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1.
1.H. Kitano, Science 295, 16621664 (2002).
http://dx.doi.org/10.1126/science.1069492
2.
2.H. Kitano, Nature 420, 206210 (2002).
http://dx.doi.org/10.1038/nature01254
3.
3.T.E. Turner, S. Schnell, and K. Burrage, Comput. Biol. Chem. 28, 165 (2004).
4.
4.M. Thattai and A. van Oudenaarden, PNAS. USA 98, 86148619 (2001).
http://dx.doi.org/10.1073/pnas.151588598
5.
5.M.B. Elowitz et al., Science 297, 11831186 (2002).
http://dx.doi.org/10.1126/science.1070919
6.
6.D.J. Wilkinson, Stochastic modelling for systems biology (Chapman & Hall/CRC, 2006).
7.
7.C. Gardiner, K. McNeil, D. Walls, and I. Matheson, J. Stat. Phys. 14, 307 (1976).
http://dx.doi.org/10.1007/BF01030197
8.
8.F. Baras and M. Malek-Mansour, Phys. Rev. E 54, 61396148 (1996).
http://dx.doi.org/10.1103/PhysRevE.54.6139
9.
9.G. Nicolis and I. Prigogine, Self-organization in non-equilibrium systems (Wiley-Interscience, New York, 1977).
10.
10.N.N. Batada et al., PNAS. USA 101(17), 64456449 (2004).
http://dx.doi.org/10.1073/pnas.0401314101
11.
11.U.S. Bhalla, Biophys. J. 87, 733 (2004).
http://dx.doi.org/10.1529/biophysj.104.040469
12.
12.M. Howard, Trends in Cell Biology 22(6), 311317 (2012).
http://dx.doi.org/10.1016/j.tcb.2012.03.002
13.
13.D.T. Gillespie, J. Phys. Chem. 81, 23402361 (1977).
http://dx.doi.org/10.1021/j100540a008
14.
14.N.G. van Kampen, Stochastic processes in physics and chemistry (Elsevier, Amsterdam, North-Holland, 2007).
15.
15.D.T. Gillespie, J. Comp. Phys. 22, 403434 (1976).
http://dx.doi.org/10.1016/0021-9991(76)90041-3
16.
16.D.T. Gillespie, J. Chem. Phys. 115, 17161733 (2001).
http://dx.doi.org/10.1063/1.1378322
17.
17.M. Rathinam et al., J. Chem. Phys. 119(24), 12784 (2003).
http://dx.doi.org/10.1063/1.1627296
18.
18.Y. Cao, D.T. Gillespie, and L. Petzold, J. Chem. Phys. 124, 044109 (2006).
http://dx.doi.org/10.1063/1.2159468
19.
19.T. Tian and K. Burrage, J. Chem. Phys. 121(21), 1035610364 (2004).
http://dx.doi.org/10.1063/1.1810475
20.
20.D.F. Anderson, J. Chem. Phys. 128(5), 054103 (2008).
http://dx.doi.org/10.1063/1.2819665
21.
21.D.F. Anderson et al., Annals of Appl. Probability 21(6), 22262262 (2011).
http://dx.doi.org/10.1214/10-AAP756
22.
22.A. Chatterjee, D.G. Vlachos, and M.A. Katsoulakis, J. Chem. Phys. 122, 024112 (2005).
http://dx.doi.org/10.1063/1.1833357
23.
23.Y. Hu and T. Li, J. Chem. Phys. 130, 124109 (2009).
http://dx.doi.org/10.1063/1.3091269
24.
24.M.F. Pettigrew and H. Resat, J. Chem. Phys. 126, 084101 (2007).
http://dx.doi.org/10.1063/1.2432326
25.
25.H. Salis and Y. Kaznessis, J. Chem. Phys. 123, 214106 (2005).
http://dx.doi.org/10.1063/1.2131050
26.
26.W.E. Weinan et al., J. Chem. Phys. 123, 194107 (2005).
http://dx.doi.org/10.1063/1.2109987
27.
27.C.V. Rao and A.P. Arkin, J. Chem. Phys. 118, 49995010 (2003).
http://dx.doi.org/10.1063/1.1545446
28.
28.E.L. Haseltine and J.B. Rawlings, J. Chem. Phys. 117, 6959 (2002).
http://dx.doi.org/10.1063/1.1505860
29.
29.H. Salis and Y. Kaznessis, J. Chem. Phys. 122, 054103 (2005).
http://dx.doi.org/10.1063/1.1835951
30.
30.A. Samant and D. Vlachos, J. Chem. Phys. 123, 144114 (2005).
http://dx.doi.org/10.1063/1.2046628
31.
31.M. Howard and A.D. Rutenberg, Phys. Rev. Lett. 90, 128102 (2003).
