Study of spatial signal transduction in bistable switches

Abstract

Bistable switch modules are among the most important fundamental motifs in signal-transduction pathways. To better understand their spatial signal transduction, we model the diffusion process in the one-dimensional (1–D) domain. We find that when none of the elements diffuse, the response of the system exhibits a spatial switch–like property. However, when one of the elements is highly diffusible, the response of the system does not show any spatial switching behavior. Furthermore, we observe that the spatial responses of the system are more sensitive to the time constant of the switch when none of the elements are diffusible. Further, a slow loop keeps the system in the high steady state more positions than that in the fast loop. Finally, we consolidate our numerical results analytically by performing a mathematical method.

Keywords

signal processing / reaction–diffusion model / nonlinear dynamics / spatial switch

References

[1] B. D. Gomperts, I. M. Kramer, and P. E. R. Tatham, Signal Transduction, London: Academic Press, 2009

[2] S. Liu, Z. W. He, and M. Zhan, Firing rates of coupled noisy excitable elements, Front. Phys. 9(1), 127 (2014)

[3] B. N. Kholodenko, Cell-signalling dynamics in time and space, Nat. Rev. Mol. Cell Biol. 7(3), 165 (2006)

[4] M. Freeman, Feedback control of intercellular signalling in development, Nature 408(6810), 313 (2000)

[5] J. E. Ferrell and W. Xiong, Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible, Chaos 11(1), 227 (2001)

[6] J. E. Jr Ferrell, Self-perpetuating states in signal transduction: Positive feedback, double-negative feedback and bistability, Curr. Opin. Cell Biol. 14(2), 140 (2002)

[7] N. I. Markevich, J. B. Hoek, and B. N. Kholodenko, Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades, J. Cell Biol. 164(3), 353 (2004)

[8] J. E. Jr Ferrell and E. M. Machleder, The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes, Science 280(5365), 895 (1998)

[9] W. Xiong and J. E. Jr Ferrell, A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision, Nature 426(6965), 460 (2003)

[10] A. Abrieu, M. Dorée, and D. Fisher, The interplay between cyclin-B-Cdc2 kinase (MPF) and MAP kinase during maturation of oocytes, J. Cell. Sci. 114(Pt 2), 257 (2001)

[11] R. Wedlich-Soldner, S. C. Wai, T. Schmidt, and R. Li, Robust cell polarity is a dynamic state established by coupling transport and GTPase signaling, J. Cell Biol. 166(6), 889 (2004)

[12] J. R. Pomerening, E. D. Sontag, and J. E. Jr Ferrell, Building a cell cycle oscillator: Hysteresis and bistability in the activation of Cdc2, Nat. Cell Biol. 5(4), 346 (2003)

[13] C. Y. Huang and J. E. Jr Ferrell, Ultrasensitivity in the mitogen-activated protein kinase cascade, Proc. Natl. Acad. Sci. USA 93(19), 10078 (1996)

[14] J. E. Jr Ferrell, How responses get more switch-like as you move down a protein kinase cascade, Trends Biochem. Sci. 22(8), 288 (1997)

[15] B. N. Kholodenko, Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades, Eur. J. Biochem. 267(6), 1583 (2000)

[16] A. Vaknin and H. C. Berg, Single-cell FRET imaging of phosphatase activity in the Escherichia coli chemotaxis system, Proc. Natl. Acad. Sci. USA 101(49), 17072 (2004)

[17] P. Kalab, K. Weis, and R. Heald, Visualization of a Ran-GTP gradient in interphase and mitotic Xenopus egg extracts, Science 295(5564), 2452 (2002)

[18] P. Niethammer, P. Bastiaens, and E. Karsenti, Stathmin-tubulin interaction gradients in motile and mitotic cells, Science 303(5665), 1862 (2004)

[19] Q. Zhao, M. Yi, and Y. Liu, Spatial distribution and dose-response relationship for different operation modes in a reaction-diffusion model of the MAPK cascade, Phys. Biol. 8(5), 055004 (2011)

[20] M. Yi, Q. Zhao, J. Tang, and C. Wang, A theoretical modeling for frequency modulation of Ca²⁺ signal on activation of MAPK cascade, Biophys. Chem. 157(1-3), 33 (2011)

[21] R. Rappaport, Cytokinesis in animal cells, Int. Rev. Cytol. 31, 169 (1971)

[22] W. J. Nelson, Adaptation of core mechanisms to generate cell polarity, Nature 422(6933), 766 (2003)

[23] I. V. Maly, H. S. Wiley, and D. A. Lauffenburger, Self-organization of polarized cell signaling via autocrine circuits: computational model analysis, Biophys. J. 86(1 Pt 1), 10 (2004)

[24] A. S. Howell, N. S. Savage, S. A. Johnson, I. Bose, A. W. Wagner, T. R. Zyla, H. F. Nijhout, M. C. Reed, A. B. Goryachev, and D. J. Lew, Singularity in polarization: rewiring yeast cells to make two buds, Cell 139(4), 731 (2009)

[25] P. A. Fletcher, Y. X. Li, and M. D. Bootman, An integrated model of electrical spiking, bursting, and calcium oscillations in GnRH neurons, Biophys. J. 96(11), 4514 (2009)

[26] M. J. Berridge, P. Lipp, and M. D. Bootman, The versatility and universality of calcium signalling, Nat. Rev. Mol. Cell Biol. 1(1), 11 (2000)

[27] N. I. Markevich, M. A. Tsyganov, J. B. Hoek, and B. N. Kholodenko, Long-range signaling by phosphoprotein waves arising from bistability in protein kinase cascades, Mol. Syst. Biol. 2, 61 (2006)

[28] S. B. van Albada and P. R. ten Wolde, Enzyme localization can drastically affect signal amplification in signal transduction pathways, PLoS Comput. Biol. 3(10), 1925 (2007)

[29] A. Alam-Nazki and J. Krishnan, An investigation of spatial signal transduction in cellular networks, BMC Syst. Biol. 6, 83 (2012)

[30] O. Brandman, J. E. Jr Ferrell, R. Li, and T. Meyer, Interlinked fast and slow positive feedback loops drive reliable cell decisions, Science 310(5747), 496 (2005)

[31] X. P. Zhang, Z. Cheng, F. Liu, and W. Wang, Linking fast and slow positive feedback loops creates an optimal bistable switch in cell signaling, Phys. Rev. E 76(3 Pt 1), 031924 (2007)

[32] G. C. Brown and B. N. Kholodenko, Spatial gradients of cellular phospho-proteins, FEBS Lett. 457(3), 452 (1999)

[33] J. D. Murray, Mathematical Biology, New York: Springer, 2008

[34] B. Kazmierczak and T. Lipniacki, Regulation of kinase activity by diffusion and feedback, J. Theor. Biol. 259(2), 291 (2009)

[35] B. Kazmierczak and T. Lipniacki, Spatial gradients in kinase cascade regulation, IET Syst. Biol. 4(6), 348 (2010)

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Higher Education Press and Springer-Verlag Berlin Heidelberg