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. 1998 Mar;74(3):1215–1228. doi: 10.1016/S0006-3495(98)77836-1

Theory for ligand rebinding at cell membrane surfaces.

B C Lagerholm 1, N L Thompson 1
PMCID: PMC1299470  PMID: 9512020

Abstract

Conditions for which a ligand reversibly bound to a cell surface dissociates and then rebinds to the surface have been theoretically examined. The coupled differential equations that describe reaction at the interface between sites on a plane and three-dimensional solution have been described previously (Thompson, N. L., T. P. Burghardt, and D. Axelrod. 1981. Biophys. J. 33:435-454). Here, we use this theoretical formalism to provide an analytical solution for the spatial and temporal dependence of the probabilities of finding a molecule on the surface or in the solution, given initial placement on the surface at the origin. This general analytical solution is used to derive a simple expression for the probability that a molecule rebinds to the surface at a given position and time after release at the origin and time zero. The probability expressions provide fundamental equations that form a basis for subsequent modeling of ligand-receptor interactions in specific geometries.

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Selected References

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  1. Axelrod D., Wang M. D. Reduction-of-dimensionality kinetics at reaction-limited cell surface receptors. Biophys J. 1994 Mar;66(3 Pt 1):588–600. doi: 10.1016/s0006-3495(94)80834-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Balgi G., Leckband D. E., Nitsche J. M. Transport effects on the kinetics of protein-surface binding. Biophys J. 1995 Jun;68(6):2251–2260. doi: 10.1016/S0006-3495(95)80407-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Berg H. C., Purcell E. M. Physics of chemoreception. Biophys J. 1977 Nov;20(2):193–219. doi: 10.1016/S0006-3495(77)85544-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Berg O. G., von Hippel P. H. Diffusion-controlled macromolecular interactions. Annu Rev Biophys Biophys Chem. 1985;14:131–160. doi: 10.1146/annurev.bb.14.060185.001023. [DOI] [PubMed] [Google Scholar]
  5. Burghardt T. P., Axelrod D. Total internal reflection/fluorescence photobleaching recovery study of serum albumin adsorption dynamics. Biophys J. 1981 Mar;33(3):455–467. doi: 10.1016/S0006-3495(81)84906-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Conibear P. B., Bagshaw C. R. Measurement of nucleotide exchange kinetics with isolated synthetic myosin filaments using flash photolysis. FEBS Lett. 1996 Feb 12;380(1-2):13–16. doi: 10.1016/0014-5793(95)01538-8. [DOI] [PubMed] [Google Scholar]
  7. DeLisi C., Wiegel F. W. Effect of nonspecific forces and finite receptor number on rate constants of ligand--cell bound-receptor interactions. Proc Natl Acad Sci U S A. 1981 Sep;78(9):5569–5572. doi: 10.1073/pnas.78.9.5569. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Duschl C., Sévin-Landais A. F., Vogel H. Surface engineering: optimization of antigen presentation in self-assembled monolayers. Biophys J. 1996 Apr;70(4):1985–1995. doi: 10.1016/S0006-3495(96)79763-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Erickson J. W., Posner R. G., Goldstein B., Holowka D., Baird B. Bivalent ligand dissociation kinetics from receptor-bound immunoglobulin E: evidence for a time-dependent increase in ligand rebinding at the cell surface. Biochemistry. 1991 Mar 5;30(9):2357–2363. doi: 10.1021/bi00223a009. [DOI] [PubMed] [Google Scholar]
