Quantitative Modelling of the Waddington Epigenetic Landscape

C.H. Waddington introduced the epigenetic landscape as a metaphor to represent cellular decision-making during development. Like a population of balls rolling down a rough hillside, developing cells follow specific trajectories (valleys) and eventually come to rest in one or another low-energy state that represents a mature cell type. Waddington depicted the topography of this landscape as determined by interactions among gene products, thereby connecting genotype to phenotype. In modern terms, each point on the landscape represents a state of the underlying genetic regulatory network, which in turn is described by a gene expression profile. In this chapter we demonstrate how the mathematical formalism of Hopfield networks can be used to model this epigenetic landscape. Hopfield networks are auto-associative artificial neural networks; input patterns are stored as attractors of the network and can be recalled from noisy or incomplete inputs. The resulting models capture the temporal dynamics of a gene regulatory network, yielding quantitative insight into cellular development and phenotype.