Ion mediated crosslink driven mucous swelling kinetics

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August 2016, 21(6): 1937-1951. doi: 10.3934/dcdsb.2016030

Ion mediated crosslink driven mucous swelling kinetics

Sarthok Sircar ^1, and Anthony Roberts ^2,

1.	School of Mathematical Sciences, 650 IW Building, North Terrace Campus, University of Adelaide, SA 5005, Australia
2.	School of Mathematical Sciences, 738 IW Building, North Terrace Campus, University of Adelaide, SA 5005, Australia

Received April 2015 Revised February 2016 Published June 2016

Abstract
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We provide qualitative predictions on the rheology of mucus of healthy individuals (Wild Type or WT-mucus) versus those infected with Cystic Fibrosis (CF-mucus) using an experimentally guided, multi-phase, multi-species ionic gel model. The theory which accounts for mucus (as polymer phase), water (as solvent phase) and ions, H$^+$, Na$^+$ and Ca$^{2+}$, is linearized to study the hydration of spherically symmetric mucus gels and calibrated against the experimental data of mucus diffusivities. Near equilibrium, the linearized form of the solution reduces to an expression similar to the well known kinetic theory of neutral gels. Numerical studies reveal that the Donnan potential is the dominating mechanism driving the mucus swelling/deswelling transition. However, the altered swelling kinetics of the Cystic Fibrosis infected mucus is not merely governed by the hydroelectric composition of the swelling media, but also due to the altered movement of electrolytes as well as due to the defective properties of the mucin polymer network.

Keywords: mucus diffusivity, cystic fibrosis, Polyelectrolyte gel, Donnan potential, binding affinity..

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.

Citation: Sarthok Sircar, Anthony Roberts. Ion mediated crosslink driven mucous swelling kinetics. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1937-1951. doi: 10.3934/dcdsb.2016030

References:

[1]	S. Baconnais, F. Delavoie, J. M. Zahm, M. Milliot, C. Terryn, N. Castillon, V. Banchet, J. Micheal, O. Danos, M. Merten, T. Chinet, K. Zierold, N. Bonnet, E. Puchelle and G. Balossier, Abnormal ion content, hydration and granule expansion of the secretory granules from cystic fibrosis airway glandular cells, Exp. Cell Res., 309 (2005), 296-304. doi: 10.1016/j.yexcr.2005.06.010.
[2]	R. Bansil and B. S. Turner, Mucin structure, aggregation, physiological functions and biomedical applications, Curr. Opin. Colloid and Interface Sci., 11 (2006), 164-170. doi: 10.1016/j.cocis.2005.11.001.
[3]	J. Barasch, B. Kiss, A. Prince, L. Saiman, D. Gruenert and Q. A. Awqati, Defective acidification of intracellular organelles in cystic fibrosis, Nature, 352 (1991), 70-73. doi: 10.1038/352070a0.
[4]	A. F. M. Barton, Handbook of polymer-liquid interaction parameters and solubility parameters, CRC press, 1990.
[5]	M. C. Calderer, H. Chen, C. Micek and Y. Mori, A dynamic model of polyelectrolyte gels, SIAM J. Appl. Math., 73 (2013), 104-133. doi: 10.1137/110855296.
[6]	K. V. Chase, D. S. Leahy, R. Martin, M. Carubelli, M. Flux and G. P. Sachdev, Respiratory mucus secretions in patients with cystic fibrosis: relationship between levels of highly sulfated mucin components and severity of disease, Clin. Chim. Acta, 132 (1983), 143-155. doi: 10.1016/0009-8981(83)90242-5.
[7]	P. W. Cheng, T. F. Boat, K. Cranfill, J. R. Yankaskas and R. C. Boucher, Increased sulfonation of glycoconjugates by cultured nasal epithelial cells from patients with cystic fibrosis, J. Clin. Invest., 84 (1989), 68-72. doi: 10.1172/JCI114171.
[8]	R. S. Crowther and C. Marriott, Counter-ion binding to mucus glycoproteins, J. Pharm. Pharmacol., 36 (1984), 21-26. doi: 10.1111/j.2042-7158.1984.tb02980.x.
[9]	M. Doi and S. F. Edwards, Theory of Polymer Dynamics, Clarendon Press, Oxford, England, 1986.
[10]	C. J. Durning and K. N. Morman, Nonlinear swelling of polymer gels, J. Chem. Phys., 98 (1993), 4275-4293. doi: 10.1063/1.465034.
[11]	P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, NY, 1953.
[12]	M. J. Holmes, N. G. Parker and M. J. W. Povey, Temperature dependence of bulk viscosity in water using acoustic spectroscopy, J. Phys.: Conf. Ser., 269 (2011), 012011, 7pp. doi: 10.1088/1742-6596/269/1/012011.
[13]	A. Katchalsky and I. Michaeli, Polyelectrolyte gels in salt solutions, J. Polym. Sci., 15 (1955), 69-86. doi: 10.1002/pol.1955.120157906.
[14]	J. P. Keener, S. Sircar and A. Fogelson, Kinetics of swelling gels, SIAM J. Appl. Math., 71 (2011), 854-875. doi: 10.1137/100796984.
[15]	J. P. Keener, S. Sircar and A. Fogelson, Influence of free energy on swelling kinetics of gels, Phys. Rev. E, 83 (2011), 041802, 11pp. doi: 10.1103/PhysRevE.83.041802.
[16]	R. Kuver, T. Wong, J. H. Klinkspoor and S. P. Lee, Absence of CFTR is associated with pleiotropic effects on mucins in mouse gallbladder epithelial cells, Am. J. Physiol. Gastrointest Liver Physiol., 291 (2006), G1148-G1154. doi: 10.1152/ajpgi.00547.2005.
[17]	R. C. Lisle, Increased expression of sulfated gp300 and acinar tissue pathology in pancreas of CFTR (-/-) mice, Am. J. Physiol., 268 (1995), G717-G723. doi: 10.1177/44.1.8543783.
[18]	S. Sircar, J. P. Keener and A. L. Fogelson, The effect of divalent vs. monovalent ions on the swelling of Mucin-like polyelectrolyte gels: Governing equations and equilibrium analysis, J. Chem. Phys., 138 (2013), 014901, 16pp. doi: 10.1063/1.4772405.
[19]	S. Sircar, E. Aisenbrey, S. J. Bryant and D. M. Bortz, Determining equilibrium osmolarity in poly(ethylene glycol)/chondrotin sulfate gels mimicking articular cartilage, J. Theor. Biol., 364 (2015), 397-406. doi: 10.1016/j.jtbi.2014.09.037.
[20]	T. Tanaka and D. Fillmore, Kinetics of swelling gels, J. Chem. Phys., 70 (1979), 1214-1218. doi: 10.1063/1.437602.
[21]	P. Verdugo, Hydration kinetics of exocytosed mucins in cultured secretory cells of the rabbit trachea: A new model, Mucus and mucosa, Ciba Foundation symposium, 109 (1984), 212-225. doi: 10.1002/9780470720905.ch15.
[22]	P. Verdugo, M. Aitken, L. Langley and M. J. Villalon, Molecular mechanism of product storage and release in mucin secretion. II. The role of extracelluar $Ca^{++}$, Biorheology, 24 (1987), 625-633. doi: www.ncbi.nlm.nih.gov/pubmed/3502764.
[23]	P. Verdugo, Goblet cells secretion and mucogenesis, Annu. Rev. Physiol., 52 (1990), 157-176. doi: 10.1146/annurev.ph.52.030190.001105.
[24]	P. Verdugo, Polymer gel phase transition in condensation-decondensation of secretory products, Adv. Polm. Sci., 110 (2005), 145-156. doi: 10.1007/BFb0021131.
[25]	P. Verdugo, Cilia, Mucus and Mucociliary Interactions, Chap 19, Marcel Decker, New York, 1998.
[26]	J. P. Villar, Mucin Granule Intraluminal Organization, Am. J. Respir. Cell Mol. Biol., 36 (2007), 183-190. doi: 10.1165/rcmb.2006-0291TR.
[27]	C. Wang, Y. Li and Z. Hu, Swelling kinetics of polymer gels, Macromolecules, 30 (1997), 4727-4732. doi: 10.1021/ma9613648.
[28]	C. W. Wolgemuth, A. Mogilner and G. Oster, The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery, Euro Biophys. J., 33 (2004), 146-158. doi: 10.1007/s00249-003-0344-5.

show all references

References:

[1]	S. Baconnais, F. Delavoie, J. M. Zahm, M. Milliot, C. Terryn, N. Castillon, V. Banchet, J. Micheal, O. Danos, M. Merten, T. Chinet, K. Zierold, N. Bonnet, E. Puchelle and G. Balossier, Abnormal ion content, hydration and granule expansion of the secretory granules from cystic fibrosis airway glandular cells, Exp. Cell Res., 309 (2005), 296-304. doi: 10.1016/j.yexcr.2005.06.010.
[2]	R. Bansil and B. S. Turner, Mucin structure, aggregation, physiological functions and biomedical applications, Curr. Opin. Colloid and Interface Sci., 11 (2006), 164-170. doi: 10.1016/j.cocis.2005.11.001.
[3]	J. Barasch, B. Kiss, A. Prince, L. Saiman, D. Gruenert and Q. A. Awqati, Defective acidification of intracellular organelles in cystic fibrosis, Nature, 352 (1991), 70-73. doi: 10.1038/352070a0.
[4]	A. F. M. Barton, Handbook of polymer-liquid interaction parameters and solubility parameters, CRC press, 1990.
[5]	M. C. Calderer, H. Chen, C. Micek and Y. Mori, A dynamic model of polyelectrolyte gels, SIAM J. Appl. Math., 73 (2013), 104-133. doi: 10.1137/110855296.
[6]	K. V. Chase, D. S. Leahy, R. Martin, M. Carubelli, M. Flux and G. P. Sachdev, Respiratory mucus secretions in patients with cystic fibrosis: relationship between levels of highly sulfated mucin components and severity of disease, Clin. Chim. Acta, 132 (1983), 143-155. doi: 10.1016/0009-8981(83)90242-5.
[7]	P. W. Cheng, T. F. Boat, K. Cranfill, J. R. Yankaskas and R. C. Boucher, Increased sulfonation of glycoconjugates by cultured nasal epithelial cells from patients with cystic fibrosis, J. Clin. Invest., 84 (1989), 68-72. doi: 10.1172/JCI114171.
[8]	R. S. Crowther and C. Marriott, Counter-ion binding to mucus glycoproteins, J. Pharm. Pharmacol., 36 (1984), 21-26. doi: 10.1111/j.2042-7158.1984.tb02980.x.
[9]	M. Doi and S. F. Edwards, Theory of Polymer Dynamics, Clarendon Press, Oxford, England, 1986.
[10]	C. J. Durning and K. N. Morman, Nonlinear swelling of polymer gels, J. Chem. Phys., 98 (1993), 4275-4293. doi: 10.1063/1.465034.
[11]	P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, NY, 1953.
[12]	M. J. Holmes, N. G. Parker and M. J. W. Povey, Temperature dependence of bulk viscosity in water using acoustic spectroscopy, J. Phys.: Conf. Ser., 269 (2011), 012011, 7pp. doi: 10.1088/1742-6596/269/1/012011.
[13]	A. Katchalsky and I. Michaeli, Polyelectrolyte gels in salt solutions, J. Polym. Sci., 15 (1955), 69-86. doi: 10.1002/pol.1955.120157906.
[14]	J. P. Keener, S. Sircar and A. Fogelson, Kinetics of swelling gels, SIAM J. Appl. Math., 71 (2011), 854-875. doi: 10.1137/100796984.
[15]	J. P. Keener, S. Sircar and A. Fogelson, Influence of free energy on swelling kinetics of gels, Phys. Rev. E, 83 (2011), 041802, 11pp. doi: 10.1103/PhysRevE.83.041802.
[16]	R. Kuver, T. Wong, J. H. Klinkspoor and S. P. Lee, Absence of CFTR is associated with pleiotropic effects on mucins in mouse gallbladder epithelial cells, Am. J. Physiol. Gastrointest Liver Physiol., 291 (2006), G1148-G1154. doi: 10.1152/ajpgi.00547.2005.
[17]	R. C. Lisle, Increased expression of sulfated gp300 and acinar tissue pathology in pancreas of CFTR (-/-) mice, Am. J. Physiol., 268 (1995), G717-G723. doi: 10.1177/44.1.8543783.
[18]	S. Sircar, J. P. Keener and A. L. Fogelson, The effect of divalent vs. monovalent ions on the swelling of Mucin-like polyelectrolyte gels: Governing equations and equilibrium analysis, J. Chem. Phys., 138 (2013), 014901, 16pp. doi: 10.1063/1.4772405.
[19]	S. Sircar, E. Aisenbrey, S. J. Bryant and D. M. Bortz, Determining equilibrium osmolarity in poly(ethylene glycol)/chondrotin sulfate gels mimicking articular cartilage, J. Theor. Biol., 364 (2015), 397-406. doi: 10.1016/j.jtbi.2014.09.037.
[20]	T. Tanaka and D. Fillmore, Kinetics of swelling gels, J. Chem. Phys., 70 (1979), 1214-1218. doi: 10.1063/1.437602.
[21]	P. Verdugo, Hydration kinetics of exocytosed mucins in cultured secretory cells of the rabbit trachea: A new model, Mucus and mucosa, Ciba Foundation symposium, 109 (1984), 212-225. doi: 10.1002/9780470720905.ch15.
[22]	P. Verdugo, M. Aitken, L. Langley and M. J. Villalon, Molecular mechanism of product storage and release in mucin secretion. II. The role of extracelluar $Ca^{++}$, Biorheology, 24 (1987), 625-633. doi: www.ncbi.nlm.nih.gov/pubmed/3502764.
[23]	P. Verdugo, Goblet cells secretion and mucogenesis, Annu. Rev. Physiol., 52 (1990), 157-176. doi: 10.1146/annurev.ph.52.030190.001105.
[24]	P. Verdugo, Polymer gel phase transition in condensation-decondensation of secretory products, Adv. Polm. Sci., 110 (2005), 145-156. doi: 10.1007/BFb0021131.
[25]	P. Verdugo, Cilia, Mucus and Mucociliary Interactions, Chap 19, Marcel Decker, New York, 1998.
[26]	J. P. Villar, Mucin Granule Intraluminal Organization, Am. J. Respir. Cell Mol. Biol., 36 (2007), 183-190. doi: 10.1165/rcmb.2006-0291TR.
[27]	C. Wang, Y. Li and Z. Hu, Swelling kinetics of polymer gels, Macromolecules, 30 (1997), 4727-4732. doi: 10.1021/ma9613648.
[28]	C. W. Wolgemuth, A. Mogilner and G. Oster, The hydration dynamics of polyelectrolyte gels with applications to cell motility and drug delivery, Euro Biophys. J., 33 (2004), 146-158. doi: 10.1007/s00249-003-0344-5.

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