  10. Erickson J., Goldstein B., Holowka D., Baird B. The effect of receptor density on the forward rate constant for binding of ligands to cell surface receptors. Biophys J. 1987 Oct;52(4):657–662. doi: 10.1016/S0006-3495(87)83258-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Forsten K. E., Lauffenburger D. A. Probability of autocrine ligand capture by cell-surface receptors: implications for ligand secretion measurements. J Comput Biol. 1994 Spring;1(1):15–23. doi: 10.1089/cmb.1994.1.15. [DOI] [PubMed] [Google Scholar]
  12. Funatsu T., Harada Y., Tokunaga M., Saito K., Yanagida T. Imaging of single fluorescent molecules and individual ATP turnovers by single myosin molecules in aqueous solution. Nature. 1995 Apr 6;374(6522):555–559. doi: 10.1038/374555a0. [DOI] [PubMed] [Google Scholar]
  13. Geurts B. J. Diffusion limited immunochemical sensing. Bull Math Biol. 1989;51(3):359–379. doi: 10.1007/BF02460114. [DOI] [PubMed] [Google Scholar]
  14. Goldstein B., Dembo M. Approximating the effects of diffusion on reversible reactions at the cell surface: ligand-receptor kinetics. Biophys J. 1995 Apr;68(4):1222–1230. doi: 10.1016/S0006-3495(95)80298-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Goldstein B., Posner R. G., Torney D. C., Erickson J., Holowka D., Baird B. Competition between solution and cell surface receptors for ligand. Dissociation of hapten bound to surface antibody in the presence of solution antibody. Biophys J. 1989 Nov;56(5):955–966. doi: 10.1016/S0006-3495(89)82741-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Hsieh H. V., Thompson N. L. Dissociation kinetics between a mouse Fc receptor (Fc gamma RII) and IgG: measurement by total internal reflection with fluorescence photobleaching recovery. Biochemistry. 1995 Sep 26;34(38):12481–12488. doi: 10.1021/bi00038a047. [DOI] [PubMed] [Google Scholar]
  17. Hsieh H. V., Thompson N. L. Theory for measuring bivalent surface binding kinetics using total internal reflection with fluorescence photobleaching recovery. Biophys J. 1994 Mar;66(3 Pt 1):898–911. doi: 10.1016/s0006-3495(94)80866-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Huang Z., Pearce K. H., Thompson N. L. Translational diffusion of bovine prothrombin fragment 1 weakly bound to supported planar membranes: measurement by total internal reflection with fluorescence pattern photobleaching recovery. Biophys J. 1994 Oct;67(4):1754–1766. doi: 10.1016/S0006-3495(94)80650-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Lauffenburger D. A., Forsten K. E., Will B., Wiley H. S. Molecular/cell engineering approach to autocrine ligand control of cell function. Ann Biomed Eng. 1995 May-Jun;23(3):208–215. doi: 10.1007/BF02584423. [DOI] [PubMed] [Google Scholar]
  20. Lookene A., Chevreuil O., Ostergaard P., Olivecrona G. Interaction of lipoprotein lipase with heparin fragments and with heparan sulfate: stoichiometry, stabilization, and kinetics. Biochemistry. 1996 Sep 17;35(37):12155–12163. doi: 10.1021/bi960008e. [DOI] [PubMed] [Google Scholar]
  21. Lánská V., Lánský P., Smith C. E. Synaptic transmission in a diffusion model for neural activity. J Theor Biol. 1994 Feb 21;166(4):393–406. doi: 10.1006/jtbi.1994.1035. [DOI] [PubMed] [Google Scholar]
  22. Model M. A., Omann G. M. Ligand-receptor interaction rates in the presence of convective mass transport. Biophys J. 1995 Nov;69(5):1712–1720. doi: 10.1016/S0006-3495(95)80041-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Nieba L., Krebber A., Plückthun A. Competition BIAcore for measuring true affinities: large differences from values determined from binding kinetics. Anal Biochem. 1996 Feb 15;234(2):155–165. doi: 10.1006/abio.1996.0067. [DOI] [PubMed] [Google Scholar]
  24. Nygren H., Stenberg M. Immunochemistry at interfaces. Immunology. 1989 Mar;66(3):321–327. [PMC free article] [PubMed] [Google Scholar]
