Simulating kinetic processes in time and space on a lattice

Mathematical Modelling of Natural Phenomena

Volumn 6, Issue 6, 2011, Pages 159-197

  Gill, J P ^a   Shaw, K M ^a   Rountree, B L ^c   Kehl, C E ^a   Chiel, H J ^a,b  

^a Department of Biology ^*  (United States)

^b Case Western Reserve University   (United States)

^c LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Artificial chemistry; Autopoiesis; Chemical reactions; Diffusion; Donnan equilibrium; Education in biomathematics; Enzyme kinetics; Kinetics; Lattice models; Lotka Volterra; Michaelis Menten; Nernst potential; Open source; Origin of life; Predator prey model; Resting potential; Simulation

Indexed keywords

ARTIFICIAL CHEMISTRIES; AUTOPOIESIS; DONNAN EQUILIBRIUM; LATTICE MODELS; LOTKA-VOLTERRA; MICHAELIS-MENTEN; NERNST POTENTIAL; OPEN-SOURCE; ORIGIN OF LIFE; PREDATOR-PREY MODELS; RESTING POTENTIAL; SIMULATION;

EDUCATION COMPUTING; ELECTROCHEMICAL PROPERTIES; ENZYME KINETICS; KINETICS; LAPTOP COMPUTERS; ORDINARY DIFFERENTIAL EQUATIONS; TEACHING;

COMPUTER SIMULATION;

EID: 80053945126     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20116609     Document Type: Article

References (34)

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.
2. P. Atkins, J. de Paula. Physical chemistry. W. H. Freeman, New York, 7th ed., 2002.
3. M. Branch, S. Wright. The Nernst/Goldman equation simulator. http://www.nernstgoldman.physiology.arizona.edu/.
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.
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.
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.
7. P. Dittrich, J. Ziegler, W. Banzhaf. Artificial chemistries-a review. Artif. Life, 7 (2001), No. 3, 225-275.
8. A. Einstein. A ber die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen. Ann. Phys.-Berlin, 17 (1905), 549-560.
9. B. M. Frezza. Deterministic versus stochastic chemical kinetics. http://demonstrations.wolfram.com/DeterministicVersusStochasticChemicalKinetics/ .
10. B. M. Frezza. Michaelis-Menten enzyme kinetics and the steady-state approximation. http://demonstrations.wolfram.com/ MichaelisMentenEnzymeKineticsAndTheSteadyStateApproximation/.
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.
12. R. Grima, S. Schnell. Modelling reaction kinetics inside cells. Essays Biochem., 45 (2008), 41-56.
13. W. S. C. Gurney, R. M. Nisbet. Ecological dynamics. Oxford Univ. Press, New York, 1998.
14. B. Hille. Ionic channels of excitable membranes. Sinauer Associates, Sunderland, MA, 3rd ed., 2001.
15. T. J. Hutton. Evolvable self-reproducing cells in a two-dimensional artificial chemistry. Artif. Life, 13 (2007), No. 1, 11-30.
16. D. Johnston, S. M. Wu. Foundations of cellular neurophysiology. MIT Press, Cambridge, 1994.
17. E. R. Kandel, J. H. Schwartz, T. M. Jessell. Principles of neural science. McGraw-Hill, 4th ed., 2000.
18. K. Kang, S. Redner. Fluctuation-dominated kinetics in diffusion-controlled reactions. Phys. Rev. A, 32 (1985), No. 1, 435-447.
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.
20. R. Kutner. Chemical diffusion in the lattice gas of non-interacting particles. Phys. Lett. A, 81 (1981), No. 4, 239-240.
21. F. Leyvraz, S. Redner. Spatial structure in diffusion-limited two-species annihilation. Phys. Rev. A, 46 (1992), No. 6, 3132-3147.
22. B. McMullin. Thirty years of computational autopoiesis: a review. Artif. Life, 10 (2004), No. 3, 277-295.
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.
24. A. A. Ovchinnikov, Y. B. Zeldovich. Role of density fluctuations in bimolecular reaction kinetics. Chem. Phys., 28 (1978), 215-218.
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.
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.
27. H. Suzuki. An approach toward emulating molecular interaction with a graph. Aust. J. Chem., 59 (2006), No. 12, 869-873.
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.
29. D. Toussaint, F. Wilczek. Particle-antiparticle annihilation in diffusive motion. J. Chem. Phys., 78 (1983), No. 5, 2642-2647.
30. J. Trefil, H. J. Morowitz, E. Smith. The origin of life. Am. Sci., 97 (2009), No. 3, 206-213.
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.
32. E. W. Weisstein. Predator-prey equations. http://demonstrations.wolfram. com/{\penalty 0}Predator{}PreyEquations/.
33. T. Weisstein. Michaelis-Menten enzyme kinetics. http://bioquest.org/ esteem/{\penalty 0}esteem-details.php?product-id=246.
34. T. Weisstein, R. Salinas, J. R. Jungck. Two-species model. http://bioquest.org/esteem/{\penalty 0}esteem-details.php?product-id=203.