Skip to main content
Log in

Mathematical Simulation of Membrane Protein Clustering for Efficient Signal Transduction

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Initiation and propagation of cell signaling depend on productive interactions among signaling proteins at the plasma membrane. These diffusion-limited interactions can be influenced by features of the membrane that introduce barriers, such as cytoskeletal corrals, or microdomains that transiently confine both transmembrane receptors and membrane-tethered peripheral proteins. Membrane topographical features can lead to clustering of receptors and other membrane components, even under very dynamic conditions. This review considers the experimental and mathematical evidence that protein clustering impacts cell signaling in complex ways. Simulation approaches used to consider these stochastic processes are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2
Figure 3

Similar content being viewed by others

References

  1. Abulrob, A., et al. Nanoscale imaging of epidermal growth factor receptor clustering: effects of inhibitors. J. Biol. Chem. 285(5):3145–3156, 2010.

    Article  PubMed  CAS  Google Scholar 

  2. Alberts, B. Molecular Biology of the Cell (5th ed.). New York: Garland Science, 2008. 1 v. (various pagings)

    Google Scholar 

  3. Allen, J. A., R. A. Halverson-Tamboli, and M. M. Rasenick. Lipid raft microdomains and neurotransmitter signalling. Nat. Rev. Neurosci. 8(2):128–140, 2007.

    Article  PubMed  CAS  Google Scholar 

  4. Andrews, S. S., and D. Bray. Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys. Biol. 1(3–4):137–151, 2004.

    Article  PubMed  CAS  Google Scholar 

  5. Auerbach, S. M. Theory and simulation of jump dynamics, diffusion and phase equilibrium in nanopores. Int. Rev. Phys. Chem. 19(2):155–198, 2000.

    Article  CAS  Google Scholar 

  6. Bader, A. N., et al. Homo-FRET imaging enables quantification of protein cluster sizes with subcellular resolution. Biophys. J. 97(9):2613–2622, 2009.

    Article  PubMed  CAS  Google Scholar 

  7. Brightman, F. A., and D. A. Fell. Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells. FEBS Lett. 482(3):169–174, 2000.

    Article  PubMed  CAS  Google Scholar 

  8. Brinkerhoff, C. J., P. J. Woolf, and J. J. Linderman. Monte Carlo simulations of receptor dynamics: insights into cell signaling. J. Mol. Histol. 35(7):667–677, 2004.

    Article  PubMed  Google Scholar 

  9. Brown, G. C., and B. N. Kholodenko. Spatial gradients of cellular phospho-proteins. FEBS Lett. 457(3):452–454, 1999.

    Article  PubMed  CAS  Google Scholar 

  10. Bublil, E. M., and Y. Yarden. The EGF receptor family: spearheading a merger of signaling and therapeutics. Curr. Opin. Cell Biol. 19(2):124–134, 2007.

    Article  PubMed  CAS  Google Scholar 

  11. Burrage, K., et al. Modelling and simulation techniques for membrane biology. Brief. Bioinform. 8(4):234–244, 2007.

    Article  PubMed  CAS  Google Scholar 

  12. Chakraborty, A. K., M. L. Dustin, and A. S. Shaw. In silico models for cellular and molecular immunology: successes, promises and challenges. Nat. Immunol. 4(10):933–936, 2003.

    Article  PubMed  CAS  Google Scholar 

  13. Chatterjee, A., et al. Time accelerated Monte Carlo simulations of biological networks using the binomial tau-leap method. Bioinformatics 21(9):2136–2137, 2005.

    Article  PubMed  CAS  Google Scholar 

  14. Chuan Kang, H., and W. Weinberg. Modeling the kinetics of heterogeneous catalysis. Chem. Rev. 95:667–676, 1995.

    Article  Google Scholar 

  15. Colicelli, J. Human RAS superfamily proteins and related GTPases. Sci. STKE 2004(250):RE13, 2004.

    Article  PubMed  Google Scholar 

  16. Coppens, M. O., A. T. Bell, and A. K. Chakraborty. Dynamic Monte-Carlo and mean-field study of the effect of strong adsorption sites on self-diffusion in zeolites. Chem. Eng. Sci. 54:3455–3463, 1999.

