Biological pattern formation in spatio-temporally fluctuating environments

The study of biological pattern-forming systems has revealed generic features that promote robustness with respect to variations between cells or populations in morphogen and protein production rates. By contrast, less is understood about how such systems respond to spatio-temporal fluctuations in morphogen concentrations within individual cells or populations over timescales faster than or similar to growth. Such fluctuations can be caused by growth, motility or changes in the external environment. Here, we formulate a general theory of biological pattern formation in spatio-temporally fluctuating environments. Using our framework, we show how pattern-forming systems can be reduced to a low-dimensional representation based on their time-dependent response to fluctuations, complementing recent work on low-dimensional representations in fixed conditions.