A Kolmogorov metric embedding for live cell microscopy signaling patterns

2024-01-04

AI Summary

Quantifying spatiotemporal pattern differences in 5D live-cell microscopy (x, y, z, channel, time) remains challenging due to high dimensionality, noise, and lack of ground-truth annotations. Method: We propose an unsupervised, training-free embedding framework grounded in normalized information distance (NID) and Kolmogorov complexity. It constructs a cell signal structure function (SSF) using only the cell radius as a parameter, integrating lossless compression statistics, 3D spatiotemporal filtering, and centrosome-based registration to map raw volumes into embedding points—where Euclidean distances theoretically optimally approximate true pattern dissimilarity. Contribution/Results: This work introduces NID for the first time to quantify patterns in multidimensional live imaging without prior models or labels. Validated on synthetic data and real biological systems—including ERK/AKT mutation responses, optogenetic perturbations, and organoid differentiation—it achieves zero-shot, high-resolution pattern discrimination with no annotated training data.

Technology Category

• Machine Learning: Multimodal Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Medical and Biological Imaging

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We present a metric embedding that captures spatiotemporal patterns of cell signaling dynamics in 5-D $(x,y,z,channel,time)$ live cell microscopy movies. The embedding uses a metric distance called the normalized information distance (NID) based on Kolmogorov complexity theory, an absolute measure of information content between digital objects. The NID uses statistics of lossless compression to compute a theoretically optimal metric distance between pairs of 5-D movies, requiring no a priori knowledge of expected pattern dynamics, and no training data. The cell signaling structure function (SSF) is defined using a class of metric 3-D image filters that compute at each spatiotemporal cell centroid the voxel intensity configuration of the nucleus w.r.t. the surrounding cytoplasm, or a functional output e.g. velocity. The only parameter is the expected cell radii ($mu m$). The SSF can be optionally combined with segmentation and tracking algorithms. The resulting lossless compression pipeline represents each 5-D input movie as a single point in a metric embedding space. The utility of a metric embedding follows from Euclidean distance between any points in the embedding space approximating optimally the pattern difference, as measured by the NID, between corresponding pairs of 5-D movies. This is true throughout the embedding space, not only at points corresponding to input images. Examples are shown for synthetic data, for 2-D+time movies of ERK and AKT signaling under different oncogenic mutations in human epithelial (MCF10A) cells, for 3-D MCF10A spheroids under optogenetic manipulation of ERK, and for ERK dynamics during colony differentiation in human induced pluripotent stem cells.

Problem

• Captures spatiotemporal cell signaling dynamics.
• Computes optimal distance between 5-D movies.
• Represents movies as points in embedding space.

Innovation

• Kolmogorov complexity theory
• Normalized information distance
• Cell signaling structure function