    Article  CAS  Google Scholar 

  17. Costa, M. N., K. Radhakrishnan, and J. S. Edwards. Monte Carlo simulations of plasma membrane corral-induced EGFR clustering. J. Biotechnol. 151(3):261–270, 2009.

    Article  Google Scholar 

  18. Costa, M. N., et al. Coupled stochastic spatial and non-spatial simulations of ErbB1 signaling pathways demonstrate the importance of spatial organization in signal transduction. PLoS ONE 4(7):e6316, 2009.

    Article  PubMed  Google Scholar 

  19. Erban, R., and S. J. Chapman. Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions. Phys. Biol. 6(4):046001, 2009.

    Article  PubMed  Google Scholar 

  20. Faeder, J., M. Blinov, and W. Hlavacek. Rules-based modeling of biochemical systems with BioNetGen. Methods Mol. Biol. 500:113–168, 2009.

    Article  PubMed  CAS  Google Scholar 

  21. Fallahi-Sichani, M., and J. J. Linderman. Lipid raft-mediated regulation of G-protein coupled receptor signaling by ligands which influence receptor dimerization: a computational study. PLoS ONE 4(8):e6604, 2009.

    Article  PubMed  Google Scholar 

  22. Friday, B. B., and A. A. Adjei. Advances in targeting the Ras/Raf/MEK/Erk mitogen-activated protein kinase cascade with MEK inhibitors for cancer therapy. Clin. Cancer Res. 14(2):342–346, 2008.

    Article  PubMed  CAS  Google Scholar 

  23. Fujioka, A., et al. Dynamics of the Ras/ERK MAPK cascade as monitored by fluorescent probes. J. Biol. Chem. 281(13):8917–8926, 2006.

    Article  PubMed  CAS  Google Scholar 

  24. Fuxe, K., and T. Kenakin. The changing world of G protein-coupled receptors. J. Recept. Signal Transduct. Res. 30(5):271, 2010.

    Article  PubMed  CAS  Google Scholar 

  25. Gibson, M. A., and J. Bruck. Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. 104:1876–1889, 2000.

    Article  CAS  Google Scholar 

  26. Gillespie, D. T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25):2340–2361, 1977.

    Article  CAS  Google Scholar 

  27. Gillespie, D. T. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58:35–55, 2007.

    Article  PubMed  CAS  Google Scholar 

  28. Gilmer, G. Computer models of crystal growth. Science 208:355–363, 1980.

    Article  PubMed  CAS  Google Scholar 

  29. Govindan, R. A review of epidermal growth factor receptor/HER2 inhibitors in the treatment of patients with non-small-cell lung cancer. Clin. Lung Cancer 11(1):8–12, 2010.

    Article  PubMed  CAS  Google Scholar 

  30. Grima, R., and S. Schnell. Modelling reaction kinetics inside cells. Essays Biochem. 45:41–56, 2008.

    Article  PubMed  CAS  Google Scholar 

  31. Hartman, N. C., and J. T. Groves. Signaling clusters in the cell membrane. Curr. Opin. Cell Biol. 23(4):370–376, 2011.

    Article  PubMed  CAS  Google Scholar 

  32. Hatakeyama, M., et al. A computational model on the modulation of mitogen-activated protein kinase (MAPK) and Akt pathways in heregulin-induced ErbB signalling. Biochem. J. 373(Pt 2):451–463, 2003.

    Article  PubMed  CAS  Google Scholar 

  33. Hlavacek, W., et al. Rules for modeling signal-transduction systems. Sci. STKE 2006:re6, 2006.

    Article  PubMed  Google Scholar 

  34. Hornberg, J. J., et al. Control of MAPK signalling: from complexity to what really matters. Oncogene 24(36):5533–5542, 2005.

    Article  PubMed  CAS  Google Scholar 

  35. Hsieh, M. Y., et al. Stochastic simulations of ErbB homo and heterodimerisation: potential impacts of receptor conformational state and spatial segregation. IET Syst. Biol. 2(5):256–272, 2008.

    Article  PubMed  Google Scholar 

  36. Hsieh, M. Y., et al. Spatio-temporal modeling of signaling protein recruitment to EGFR. BMC Syst. Biol. 4:57, 2010.

    Article  PubMed  Google Scholar 

  37. Hynes, N. E., and G. MacDonald. ErbB receptors and signaling pathways in cancer. Curr. Opin. Cell Biol. 21(2):177–184, 2009.

