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A dynamic model describing heterotrophic culture of chorella and its stability analysis
Mathematical analysis of steady-state solutions in compartment and continuum models of cell polarization
1. | Department of Mathematics, Center for Complex Biological Systems & Center for Mathematical and Computational Biology, University of California, Irvine, CA 92697, United States |
2. | Department of Mathematics, Mathematica Biosciences Institute, The Ohio State University, Columbus, OH 43221, United States |
3. | Developmental and Cell Biology, Center for Complex Biological Systems & Center for Mathematical and Computational Biology, University of California, Irvina, CA 92697, United States |
4. | Department of Mathematics, Center for Complex Biological Systems & Center for Mathematical and Computational Biology, University of California, Irvine, California, 92697-3875 |
References:
[1] |
G. L. Atkins, "Multicompartment Models for Biological Systems," Willmer Brothers Limited, Birkenhead, Great Britain, 1969. |
[2] |
D. M. Bryant and K. E. Mostov, From cells to organs: Building polarized tissue, Nature Rev. Mol. Cell Biol., 9 (2008), 887-901.
doi: 10.1038/nrm2523. |
[3] |
C.-S. Chou, Q. Nie and T. M. Yi, Modeling robustness tradeoffs in yeast cell polarization induced by spatial gradients, PLoS One, 3 (2008), e3103.
doi: 10.1371/journal.pone.0003103. |
[4] |
A. Dawes and L. Edelstein-Keshet, Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a 1D model of a motile cell, Biophys. J., 92 (2007), 1-25.
doi: 10.1529/biophysj.106.090514. |
[5] |
P. Devreotes and C. Janetopoulos, Eukaryotic chemotaxis: Distinctions between directional sensing and polarization, J. Biol. Chem., 278 (2003), 20445-20448.
doi: 10.1074/jbc.R300010200. |
[6] |
J. Dobbelaere and Y. Barral, Spatial coordination of cytokinetic events by compartmentalization of the cell cortex, Science, 305 (2004), 393-396.
doi: 10.1126/science.1099892. |
[7] |
D. G. Drubin and W. J. Nelson, Origins of cell polarity, Cell, 84 (1996), 335-344.
doi: 10.1016/S0092-8674(00)81278-7. |
[8] |
A. B. Goryachev and A. V. Pokhilko, Dynamics of cdc42 network embodies a turing-type mechanism of yeast cell polarity, FEBS Lett., 582 (2008), 1437-1443.
doi: 10.1016/j.febslet.2008.03.029. |
[9] |
J. Haugh and I. Schneider, Spatial analysis of 3' phosphoinositide signaling in living fibroblasts: I. Uniform stimulation model and bounds on dimensionless groups, Biophys. J., 86 (2004), 589-598.
doi: 10.1016/S0006-3495(04)74137-5. |
[10] |
P. A. Iglesias and A. Levchenko, Modeling the cell's guidance system, Sci STKE, 2002 (2002), re12.
doi: 10.1126/stke.2002.148.re12. |
[11] |
A. Jilkine, A. F. M. Marée and L. Edelstein-Keshet, Mathematical model for spatial segregation of the Rho-family GTPases based on inhibitory crosstalk, Bull. Math. Biol., 69 (2007), 1943-1978.
doi: 10.1007/s11538-007-9200-6. |
[12] |
J. Krishnan and P. A. Iglesias, Uncovering directional sensing: Where are we headed?, Syst. Biol. (Stevenage), 1 (2004), 54-61.
doi: 10.1049/sb:20045001. |
[13] |
J. Krishnan and P. Iglesias, A modeling framework describing the enzyme regulation of membrane lipids underlying gradient perception in Dictyostelium cells, J. Theor. Biol., 229 (2004), 85-99.
doi: 10.1016/j.jtbi.2004.03.005. |
[14] |
A. Levchenko and P. A. Iglesias, Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils, Biophys. J., 82 (2002), 50-63.
doi: 10.1016/S0006-3495(02)75373-3. |
[15] |
I. Maly, H. Wiley and D. Lauffenburger, Self-organization of polarized cell signaling via autocrine circuits: Computational model analysis, Biophys. J., 86 (2004), 10-22.
doi: 10.1016/S0006-3495(04)74079-5. |
[16] |
A. Marée, A. Jilkine, A. Dawes, V. Grieneisen and L. Edelstein-Keshet, Polarization and movement of keratocytes: A multiscale modeling approach, Bull. Math. Biol., 68 (2006), 1169-1211. |
[17] |
F. R. Maxfield, Plasma membrane microdomains, Curr Opin Cell Biol, 14 (2002), 483-487.
doi: 10.1016/S0955-0674(02)00351-4. |
[18] |
H. Meinhardt, "Models of Biological Pattern Formation," Academic Press, London, 1982. |
[19] |
H. Meinhardt, Orientation of chemotactic cells and growth cones: Models and mechanisms, J. Cell Sci., 112 (1999), 2867-2874. |
[20] |
I. Mellman and W. J. Nelson, Coordinated protein sorting, targeting and distribution in polarized cells, Nature Rev. Mol. Cell Biol., 9 (2008), 833-845.
