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The expression of a few key genes determines the body plan of the fruit fly. We show that the spatial expression patterns for several of these genes scale precisely with embryo size. Discrete positional markers such as the peaks in striped patterns or the boundaries of expression domains have positions along the embryo’s major axis proportional to embryo length, accurate to within 1%. Further, the information (in bits) that graded patterns of expression provide about a cell’s position can be decomposed into information about fractional or scaled position and information about absolute position or embryo length; all information available is about scaled position, with $<$2% error. These findings imply that the underlying genetic network’s behavior exhibits scale invariance in a more precise mathematical sense. We argue that models that can explain this scale invariance also have a “zero mode” in the dynamics of gene expression, and this connects to observations on the spatial correlation of fluctuations in expression levels. 

In a developing embryo, information about the position of cells is encoded in the concentrations of morphogen molecules. In the fruit fly, the local concentrations of just a handful of proteins encoded by the gap genes are sufficient to specify position with a precision comparable to the spacing between cells along the anterior-posterior axis. This matches the precision of downstream events such as the striped patterns of expression in the pair-rule genes, but is not quite sufficient to define unique identities for individual cells. We demonstrate theoretically that this information gap can be bridged if positional errors are spatially correlated, with correlation lengths approximately $20\%$of the embryo length. We then show experimentally that these correlations are present, with the required strength, in the fluctuating positions of the pair-rule stripes, and this can be traced back to the gap genes. Taking account of these correlations, the available information matches the information needed for unique cellular specification, within error bars of approximately $2\%$. These observation support a precisionist view of information flow through the underlying genetic networks, in which accurate signals are available from the start and preserved as they are transformed into the final spatial patterns. Published by the American Physical Society2024 

Abstract The mechanical properties of the cellular nucleus are extensively studied as they play a critical role in important processes, such as cell migration, gene transcription, and stem cell differentiation. While the mechanical properties of the isolated nucleus have been tested, there is a lack of measurements about the mechanical behavior of the nucleus within intact cells and specifically about the interplay of internal nuclear components with the intracellular microenvironment, because current testing methods are based on contact and only allow studying the nucleus after isolation from a cell or disruption of cytoskeleton. Here, all‐optical Brillouin microscopy and 3D chemomechanical modeling are used to investigate the regulation of nuclear mechanics in physiological conditions. It is observed that the nuclear modulus can be modulated by epigenetic regulation targeting internal nuclear nanostructures such as lamin A/C and chromatin. It is also found that nuclear modulus is strongly regulated by cytoskeletal behavior through a robust mechanism conserved in different culturing conditions. Given the active role of cytoskeletal modulation in nearly all cell functions, this work will enable to reveal highly relevant mechanisms of nuclear mechanical regulations in physiological and pathological conditions.