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Equilibrium submanifold for a biological system
1. | Department of Mathematics, Louisiana State University, Baton Rouge, LA 7080, United States |
2. | Department of Biology, Louisiana State University, Baton Rouge, LA 70803, United States |
References:
[1] |
B. Alberts, J. Lewins, M. Raff, K. Roberts and P. Walter, editor., Intracellular vesicular traffic, in "Molecular Biology of the Cell," Fifth ed. New York, Garland Science, (2008), 749-812. |
[2] |
V. I. Arnold, "Ordinary Differential Equations," Springer, New York, 2006. |
[3] |
B. Aulbach, "Continuous and Discrete Dynamics Near Manifolds of Equilibria," Lecture Notes in Mathematics, 1058. Springer-Verlag, Berlin, 1984. |
[4] |
J. Bonifacino and B. Glick, The mechanisms of vesicle budding and fusion, Cell, 116 (2004), 153-166. |
[5] |
H. Cai, K. Reinisch and S. Ferro-Novick, Coats, tethers, Rabs, and SNAREs work together to mediate the intracellular destination of a transport vesicle, Dev. Cell, 12 (2007), 671-682.
doi: 10.1016/j.devcel.2007.04.005. |
[6] |
T. Chen, H. He and G. Church, Modeling gene expression with differential equations, "Pacific Symposium on Biocomputing' 99," World Scientific (2000), 29-40. |
[7] |
N. C. Collins, H. Thordal-Christensen, V. Lipka, S. Bau, E. Kombrink, J. L Qiu, R. Huckelhoven, M. Stein, A. Freialdenhoven, S. C. Somerville and P. Schulze-Lefert, SNARE-protein-mediated disease resistance at the plant cell wall, Nature, 425 (2003), 973-977.
doi: 10.1038/nature02076. |
[8] |
N. Kato, H. He and A. Steger, A systems model of vesicle trafficking in Arabidopsis pollen tubes, Plant Physiol., 152 (2010), 590-601.
doi: 10.1104/pp.109.148700. |
[9] |
M. de Maio, Therapeutic uses of botulinum toxin: From facial palsy to autonomic disorders, Expert. Opin. Biol. Ther., 8 (2008), 791-798.
doi: 10.1517/14712598.8.6.791. |
[10] |
H. Gong, D. Sengupta, A. Linstedt and R. Schwartz, Simulated de novo assembly of Golgi compartments by selective cargo capture during vesicle budding and targeted vesicle fusion, Biophysical Journal, 95 (2008), 1674-1688.
doi: 10.1529/biophysj.107.127498. |
[11] |
R. Heinrich and T. Rapoport, Generation of nonidentical compartments in vesicular transport systems, Journal of Cell Biology, 168 (2005), 271-280.
doi: 10.1083/jcb.200409087. |
[12] |
R. Jahn and R. H. Scheller, SNAREs-engines for membrane fusion, Nat. Rev. Mol. Cell Biol., 7 (2006), 631-643.
doi: 10.1038/nrm2002. |
[13] |
J. Samaj, J. Muller, M. Beck, N. Bohm and D. Menzel, Vesicular trafficking, cytoskeleton and signalling in root hairs and pollen tubes, Trends Plant Sci., 11 ( 2006), 594-600.
doi: 10.1016/j.tplants.2006.10.002. |
[14] |
C. Taubes, "Modeling Differential Equations in Biology," Second edition. Cambridge University Press, Cambridge, 2008 |
[15] |
J. H. Williams, Novelties of the flowering plant pollen tube underlie diversification of a key life history stage, Proc. Natl. Acad. Sci. USA, 105 (2008), 11259-11263.
doi: 10.1073/pnas.0800036105. |
show all references
References:
[1] |
B. Alberts, J. Lewins, M. Raff, K. Roberts and P. Walter, editor., Intracellular vesicular traffic, in "Molecular Biology of the Cell," Fifth ed. New York, Garland Science, (2008), 749-812. |
[2] |
V. I. Arnold, "Ordinary Differential Equations," Springer, New York, 2006. |
[3] |
B. Aulbach, "Continuous and Discrete Dynamics Near Manifolds of Equilibria," Lecture Notes in Mathematics, 1058. Springer-Verlag, Berlin, 1984. |
[4] |
J. Bonifacino and B. Glick, The mechanisms of vesicle budding and fusion, Cell, 116 (2004), 153-166. |
[5] |
H. Cai, K. Reinisch and S. Ferro-Novick, Coats, tethers, Rabs, and SNAREs work together to mediate the intracellular destination of a transport vesicle, Dev. Cell, 12 (2007), 671-682.
doi: 10.1016/j.devcel.2007.04.005. |
[6] |
T. Chen, H. He and G. Church, Modeling gene expression with differential equations, "Pacific Symposium on Biocomputing' 99," World Scientific (2000), 29-40. |
[7] |
N. C. Collins, H. Thordal-Christensen, V. Lipka, S. Bau, E. Kombrink, J. L Qiu, R. Huckelhoven, M. Stein, A. Freialdenhoven, S. C. Somerville and P. Schulze-Lefert, SNARE-protein-mediated disease resistance at the plant cell wall, Nature, 425 (2003), 973-977.
doi: 10.1038/nature02076. |
[8] |
N. Kato, H. He and A. Steger, A systems model of vesicle trafficking in Arabidopsis pollen tubes, Plant Physiol., 152 (2010), 590-601.
doi: 10.1104/pp.109.148700. |
[9] |
M. de Maio, Therapeutic uses of botulinum toxin: From facial palsy to autonomic disorders, Expert. Opin. Biol. Ther., 8 (2008), 791-798.
doi: 10.1517/14712598.8.6.791. |
[10] |
H. Gong, D. Sengupta, A. Linstedt and R. Schwartz, Simulated de novo assembly of Golgi compartments by selective cargo capture during vesicle budding and targeted vesicle fusion, Biophysical Journal, 95 (2008), 1674-1688.
doi: 10.1529/biophysj.107.127498. |
[11] |
R. Heinrich and T. Rapoport, Generation of nonidentical compartments in vesicular transport systems, Journal of Cell Biology, 168 (2005), 271-280.
doi: 10.1083/jcb.200409087. |
[12] |
R. Jahn and R. H. Scheller, SNAREs-engines for membrane fusion, Nat. Rev. Mol. Cell Biol., 7 (2006), 631-643.
doi: 10.1038/nrm2002. |
[13] |
J. Samaj, J. Muller, M. Beck, N. Bohm and D. Menzel, Vesicular trafficking, cytoskeleton and signalling in root hairs and pollen tubes, Trends Plant Sci., 11 ( 2006), 594-600.
doi: 10.1016/j.tplants.2006.10.002. |
[14] |
C. Taubes, "Modeling Differential Equations in Biology," Second edition. Cambridge University Press, Cambridge, 2008 |
[15] |
J. H. Williams, Novelties of the flowering plant pollen tube underlie diversification of a key life history stage, Proc. Natl. Acad. Sci. USA, 105 (2008), 11259-11263.
doi: 10.1073/pnas.0800036105. |
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