    Article  PubMed  CAS  Google Scholar 

  38. Insel, P. A., et al. Impact of GPCRs in clinical medicine: monogenic diseases, genetic variants and drug targets. Biochim. Biophys. Acta 1768(4):994–1005, 2007.

    Article  PubMed  CAS  Google Scholar 

  39. Keating, E., A. Nohe, and N. O. Petersen. Studies of distribution, location and dynamic properties of EGFR on the cell surface measured by image correlation spectroscopy. Eur. Biophys. J. 37(4):469–481, 2008.

    Article  PubMed  CAS  Google Scholar 

  40. Kholodenko, B. N., J. F. Hancock, and W. Kolch. Signalling ballet in space and time. Nat. Rev. Mol. Cell Biol. 11(6):414–426, 2010.

    Article  PubMed  CAS  Google Scholar 

  41. Kholodenko, B. N., et al. Quantification of short term signaling by the epidermal growth factor receptor. J. Biol. Chem. 274(42):30169–30181, 1999.

    Article  PubMed  CAS  Google Scholar 

  42. Kitaura, J., et al. Evidence that IgE molecules mediate a spectrum of effects on mast cell survival and activation via aggregation of the FcepsilonRI. Proc. Natl. Acad. Sci. USA 100(22):12911–12916, 2003.

    Article  PubMed  CAS  Google Scholar 

  43. Kusumi, A., et al. Paradigm shift of the plasma membrane concept from the two-dimensional continuum fluid to the partitioned fluid: high-speed single-molecule tracking of membrane molecules. Annu. Rev. Biophys. Biomol. Struct. 34:351–378, 2005.

    Article  PubMed  CAS  Google Scholar 

  44. Lambert, N. A. GPCR dimers fall apart. Sci. Signal. 3(115):pe12, 2010.

    Article  PubMed  Google Scholar 

  45. Li, H., et al. Algorithms and software for stochastic simulation of biochemical reacting systems. Biotechnol. Prog. 24(1):56–61, 2008.

    Article  PubMed  Google Scholar 

  46. Lidke, D. S., and B. S. Wilson. Caught in the act: quantifying protein behaviour in living cells. Trends Cell Biol. 19(11):566–574, 2009.

    Article  PubMed  CAS  Google Scholar 

  47. Lillemeier, B. F., et al. TCR and Lat are expressed on separate protein islands on T cell membranes and concatenate during activation. Nat. Immunol. 11(1):90–96, 2010.

    Article  PubMed  CAS  Google Scholar 

  48. Linderman, J. J. Modeling of G-protein-coupled receptor signaling pathways. J. Biol. Chem. 284(9):5427–5431, 2009.

    Article  PubMed  CAS  Google Scholar 

  49. Lo, H. W. Nuclear mode of the EGFR signaling network: biology, prognostic value, and therapeutic implications. Discov. Med. 10(50):44–51, 2010.

    PubMed  Google Scholar 

  50. Low-Nam, S. T., et al. ErbB1 dimerization is promoted by domain co-confinement and stabilized by ligand binding. Nat. Struct. Mol. Biol. 18(11):1244–1249, 2011.

    Article  PubMed  CAS  Google Scholar 

  51. Mayawala, K., C. A. Gelmi, and J. S. Edwards. MAPK cascade possesses decoupled controllability of signal amplification and duration. Biophys. J. 87(5):L01–L02, 2004.

    Article  PubMed  Google Scholar 

  52. Mayawala, K., D. G. Vlachos, and J. S. Edwards. Heterogeneities in EGF receptor density at the cell surface can lead to concave up scatchard plot of EGF binding. FEBS Lett. 579(14):3043–3047, 2005.

    Article  PubMed  CAS  Google Scholar 

  53. Mayawala, K., D. G. Vlachos, and J. S. Edwards. Computational modeling reveals molecular details of epidermal growth factor binding. BMC Cell Biol. 6:41, 2005.

    Article  PubMed  Google Scholar 

  54. Mayawala, K., D. G. Vlachos, and J. S. Edwards. Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations. Biophys. Chem. 121(3):194–208, 2006.

    Article  PubMed  CAS  Google Scholar 

  55. Miura, Y., K. Hanada, and T. L. Jones. G(s) signaling is intact after disruption of lipid rafts. Biochemistry 40(50):15418–15423, 2001.

