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. 1998 May;74(5):2259–2271. doi: 10.1016/S0006-3495(98)77935-4

A model for diffusive transport through a spherical interface probed by pulsed-field gradient NMR.

W S Price 1, A V Barzykin 1, K Hayamizu 1, M Tachiya 1
PMCID: PMC1299569  PMID: 9591653

Abstract

In biological systems, because of higher intracellular viscosity and/or the restriction of the diffusion space inside cells, the (apparent) diffusion coefficient of an intracellular species (e.g., water) is generally smaller than when it is in the extracellular medium. This difference affects the spin-echo signal attenuation in the pulsed field gradient NMR experiment and thus affords a means of separating the intracellular from the extracellular species, thereby providing a basis for studying transmembrane transport. Such experiments have commonly been analyzed using the macroscopic model of Kärger (see Adv. Magn. Reson. 21:1-89 (1988)). In our previous study, we considered a microscopic model of diffusive transport through a spherical interface using the short gradient pulse approximation (J. Magn. Reson. A114:39-46 (1995)). The spins in the external medium were modeled with the "partially absorbing wall" condition or as having a small but finite lifetime. In the present paper, we extend our treatment to the case in which there is no limitation upon the lifetime in either medium. We also consider a simple modification of Kärger's model that more properly accounts for the restricted intracellular diffusion. Importantly, it was found that the exact solution within the short gradient pulse approximation developed here and the modified Kärger model are in close agreement in the (experimentally relevant) long-time limit. The results of this study show that when there is no limitation upon the lifetime of the transported species in either phase, the spin-echo attenuation curve is very sensitive to transport.

