Hillenbrand, Patrick; Gerland, Ulrich; Tkacik, GasperISTA
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to infer their global position within a tissue or an organism by reading out local gene expression levels. The patterning system is thus said to encode positional information, a concept that was formalized recently in the framework of information theory. Here we introduce a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolpert's paradigmatic "French Flag" model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise. Our model, a variant of an Ising spin system, allows us to systematically explore expression patterns that optimally encode positional information. We find that optimal patterning systems use positional cues, as in the French Flag model, together with gene-gene interactions to generate combinatorial codes for position which we call "Counter" patterns. Counter patterns can also be stabilized against noise and variations in system size or morphogen dosage by longer-range spatial interactions of the type invoked in the Turing model. The simple setup proposed here qualitatively captures many of the experimentally observed properties of biological patterning systems and allows them to be studied in a single, theoretically consistent framework.
The authors would like to thank Thomas Sokolowski and Filipe Tostevin for helpful discussions. PH and UG were funded by the German Excellence Initiative via the program "Nanosystems Initiative Munich" (https://www.nano-initiative-munich.de) and the German Research Foundation via the SFB 1032 "Nanoagents for Spatiotemporal Control of Molecular and Cellular Reactions" (http://www.sfb1032.physik.uni-muenchen.de). GT was funded by the Austrian Science Fund (FWF P 28844) (http://www.fwf.ac.at).
Hillenbrand P, Gerland U, Tkačik G. Beyond the French flag model: Exploiting spatial and gene regulatory interactions for positional information. PLoS One. 2016;11(9). doi:10.1371/journal.pone.0163628
Hillenbrand, P., Gerland, U., & Tkačik, G. (2016). Beyond the French flag model: Exploiting spatial and gene regulatory interactions for positional information. PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0163628
Hillenbrand, Patrick, Ulrich Gerland, and Gašper Tkačik. “Beyond the French Flag Model: Exploiting Spatial and Gene Regulatory Interactions for Positional Information.” PLoS One. Public Library of Science, 2016. https://doi.org/10.1371/journal.pone.0163628.
P. Hillenbrand, U. Gerland, and G. Tkačik, “Beyond the French flag model: Exploiting spatial and gene regulatory interactions for positional information,” PLoS One, vol. 11, no. 9. Public Library of Science, 2016.
Hillenbrand P, Gerland U, Tkačik G. 2016. Beyond the French flag model: Exploiting spatial and gene regulatory interactions for positional information. PLoS One. 11(9), e0163628.
Hillenbrand, Patrick, et al. “Beyond the French Flag Model: Exploiting Spatial and Gene Regulatory Interactions for Positional Information.” PLoS One, vol. 11, no. 9, e0163628, Public Library of Science, 2016, doi:10.1371/journal.pone.0163628.
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