Free Access
Math. Model. Nat. Phenom.
Volume 6, Number 6, 2011
Biomathematics Education
Page(s) 159 - 197
Section Discrete Modeling
Published online 05 October 2011
  1. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter. Molecular biology of the cell. Garland Science, New York, 4th ed., 2002. [Google Scholar]
  2. P. Atkins, J. de Paula. Physical chemistry. W. H. Freeman, New York, 7th ed., 2002. [Google Scholar]
  3. M. Branch, S. Wright. The Nernst/Goldman equation simulator. [Google Scholar]
  4. B. R. Brooks, C. L. Brooks, A. D. Mackerell, L. Nilsson, R. J. Petrella, B. Roux, Y. Won, G. Archontis, C. Bartels, S. Boresch, A. Caflisch, L. Caves, Q. Cui, A. R. Dinner, M. Feig, S. Fischer, J. Gao, M. Hodoscek, W. Im, K. Kuczera, T. Lazaridis, J. Ma, V. Ovchinnikov, E. Paci, R. W. Pastor, C. B. Post, J. Z. Pu, M. Schaefer, B. Tidor, R. M. Venable, H. L. Woodcock, X. Wu, W. Yang, D. M. York, M. Karplus. CHARMM: the biomolecular simulation program. J. Comput. Chem., 30 (2009), No. 10, 1545–1614. [CrossRef] [PubMed] [Google Scholar]
  5. H. Casanova, F. Berman, T. Bartol, E. Gokcay, T. Sejnowski, A. Birnbaum, J. Dongarra, M. Miller, M. Ellisman, M. Faerman, G. Obertelli, R. Wolski, S. Pomerantz, J. Stiles. The virtual instrument: support for grid-enabled MCell simulations. Int. J. High Perform. C., 18 (2004), No. 1, 3–17. [CrossRef] [Google Scholar]
  6. P. S. di Fenizio, P. Dittrich, W. Banzhaf. Spontaneous formation of proto-cells in an universal artificial chemistry on a planar graph. In: J. Keleman, P. Sosik, editors. Advances in Artificial Life. 6th European Conference, ECAL 2001, 2001 Sep 10–14, Prague, Czech Republic. Lect. Notes Comput. Sc., 2159 (2001), 206–215. [Google Scholar]
  7. P. Dittrich, J. Ziegler, W. Banzhaf. Artificial chemistries - a review. Artif. Life, 7 (2001), No. 3, 225–275. [CrossRef] [PubMed] [Google Scholar]
  8. A. Einstein. Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen. Ann. Phys.-Berlin, 17 (1905), 549–560. [CrossRef] [Google Scholar]
  9. B. M. Frezza. Deterministic versus stochastic chemical kinetics. [Google Scholar]
  10. B. M. Frezza. Michaelis-Menten enzyme kinetics and the steady-state approximation. [Google Scholar]
  11. R. F. Galán. Analytical calculation of the frequency shift in phase oscillators driven by colored noise: implications for electrical engineering and neuroscience. Phys. Rev. E, 80 (2009), No. 3, 036113. [CrossRef] [Google Scholar]
  12. R. Grima, S. Schnell. Modelling reaction kinetics inside cells. Essays Biochem., 45 (2008), 41–56. [CrossRef] [PubMed] [Google Scholar]
  13. W. S. C. Gurney, R. M. Nisbet. Ecological dynamics. Oxford Univ. Press, New York, 1998. [Google Scholar]
  14. B. Hille. Ionic channels of excitable membranes. Sinauer Associates, Sunderland, MA, 3rd ed., 2001. [Google Scholar]
  15. T. J. Hutton. Evolvable self-reproducing cells in a two-dimensional artificial chemistry. Artif. Life, 13 (2007), No. 1, 11–30. [CrossRef] [PubMed] [Google Scholar]
  16. D. Johnston, S. M. Wu. Foundations of cellular neurophysiology. MIT Press, Cambridge, 1994. [Google Scholar]
