129008.
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Ryerson, S., Enciso, G.A. Ultrasensitivity in independent multisite systems. J. Math. Biol. 69, 977–999 (2014). https://doi.org/10.1007/s00285-013-0727-x
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DOI: https://doi.org/10.1007/s00285-013-0727-x
Keywords
- Multisite system
- Phosphorylation
- Signal transduction
- Ultrasensitivity
- Cooperativity
- Allostery
- Bacterial chemotaxis