Topological Data Analysis of Spatial Patterning in Heterogeneous Cell Populations: Clustering and Sorting with Varying Cell-Cell Adhesion

TL;DR

This paper introduces an efficient topological data analysis method using persistence images combined with autoencoders and hierarchical clustering to classify complex tissue architectures based on cell adhesion patterns.

Contribution

It presents a novel, computationally efficient approach for classifying multicellular spatial patterns using persistence images and machine learning techniques.

Findings

High classification accuracy for constant cell number simulations.

Normalization of persistence images improves classification with varying cell numbers.

Incorporating diverse topological features enhances classification accuracy.

Abstract

Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other cell types. However, automated and unsupervised classification of these multicellular spatial patterns remains challenging, particularly given their structural diversity and biological variability. Recent developments based on topological data analysis are intriguing to reveal similarities in tissue architecture, but these methods remain computationally expensive. In this article, we show that multicellular patterns organized from two interacting cell types can be efficiently represented through persistence images. Our optimized combination of dimensionality reduction via autoencoders, combined with hierarchical clustering, achieved high classification accuracy for simulations with constant cell numbers. We further demonstrate that persistence images can be normalized to improve classification for simulations with varying cell numbers due to proliferation. Finally, we systematically consider the importance of incorporating different topological features as well as information about each cell type to improve classification accuracy. We envision that topological machine learning based on persistence images will enable versatile and robust classification of complex tissue architectures that occur in development and disease.