Intrinsic Noise Profoundly Alters the Dynamics and Steady State of Morphogen-Controlled Bistable Genetic Switches

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.Author Summary: The bistable switch, a common regulatory sub-network, is found in many biological processes. It consists of cross-repressing components that generate a switch-like transition between two possible states. In developing tissues, bistable switches, created by cross-repressing 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. Here we use mathematical models to analyse the temporal response of such a system. 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. One of the techniques we use, Minimum Action Path theory, identifies key features of the switch without computationally expensive calculations. The results reveal a noise driven switching wave that propels the stripe boundary away from the morphogen source to eventually settle, at steady state, further from the morphogen source than in the deterministic description. Together the analysis highlights the importance dynamics in patterning and demonstrates a set of mathematical tools for studying this problem.