Are we in the Times of Theoretical Biology?
DOI:
https://doi.org/10.3989/arbor.2010.746n1255Keywords:
Theoretical biology, stochasticity, pattern formation, kinetic modelsAbstract
During the last times there has been an increasing interest by physicists and mathematicians in the study of problems allowing to understand biological questions. On the other hand, progress in experimental techniques are making possible to obtain a huge amound of information about the mechanisms used by cells. In this article some mathematical research lines whose study has been motivated by biological problems are described.
Downloads
References
1 W. Alt, “Biased random walks models for chemotaxis and related diffusion approximations”, J. Math. Biol. 9, 147-177, 1980. doi:10.1007/BF00275919 PMid:7365332
2 W. Alt y M. Dembo, “Cytoplasm dynamics and cell motion: Two phase flow models”, Mathematical Biosciences 156, 207-228, 1999. doi:10.1016/S0025-5564(98)10067-6
3 D. Andreucci, P. Bisegna, G. Caruso, H. E. Hamm y E. DiBenedetto, “Mathematical models of the spatio-temporal dynamics of second messengers in visual transduction”, Biophysical J. 85, 1358-1376, 2003. doi:10.1016/S0006-3495(03)74570-6
4 A.L. Barabási, Linked: The New Science of Networks, Perseus, Cambridge, MA, 2002.
5 H. C. Berg, Random walks in biology, Princeton Univ. Press, 1993.
6 T. Bollenbach, K. Kruse, P. Pantazis, M. González-Gaitán, F. Jülicher, “Robust formation of morphogen gradients”, Phys. Rev. Lett. 94, 2005.
7 E. O. Budrene y H. C. Berg, “Dynamics of formation of symmetrical patterns by chemotactic bacteria”, Nature 376, 49-53, 1995. doi:10.1038/376049a0 PMid:7596432
8 D’Arcy Thompson, On Growth and Form, Cambridge University Press, 1942.
9 R. B. Dickinson y R. T. Tranquillo, “Transport equations and indices for random and biased cell migration based on single cell properties”, SIAM J. Appl. Math. 55, 5, 1419-1454, 1995. doi:10.1137/S003613999223733X
10 S. Douady y Y. Couder, “Phyllotaxis as a physical self-organized growth process”, Phys. Rev. Lett. 68, 2098-2101, 1992. doi:10.1103/PhysRevLett.68.2098 PMid:10045303
11 R. Erban, I. G. Kevrekidis, David Adalsteinsson, Timothy C. Elston, “Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation”, Journal of Chemical Physics, Volume 124, Issue 8, 084106, 17 pages, 2006.
12 R. Erban and J. Chapman, “Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions”, Physical Biology, vol. 6, n.º 4, 046001, 2009.
13 M. Feinberg, “The existence and uniqueness of steady states for a class of chemical reaction networks”, Arch. Rat. Mech. Anal., 132, 311-370, 1995. doi:10.1007/BF00375614
14 Y. C. Fung, Biomechanics, Springer Verlag, 1984.
15 E. Geigant y M. Stoll, “Bifurcation analysis of an orientational aggregation model”, J. Math. Biol. 46 (6), 537-563, 2003. doi:10.1007/s00285-002-0187-1 PMid:12783181
16 D. T. Gillespie, “A general method for numerically simulating the stochastic time evolution of coupled chemical reactions”, J. Comput. Phys. 22: 403-34, 1976. doi:10.1016/0021-9991(76)90041-3
17 A. Marciniak-Czochra, “Receptorbased models with diffusion-driven instability for pattern formation in hydra”, J. Biol. Sys. 11: 293-324, 2003. doi:10.1142/S0218339003000889
18 H. Meinhardt, A. Gierer, “Applications of a theory of biological pattern formation based on lateral inhibition”, J. Cell Sci. 15, 321-346, 1974. PMid:4859215
19 N. Mittal, E. O. Budrene, M. P. Brenner y A. van Oudenaarden, “Motility of Escherilia coli cells in clusters formed by chemotactic aggregation”, Proc. Nat. Acad. Sci. 100, 23, 13259-13263, 2003. doi:10.1073/pnas.2233626100 PMid:14597724 PMCid:263772
20 A. Mogilner y L. Edelstein-Keshet, “Spatio-angular order in populations of self-aligning objects: formation of oriented patches”, Phys. D 89, 3-4, 346-367, 1996.
21 C. Nüsslein-Volhard, Coming to Life, How genes drive development, Kales Press, 2006.
22 H. G. Othmer and A. Stevens, “Aggregation, blow-up and collapse. The ABC’s of taxis in reinforced random walks”, SIAM J. Appl. Math. 57, 4, 1044-1081, 1997.
23 C. S. Patlak, “Random walk with persistence and external bias”, Bull. Math. Biophysics 15, 311-338, 1957. doi:10.1007/BF02476407
24 J. A. Sherratt, P. K. Maini, W. Jäger, W. Müller, “A receptor based model for pattern formation in hydra”, Forma 10, 77-95, 1995.
25 G. Shinar, U. Alon y M. Feinberg, “Sensitivity and robustness in chemical reaction networks”, SIAM J. Appl. Math., vol. 69, 4, 977-998, 2009. doi:10.1137/080719820
26 E. Schrödinger (1944): What is life?, Cambridge University Press.
27 A. Stevens y J. J. L. Velázquez, “PDEs and Non-diffusive structures”, Nonlinearity, 21 T283-T289, 2008.
28 A. Trembley, Memoires pour servir à l’histoire d’un genre de polypes d’eau douce, à bras en forme de cornes, Jean and Herman Verbeek, Leiden, 1744.
29 A. M. Turing, “The chemical basis of morphogenesis”, Phil. Trans. Roy. Soc., B 237 37-72, 1952.
30 S. Vogel, Life in Moving Fluids: The Physical Biology of Flow, Princeton Univ. Press, 1996.
31 A. Wagner, Robustness and Evolvability in Living Systems, Princeton University Press, 2005.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2010 Consejo Superior de Investigaciones Científicas (CSIC)

This work is licensed under a Creative Commons Attribution 4.0 International License.
© CSIC. Manuscripts published in both the printed and online versions of this Journal are the property of Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a “Creative Commons Attribution 4.0 International” (CC BY 4.0) License. You may read the basic information and the legal text of the license. The indication of the CC BY 4.0 License must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the published by the Editor, is not allowed.