-
Previous Article
Migration and orientation of endothelial cells on micropatterned polymers: A simple model based on classical mechanics
- DCDS-B Home
- This Issue
-
Next Article
Multidimensional stability of disturbed pyramidal traveling fronts in the Allen-Cahn equation
On an ODE-PDE coupling model of the mitochondrial swelling process
1. | Institute of Computational Biology, Helmholtz Center Munich, Ingolstädter, Landstrasse 1, 85764 Neuherberg, Germany |
2. | Helmholtz Zentrum München, Institute of Computational Biology, Ingolstädter Landstrasse1, D-85764 Neuherberg, |
3. | Department of Applied Physics, Waseda University, 3-4-1, Okubo, Tokyo, 169-8555 |
4. | Institute of Molecular Toxicology and Pharmscology, Helmholtz Center Munich, Ingolstädter, Landstrasse 1, 85764 Neuherberg, Germany, Germany |
References:
[1] |
B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts and P. Walter, Molecular Biology of the Cell, 5th edition, Garland Science, 2007. |
[2] |
M. A. Aon, S. Cortassa, E. Marban and B. O'Rourke, Synchronized whole cell oscillations in mitochondrial metabolism triggered by a local release of reactive oxygen species in cardiac myocytes, Journal of Biological Chemistry, 278 (2003), 44735-44744.
doi: 10.1074/jbc.M302673200. |
[3] |
M. A. Aon, S. Cortassa and B. O'Rourke, Percolation and criticality in a mitochondrial network, Proceedings of the National Academy of Sciences of USA, 101 (2004), 4447-4452.
doi: 10.1073/pnas.0307156101. |
[4] |
A. Babin and M. Vishik, Attractors of Evolution Equations, North Holland, 1992. |
[5] |
S. Baranov, I. Stavrovskaya, A. Brown, A. Tyryshkin and B. Kristal, Kinetic model for $Ca^{2+}$-induced permeability transition in energized liver mitochondria discriminates between inhibitor mechanisms, Journal of Biological Chemistry, 283 (2008), 665-676. |
[6] |
H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions Dans Les Espaces de Hilbert, vol. 5, North Holland, 1973. |
[7] |
H. Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011. |
[8] |
G. Calamita, D. Ferri, P. Gena, G. Liquori, A. Cavalier, D. Thomas and M. Svelto, The inner mitochondrial membrane has aquaporin-8 water channels and is highly permeable to water, Journal of Biological Chemistry, 280 (2005), 17149-17153.
doi: 10.1074/jbc.C400595200. |
[9] |
V. Chepyzhov and M. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, 2002. |
[10] |
S. Eisenhofer, A Coupled System of Ordinary and Partial Differential Equations Modeling the Swelling of Mitochondria,, PhD Thesis, ().
|
[11] |
S. Eisenhofer, F. Toókos, B. A. Hense, S. Schulz, F. Filbir and H. Zischka, A mathematical model of mitochondrial swelling, BMC Research Notes, 3 (2010), p67.
doi: 10.1186/1756-0500-3-67. |
[12] |
D. Gilbarg and T. N. S., Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, 1983. |
[13] |
D. Green and G. Kroemer, The pathophysiology of mitochondrial cell death, Science, 305 (2004), 626-629.
doi: 10.1126/science.1099320. |
[14] |
D. Hunter, R. Haworth and J. Southard, Relationship between configuration, function, and permeability in calcium-treated mitochondria, Journal of Biological Chemistry, 251 (1976), 5069-5077. |
[15] |
G. Kroemer, L. Galluzzi and C. Brenner, Mitochondrial membrane permeabilization in cell death, Physiological Reviews, 87 (2007), 99-163.
doi: 10.1152/physrev.00013.2006. |
[16] |
G. Leoni and M. Morini, Necessary and sufficient conditions for the chain rule in $W_{loc}^{1,1}(\mathbbR^n ; \mathbbR^d)$ and $BV_{loc}(\mathbbR^n ; \mathbbR^d )$, J. Eur. Math. Soc., 9 (2007), 219-252.
doi: 10.4171/JEMS/78. |
[17] |
S. Massari, Kinetic analysis of the mitochondrial permeability transition, Journal of Biological Chemistry, 271 (1996), 31942-31948. |
[18] |
S. Naghdi, M. Waldeck-Weiermair, I. Fertschai, M. Poteser, W. Graier and R. Malli, Mitochondrial $Ca^{2+}$ uptake and not mitochondrial motility is required for STIM1-Orai1-dependent store-operated $Ca^{2+}$ entry, Journal of Cell Science, 123 (2010), 2553-2564. |
[19] |
M. Ôtani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, Cauchy problems, Journal of Differential Equations, 46 (1982), 268-299.
