American Institute of Mathematical Sciences

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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

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 & 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.  doi: 10.1016/j.yexcr.2005.06.010.  Google Scholar

[2]

R. Bansil and B. S. Turner, Mucin structure, aggregation, physiological functions and biomedical applications,, Curr. Opin. Colloid and Interface Sci., 11 (2006), 164.  doi: 10.1016/j.cocis.2005.11.001.  Google Scholar

[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.  doi: 10.1038/352070a0.  Google Scholar

[4]

A. F. M. Barton, Handbook of polymer-liquid interaction parameters and solubility parameters,, CRC press, (1990).   Google Scholar

[5]

M. C. Calderer, H. Chen, C. Micek and Y. Mori, A dynamic model of polyelectrolyte gels,, SIAM J. Appl. Math., 73 (2013), 104.  doi: 10.1137/110855296.  Google Scholar

[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.  doi: 10.1016/0009-8981(83)90242-5.  Google Scholar

[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.  doi: 10.1172/JCI114171.  Google Scholar

[8]

R. S. Crowther and C. Marriott, Counter-ion binding to mucus glycoproteins,, J. Pharm. Pharmacol., 36 (1984), 21.  doi: 10.1111/j.2042-7158.1984.tb02980.x.  Google Scholar

[9]

M. Doi and S. F. Edwards, Theory of Polymer Dynamics,, Clarendon Press, (1986).   Google Scholar

[10]

C. J. Durning and K. N. Morman, Nonlinear swelling of polymer gels,, J. Chem. Phys., 98 (1993), 4275.  doi: 10.1063/1.465034.  Google Scholar

[11]

P. J. Flory, Principles of Polymer Chemistry,, Cornell University Press, (1953).   Google Scholar

[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).  doi: 10.1088/1742-6596/269/1/012011.  Google Scholar

[13]

A. Katchalsky and I. Michaeli, Polyelectrolyte gels in salt solutions,, J. Polym. Sci., 15 (1955), 69.  doi: 10.1002/pol.1955.120157906.  Google Scholar

[14]

J. P. Keener, S. Sircar and A. Fogelson, Kinetics of swelling gels,, SIAM J. Appl. Math., 71 (2011), 854.  doi: 10.1137/100796984.  Google Scholar

[15]

J. P. Keener, S. Sircar and A. Fogelson, Influence of free energy on swelling kinetics of gels,, Phys. Rev. E, 83 (2011).  doi: 10.1103/PhysRevE.83.041802.  Google Scholar

[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).  doi: 10.1152/ajpgi.00547.2005.  Google Scholar

[17]

R. C. Lisle, Increased expression of sulfated gp300 and acinar tissue pathology in pancreas of CFTR (-/-) mice,, Am. J. Physiol., 268 (1995).  doi: 10.1177/44.1.8543783.  Google Scholar

[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).  doi: 10.1063/1.4772405.  Google Scholar

[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.  doi: 10.1016/j.jtbi.2014.09.037.  Google Scholar

[20]

T. Tanaka and D. Fillmore, Kinetics of swelling gels,, J. Chem. Phys., 70 (1979), 1214.  doi: 10.1063/1.437602.  Google Scholar

[21]

P. Verdugo, Hydration kinetics of exocytosed mucins in cultured secretory cells of the rabbit trachea: A new model,, Mucus and mucosa, 109 (1984), 212.  doi: 10.1002/9780470720905.ch15.  Google Scholar

[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.  doi: www.ncbi.nlm.nih.gov/pubmed/3502764.  Google Scholar

[23]

P. Verdugo, Goblet cells secretion and mucogenesis,, Annu. Rev. Physiol., 52 (1990), 157.  doi: 10.1146/annurev.ph.52.030190.001105.  Google Scholar

[24]

P. Verdugo, Polymer gel phase transition in condensation-decondensation of secretory products,, Adv. Polm. Sci., 110 (2005), 145.  doi: 10.1007/BFb0021131.  Google Scholar

[25]

P. Verdugo, Cilia, Mucus and Mucociliary Interactions,, Chap 19, (1998).   Google Scholar

[26]

J. P. Villar, Mucin Granule Intraluminal Organization,, Am. J. Respir. Cell Mol. Biol., 36 (2007), 183.  doi: 10.1165/rcmb.2006-0291TR.  Google Scholar

[27]

C. Wang, Y. Li and Z. Hu, Swelling kinetics of polymer gels,, Macromolecules, 30 (1997), 4727.  doi: 10.1021/ma9613648.  Google Scholar

[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.  doi: 10.1007/s00249-003-0344-5.  Google Scholar

