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Calcium waves with mechano-chemical couplings
1. | Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland |
2. | Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland |
References:
[1] |
D. Bia, R. Armentano, D. Craiem, J. Grignola, F. Gines, A. Simon and J. Levenson, Smooth muscle role on pulmonary arterial function during acute pulmonary hypertension in sheep,, Acta Physiol. Scand., 181 (2004), 359.
doi: 10.1111/j.1365-201X.2004.01294.x. |
[2] |
E. C. M. Crooks, On the Vol'pert theory of travelling wave solutions for parabolic equations,, Nonlinear Analysis TM & A, 26 (1996), 1621.
doi: 10.1016/0362-546X(95)00038-W. |
[3] |
P. B. Dobrin and J. M. Doyle, Vascular smooth muscle and the anisotropy of dog carotid artery,, Circ. Res., 27 (1970), 105.
doi: 10.1161/01.RES.27.1.105. |
[4] |
A. Doyle, W. Marganski and J. Lee, Calcium transients induce spatially coordinated increases in traction force during the movement of fish keratocytes,, Journal of Cell Science, 117 (2004), 2203.
doi: 10.1242/jcs.01087. |
[5] |
M. Falcke, Reading the patterns in living cells - the physics of $Ca^{2+}$ signaling,, Advances in Physics, 53 (2004), 255. Google Scholar |
[6] |
G. Flores, A. Minzoni, K. Mischaikov and V. Moll, Post-fertilization travelling waves on eggs,, Nonlinear Analysis: Theory, 36 (1999), 45.
doi: 10.1016/S0362-546X(97)00696-2. |
[7] |
D. Hong, D. Jaron, D. G. Buerk and K. A. Barbee, Heterogeneous response of microvascular endothelial cells to shear stress,, Am. J. Physiol. (Heart Circ. Physiol.), 290 (2006), 2498.
doi: 10.1152/ajpheart.00828.2005. |
[8] |
L. F. Jaffe, The path of calcium in cytosolic calcium oscillations: A unifying hypothesis,, Proc. Natl. Acad. Sci. USA, 88 (1991), 9883.
doi: 10.1073/pnas.88.21.9883. |
[9] |
L. F. Jaffe, Stretch-activated calcium channels relay fast calcium waves propagated by calcium-induced calcium influx,, Biol. Cell, 99 (2007), 75.
doi: 10.1042/BC20060031. |
[10] |
N. R. Jorgensen, S. C. Teilmann, Z. Henriksen, R. Civitelli, O. H. Sorensen and T. H. Steinberg, Activation of L-type calcium channels is required for gap junction-mediated intercellular calcium signaling in osteoblastic cells,, J. Biological Chemistry, 278 (2003), 4082.
doi: 10.1074/jbc.M205880200. |
[11] |
B. Kazmierczak and Z. Peradzynski, Calcium waves with fast buffers and mechanical effects,, Journal of Mathematical Biology, 62 (2011), 1.
doi: 10.1007/s00285-009-0323-2. |
[12] |
B. Kazmierczak and V. Volpert, Calcium waves in systems with immobile buffers as a limit of waves for systems with non zero diffusion,, Nonlinearity, 21 (2008), 71.
doi: 10.1088/0951-7715/21/1/004. |
[13] |
B. Kazmierczak and V. Volpert, Travelling calcium waves in systems with non-diffusing buffers,, Mathematical Models and Methods in Applied Sciences, 18 (2008), 883.
doi: 10.1142/S0218202508002899. |
[14] |
B. Kazmierczak and V. Volpert, Existence of heteroclinic orbits for systems satisfying monotonicity conditions,, Nonlinear Analysis: Theory, 55 (2003), 467.