doi: 10.1016/0022-0396(82)90119-X. |
[20] |
P. Petit, M. Goubern, P. Diolez, S. Susin, N. Zamzami and G. Kroemer, Disruption of the outer mitochondrial membrane as a result of large amplitude swelling: The impact of irreversible permeability transition, FEBS letters, 426 (1998), 111-116.
doi: 10.1016/S0014-5793(98)00318-4. |
[21] |
V. Petronilli, C. Cola, S. Massari, R. Colonna and P. Bernardi, Physiological effectors modify voltage sensing by the cyclosporin A-sensitive permeability transition pore of mitochondria, Journal of Biological Chemistry, 268 (1993), 21939-21945. |
[22] |
A. Pokhilko, F. Ataullakhanov and E. Holmuhamedov, Mathematical model of mitochondrial ionic homeostasis: Three modes of $Ca^{2+}$ transport, Journal of Theoretical Biology, 243 (2006), 152-169.
doi: 10.1016/j.jtbi.2006.05.025. |
[23] |
R. Rizzuto, S. Marchi, M. Bonora, P. Aguiari, A. Bononi, D. De Stefani, C. Giorgi, S. Leo, A. Rimessi, R. Siviero, E. Zecchini and P. Pinton, $Ca^{2+}$ transfer from the ER to mitochondria: When, how and why, Biochimica et Biophysica Acta (BBA)-Bioenergetics, 1787 (2009), 1342-1351. |
[24] |
R. Rizzuto and T. Pozzan, Microdomains of intracellular $Ca^{2+}$: Molecular determinants and functional consequences, Physiological Reviews, 86 (2006), 369-408. |
[25] |
V. Selivanov, F. Ichas, E. Holmuhamedov, L. Jouaville, Y. Evtodienko and J. Mazat, A model of mitochondrial $Ca^{2+}$-induced $Ca^{2+}$ release simulating the $Ca^{2+}$ oscillations and spikes generated by mitochondria, Biophysical Chemistry, 72 (1998), 111-121. |
[26] |
H. Zischka, N. Larochette, F. Hoffmann, D. Hamöller, N. Jägemann, J. Lichtmannegger, L. Jennen, J. Müller-Höcker, F. Roggel, M. Göttlicher, A. M. Vollmar and G. Kroemer, Electrophoretic analysis of the mitochondrial outer membrane rupture induced by permeability transition, Analytical Chemistry, 80 (2008), 5051-5058. |
show all references
References:
[1] |
B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts and P. Walter, Molecular Biology of the Cell, 5th edition, Garland Science, 2007. |
[2] |
M. A. Aon, S. Cortassa, E. Marban and B. O'Rourke, Synchronized whole cell oscillations in mitochondrial metabolism triggered by a local release of reactive oxygen species in cardiac myocytes, Journal of Biological Chemistry, 278 (2003), 44735-44744.
doi: 10.1074/jbc.M302673200. |
[3] |
M. A. Aon, S. Cortassa and B. O'Rourke, Percolation and criticality in a mitochondrial network, Proceedings of the National Academy of Sciences of USA, 101 (2004), 4447-4452.
doi: 10.1073/pnas.0307156101. |
[4] |
A. Babin and M. Vishik, Attractors of Evolution Equations, North Holland, 1992. |
[5] |
S. Baranov, I. Stavrovskaya, A. Brown, A. Tyryshkin and B. Kristal, Kinetic model for $Ca^{2+}$-induced permeability transition in energized liver mitochondria discriminates between inhibitor mechanisms, Journal of Biological Chemistry, 283 (2008), 665-676. |
[6] |
H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions Dans Les Espaces de Hilbert, vol. 5, North Holland, 1973. |
[7] |
H. Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011. |
[8] |
G. Calamita, D. Ferri, P. Gena, G. Liquori, A. Cavalier, D. Thomas and M. Svelto, The inner mitochondrial membrane has aquaporin-8 water channels and is highly permeable to water, Journal of Biological Chemistry, 280 (2005), 17149-17153.
doi: 10.1074/jbc.C400595200. |
[9] |
V. Chepyzhov and M. Vishik, Attractors for Equations of Mathematical Physics, American Mathematical Society, 2002. |
[10] |
S. Eisenhofer, A Coupled System of Ordinary and Partial Differential Equations Modeling the Swelling of Mitochondria,, PhD Thesis, ().
