Latent space of a small genetic network: Geometry of dynamics and information
Rabea Seyboldt, Juliette Lavoie, Adrien Henry, Jules Vanaret, Mariela D. Petkova, Thomas Gregor, and Paul François. Proceedings of the National Academy of Science 119 (26): e2113651119 (2022).
Significance
In living systems all processes are intrinsically dynamic. But even the most basic biological dynamics are of such high-dimensional character that it is often difficult to deduce representations containing the most essential features with high predictive power. Here we consider the dynamics of a small genetic network driving early fly development and derive a picture representation that intuitively encodes the biological notion of positional information. We show how gene regulation and network circuitry are associated with geometric features in this picture, and how a parsimonious model for fly development separating time and space emerges naturally. Our work illustrates how small, informative representations of biological data serve for intuitive interpretation of complex biological regulation and dynamics.
Abstract
The high-dimensional character of most biological systems presents genuine challenges for modeling and prediction. Here we propose a neural network–based approach for dimensionality reduction and analysis of biological gene expression data, using, as a case study, a well-known genetic network in the early Drosophila embryo, the gap gene patterning system. We build an autoencoder compressing the dynamics of spatial gap gene expression into a two-dimensional (2D) latent map. The resulting 2D dynamics suggests an almost linear model, with a small bare set of essential interactions. Maternally defined spatial modes control gap genes positioning, without the classically assumed intricate set of repressive gap gene interactions. This, surprisingly, predicts minimal changes of neighboring gap domains when knocking out gap genes, consistent with previous observations. Latent space geometries in maternal mutants are also consistent with the existence of such spatial modes. Finally, we show how positional information is well defined and interpretable as a polar angle in latent space. Our work illustrates how optimization of small neural networks on medium-sized biological datasets is sufficiently informative to capture essential underlying mechanisms of network function.
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