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Nonlinear stability of stationary points in the problem of Robe
Ion mediated crosslink driven mucous swelling kinetics
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 |
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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