Simulating Kinetic Processes in Time and Space on a Lattice

J. P. Gill; K. M. Shaw; B. L. Rountree; C. E. Kehl; H. J. Chiel

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 6, page 159-197
  • ISSN: 0973-5348

Abstract

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We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that this can be used for simulating fundamental molecular and chemical processes and even simplified models of predator–prey interactions. By giving the simulated entities spatial extent in the lattice, the particles do not interpenetrate, and clusters of particles can spatially exclude one another. Our simulation demonstrates that spatial inhomogeneity leads to different results than those that are obtained by using standard ordinary differential equation models, as previously reported.

How to cite

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Gill, J. P., et al. "Simulating Kinetic Processes in Time and Space on a Lattice." Mathematical Modelling of Natural Phenomena 6.6 (2011): 159-197. <http://eudml.org/doc/222312>.

@article{Gill2011,
abstract = {We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that this can be used for simulating fundamental molecular and chemical processes and even simplified models of predator–prey interactions. By giving the simulated entities spatial extent in the lattice, the particles do not interpenetrate, and clusters of particles can spatially exclude one another. Our simulation demonstrates that spatial inhomogeneity leads to different results than those that are obtained by using standard ordinary differential equation models, as previously reported. },
author = {Gill, J. P., Shaw, K. M., Rountree, B. L., Kehl, C. E., Chiel, H. J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {education in biomathematics; lattice models; artificial chemistry; simulation; open-source; autopoiesis; origin of life; diffusion; Nernst potential; resting potential; Donnan equilibrium; chemical reactions; kinetics; Michaelis–Menten; enzyme kinetics; Lotka–Volterra; predator–prey model; Michaelis-Menten; Lotka-Volterra; predator-prey model; biomathematics education},
language = {eng},
month = {10},
number = {6},
pages = {159-197},
publisher = {EDP Sciences},
title = {Simulating Kinetic Processes in Time and Space on a Lattice},
url = {http://eudml.org/doc/222312},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Gill, J. P.
AU - Shaw, K. M.
AU - Rountree, B. L.
AU - Kehl, C. E.
AU - Chiel, H. J.
TI - Simulating Kinetic Processes in Time and Space on a Lattice
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/10//
PB - EDP Sciences
VL - 6
IS - 6
SP - 159
EP - 197
AB - We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that this can be used for simulating fundamental molecular and chemical processes and even simplified models of predator–prey interactions. By giving the simulated entities spatial extent in the lattice, the particles do not interpenetrate, and clusters of particles can spatially exclude one another. Our simulation demonstrates that spatial inhomogeneity leads to different results than those that are obtained by using standard ordinary differential equation models, as previously reported.
LA - eng
KW - education in biomathematics; lattice models; artificial chemistry; simulation; open-source; autopoiesis; origin of life; diffusion; Nernst potential; resting potential; Donnan equilibrium; chemical reactions; kinetics; Michaelis–Menten; enzyme kinetics; Lotka–Volterra; predator–prey model; Michaelis-Menten; Lotka-Volterra; predator-prey model; biomathematics education
UR - http://eudml.org/doc/222312
ER -

References

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  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. .  URIhttp://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. Über 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. .  URIhttp://demonstrations.wolfram.com/DeterministicVersusStochasticChemicalKinetics/
  10. B. M. Frezza. Michaelis-Menten enzyme kinetics and the steady-state approximation. .  URIhttp://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. .  URIhttp://demonstrations.wolfram.com/PredatorPreyEquations/
  33. T. Weisstein. Michaelis-Menten enzyme kinetics. .  URIhttp://bioquest.org/esteem/esteemdetails.php?productid=246
  34. T. Weisstein, R. Salinas, J. R. Jungck. Two-species model. .  URIhttp://bioquest.org/esteem/esteemdetails.php?productid=203

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