|
[11] |
S. Eisenhofer, F. Toókos, B. A. Hense, S. Schulz, F. Filbir and H. Zischka, A mathematical model of mitochondrial swelling, BMC Research Notes, 3 (2010), p67.
doi: 10.1186/1756-0500-3-67. |
[12] |
D. Gilbarg and T. N. S., Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, 1983. |
[13] |
D. Green and G. Kroemer, The pathophysiology of mitochondrial cell death, Science, 305 (2004), 626-629.
doi: 10.1126/science.1099320. |
[14] |
D. Hunter, R. Haworth and J. Southard, Relationship between configuration, function, and permeability in calcium-treated mitochondria, Journal of Biological Chemistry, 251 (1976), 5069-5077. |
[15] |
G. Kroemer, L. Galluzzi and C. Brenner, Mitochondrial membrane permeabilization in cell death, Physiological Reviews, 87 (2007), 99-163.
doi: 10.1152/physrev.00013.2006. |
[16] |
G. Leoni and M. Morini, Necessary and sufficient conditions for the chain rule in $W_{loc}^{1,1}(\mathbbR^n ; \mathbbR^d)$ and $BV_{loc}(\mathbbR^n ; \mathbbR^d )$, J. Eur. Math. Soc., 9 (2007), 219-252.
doi: 10.4171/JEMS/78. |
[17] |
S. Massari, Kinetic analysis of the mitochondrial permeability transition, Journal of Biological Chemistry, 271 (1996), 31942-31948. |
[18] |
S. Naghdi, M. Waldeck-Weiermair, I. Fertschai, M. Poteser, W. Graier and R. Malli, Mitochondrial $Ca^{2+}$ uptake and not mitochondrial motility is required for STIM1-Orai1-dependent store-operated $Ca^{2+}$ entry, Journal of Cell Science, 123 (2010), 2553-2564. |
[19] |
M. Ôtani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdifferential operators, Cauchy problems, Journal of Differential Equations, 46 (1982), 268-299.
doi: 10.1016/0022-0396(82)90119-X. |
[20] |
P. Petit, M. Goubern, P. Diolez, S. Susin, N. Zamzami and G. Kroemer, Disruption of the outer mitochondrial membrane as a result of large amplitude swelling: The impact of irreversible permeability transition, FEBS letters, 426 (1998), 111-116.
doi: 10.1016/S0014-5793(98)00318-4. |
[21] |
V. Petronilli, C. Cola, S. Massari, R. Colonna and P. Bernardi, Physiological effectors modify voltage sensing by the cyclosporin A-sensitive permeability transition pore of mitochondria, Journal of Biological Chemistry, 268 (1993), 21939-21945. |
[22] |
A. Pokhilko, F. Ataullakhanov and E. Holmuhamedov, Mathematical model of mitochondrial ionic homeostasis: Three modes of $Ca^{2+}$ transport, Journal of Theoretical Biology, 243 (2006), 152-169.
doi: 10.1016/j.jtbi.2006.05.025. |
[23] |
R. Rizzuto, S. Marchi, M. Bonora, P. Aguiari, A. Bononi, D. De Stefani, C. Giorgi, S. Leo, A. Rimessi, R. Siviero, E. Zecchini and P. Pinton, $Ca^{2+}$ transfer from the ER to mitochondria: When, how and why, Biochimica et Biophysica Acta (BBA)-Bioenergetics, 1787 (2009), 1342-1351. |
[24] |
R. Rizzuto and T. Pozzan, Microdomains of intracellular $Ca^{2+}$: Molecular determinants and functional consequences, Physiological Reviews, 86 (2006), 369-408. |
[25] |
V. Selivanov, F. Ichas, E. Holmuhamedov, L. Jouaville, Y. Evtodienko and J. Mazat, A model of mitochondrial $Ca^{2+}$-induced $Ca^{2+}$ release simulating the $Ca^{2+}$ oscillations and spikes generated by mitochondria, Biophysical Chemistry, 72 (1998), 111-121. |
[26] |
H. Zischka, N. Larochette, F. Hoffmann, D. Hamöller, N. Jägemann, J. Lichtmannegger, L. Jennen, J. Müller-Höcker, F. Roggel, M. Göttlicher, A. M. Vollmar and G. Kroemer, Electrophoretic analysis of the mitochondrial outer membrane rupture induced by permeability transition, Analytical Chemistry, 80 (2008), 5051-5058. |
[1] |
Chang Zhang, Fang Li, Jinqiao Duan. Long-time behavior of a class of nonlocal partial differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 749-763. doi: 10.3934/dcdsb.2018041 |
[2] |
