(B-66) Capturing Spatiotemporal Signaling Patterns in Cellular Data with Geometric Scattering Trajectory Homology

Introduction::Cell signaling plays a critical role in orchestrating the complex interactions and processes necessary for the proper functioning and survival of organisms. This intricate communication system allows cells to perceive and respond to their ever-changing environment by transmitting and processing information through a series of biochemical reactions. Although many signaling molecules and pathways have been identified, the dynamics of signaling processes, including their initiation, propagation, termination, and adaptation, are not yet fully understood. Cellular signaling networks are highly complex, involving numerous molecules, pathways, and feedback loops. These networks often show emergent properties that cannot be easily determined from the behavior of their individual components. Moreover, signaling dynamics are often non-linear and context-dependent, making it difficult to predict their outcomes based on simple linear models or assumptions.


To facilitate a quantitative understanding of complex spatiotemporal signaling activity, we developed Geometric Scattering Trajectory Homology (GSTH), a general framework that converts time-lapse signals on a cell adjacency graph into a low-dimensional trajectory. By accounting for the multi-scale nature of cellular interactions and the temporal fluctuations of signaling events, GSTH uncovers the intricate mechanisms that govern cellular communication and coordination. We tested this framework using a variety of computational models and experimental data. Our findings demonstrate that the GSTH-generated trajectory is related to the degree of synchrony, speed, and quasi-periodicity of the underlying signaling pattern. We recovered model parameters and experimental conditions by training neural networks on the trajectory, showing that our approach preserves information that characterizes various cell types, tissues, and drug treatments.



Materials and Methods:: The GSTH framework integrates geometric scattering and topological data analysis (TDA) to provide a comprehensive understanding of complex cellular interactions. This combination allows for the effective capture of both local and global patterns, as well as a robust analysis of the underlying topology. First, we construct a graph from cell positions with the time-lapse signal as node features. We then apply geometric scattering to quantify the spatiotemporal features of signaling dynamics. Geometric scattering employs wavelet-based transformations to extract multiscale representations of the signaling data, capturing the intricate hierarchical structures present in the spatial organization of cells and the temporal evolution of signaling events. These features provide a rich, multiscale characterization of the spatiotemporal patterns that are essential for understanding the complex dynamics of cellular processes.


We obtain a low dimensional trajectory of the signaling dynamics using PHATE, a manifold-geometry preserving dimensionality reduction technique. The trajectory is generated by embedding geometric scattering features for each time point. Next, we use TDA to study the higher-order properties of the PHATE trajectory by computing the persistent homology of the signal embeddings. TDA is a powerful tool for investigating the shape and connectivity of data, providing a robust, scale-invariant representation of the underlying structure. Persistent homology, a key technique within TDA, is used to capture the topological features of the data across multiple scales, revealing hidden patterns and relationships in cell signaling dynamics.



Results, Conclusions, and Discussions:: We tested the proposed GSTH framework on simulations of collective oscillatory behavior and calcium signaling in the Drosophila wing imaginal disc. First, we simulated a system of coupled oscillators at varying coupling strengths to generate signals with varying degrees of synchrony. Our results show that the low-dimensional signal embeddings produced by GSTH converge over time as the oscillators get synchronized. We can observe this behavior visually by plotting the PHATE trajectories, which ‘stall’ as the oscillators become synchronized. Next, we simulate four different patterns of calcium signaling by varying the rate of production of inositol trisphosphate (IP3) in a mathematical model of intercellular calcium signaling in the Drosophila wing imaginal disc. We show that intermittent spiking and uncoordinated transient signaling produce gaps in the PHATE trajectory, which are detected using TDA. On the other hand, spatially and temporally coordinated signaling produces smooth trajectories without gaps. We demonstrate that the model parameters used to generate the simulation can be recovered using a neural network trained on geometric scattering features, highlighting the predictive capability of our model.


Finally, we apply GSTH to three experimental datasets, consisting of: (1) calcium signaling in the basal stem cell layer of the mouse epidermis, (2) ERK signaling in oncogenic mammary epithelial cells, and (3) calcium signaling in the prefrontal visual cortex of mice. We show that GSTH can accurately classify control versus perturbations in the first two datasets with over 90% accuracy, and recover the visual stimuli presented to mice in the third dataset with over 85% accuracy.


Geometrical and topological analysis of spatiotemporal signaling can be used to understand the complex dynamics of biological systems, such as how cells process information and coordinate their behavior. By combining geometric scattering and topological data analysis, our framework can integrate local and global information, as well as geometrical and topological properties, to provide a more comprehensive understanding of spatiotemporal patterns in cell signaling. This innovative approach paves the way for the development of predictive models, improved therapeutic strategies, and a deeper understanding of the complex processes governing cellular communication and coordination.



Acknowledgements (Optional): : Research reported in this abstract was supported by a 55108527- Howard Hughes Medical Institute Scholar award, the National Institute Of Arthritis And Musculoskeletal And Skin Diseases of the NIH under award numbers R01AR063663, R01AR067755, and R01AR072668, and the National Institute On Aging of the National Institutes of Health under Award Number DP1AG066590. J.L. Moore was supported by the Lo Graduate Fellowship for Excellence in Stem Cell Research and NIH grant numbers 2T32GM007499 and 5T32HD007149. D. Bhaskar was supported by a Yale-Boehringer Ingelheim Biomedical Data Science Fellowship. S. Krishnaswamy received funding from the NIH (grants R01GM135929, R01GM130847, and R01HD100035), National Science Foundation Career Grant (2047856), and the Sloan Fellowship (grant FG-2021-15883). This project has been made possible in part by grant number 2019- 202662 from the Chan Zuckerberg Foundation.



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