http://dx.doi.org/10.1103/PhysRevLett.90.128102
32.
32.S.A. Isaacson and C.S. Peskin, SIAM J. Sci. Comput. 28, 4774 (2006).
http://dx.doi.org/10.1137/040605060
33.
33.A.B. Sturzia and C.J. Lumsden, J. Comput. Phys. 127, 196207 (1996).
http://dx.doi.org/10.1006/jcph.1996.0168
34.
34.D. Fange and J. Elf, PLOS Comput. Biol. 2, 637 (2006).
35.
35.J. Elf and M. Ehrenberg, Systems Biology 1(2), 230236 (2004).
http://dx.doi.org/10.1049/sb:20045021
36.
36.D.T. Gillespie et al., J. Chem. Phys. 138, 170901 (2013).
http://dx.doi.org/10.1063/1.4801941
37.
37.T. Marquez-Lago and K. Burrage, J. Chem. Phys. 127, 104101 (2007).
http://dx.doi.org/10.1063/1.2771548
38.
38.D. Rossinelli, B. Bayati, and P. Koumoutsakos, Chem. Phys. Letters 451(1-3), 136140 (2008).
http://dx.doi.org/10.1016/j.cplett.2007.11.055
39.
39.W. Koh and K.T. Blackwell, J. Chem. Phys. 134, 154103 (2011).
http://dx.doi.org/10.1063/1.3572335
40.
40.L. Ferm, A. Hellander, and P. Lötstedt, J. Comput. Phys. 229, 343360 (2010).
http://dx.doi.org/10.1016/j.jcp.2009.09.030
41.
41.S. Lampoudi et al., J. Chem. Phys. 130, 094104 (2009).
http://dx.doi.org/10.1063/1.3074302
42.
42.W. Koh and K.T. Blackwell, J. Chem. Phys. 137, 154111 (2012).
http://dx.doi.org/10.1063/1.4758459
43.
43.S. Ilie and A. Teslya, J. Chem. Phys. 136, 184101 (2012).
http://dx.doi.org/10.1063/1.4711143
44.
44.V. Sotiropoulos and Y.N. Kaznessis, J. Chem. Phys. 128, 014103 (2008).
http://dx.doi.org/10.1063/1.2812240
45.
45.S. Ilie, J. Chem. Phys. 137, 234110 (2012).
http://dx.doi.org/10.1063/1.4771660
46.
46.E. Hairer, S.P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I, 2nd ed. (Springer, Berlin, 2009).
47.
47.K. Burrage and P.M. Burrage, SIAM J. Sci. Comput. 24(3), 848864 (2002).
http://dx.doi.org/10.1137/S1064827500376922
48.
48.S. Ilie, K.R. Jackson, and W.H. Enright, Numer. Algorithms 68(4), 791812 (2015).
http://dx.doi.org/10.1007/s11075-014-9872-6
49.
49.K. Burrage, P.M. Burrage, and T. Tian, Proc. R. Soc. Lond. A 460, 373402 (2004).
http://dx.doi.org/10.1098/rspa.2003.1247
50.
50.Y. Cao and R. Erban, Bull. Math. Biology 76(12), 30513069 (2014).
51.
51.R. Erban, S.J. Chapman, and P.K. Maini, arXiv:0704.1908v2 (2007).
52.
52.G. Söderlind, Numer. Algorithms 31, 281310 (2002).
http://dx.doi.org/10.1023/A:1021160023092
53.
53.P.M. Burrage et al., J. Comput. Appl. Math. 170, 317336 (2004).
http://dx.doi.org/10.1016/j.cam.2004.01.027
54.
54.R. Strehl and S. Ilie, J. Chem. Phys. 143, 234108 (2015).
http://dx.doi.org/10.1063/1.4937491
55.
55.K. Takahashi, S. Tănase-Nicola, and P.R. ten Wolde, PNAS USA 107, 2473 (2010).
http://dx.doi.org/10.1073/pnas.0906885107
56.
56.S. Hellander, A. Hellander, and L. Petzold, Physical Review E 91, 023312 (2015).
http://dx.doi.org/10.1103/PhysRevE.91.023312
57.
57.R. Erban and S.J. Chapman, Physical Biology 6, 046001 (2009).
http://dx.doi.org/10.1088/1478-3975/6/4/046001
58.
58.M.H. Sung and J.G. McNally, Wiley Interdisciplinary Reviews: Systems Biology and Medicine 3(2), 167182 (2011).
http://dx.doi.org/10.1002/wsbm.108
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/content/aip/journal/adva/6/3/10.1063/1.4944952
2016-03-24
2016-12-05

Abstract

Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.

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