Detection and characterization of chemotaxis without cell tracking

Abstract

Swarming has been observed in various biological systems from collective animal movements to immune cells. In the cellular context, swarming is driven by the secretion of chemotactic factors. Despite the critical role of chemotactic swarming, few methods to robustly identify and quantify this phenomenon exist. Here, we present a novel method for the analysis of time series of positional data generated from realizations of agent-based processes. We convert the positional data for each individual time point to a function measuring agent aggregation around a given area of interest, hence generating a functional time series. The functional time series, and a more easily visualized swarming metric of agent aggregation derived from these functions, provide useful information regarding the evolution of the underlying process over time. We extend our method to build upon the modelling of collective motility using drift–diffusion partial differential equations (PDEs). Using a functional linear model, we are able to use the functional time series to estimate the drift and diffusivity terms associated with the underlying PDE. By producing an accurate estimate for the drift coefficient, we can infer the strength and range of attraction or repulsion exerted on agents, as in chemotaxis. Our approach relies solely on using agent positional data. The spatial distribution of diffusing chemokines is not required, nor do individual agents need to be tracked over time. We demonstrate our approach using random walk simulations of chemotaxis and experiments investigating cytotoxic T cells interacting with tumouroids.

The Critical Importance of Spatial and Temporal Scales in Designing and Interpreting Immune Cell Migration Assays

“…Recently, an example of a hybrid experimental-mathematical continuum approach can be found in the work of Hywood et al [ 137 ]. They derived density relationships from a Fokker-Planck model, and, by estimating these relationships from microscopy data, they were able to estimate motility and chemotaxis using cell densities instead of cell tracking.…”

“…However, if work could address this weakness, this approach would mitigate some scale phenomena by reducing the required spatial resolution and allow an increase in the temporal resolution. Recently, an example of a hybrid experimental-mathematical continuum approach can be found in the work of Hywood et al [137]. They derived density relationships from a Fokker-Planck model, and, by estimating these relationships from microscopy data, they were able to estimate motility and chemotaxis using cell densities instead of cell tracking.…”

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation

“…However, working with cell trajectory data can be challenging, and these challenges include time consuming effort to manually track cells and the need for the cell density to be low to make cell tracking easier. Models that can avoid using cell trajectory data are an active area of research [ 11 ], but we find using the Simpson et al [ 7 ] model, which incorporates cell trajectory data, leads to a good outcome.…”

Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using Approximate Bayesian Computation

“…However, working with cell trajectory data can be challenging, and these challenges include time consuming effort to manually track cells and the need for the cell density to be low to make cell tracking easier. Models which can avoid using cell trajectory data is an active area of research (Hywood et al, 2021), but we find using the Simpson et al (2018) model which incorporates cell trajectory data leads to a good outcome.…”