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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v6.i1.70
pages 77-86

Modeling Intrinsic Noise and Delays in Chemical Kinetics of Coupled Autoregulated Oscillating Cells

Andre Leier
Institute for Molecular Bioscience, University of Queensland, Brisbane, QLD 4072 Australia
Tatiana T. Marquez-Lago
Institute for Molecular Bioscience, University of Queensland, Brisbane, QLD 4072 Australia
Kevin Burrage
Institute for Molecular Bioscience, University of Queensland, Brisbane, QLD 4072 Australia
Pamela Burrage
Institute for Molecular Bioscience, University of Queensland, Brisbane, QLD 4072 Australia

ABSTRACT

Delays are an important feature in temporal models of genetic regulation due to slow biochemical processes, such as transcription and translation. In this paper, we show how to model intrinsic noise effects in a delayed setting by either using a delay stochastic simulation algorithm (DSSA) or, for larger and more complex systems, a generalized Binomial τ-leap method (Bτ-DSSA). As a particular application, we apply these ideas to modeling somite segmentation in zebra fish across a number of cells in which two linked oscillatory genes (her1 and her7) are synchronized via Notch signaling between the cells.