    Article  PubMed  CAS  Google Scholar 

  56. Nagy, P., et al. Lipid rafts and the local density of ErbB proteins influence the biological role of homo- and heteroassociations of ErbB2. J. Cell Sci. 115(Pt 22):4251–4262, 2002.

    Article  PubMed  CAS  Google Scholar 

  57. Orton, R. J., et al. Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway. Biochem. J. 392(Pt 2):249–261, 2005.

    PubMed  CAS  Google Scholar 

  58. Pike, L. J. Lipid rafts: bringing order to chaos. J. Lipid Res. 44(4):655–667, 2003.

    Article  PubMed  CAS  Google Scholar 

  59. Plowman, S. J., et al. H-ras, K-ras, and inner plasma membrane raft proteins operate in nanoclusters with differential dependence on the actin cytoskeleton. Proc. Natl. Acad. Sci. USA 102(43):15500–15505, 2005.

    Article  PubMed  CAS  Google Scholar 

  60. Radhakrishnan, K. Combustion kinetics and sensitivity analysis. In: Numerical Approaches to Combustion Modeling, edited by E. S. Oran, and J. P. Boris. Washington, DC: AIAA, 1991, pp. 83–128.

    Google Scholar 

  61. Radhakrishnan, K., et al. Sensitivity analysis predicts that the ERK–pMEK interaction regulates ERK nuclear translocation. IET Syst. Biol. 3(5):329–341, 2009.

    Article  PubMed  CAS  Google Scholar 

  62. Radhakrishnan, K., et al. Quantitative understanding of cell signaling: the importance of membrane organization. Curr. Opin. Biotechnol. 21(5):677–682, 2010.

    Article  PubMed  CAS  Google Scholar 

  63. Reddy, A. S., S. Chilukuri, and S. Raychaudhuri. The network of receptors characterize B cell receptor micro- and macroclustering in a Monte Carlo model. J. Phys. Chem. B 114(1):487–494, 2010.

    Article  PubMed  CAS  Google Scholar 

  64. Resat, H., L. Petzold, and M. F. Pettigrew. Kinetic modeling of biological systems. Methods Mol. Biol. 541:311–335, 2009.

    Article  PubMed  CAS  Google Scholar 

  65. Rosenbaum, D. M., S. G. Rasmussen, and B. K. Kobilka. The structure and function of G-protein-coupled receptors. Nature 459(7245):356–363, 2009.

    Article  PubMed  CAS  Google Scholar 

  66. Saffarian, S., et al. Oligomerization of the EGF receptor investigated by live cell fluorescence intensity distribution analysis. Biophys. J. 93(3):1021–1031, 2007.

    Article  PubMed  CAS  Google Scholar 

  67. Santamaria, F., et al. Quantifying the effects of elastic collisions and non-covalent binding on glutamate receptor trafficking in the post-synaptic density. PLoS Comput. Biol. 6(5):e1000780, 2010.

    Article  PubMed  Google Scholar 

  68. Sasagawa, S., et al. Prediction and validation of the distinct dynamics of transient and sustained ERK activation. Nat. Cell Biol. 7(4):365–373, 2005.

    Article  PubMed  CAS  Google Scholar 

  69. Schoeberl, B., et al. Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat. Biotechnol. 20(4):370–375, 2002.

    Article  PubMed  Google Scholar 

  70. Shalom-Feuerstein, R., et al. K-ras nanoclustering is subverted by overexpression of the scaffold protein galectin-3. Cancer Res. 68(16):6608–6616, 2008.

    Article  PubMed  CAS  Google Scholar 

  71. Slepchenko, B. M., et al. Quantitative cell biology with the virtual cell. Trends Cell Biol. 13(11):570–576, 2003.

    Article  PubMed  CAS  Google Scholar 

  72. Suzuki, K., et al. Rapid hop diffusion of a G-protein-coupled receptor in the plasma membrane as revealed by single-molecule techniques. Biophys. J. 88(5):3659–3680, 2005.

    Article  PubMed  CAS  Google Scholar 

  73. Szabo, A., et al. Quantitative characterization of the large-scale association of ErbB1 and ErbB2 by flow cytometric homo-FRET measurements. Biophys. J. 95(4):2086–2096, 2008.