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.  doi: 10.1016/j.yexcr.2005.06.010.  Google Scholar

[2]

R. Bansil and B. S. Turner, Mucin structure, aggregation, physiological functions and biomedical applications,, Curr. Opin. Colloid and Interface Sci., 11 (2006), 164.  doi: 10.1016/j.cocis.2005.11.001.  Google Scholar

[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.  doi: 10.1038/352070a0.  Google Scholar

[4]

A. F. M. Barton, Handbook of polymer-liquid interaction parameters and solubility parameters,, CRC press, (1990).   Google Scholar

[5]

M. C. Calderer, H. Chen, C. Micek and Y. Mori, A dynamic model of polyelectrolyte gels,, SIAM J. Appl. Math., 73 (2013), 104.  doi: 10.1137/110855296.  Google Scholar

[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.  doi: 10.1016/0009-8981(83)90242-5.  Google Scholar

[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.  doi: 10.1172/JCI114171.  Google Scholar

[8]

R. S. Crowther and C. Marriott, Counter-ion binding to mucus glycoproteins,, J. Pharm. Pharmacol., 36 (1984), 21.  doi: 10.1111/j.2042-7158.1984.tb02980.x.  Google Scholar

[9]

M. Doi and S. F. Edwards, Theory of Polymer Dynamics,, Clarendon Press, (1986).   Google Scholar

[10]

C. J. Durning and K. N. Morman, Nonlinear swelling of polymer gels,, J. Chem. Phys., 98 (1993), 4275.  doi: 10.1063/1.465034.  Google Scholar

[11]

P. J. Flory, Principles of Polymer Chemistry,, Cornell University Press, (1953).   Google Scholar

[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).  doi: 10.1088/1742-6596/269/1/012011.  Google Scholar

[13]

A. Katchalsky and I. Michaeli, Polyelectrolyte gels in salt solutions,, J. Polym. Sci., 15 (1955), 69.  doi: 10.1002/pol.1955.120157906.  Google Scholar

[14]

J. P. Keener, S. Sircar and A. Fogelson, Kinetics of swelling gels,, SIAM J. Appl. Math., 71 (2011), 854.  doi: 10.1137/100796984.  Google Scholar

[15]

J. P. Keener, S. Sircar and A. Fogelson, Influence of free energy on swelling kinetics of gels,, Phys. Rev. E, 83 (2011).  doi: 10.1103/PhysRevE.83.041802.  Google Scholar

[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).  doi: 10.1152/ajpgi.00547.2005.  Google Scholar

[17]

R. C. Lisle, Increased expression of sulfated gp300 and acinar tissue pathology in pancreas of CFTR (-/-) mice,, Am. J. Physiol., 268 (1995).  doi: 10.1177/44.1.8543783.  Google Scholar

[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).  doi: 10.1063/1.4772405.  Google Scholar

[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.  doi: 10.1016/j.jtbi.2014.09.037.  Google Scholar

[20]

T. Tanaka and D. Fillmore, Kinetics of swelling gels,, J. Chem. Phys., 70 (1979), 1214.  doi: 10.1063/1.437602.  Google Scholar

[21]

P. Verdugo, Hydration kinetics of exocytosed mucins in cultured secretory cells of the rabbit trachea: A new model,, Mucus and mucosa, 109 (1984), 212.  doi: 10.1002/9780470720905.ch15.  Google Scholar

[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.  doi: www.ncbi.nlm.nih.gov/pubmed/3502764.  Google Scholar

[23]

P. Verdugo, Goblet cells secretion and mucogenesis,, Annu. Rev. Physiol., 52 (1990), 157.  doi: 10.1146/annurev.ph.52.030190.001105.  Google Scholar

[24]

P. Verdugo, Polymer gel phase transition in condensation-decondensation of secretory products,, Adv. Polm. Sci., 110 (2005), 145.  doi: 10.1007/BFb0021131.  Google Scholar

[25]

P. Verdugo, Cilia, Mucus and Mucociliary Interactions,, Chap 19, (1998).   Google Scholar

[26]

J. P. Villar, Mucin Granule Intraluminal Organization,, Am. J. Respir. Cell Mol. Biol., 36 (2007), 183.  doi: 10.1165/rcmb.2006-0291TR.  Google Scholar

[27]

C. Wang, Y. Li and Z. Hu, Swelling kinetics of polymer gels,, Macromolecules, 30 (1997), 4727.  doi: 10.1021/ma9613648.  Google Scholar

[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.  doi: 10.1007/s00249-003-0344-5.  Google Scholar

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