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A practical introduction to stochastic modelling of reaction-diffusion processes is presented.
S. Chandrasekhar, Stochastic problems in physics and astronomy , Reviews of Modern Physics 15
1943
Earlier work this paper cites.
A. Turing, The chemical basis of morphogenesis , Phil. Trans. Roy. Soc. Lond. 237
1952
Earlier work this paper cites.
A. Gierer and H. Meinhardt, A theory of biological pattern formation , Kybernetik 12
1972
Earlier work this paper cites.
F. Schlögl, Chemical reaction models for non-equilibrium phase transitions , Zeitschrift für Physik 253
1972
Earlier work this paper cites.
L. Arnold, Stochastic Differential Equations, theory and applications , Wiley-Interscience Publication, 1974
1974
Earlier work this paper cites.
D. Gillespie, Exact stochastic simulation of coupled chemical reactions , Journal of Physical Chemistry 81
1977
Earlier work this paper cites.
J. Schnakenberg, Simple chemical reaction systems with limit cycle behaviour , Journal of Theoretical Biology 81
1979
Earlier work this paper cites.
H. Berg, Random Walks in Biology , Princeton University Press, 1983
1983
Earlier work this paper cites.
E. Zauderer, Partial Differential Equations of Applied Mathematics , John Wiley & Sons, 1983
1983
Earlier work this paper cites.
G.W. Gardiner, Handbook of Stochastic Processes for physics, chemistry and natural sciences , 2 ed., Springer Verlag, 1985
1985
Earlier work this paper cites.
H. Othmer, S. Dunbar, and W Alt, Models of dispersal in biological systems , Journal of Mathematical Biology 26
1988
Earlier work this paper cites.
H. Risken, The Fokker-Planck Equation, methods of solution and applications , Springer-Verlag, 1989
1989
Earlier work this paper cites.
A. Stundzia and C. Lumsden, Stochastic simulation of coupled reaction-diffusion processes , Journal of Computational Physics 127
1996
Earlier work this paper cites.
T. Gardner, C. Cantor, and J. Collins, Construction of a genetic toggle switch in E. coli , Nature 403
2000
Cited alongside, same era.
M. Gibson and J. Bruck, Efficient exact stochastic simulation of chemical systems with many species and many channels , Journal of Physical Chemistry A 104
2000
Cited alongside, same era.
J. Paulsson, O. Berg, and M. Ehrenberg, Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation , Proceedings of the National Academy of Sciences USA 97
2000
Cited alongside, same era.
D.J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations , SIAM Review 43
2001
Cited alongside, same era.
T. Kepler and T. Elston, Stochasticity in transcriptional regulation: Origins, consequences and mathematical representations , Biophysical Journal 81
2001
C. Gadgil, C. Lee, and H. Othmer, A stochastic analysis of first-order reaction networks , Bulletin of Mathematical Biology 67
2005
Later among the works it cites.
J. Hattne, D. Fange, and J. Elf, Stochastic reaction-diffusion simulation with MesoRD , Bioinformatics 21
2005
Later among the works it cites.
C. Muratov, E. Vanden-Eijnden, and W. E, Self-induced stochastic resonance in excitable systems , Physica D 210
2005
Later among the works it cites.
G. Reeves, R. Kalifa, D. Klein, M. Lemmon, and S. Shvartsmann, Computational analysis of EGFR inhibition by Argos , Developmental biology 284
2005
Later among the works it cites.
O. Shimmi, D. Umulis, H. Othmer, and M. Connor, Faciliated transport of a Dpp/Scw heterodimer by Sog/Tsg leads to robust patterning of the Drosophila blastoderm embryo , Cell 120
2005
Later among the works it cites.
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Cited alongside, same era.
M. Elowitz, A. Levine, E. Siggia, and P. Swain, Stochastic gene expression in a single cell , Science 297
2002
Cited alongside, same era.
J. Hasty, D. McMillen, and J. Collins, Engineered gene circuits , Nature 420
2002
Cited alongside, same era.
J. Murray, Mathematical Biology , Springer Verlag, 2002
2002
Cited alongside, same era.
C. Rao, D. Wolf, and A. Arkin, Control, exploitation and tolerance of intracellular noise , Nature 420
2002
Cited alongside, same era.
L. Wolpert, R. Beddington, T. Jessel, P. Lawrence, E. Meyerowitz, and J. Smith, Principles of Development , Oxford University Press, 2002
2002
Cited alongside, same era.
I. Kevrekidis, C. Gear, J. Hyman, P. Kevrekidis, O. Runborg, and K. Theodoropoulos, Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis , Communications in Mathematical Sciences 1
2003
Cited alongside, same era.
S. Andrews and D. Bray, Stochastic simulation of chemical reactions with spatial resolution and single molecule detail , Physical Biology 1
2004
Cited alongside, same era.
R. DeVille, C. Muratov, and E. Vanden-Eijnden, Non-meanfield deterministic limits in chemical reaction kinetics , Journal of Chemical Physics 124
2006
Later among the works it cites.
R. Erban, I. Kevrekidis, D. Adalsteinsson, and T. Elston, Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation , Journal of Chemical Physics 124
2006
Later among the works it cites.
S. Isaacson and C. Peskin, Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations , SIAM Journal on Scientific Computing 28
2006
Later among the works it cites.
L. Qiao, R. Erban, C. Kelley, and I. Kevrekidis, Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computation , Journal of Chemical Physics 125
2006
Later among the works it cites.
M. Samoilov and A. Arkin, Deviant effects in molecular reaction pathways , Nature Biotechnology 24
2006
Later among the works it cites.
S. Sick, S. Reinker, J. Timmer, and T. Schlake, WNT and DKK determine hair follicle spacing through a reaction-diffusion mechanism , Science 314
2006
Later among the works it cites.
R. Erban and S. J. Chapman, Reactive boundary conditions for stochastic simulations of reaction-diffusion processes , Physical Biology 4
2007
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