Fluctuations in morphogens often lead to gene expression domains with rough boundaries during development. A mechanism is described whereby intracellular noise can help coordinate cellular decisions during patterning and thereby sharpen expression boundaries.

The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations [M. Flegg, J. Chapman, and R. Erban, J. Roy. Soc. Interface, 9 (2012), pp. 859-868]. It is a multiscale (hybrid) algorithm which uses stochastic reaction-diffusion models with different levels of detail in different parts of the computational domain. The coupling condition on the interface between different modeling regimes of the TRM was previously derived for onedimensional models. In this paper, the TRM is generalized to higher dimensional reaction-diffusion systems. Coupling Brownian dynamics models with compartment-based models on regular (square) two-dimensional lattices is studied in detail. In this case, the interface between different modeling regimes contains either flat parts or right-angle corners. Both cases are studied in the paper. For flat interfaces, it is shown that the one-dimensional theory can be used along the line perpendicular to the TRM interface. In the direction tangential to the interface, two choices of the TRM parameters are presented. Their applicability depends on the compartment size and the time step used in the molecular-based regime. The two-dimensional generalization of the TRM is also discussed in the case of corners.

Morphogen gradients induce sharply defined domains of gene expression in a concentration-dependent manner, yet how cells interpret these signals in the face of spatial and temporal noise remains unclear. Using fluorescence lifetime imaging microscopy (FLIM) and phasor analysis to measure endogenous retinoic acid (RA) directly in vivo, we have investigated the amplitude of noise in RA signaling, and how modulation of this noise affects patterning of hindbrain segments (rhombomeres) in the zebrafish embryo. We demonstrate that RA forms a noisy gradient during critical stages of hindbrain patterning and that cells use distinct intracellular binding proteins to attenuate noise in RA levels. Increasing noise disrupts sharpening of rhombomere boundaries and proper patterning of the hindbrain. These findings reveal novel cellular mechanisms of noise regulation, which are likely to play important roles in other aspects of physiology and disease.DOI: http://dx.doi.org/10.7554/eLife.14034.001

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How to choose the computational compartment or cell size for the stochastic simulation of a reaction–diffusion system is still an open problem, and a number of criteria have been suggested. A generalized measure of the noise for finite-dimensional systems based on the largest eigenvalue of the covariance matrix of the number of molecules of all species has been suggested as a measure of the overall fluctuations in a multivariate system, and we apply it here to a discretized reaction–diffusion system. We show that for a broad class of first-order reaction networks this measure converges to the square root of the reciprocal of the smallest mean species number in a compartment at the steady state. We show that a suitably re-normalized measure stabilizes as the volume of a cell approaches zero, which leads to a criterion for the maximum volume of the compartments in a computational grid. We then derive a new criterion based on the sensitivity of the entire network, not just of the fastest step, that predicts a grid size that assures that the concentrations of all species converge to a spatially-uniform solution. This criterion applies for all orders of reactions and for reaction rate functions derived from singular perturbation or other reduction methods, and encompasses both diffusing and non-diffusing species. We show that this predicts the maximal allowable volume found in a linear problem, and we illustrate our results with an example motivated by anterior-posterior pattern formation in Drosophila, and with several other examples.