doi: 10.1016/S0362-546X(03)00247-5. |
[15] |
J. Keener and J. Sneyd, "Mathematical Physiology,", Springer-Verlag, (1998).
|
[16] |
J. D. Murray, "Mathematical Biology,", 2nd edition, (1993).
doi: 10.1007/b98869. |
[17] |
K. J. Palmer, Exponential dichotomies and transversal homoclinic points,, J. Diff. Equat., 20 (1984), 225.
doi: 10.1016/0022-0396(84)90082-2. |
[18] |
Z. Peradzynski, Diffusion of calcium in biological tissues and accompanying mechano-chemical effects,, Arch. Mech., 62 (2010), 423.
|
[19] |
Z. Peradzynski and B. Kazmierczak, On mechano-chemical calcium waves,, Archive of Applied Mechanics, 74 (2005), 827.
doi: 10.1007/s00419-005-0392-7. |
[20] |
K. Piechor, Reaction-diffusion equation modelling calcium waves with fast buffering in visco-elastic environment,, Arch. Mech., 64 (2012), 477. Google Scholar |
[21] |
M. Sato, N. Ohshima and R. M. Nerem, Viscoelastic properties of cultured porcine aortic endothelial cells exposed to shear stress,, Journal of Biomechanics, 29 (1996), 461.
doi: 10.1016/0021-9290(95)00069-0. |
[22] |
J. Sneyd, P. D. Dalez and A. Duffy, Traveling waves in buffered systems: Applications to calcium waves,, SIAM J. Appl. Math., 58 (1998), 1178.
doi: 10.1137/S0036139996305074. |
[23] |
A. E. Taylor, "Introduction to Functional Analysis,", J. Wiley and Sons, (1958).
|
[24] |
A. Volpert, V. Volpert and V. Volpert, "Traveling Wave Solutions of Parabolic Systems,", AMS, (1994). Google Scholar |
[25] |
S. H. Young, H. S. Ennes, J. A. McRoberts, V. V. Chaban, S. K. Dea and E. A. Mayer, Calcium waves in colonic myocytes produced by mechanical and receptor-mediated stimulation,, Am. J. Physiol. Gastrointest. Liver Physiol., 276 (1999), 1204. Google Scholar |
show all references
References:
[1] |
D. Bia, R. Armentano, D. Craiem, J. Grignola, F. Gines, A. Simon and J. Levenson, Smooth muscle role on pulmonary arterial function during acute pulmonary hypertension in sheep,, Acta Physiol. Scand., 181 (2004), 359.
doi: 10.1111/j.1365-201X.2004.01294.x. |
[2] |
E. C. M. Crooks, On the Vol'pert theory of travelling wave solutions for parabolic equations,, Nonlinear Analysis TM & A, 26 (1996), 1621.
doi: 10.1016/0362-546X(95)00038-W. |
[3] |
P. B. Dobrin and J. M. Doyle, Vascular smooth muscle and the anisotropy of dog carotid artery,, Circ. Res., 27 (1970), 105.
doi: 10.1161/01.RES.27.1.105. |
[4] |
A. Doyle, W. Marganski and J. Lee, Calcium transients induce spatially coordinated increases in traction force during the movement of fish keratocytes,, Journal of Cell Science, 117 (2004), 2203.
doi: 10.1242/jcs.01087. |
[5] |
M. Falcke, Reading the patterns in living cells - the physics of $Ca^{2+}$ signaling,, Advances in Physics, 53 (2004), 255. Google Scholar |
[6] |
G. Flores, A. Minzoni, K. Mischaikov and V. Moll, Post-fertilization travelling waves on eggs,, Nonlinear Analysis: Theory, 36 (1999), 45.
doi: 10.1016/S0362-546X(97)00696-2. |
[7] |
D. Hong, D. Jaron, D. G. Buerk and K. A. Barbee, Heterogeneous response of microvascular endothelial cells to shear stress,, Am. J. Physiol. (Heart Circ. Physiol.), 290 (2006), 2498.
doi: 10.1152/ajpheart.00828.2005. |
[8] |
L. F. Jaffe, The path of calcium in cytosolic calcium oscillations: A unifying hypothesis,, Proc. Natl. Acad. Sci. USA, 88 (1991), 9883.
