Abstract
During tissue development, patterns of gene expression determine the spatial arrangement of cell types. In many cases, gradients of secreted signalling molecules—morphogens—guide this process by controlling downstream transcriptional networks. A mechanism commonly used in these networks to convert the continuous information provided by the gradient into discrete transitions between adjacent cell types is the genetic toggle switch, composed of cross-repressing transcriptional determinants. Previous analyses have emphasised the steady state output of these mechanisms. Here, we explore the dynamics of the toggle switch and use exact numerical simulations of the kinetic reactions, the corresponding Chemical Langevin Equation, and Minimum Action Path theory to establish a framework for studying the effect of gene expression noise on patterning time and boundary position. This provides insight into the time scale, gene expression trajectories and directionality of stochastic switching events between cell states. Taking gene expression noise into account predicts that the final boundary position of a morphogen-induced toggle switch, although robust to changes in the details of the noise, is distinct from that of the deterministic system. Moreover, the dramatic increase in patterning time close to the boundary predicted from the deterministic case is substantially reduced. The resulting stochastic switching introduces differences in patterning time along the morphogen gradient that result in a patterning wave propagating away from the morphogen source with a velocity determined by the intrinsic noise. The wave sharpens and slows as it advances and may never reach steady state in a biologically relevant time. This could explain experimentally observed dynamics of pattern formation. Together the analysis reveals the importance of dynamical transients for understanding morphogen-driven transcriptional networks and indicates that gene expression noise can qualitatively alter developmental patterning.
Highlights
Tissue development relies on the spatially and temporally organised allocation of cell identity, with each cell adopting an identity appropriate for its position within the tissue
The patterning time of a deterministic bistable switch varies with morphogen level For a genetic toggle switch such as that described by Eq (1), bistability means that the final steady state is determined by the level of the signal and the initial condition of the system
In the absence of noise, the response of the system to the signal M can be divided into a bistable regime (MB < M < MA) where the steady state is dependent on the initial conditions, and two monostable regimes (M > MA and M < MB) where the final state of the system, A or B, is independent of the initial conditions
Summary
The bistable switch, a common regulatory sub-network, is found in many biological processes. Bistable switches, created by crossrepressing transcriptional determinants, are often controlled by gradients of secreted signalling molecules—morphogens. These provide a mechanism to convert a morphogen gradient into stripes of gene expression that determine the arrangement of distinct cell types. We find that the behaviour is highly dependent on the intrinsic fluctuations that result from the stochastic nature of gene expression. This noise has a marked effect on both patterning time and the location of the stripe boundary. Together the analysis highlights the importance dynamics in patterning and demonstrates a set of mathematical tools for studying this problem
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