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

In: Modeling, Simulation and Optimization of Complex Processes

Author

Listed:
  • Markus Hegland

    (ANU and ARC Centre in Bioinformatics, Mathematical Sciences Institute)

  • Conrad Burden

    (ANU, Mathematical Sciences Institute and John Curtin School of Medical Research)

  • Lucia Santoso

    (ANU and ARC Centre in Bioinformatics, Mathematical Sciences Institute)

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.

Suggested Citation

  • Markus Hegland & Conrad Burden & Lucia Santoso, 2008. "Modelling Gene Regulatory Networks Using Galerkin Techniques Based on State Space Aggregation and Sparse Grids," Springer Books, in: Hans Georg Bock & Ekaterina Kostina & Hoang Xuan Phu & Rolf Rannacher (ed.), Modeling, Simulation and Optimization of Complex Processes, pages 259-272, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-79409-7_17
    DOI: 10.1007/978-3-540-79409-7_17
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