Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-25T00:59:21.726Z Has data issue: false hasContentIssue false
  • English
  • Français

Boosted Hybrid Method for Solving Chemical Reaction Systems with Multiple Scales in Time and Population Size

Published online by Cambridge University Press:  20 August 2015

Yucheng Hu ,
Assyr Abdulle  and
Tiejun Li
Yucheng Hu*
Affiliation:
Laboratory of Mathematics and Applied Mathematics and School of Mathematical Sciences, Peking University, Beijing 100871, China
Assyr Abdulle*
Affiliation:
Mathematics Section, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Tiejun Li*
Affiliation:
Laboratory of Mathematics and Applied Mathematics and School of Mathematical Sciences, Peking University, Beijing 100871, China
*
Corresponding author.Email:huyc@pku.edu.cn
Email:assyr.abdulle@epfl.ch
Email:tieli@pku.edu.cn
Get access

Abstract

A new algorithm, called boosted hybrid method, is proposed for the simulation of chemical reaction systems with scale-separation in time and disparity in species population. For such stiff systems, the algorithm can automatically identify scale-separation in time and slow down the fast reactions while maintaining a good approximation to the original effective dynamics. This technique is called boosting. As disparity in species population may still exist in the boosted system, we propose a hybrid strategy based on coarse-graining methods, such as the tau-leaping method, to accelerate the reactions among large population species. The combination of the boosting strategy and the hybrid method allow for an efficient and adaptive simulation of complex chemical reactions. The new method does not need a priori knowledge of the system and can also be used for systems with hierarchical multiple time scales. Numerical experiments illustrate the versatility and efficiency of the method.

Keywords

65C0565C20Chemical reactionmultiscaleboostinghybrid method
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 4 , October 2012 , pp. 981 - 1005
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Guido, N., Wang, X., Adalsteinsson, D., McMillen, D., Hasty, J., Cantor, C., Elston, T., and Collins, J., Nature 439, 856 (2006).Google Scholar
[2]Elowitz, M., Levine, A., Siggia, E., and Swain, P., Science 297, 1183 (2002).Google Scholar
[3]Endy, D. and Brent, R., Nature 409, 391 (2001).Google Scholar
[4]Li, H., Cao, Y., Petzold, L., and Gillespie, D., Biotech. Prog. 24, 56 (2008).Google Scholar
[5]Arkin, A., Ross, J., and McAdams, H., Genetics 149, 1633 (1998).Google Scholar
[6]Adalsteinsson, D., McMillen, D., and Elston, T., BMC Bioinformatics 5, 24 (2004).Google Scholar
[7]Gillespie, D., J. Chem. Phys. 115, 1716 (2001).Google Scholar
[8]Haseltine, E. and Rawlings, J., J. Chem. Phys. 117, 6959 (2002).Google Scholar
[9]Gillespie, D., J. Comput. Phys 22, 403 (1976).CrossRefGoogle Scholar
[10]Gillespie, D., J. Phys. Chem. 81, 2340 (1977).Google Scholar
[11]Cao, Y., Petzold, L., and Rathinam, M., J. Chem. Phys. 121, 12169 (2004).Google Scholar
[12]Abdulle, A. and Li, T., Comm. Math. Sci. 6, 845 (2008).Google Scholar
[13]Abdulle, A., Hu, Y., and Li, T., J. Comp. Math. 28, 195 (2010).Google Scholar
[14]Li, T., Abdulle, A., and W. E, Comm. Comp. Phys. 3, 295 (2008).Google Scholar
[15] W. E and Engquist, B., Comm. Math. Sci. 1, 87 (2003).Google Scholar
[16]Rao, C. and Arkin, A., J. Chem. Phys. 118, 4999 (2003).CrossRefGoogle Scholar
[17]Cao, Y., Petzold, L., and Gillespie, D., J. Chem. Phys. 122, 14116 (2005).Google Scholar
[18] W. E, Liu, D., and Vanden-Eijnden, E., J. Chem. Phys. 123, 194107 (2005).Google Scholar
[19]Takahashi, K., Kaizu, K., Hu, B., and Tomita, M., Bioinformatics 20, 538 (2004).CrossRefGoogle Scholar
[20]Salis, H. and Kaznessis, Y., J. Chem. Phys. 122, 054103 (2005).Google Scholar
[21]Bracciali, A., Brunelli, M., Cataldo, E., and Degano, P., BMC Bioinformatics 9, S7 (2008).CrossRefGoogle Scholar
[22]Vasudeva, K. and Bhalla, U., Bioinformatics 20, 78 (2004).Google Scholar
[23]Burrage, K., Tian, T., and Burrage, P., Prog. Biophys. Mol. Bio. 85, 217 (2004).Google Scholar
[24]Samant, A. and Vlachos, D., J. Chem. Phys. 123, 144114 (2005).CrossRefGoogle Scholar
[25]Salis, H. and Kaznessis, Y., J. Chem. Phys. 123, 214106 (2005).Google Scholar
[26]Higham, D., SIAM Rev. 50, 347 (2008).Google Scholar
[27]Cao, Y., Gillespie, D., and Petzold, L., J. Chem. Phys. 126, 224101 (2007).Google Scholar
[28]Samant, A., Ogunnaike, B., and Vlachos, D., BMC Bioinformatics 8, 175 (2007).Google Scholar
[29]Vanden-Eijnden, E., Comm. Math. Sci. 5, 4951 (2007).Google Scholar
[30]Ren, W., Comm. Math. Sci. 5, 1027 (2007).Google Scholar
[31]Cao, Y., Gillespie, D., and Petzold, L., J. Chem. Phys. 124, 44109 (2006).Google Scholar
[32]Cao, Y., Gillespie, D., and Petzold, L., J. Chem. Phys. 123, 054104 (2005).Google Scholar
[33]Kepler, T. and Elston, T., Biophys. J. 81, 3116 (2001).Google Scholar
[34]Cao, Y., Li, H., and Petzold, L., J. Chem. Phys. 121, 4059 (2004).Google Scholar
[35]McCollum, J., Peterson, G., Cox, C., Simpson, M., and Samatova, N., Comput. Biol. Chem. 30, 39 (2006).Google Scholar
[36]Sinitsyn, N., Hengartner, N., and Nemenman, I., Proc. Natl. Acad. Sci. 106, 10546 (2009).Google Scholar