doi: 10.1038/nrm2525. |
[21] |
Y. Mori, A. Jilkine and L. Edelstein-Keshet, Wave-pinning and cell polarity from a bistable reaction-diffusion system, Biophys J., 94 (2008), 3684-3697.
doi: 10.1529/biophysj.107.120824. |
[22] |
A. Narang, Spontaneous polarization in eukaryotic gradient sensing: A mathematical model based on mutual inhibition of frontness and backness pathways, J. Theor. Biol., 240 (2006), 538-553.
doi: 10.1016/j.jtbi.2005.10.022. |
[23] |
M. Onsum and C. V. Rao, A mathematical model for neutrophil gradient sensing and polarization, PLoS Comput. Biol., 3 (2007), 436-450.
doi: 10.1371/journal.pcbi.0030036. |
[24] |
M. Otsuji, S. Ishihara, C. Co, K. Kaibuchi, A. Mochizuki and S. Kuroda, A mass conserved reaction-diffusion system captures properties of cell polarity, PLoS Comput. Biol., 3 (2007), 1040-1054.
doi: 10.1371/journal.pcbi.0030108. |
[25] |
D. Pruyne and A. Bretscher, Polarization of cell growth in yeast I. Establishment and maintenance of polarity states, J. Cell Sci., 113 (2000), 365-375. |
[26] |
Y. Sakumura, Y. Tsukada, N. Yamamoto and S. Ishii, A molecular model for axon guidance based on cross talk between Rho GTPases, Biophys. J., 89 (2005), 812-822.
doi: 10.1529/biophysj.104.055624. |
[27] |
R. Skupsky, W. Losert and R. Nossal, Distinguishing modes of eukaryotic gradient sensing, Biophys. J., 89 (2005), 2806-2823.
doi: 10.1529/biophysj.105.061564. |
[28] |
K. Subramanian and A. Narang, A mechanistic model for eukaryotic gradient sensing: Spontaneous and induced phosphoinositide polarization, J. Theor. Biol., 231 (2004), 49-67.
doi: 10.1016/j.jtbi.2004.05.024. |
[29] |
D. W. Thompson, "On Growth and Form," Dover, New York, 1992. |
[30] |
M. Tomishige, Y. Sako and A. Kusumi, Regulation mechanism of the lateral diffusion of Band 3 in erythrocyte membranes by the membrane skeleton, J. Cell Biol., 142 (1998), 989-1000.
doi: 10.1083/jcb.142.4.989. |
[31] |
A. M. Turing, The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. Lond. B, 237 (1952), 37-72.
doi: 10.1098/rstb.1952.0012. |
[32] |
M. Vicente-Manzanares and F. Sánchez-Madrid, Cell polarization: A comparative cell biology and immunological view, Clin. Dev. Immunol., 7 (2000), 51-65. |
show all references
References:
[1] |
G. L. Atkins, "Multicompartment Models for Biological Systems," Willmer Brothers Limited, Birkenhead, Great Britain, 1969. |
[2] |
D. M. Bryant and K. E. Mostov, From cells to organs: Building polarized tissue, Nature Rev. Mol. Cell Biol., 9 (2008), 887-901.
doi: 10.1038/nrm2523. |
[3] |
C.-S. Chou, Q. Nie and T. M. Yi, Modeling robustness tradeoffs in yeast cell polarization induced by spatial gradients, PLoS One, 3 (2008), e3103.
doi: 10.1371/journal.pone.0003103. |
[4] |
A. Dawes and L. Edelstein-Keshet, Phosphoinositides and Rho proteins spatially regulate actin polymerization to initiate and maintain directed movement in a 1D model of a motile cell, Biophys. J., 92 (2007), 1-25.
doi: 10.1529/biophysj.106.090514. |
[5] |
P. Devreotes and C. Janetopoulos, Eukaryotic chemotaxis: Distinctions between directional sensing and polarization, J. Biol. Chem., 278 (2003), 20445-20448.
doi: 10.1074/jbc.R300010200. |
[6] |
J. Dobbelaere and Y. Barral, Spatial coordination of cytokinetic events by compartmentalization of the cell cortex, Science, 305 (2004), 393-396.
doi: 10.1126/science.1099892. |
[7] |
D. G. Drubin and W. J. Nelson, Origins of cell polarity, Cell, 84 (1996), 335-344.
doi: 10.1016/S0092-8674(00)81278-7. |
[8] |
A. B. Goryachev and A. V. Pokhilko, Dynamics of cdc42 network embodies a turing-type mechanism of yeast cell polarity, FEBS Lett., 582 (2008), 1437-1443.
doi: 10.1016/j.febslet.2008.03.029. |
[9] |
J. Haugh and I. Schneider, Spatial analysis of 3' phosphoinositide signaling in living fibroblasts: I. Uniform stimulation model and bounds on dimensionless groups, Biophys. J., 86 (2004), 589-598.