  25. O'Shannessy D. J., Winzor D. J. Interpretation of deviations from pseudo-first-order kinetic behavior in the characterization of ligand binding by biosensor technology. Anal Biochem. 1996 May 1;236(2):275–283. doi: 10.1006/abio.1996.0167. [DOI] [PubMed] [Google Scholar]
  26. Otis T. S., Wu Y. C., Trussell L. O. Delayed clearance of transmitter and the role of glutamate transporters at synapses with multiple release sites. J Neurosci. 1996 Mar 1;16(5):1634–1644. doi: 10.1523/JNEUROSCI.16-05-01634.1996. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Pearce K. H., Hiskey R. G., Thompson N. L. Surface binding kinetics of prothrombin fragment 1 on planar membranes measured by total internal reflection fluorescence microscopy. Biochemistry. 1992 Jul 7;31(26):5983–5995. doi: 10.1021/bi00141a005. [DOI] [PubMed] [Google Scholar]
  28. Pisarchick M. L., Gesty D., Thompson N. L. Binding kinetics of an anti-dinitrophenyl monoclonal Fab on supported phospholipid monolayers measured by total internal reflection with fluorescence photobleaching recovery. Biophys J. 1992 Jul;63(1):215–223. doi: 10.1016/S0006-3495(92)81592-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Sadana A., Madagula A. A fractal analysis of external diffusion limited first-order kinetics for the binding of antigen by immobilized antibody. Biosens Bioelectron. 1994;9(1):45–55. doi: 10.1016/0956-5663(94)80014-6. [DOI] [PubMed] [Google Scholar]
  30. Schuck P., Minton A. P. Analysis of mass transport-limited binding kinetics in evanescent wave biosensors. Anal Biochem. 1996 Sep 5;240(2):262–272. doi: 10.1006/abio.1996.0356. [DOI] [PubMed] [Google Scholar]
  31. Shoup D., Szabo A. Role of diffusion in ligand binding to macromolecules and cell-bound receptors. Biophys J. 1982 Oct;40(1):33–39. doi: 10.1016/S0006-3495(82)84455-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Thompson N. L., Axelrod D. Immunoglobulin surface-binding kinetics studied by total internal reflection with fluorescence correlation spectroscopy. Biophys J. 1983 Jul;43(1):103–114. doi: 10.1016/S0006-3495(83)84328-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Thompson N. L., Burghardt T. P., Axelrod D. Measuring surface dynamics of biomolecules by total internal reflection fluorescence with photobleaching recovery or correlation spectroscopy. Biophys J. 1981 Mar;33(3):435–454. doi: 10.1016/S0006-3495(81)84905-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Thompson N. L. Surface binding rates of nonfluorescent molecules may be obtained by total internal reflection with fluorescence correlation spectroscopy. Biophys J. 1982 Jun;38(3):327–329. doi: 10.1016/S0006-3495(82)84567-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Vale R. D., Funatsu T., Pierce D. W., Romberg L., Harada Y., Yanagida T. Direct observation of single kinesin molecules moving along microtubules. Nature. 1996 Apr 4;380(6573):451–453. doi: 10.1038/380451a0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Wang D., Gou S. Y., Axelrod D. Reaction rate enhancement by surface diffusion of adsorbates. Biophys Chem. 1992 Jun;43(2):117–137. doi: 10.1016/0301-4622(92)80027-3. [DOI] [PubMed] [Google Scholar]
  37. Xu X. H., Yeung E. S. Direct measurement of single-molecule diffusion and photodecomposition in free solution. Science. 1997 Feb 21;275(5303):1106–1109. doi: 10.1126/science.275.5303.1106. [DOI] [PubMed] [Google Scholar]
  38. Zwanzig R. Diffusion-controlled ligand binding to spheres partially covered by receptors: an effective medium treatment. Proc Natl Acad Sci U S A. 1990 Aug;87(15):5856–5857. doi: 10.1073/pnas.87.15.5856. [DOI] [PMC free article] [PubMed] [Google Scholar]

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