doi: 10.1073/pnas.88.21.9883. |
[9] |
L. F. Jaffe, Stretch-activated calcium channels relay fast calcium waves propagated by calcium-induced calcium influx,, Biol. Cell, 99 (2007), 75.
doi: 10.1042/BC20060031. |
[10] |
N. R. Jorgensen, S. C. Teilmann, Z. Henriksen, R. Civitelli, O. H. Sorensen and T. H. Steinberg, Activation of L-type calcium channels is required for gap junction-mediated intercellular calcium signaling in osteoblastic cells,, J. Biological Chemistry, 278 (2003), 4082.
doi: 10.1074/jbc.M205880200. |
[11] |
B. Kazmierczak and Z. Peradzynski, Calcium waves with fast buffers and mechanical effects,, Journal of Mathematical Biology, 62 (2011), 1.
doi: 10.1007/s00285-009-0323-2. |
[12] |
B. Kazmierczak and V. Volpert, Calcium waves in systems with immobile buffers as a limit of waves for systems with non zero diffusion,, Nonlinearity, 21 (2008), 71.
doi: 10.1088/0951-7715/21/1/004. |
[13] |
B. Kazmierczak and V. Volpert, Travelling calcium waves in systems with non-diffusing buffers,, Mathematical Models and Methods in Applied Sciences, 18 (2008), 883.
doi: 10.1142/S0218202508002899. |
[14] |
B. Kazmierczak and V. Volpert, Existence of heteroclinic orbits for systems satisfying monotonicity conditions,, Nonlinear Analysis: Theory, 55 (2003), 467.
doi: 10.1016/S0362-546X(03)00247-5. |
[15] |
J. Keener and J. Sneyd, "Mathematical Physiology,", Springer-Verlag, (1998).
|
[16] |
J. D. Murray, "Mathematical Biology,", 2nd edition, (1993).
doi: 10.1007/b98869. |
[17] |
K. J. Palmer, Exponential dichotomies and transversal homoclinic points,, J. Diff. Equat., 20 (1984), 225.
doi: 10.1016/0022-0396(84)90082-2. |
[18] |
Z. Peradzynski, Diffusion of calcium in biological tissues and accompanying mechano-chemical effects,, Arch. Mech., 62 (2010), 423.
|
[19] |
Z. Peradzynski and B. Kazmierczak, On mechano-chemical calcium waves,, Archive of Applied Mechanics, 74 (2005), 827.
doi: 10.1007/s00419-005-0392-7. |
[20] |
K. Piechor, Reaction-diffusion equation modelling calcium waves with fast buffering in visco-elastic environment,, Arch. Mech., 64 (2012), 477. Google Scholar |
[21] |
M. Sato, N. Ohshima and R. M. Nerem, Viscoelastic properties of cultured porcine aortic endothelial cells exposed to shear stress,, Journal of Biomechanics, 29 (1996), 461.
doi: 10.1016/0021-9290(95)00069-0. |
[22] |
J. Sneyd, P. D. Dalez and A. Duffy, Traveling waves in buffered systems: Applications to calcium waves,, SIAM J. Appl. Math., 58 (1998), 1178.
doi: 10.1137/S0036139996305074. |
[23] |
A. E. Taylor, "Introduction to Functional Analysis,", J. Wiley and Sons, (1958).
|
[24] |
A. Volpert, V. Volpert and V. Volpert, "Traveling Wave Solutions of Parabolic Systems,", AMS, (1994). Google Scholar |
[25] |
S. H. Young, H. S. Ennes, J. A. McRoberts, V. V. Chaban, S. K. Dea and E. A. Mayer, Calcium waves in colonic myocytes produced by mechanical and receptor-mediated stimulation,, Am. J. Physiol. Gastrointest. Liver Physiol., 276 (1999), 1204. Google Scholar |
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