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Selected References

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  1. Andrasko J. Water diffusion permeability of human erythrocytes studied by a pulsed gradient NMR technique. Biochim Biophys Acta. 1976 Apr 23;428(2):304–311. doi: 10.1016/0304-4165(76)90038-6. [DOI] [PubMed] [Google Scholar]
  2. Andreasson B., Nordenskiöld L., Schultz J. Interactions of spermidine and methylspermidine with DNA studied by nuclear magnetic resonance self-diffusion measurements. Biophys J. 1996 Jun;70(6):2847–2856. doi: 10.1016/S0006-3495(96)79854-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Callaghan PT. A simple matrix formalism for spin echo analysis of restricted diffusion under generalized gradient waveforms . J Magn Reson. 1997 Nov;129(1):74–84. doi: 10.1006/jmre.1997.1233. [DOI] [PubMed] [Google Scholar]
  4. Callaghan PT, Coy A. Evidence for reptational motion and the entanglement tube in semidilute polymer solutions. Phys Rev Lett. 1992 May 25;68(21):3176–3179. doi: 10.1103/PhysRevLett.68.3176. [DOI] [PubMed] [Google Scholar]
  5. Chapman B. E., Kirk K., Kuchel P. W. Bicarbonate exchange kinetics at equilibrium across the erythrocyte membrane by 13C NMR. Biochem Biophys Res Commun. 1986 Apr 14;136(1):266–272. doi: 10.1016/0006-291x(86)90904-6. [DOI] [PubMed] [Google Scholar]
  6. Cory D. G., Garroway A. N. Measurement of translational displacement probabilities by NMR: an indicator of compartmentation. Magn Reson Med. 1990 Jun;14(3):435–444. doi: 10.1002/mrm.1910140303. [DOI] [PubMed] [Google Scholar]
  7. Endre Z. H., Kuchel P. W., Chapman B. E. Cell volume dependence of 1H spin-echo NMR signals in human erythrocyte suspensions. The influence of in situ field gradients. Biochim Biophys Acta. 1984 Mar 23;803(3):137–144. doi: 10.1016/0167-4889(84)90003-x. [DOI] [PubMed] [Google Scholar]
  8. Kuchel P. W., Coy A., Stilbs P. NMR "diffusion-diffraction" of water revealing alignment of erythrocytes in a magnetic field and their dimensions and membrane transport characteristics. Magn Reson Med. 1997 May;37(5):637–643. doi: 10.1002/mrm.1910370502. [DOI] [PubMed] [Google Scholar]
  9. Kuchel P. W. Spin-exchange NMR spectroscopy in studies of the kinetics of enzymes and membrane transport. NMR Biomed. 1990 Jun;3(3):102–119. doi: 10.1002/nbm.1940030303. [DOI] [PubMed] [Google Scholar]
  10. Kuchel PW, Lennon AJ, Durrant C. Analytical Solutions and Simulations for Spin-Echo Measurements of Diffusion of Spins in a Sphere with Surface and Bulk Relaxation. J Magn Reson B. 1996 Jul;112(1):1–17. doi: 10.1006/jmrb.1996.0103. [DOI] [PubMed] [Google Scholar]
  11. Lennon A. J., Scott N. R., Chapman B. E., Kuchel P. W. Hemoglobin affinity for 2,3-bisphosphoglycerate in solutions and intact erythrocytes: studies using pulsed-field gradient nuclear magnetic resonance and Monte Carlo simulations. Biophys J. 1994 Nov;67(5):2096–2109. doi: 10.1016/S0006-3495(94)80693-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Mitra PP, Sen PN. Effects of microgeometry and surface relaxation on NMR pulsed-field-gradient experiments: Simple pore geometries. Phys Rev B Condens Matter. 1992 Jan 1;45(1):143–156. doi: 10.1103/physrevb.45.143. [DOI] [PubMed] [Google Scholar]
  13. Perng W. C., Price W. S., Hsu K., Hwang L. P. The effects of hypothermia on the intracellular pH of erythrocytes studied using 31P NMR and endogenous compounds. Eur J Clin Chem Clin Biochem. 1993 Jul;31(7):413–418. doi: 10.1515/cclm.1993.31.7.413. [DOI] [PubMed] [Google Scholar]
  14. Potter K., Kleinberg R. L., Brockman F. J., McFarland E. W. Assay for bacteria in porous media by diffusion-weighted NMR. J Magn Reson B. 1996 Oct;113(1):9–15. doi: 10.1006/jmrb.1996.0149. [DOI] [PubMed] [Google Scholar]
  15. Price W. S., Arata Y. The manipulation of water relaxation and water suppression in biological systems using the water-PRESS pulse sequence. J Magn Reson B. 1996 Aug;112(2):190–192. doi: 10.1006/jmrb.1996.0129. [DOI] [PubMed] [Google Scholar]
  16. Price W. S., Hayamizu K., Arata Y. Optimization of the water-PRESS pulse sequence and its integration into pulse sequences for studying biological macromolecules. J Magn Reson. 1997 Jun;126(2):256–265. doi: 10.1006/jmre.1997.1166. [DOI] [PubMed] [Google Scholar]
  17. Price W. S., Kuchel P. W., Cornell B. A. Microviscosity of human erythrocytes studied with hypophosphite and 31P-NMR. Biophys Chem. 1989 Jul;33(3):205–215. doi: 10.1016/0301-4622(89)80022-5. [DOI] [PubMed] [Google Scholar]
  18. Price W. S., Kuchel P. W. Hypophosphite transport in human erythrocytes studied by overdetermined one-dimensional NMR exchange analysis. NMR Biomed. 1990 Apr;3(2):59–63. doi: 10.1002/nbm.1940030203. [DOI] [PubMed] [Google Scholar]
  19. Price W. S., Nara M., Arata Y. A pulsed field gradient NMR study of the aggregation and hydration of parvalbumin. Biophys Chem. 1997 Apr 22;65(2-3):179–187. doi: 10.1016/s0301-4622(97)00003-3. [DOI] [PubMed] [Google Scholar]
  20. Price W. S., Perng B. C., Tsai C. L., Hwang L. P. Microviscosity of human erythrocytes studied using hypophosphite two-spin order relaxation. Biophys J. 1992 Mar;61(3):621–630. doi: 10.1016/S0006-3495(92)81867-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Sen PN, Schwartz LM, Mitra PP, Halperin BI. Surface relaxation and the long-time diffusion coefficient in porous media: Periodic geometries. Phys Rev B Condens Matter. 1994 Jan 1;49(1):215–225. doi: 10.1103/physrevb.49.215. [DOI] [PubMed] [Google Scholar]
  22. Van Zijl P. C., Moonen C. T., Faustino P., Pekar J., Kaplan O., Cohen J. S. Complete separation of intracellular and extracellular information in NMR spectra of perfused cells by diffusion-weighted spectroscopy. Proc Natl Acad Sci U S A. 1991 Apr 15;88(8):3228–3232. doi: 10.1073/pnas.88.8.3228. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Wassall S. R. Pulsed field gradient-spin echo NMR studies of water diffusion in a phospholipid model membrane. Biophys J. 1996 Nov;71(5):2724–2732. doi: 10.1016/S0006-3495(96)79463-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Zwanzig R., Szabo A. Time dependent rate of diffusion-influenced ligand binding to receptors on cell surfaces. Biophys J. 1991 Sep;60(3):671–678. doi: 10.1016/S0006-3495(91)82096-3. [DOI] [PMC free article] [PubMed] [Google Scholar]

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