doi: 10.1016/S0006-3495(04)74137-5. |
[10] |
P. A. Iglesias and A. Levchenko, Modeling the cell's guidance system, Sci STKE, 2002 (2002), re12.
doi: 10.1126/stke.2002.148.re12. |
[11] |
A. Jilkine, A. F. M. Marée and L. Edelstein-Keshet, Mathematical model for spatial segregation of the Rho-family GTPases based on inhibitory crosstalk, Bull. Math. Biol., 69 (2007), 1943-1978.
doi: 10.1007/s11538-007-9200-6. |
[12] |
J. Krishnan and P. A. Iglesias, Uncovering directional sensing: Where are we headed?, Syst. Biol. (Stevenage), 1 (2004), 54-61.
doi: 10.1049/sb:20045001. |
[13] |
J. Krishnan and P. Iglesias, A modeling framework describing the enzyme regulation of membrane lipids underlying gradient perception in Dictyostelium cells, J. Theor. Biol., 229 (2004), 85-99.
doi: 10.1016/j.jtbi.2004.03.005. |
[14] |
A. Levchenko and P. A. Iglesias, Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils, Biophys. J., 82 (2002), 50-63.
doi: 10.1016/S0006-3495(02)75373-3. |
[15] |
I. Maly, H. Wiley and D. Lauffenburger, Self-organization of polarized cell signaling via autocrine circuits: Computational model analysis, Biophys. J., 86 (2004), 10-22.
doi: 10.1016/S0006-3495(04)74079-5. |
[16] |
A. Marée, A. Jilkine, A. Dawes, V. Grieneisen and L. Edelstein-Keshet, Polarization and movement of keratocytes: A multiscale modeling approach, Bull. Math. Biol., 68 (2006), 1169-1211. |
[17] |
F. R. Maxfield, Plasma membrane microdomains, Curr Opin Cell Biol, 14 (2002), 483-487.
doi: 10.1016/S0955-0674(02)00351-4. |
[18] |
H. Meinhardt, "Models of Biological Pattern Formation," Academic Press, London, 1982. |
[19] |
H. Meinhardt, Orientation of chemotactic cells and growth cones: Models and mechanisms, J. Cell Sci., 112 (1999), 2867-2874. |
[20] |
I. Mellman and W. J. Nelson, Coordinated protein sorting, targeting and distribution in polarized cells, Nature Rev. Mol. Cell Biol., 9 (2008), 833-845.
doi: 10.1038/nrm2525. |
[21] |
Y. Mori, A. Jilkine and L. Edelstein-Keshet, Wave-pinning and cell polarity from a bistable reaction-diffusion system, Biophys J., 94 (2008), 3684-3697.
doi: 10.1529/biophysj.107.120824. |
[22] |
A. Narang, Spontaneous polarization in eukaryotic gradient sensing: A mathematical model based on mutual inhibition of frontness and backness pathways, J. Theor. Biol., 240 (2006), 538-553.
doi: 10.1016/j.jtbi.2005.10.022. |
[23] |
M. Onsum and C. V. Rao, A mathematical model for neutrophil gradient sensing and polarization, PLoS Comput. Biol., 3 (2007), 436-450.
doi: 10.1371/journal.pcbi.0030036. |
[24] |
M. Otsuji, S. Ishihara, C. Co, K. Kaibuchi, A. Mochizuki and S. Kuroda, A mass conserved reaction-diffusion system captures properties of cell polarity, PLoS Comput. Biol., 3 (2007), 1040-1054.
doi: 10.1371/journal.pcbi.0030108. |
[25] |
D. Pruyne and A. Bretscher, Polarization of cell growth in yeast I. Establishment and maintenance of polarity states, J. Cell Sci., 113 (2000), 365-375. |
[26] |
Y. Sakumura, Y. Tsukada, N. Yamamoto and S. Ishii, A molecular model for axon guidance based on cross talk between Rho GTPases, Biophys. J., 89 (2005), 812-822.
doi: 10.1529/biophysj.104.055624. |
[27] |
R. Skupsky, W. Losert and R. Nossal, Distinguishing modes of eukaryotic gradient sensing, Biophys. J., 89 (2005), 2806-2823.
doi: 10.1529/biophysj.105.061564. |
[28] |
K. Subramanian and A. Narang, A mechanistic model for eukaryotic gradient sensing: Spontaneous and induced phosphoinositide polarization, J. Theor. Biol., 231 (2004), 49-67.
doi: 10.1016/j.jtbi.2004.05.024. |
[29] |
D. W. Thompson, "On Growth and Form," Dover, New York, 1992. |
[30] |
M. Tomishige, Y. Sako and A. Kusumi, Regulation mechanism of the lateral diffusion of Band 3 in erythrocyte membranes by the membrane skeleton, J. Cell Biol., 142 (1998), 989-1000.
doi: 10.1083/jcb.142.4.989. |
[31] |
A. M. Turing, The chemical basis of morphogenesis, Phil. Trans. Roy. Soc. Lond. B, 237 (1952), 37-72.
doi: 10.1098/rstb.1952.0012. |
[32] |
M. Vicente-Manzanares and F. Sánchez-Madrid, Cell polarization: A comparative cell biology and immunological view, Clin. Dev. Immunol., 7 (2000), 51-65. |
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