    Article  PubMed  CAS  Google Scholar 

  74. Telesco, S. E., and R. Radhakrishnan. Structural systems biology and multiscale signaling models. Ann. Biomed. Eng., 2012. doi:10.1007/s10439-012-0576-6

  75. ten Klooster, J. P., and P. L. Hordijk. Targeting and localized signalling by small GTPases. Biol. Cell 99(1):1–12, 2007.

    Article  PubMed  Google Scholar 

  76. Tian, T., et al. Plasma membrane nanoswitches generate high-fidelity Ras signal transduction. Nat. Cell Biol. 9(8):905–914, 2007.

    Article  PubMed  CAS  Google Scholar 

  77. Tian, T., et al. Mathematical modeling of K-Ras nanocluster formation on the plasma membrane. Biophys. J. 99(2):534–543, 2010.

    Article  PubMed  CAS  Google Scholar 

  78. Tolle, D. P., and N. Le Novere. Meredys, a multi-compartment reaction–diffusion simulator using multistate realistic molecular complexes. BMC Syst. Biol. 4:24, 2010.

    Article  PubMed  Google Scholar 

  79. Tolle, D. P., and N. Le Novere. Brownian diffusion of AMPA receptors is sufficient to explain fast onset of LTP. BMC Syst. Biol. 4:25, 2010.

    Article  PubMed  Google Scholar 

  80. Turner, T. E., S. Schnell, and K. Burrage. Stochastic approaches for modelling in vivo reactions. Comput. Biol. Chem. 28(3):165–178, 2004.

    Article  PubMed  CAS  Google Scholar 

  81. Vigil, D., et al. Ras superfamily GEFs and GAPs: validated and tractable targets for cancer therapy? Nat. Rev. Cancer 10(12):842–857, 2010.

    Article  PubMed  CAS  Google Scholar 

  82. Vilardaga, J. P., et al. G-protein-coupled receptor heteromer dynamics. J. Cell Sci. 123(Pt 24):4215–4220, 2010.

    Article  PubMed  CAS  Google Scholar 

  83. Waller, A., et al. Receptor binding kinetics and cellular responses of six N-formyl peptide agonists in human neutrophils. Biochemistry 43(25):8204–8216, 2004.

    Article  PubMed  CAS  Google Scholar 

  84. Wells, N. P., et al. Time-resolved three-dimensional molecular tracking in live cells. Nano Lett. 10(11):4732–4737, 2010.

    Article  PubMed  CAS  Google Scholar 

  85. Wennerberg, K., K. L. Rossman, and C. J. Der. The Ras superfamily at a glance. J. Cell Sci. 118(Pt 5):843–846, 2005.

    Article  PubMed  CAS  Google Scholar 

  86. Wiley, H. S., S. Y. Shvartsman, and D. A. Lauffenburger. Computational modeling of the EGF-receptor system: a paradigm for systems biology. Trends Cell Biol. 13(1):43–50, 2003.

    Article  PubMed  CAS  Google Scholar 

  87. Wilson, B. S., J. M. Oliver, and D. S. Lidke. Spatio-temporal signaling in mast cells. Adv. Exp. Med. Biol. 716:91–106, 2010.

    Article  Google Scholar 

  88. Wilson, B. S., et al. Exploring membrane domains using native membrane sheets and transmission electron microscopy. Methods Mol. Biol. 398:245–261, 2007.

    Article  PubMed  CAS  Google Scholar 

  89. Yang, S., et al. Mapping ErbB receptors on breast cancer cell membranes during signal transduction. J. Cell Sci. 120(Pt 16):2763–2773, 2007.

    Article  PubMed  CAS  Google Scholar 

  90. Zhdanov, V. P., and B. Kasemo. Kinetic phase transitions in simple reactions on solid surfaces. Surf. Sci. Rep. 20:111–189, 1994.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work was supported by NIH R01CA119323 (to BW), NIH P50GM085273 (the New Mexico Spatiotemporal Modeling Center), and NIH K25CA131558 (to AH).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bridget S. Wilson.

Additional information

Associate Editor Michael R. King oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Radhakrishnan, K., Halász, Á., McCabe, M.M. et al. Mathematical Simulation of Membrane Protein Clustering for Efficient Signal Transduction. Ann Biomed Eng 40, 2307–2318 (2012). https://doi.org/10.1007/s10439-012-0599-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-012-0599-z

Keywords

Navigation