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Modelling Gene Regulatory Networks Using Galerkin Techniques Based on State Space Aggregation and Sparse Grids

  • Markus Hegland
  • Conrad Burden
  • Lucia Santoso

Abstract

An important driver of the dynamics of gene regulatory networks is noise generated by transcription and translation processes involving genes and their products. As relatively small numbers of copies of each substrate are involved, such systems are best described by stochastic models. With these models, the stochastic master equations, one can follow the time development of the probability distributions for the states defined by the vectors of copy numbers of each substance. Challenges are posed by the large discrete state spaces, and are mainly due to high dimensionality.

In order to address this challenge we propose effective approximation techniques, and, in particular, numerical techniques to solve the master equations. Two theoretical results show that the numerical methods are optimal. The techniques are combined with sparse grids to give an effective method to solve high-dimensional problems.

Keywords

Master Equation Gene Regulatory Network Sparse Grid Promoter Site Chemical Master Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Markus Hegland
    • 1
  • Conrad Burden
    • 2
  • Lucia Santoso
    • 1
  1. 1.Mathematical Sciences InstituteANU and ARC Centre in BioinformaticsAustralia
  2. 2.Mathematical Sciences Institute and John Curtin School of Medical ResearchANUAustralia

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