A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems

Burrage, Kevin, Hegland, M., Macnamara, Shev, & Sidje, Roger (2006) A Krylov-based finite state projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems. In Langville, A. N. & Stewart, W. J. (Eds.) Proceedings of the Markov 150th Anniversary Conference, Boston Books, Charleston, South Carolina, pp. 21-38.


Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

Impact and interest:

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

ID Code: 46148
Item Type: Conference Paper
Refereed: Yes
ISBN: 9781932482355 (online ebook) 9781932482348 (print)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Deposited On: 27 Sep 2011 01:03
Last Modified: 27 Sep 2011 01:03

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page