Matthias Gerdts, Sven-Joachim Kimmerle. Numerical optimal control of a coupled ODE-PDE model of a truck with a fluid basin. Conference Publications, 2015, 2015 (special) : 515-524. doi: 10.3934/proc.2015.0515 |
[3] |
Igor Chueshov, Stanislav Kolbasin. Long-time dynamics in plate models with strong nonlinear damping. Communications on Pure and Applied Analysis, 2012, 11 (2) : 659-674. doi: 10.3934/cpaa.2012.11.659 |
[4] |
Marcio Antonio Jorge da Silva, Vando Narciso. Long-time dynamics for a class of extensible beams with nonlocal nonlinear damping*. Evolution Equations and Control Theory, 2017, 6 (3) : 437-470. doi: 10.3934/eect.2017023 |
[5] |
Pelin G. Geredeli, Azer Khanmamedov. Long-time dynamics of the parabolic $p$-Laplacian equation. Communications on Pure and Applied Analysis, 2013, 12 (2) : 735-754. doi: 10.3934/cpaa.2013.12.735 |
[6] |
Rong Wang, Yihong Du. Long-time dynamics of a diffusive epidemic model with free boundaries. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 2201-2238. doi: 10.3934/dcdsb.2020360 |
[7] |
Tristan Roget. On the long-time behaviour of age and trait structured population dynamics. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2551-2576. doi: 10.3934/dcdsb.2018265 |
[8] |
Linghai Zhang. Long-time asymptotic behaviors of solutions of $N$-dimensional dissipative partial differential equations. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 1025-1042. doi: 10.3934/dcds.2002.8.1025 |
[9] |
Andrea Giorgini. On the Swift-Hohenberg equation with slow and fast dynamics: well-posedness and long-time behavior. Communications on Pure and Applied Analysis, 2016, 15 (1) : 219-241. doi: 10.3934/cpaa.2016.15.219 |
[10] |
Francesca Bucci, Igor Chueshov. Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 557-586. doi: 10.3934/dcds.2008.22.557 |
[11] |
Irena Lasiecka, To Fu Ma, Rodrigo Nunes Monteiro. Long-time dynamics of vectorial von Karman system with nonlinear thermal effects and free boundary conditions. Discrete and Continuous Dynamical Systems - B, 2018, 23 (3) : 1037-1072. doi: 10.3934/dcdsb.2018141 |
[12] |
Xinguang Yang, Baowei Feng, Thales Maier de Souza, Taige Wang. Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 363-386. doi: 10.3934/dcdsb.2018084 |
[13] |
Manuel Núñez. The long-time evolution of mean field magnetohydrodynamics. Discrete and Continuous Dynamical Systems - B, 2004, 4 (2) : 465-478. doi: 10.3934/dcdsb.2004.4.465 |
[14] |
Adam Bobrowski, Katarzyna Morawska. From a PDE model to an ODE model of dynamics of synaptic depression. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2313-2327. doi: 10.3934/dcdsb.2012.17.2313 |
[15] |
Fatiha Alabau-Boussouira. On the influence of the coupling on the dynamics of single-observed cascade systems of PDE's. Mathematical Control and Related Fields, 2015, 5 (1) : 1-30. doi: 10.3934/mcrf.2015.5.1 |
[16] |
Mouhamadou Aliou M. T. Baldé, Diaraf Seck. Coupling the shallow water equation with a long term dynamics of sand dunes. Discrete and Continuous Dynamical Systems - S, 2016, 9 (5) : 1521-1551. doi: 10.3934/dcdss.2016061 |
[17] |
Jean-Paul Chehab, Pierre Garnier, Youcef Mammeri. Long-time behavior of solutions of a BBM equation with generalized damping. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 1897-1915. doi: 10.3934/dcdsb.2015.20.1897 |
[18] |
Yang Liu. Long-time behavior of a class of viscoelastic plate equations. Electronic Research Archive, 2020, 28 (1) : 311-326. doi: 10.3934/era.2020018 |
[19] |
A. Kh. Khanmamedov. Long-time behaviour of doubly nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1373-1400. doi: 10.3934/cpaa.2009.8.1373 |
[20] |
Yihong Du, Yoshio Yamada. On the long-time limit of positive solutions to the degenerate logistic equation. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 123-132. doi: 10.3934/dcds.2009.25.123 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]