Tracking collective cell motion by topological data analysis

Abstract

By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.

Noise robustness of persistent homology on greyscale images, across filtrations and signatures

“…Over the past two decades, persistent homology has found many applications in data science, e.g., in the analysis of local behaviour of the space of natural images [7], analysis of images of hepatic lesions [8], human and monkey fibrin [9], fingerprints [10], or diabetic retinopathy images [11], analysis of 3D shapes [12,13], neuronal morphology [14], brain artery trees [15,16], fMRI data [17][18][19], protein binding [20], genomic data [21] orthodontic data [22], coverage in sensor networks [23], plant morphology [24], fluid dynamics [25], dynamical systems describing the movement of biological aggregations [26], cell motion [27], models of biological experiments [28], force networks in granular media [29], structure of amorphous and nanoporous materials [30,31], spatial structure of the locus of afferent neuron terminals in crickets [32], or spread of the Zika virus [33]. An exhaustive collection of applications of topological data analysis to real data can be found at [34].…”

Persistent homology and the shape of evolutionary games

“…We have introduced persistent homology as a novel methodology to the study of spatially extended games. While previous work have used PH to analyze time series of data in other contexts (Bonilla et al, 2020;Pereira and de Mello, 2015;Khasawneh and Munch, 2014), we have demonstrated how it is relevant for understanding spatial notions of evolutionary stability. In Section 2.2, we described three basic shapes that correspond to the stability and instability of strategies in a 2D lattice game (Fig.…”

“…It is particularly useful to apply PH to data where connections, holes, and voids play an important role for understanding the studied phenomenon. To that end, PH has been used to detect group alignment and clustering events in biological aggregation models (Topaz et al, 2015), quantify the variability of zebrafish patterns in silico (McGuirl et al, 2020), automatically characterize and compare aspects of collective cell motion (Bonilla et al, 2020), model and quantify protein flexibility (Xia and Wei, 2014), describe atomic configurations in amorphous solids (Hiraoka et al, 2016), and characterize the both clonal and reticulate evolution of RNA viruses (Chan et al, 2013).…”

Anomalous Angiogenesis in Retina

“…Experiments to quantify the adhesion of the new cells generated by pluripotent stem cells and their ability to stop angiogenesis would be needed. Our passive model of RPE cells could be replaced by a vertex model of the epithelium able to describe wound healing [63]. Including reversible EMT signaling pathways [30] in future models would be desirable and could bring about new therapies.…”