  17. E. R. Kandel, J. H. Schwartz, T. M. Jessell. Principles of neural science. McGraw-Hill, 4th ed., 2000. [Google Scholar]
  18. K. Kang, S. Redner. Fluctuation-dominated kinetics in diffusion-controlled reactions. Phys. Rev. A, 32 (1985), No. 1, 435–447. [CrossRef] [PubMed] [Google Scholar]
  19. Z. Konkoli. Diffusion controlled reactions, fluctuation dominated kinetics, and living cell biochemistry. In: S. B. Cooper, V. Danors, editors. Computational Models from Nature. 5th Workshop on Developments in Computational Models, DCM 2009, 2009 Jul 11, Rhodes, Greece. EPTCS, 9 (2009), 98–107. [Google Scholar]
  20. R. Kutner. Chemical diffusion in the lattice gas of non-interacting particles. Phys. Lett. A, 81 (1981), No. 4, 239–240. [CrossRef] [Google Scholar]
  21. F. Leyvraz, S. Redner. Spatial structure in diffusion-limited two-species annihilation. Phys. Rev. A, 46 (1992), No. 6, 3132–3147. [CrossRef] [PubMed] [Google Scholar]
  22. B. McMullin. Thirty years of computational autopoiesis: a review. Artif. Life, 10 (2004), No. 3, 277–295. [CrossRef] [PubMed] [Google Scholar]
  23. P. H. Nelson, A. B. Kaiser, D. M. Bibby. Simulation of diffusion and adsorption in zeolites. J. Catal., 127 (1991), No. 1, 101–112. [CrossRef] [Google Scholar]
  24. A. A. Ovchinnikov, Y. B. Zeldovich. Role of density fluctuations in bimolecular reaction kinetics. Chem. Phys., 28 (1978), 215–218. [CrossRef] [Google Scholar]
  25. J. C. Phillips, R. Braun, W. Wang, J. Gumbart, E. Tajkhorshid, E. Villa, C. Chipot, R. D. Skeel, L. Kalé, K. Schulten. Scalable molecular dynamics with NAMD. J. Comput. Chem., 26 (2005), No. 16, 1781–1802. [CrossRef] [PubMed] [Google Scholar]
  26. S. Schnell, T. E. Turner. Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog. Biophys. Mol. Bio., 85 (2004), 235–260. [CrossRef] [Google Scholar]
  27. H. Suzuki. An approach toward emulating molecular interaction with a graph. Aust. J. Chem., 59 (2006), No. 12, 869–873. [CrossRef] [Google Scholar]
  28. K. Takahashi, N. Ishikawa, Y. Sadamoto, H. Sasamoto, S. Ohta, A. Shiozawa, F. Miyoshi, Y. Naito, Y. Nakayama, M. Tomita. E-Cell 2: multi-platform E-Cell simulation system. Bioinformatics, 19 (2003), No. 13, 1727–1729. [CrossRef] [PubMed] [Google Scholar]
  29. D. Toussaint, F. Wilczek. Particle-antiparticle annihilation in diffusive motion. J. Chem. Phys., 78 (1983), No. 5, 2642–2647. [CrossRef] [Google Scholar]
  30. J. Trefil, H. J. Morowitz, E. Smith. The origin of life. Am. Sci., 97 (2009), No. 3, 206–213. [CrossRef] [Google Scholar]
  31. F. Varela, H. Maturana, R. Uribe. Autopoiesis: the organization of living systems, its characterization and a model. Biosystems, 5 (1974), No. 4, 187–196. [CrossRef] [PubMed] [Google Scholar]
  32. E. W. Weisstein. Predator-prey equations.{\penalty 0}Predator{}PreyEquations/. [Google Scholar]
  33. T. Weisstein. Michaelis-Menten enzyme kinetics.{\penalty 0}esteem_details.php?product_id=246. [Google Scholar]
  34. T. Weisstein, R. Salinas, J. R. Jungck. Two-species model.{\penalty 0}esteem_details.php?product_id=203. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.