Multicellular mathematical models of somitogenesis

Abstract

Somitogenesis is an important pattern formation process in the developmental biology of vertebrates. The phenomenon has received wide attention from experimental, theoretical, and computational biologists. Numerous mathematical models of the process have been proposed, with the clock and wavefront mechanism rising to prominence over the last ten years. This work presents two multicellular mathematical models of somitogenesis. The first is a phenomenological phase oscillator model that reproduces both the clock and wavefront aspects of somitogenesis, but lacks a biological basis. The second is a biologically informed delay differential equation model of the clock-wave that is produced by coordinated oscillatory gene expression across many cells. Careful and efficient model construction, parameter estimation, and model validation identify important nonlinear mechanisms in the genetic control circuit of the somitogenesis clock. In particular, a graded control protein combined with differential decay of clock protein monomers and dimers is found to be a key mechanism for slowing oscillations and generating experimentally observed waves of gene expression. This represents a mode of combinatorial control that has not been previously examined in somitogenesis, and warrants further experimental and theoretical investigation.