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A key challenge in understanding subcellular organization is quantifying interpretable measurements of intracellular structures with complex multi-piece morphologies in an objective, robust and generalizable manner. Here we introduce a morphology-appropriate representation learning framework that uses 3D rotation invariant autoencoders and point clouds. This framework is used to learn representations of complex multi-piece morphologies that are independent of orientation, compact, and easy to interpret. We apply our framework to intracellular structures with punctate morphologies (e.g. DNA replication foci) and polymorphic morphologies (e.g. nucleoli). We systematically compare our framework to image-based autoencoders across several intracellular structure datasets, including a synthetic dataset with pre-defined rules of organization. We explore the trade-offs in the performance of different models by performing multi-metric benchmarking across efficiency, generative capability, and representation expressivity metrics. We find that our framework, which embraces the underlying morphology of multi-piece structures, facilitates the unsupervised discovery of sub-clusters for each structure. We show how our approach can also be applied to phenotypic profiling using a dataset of nucleolar images following drug perturbations. We implement and provide all representation learning models using CytoDL, a python package for flexible and configurable deep learning experiments., Competing Interests: Declaration of interests The authors declare no competing interests.

To investigate the fundamental question of how cellular variations arise across spatiotemporal scales in a population of identical healthy cells, we focused on nuclear growth in hiPS cell colonies as a model system. We generated a 3D timelapse dataset of thousands of nuclei over multiple days, and developed open-source tools for image and data analysis and an interactive timelapse viewer for exploring quantitative features of nuclear size and shape. We performed a data-driven analysis of nuclear growth variations across timescales. We found that individual nuclear volume growth trajectories arise from short timescale variations attributable to their spatiotemporal context within the colony. We identified a strikingly time-invariant volume compensation relationship between nuclear growth duration and starting volume across the population. Notably, we discovered that inheritance plays a crucial role in determining these two key nuclear growth features while other growth features are determined by their spatiotemporal context and are not inherited., Competing Interests: Declaration of interests The authors declare no competing interests.