Stochastic delay models for molecular clocks and somite formation

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 tau-leap method (Bt-DSSA). As a particular application we apply these ideas to modeling somite segmentation in zebrafish across a number of cells in which two linked oscillatory genes her1 and her7 are synchronized via Notch signaling between the cells.