Exploring Complex Biological Systems Using Topological Data Analysis
Introduction
Novel approaches leveraging #topological #data #analysis (#TDA) can shed light on intriguing phenomena in complex biological (and other!) systems. Here is some brand new work in this realm, which I was privileged to do in collaboration with Golnar Gharooni-Fard, Morgan Byers, Varad Deshmukh, Liz Bradley, Carissa Mayo, and Orit Peleg. This work explores the spatiotemporal movement patterns of honeybees, but the data pipeline we develop has potential application far beyond that context.
Understanding Topological Data Analysis
TDA is a powerful mathematical framework that enables the characterization of complex data. One core tool of TDA is "persistent homology," an approach that analyzes the "shape" of data at variable resolutions, connecting points within a certain distance and counting topological features. Persistent homology provides a detailed signature of the structure of a data point cloud, allowing for insights into the underlying patterns. If you would like to learn more about TDA, here are some resources:
Exploring Bees' Trophallaxis Behavior:
Have you ever pondered how honeybees efficiently manage their food exchange? Our work delves into trophallaxis, the process by which bees directly exchange food among each other. To gain insights into this remarkable behavior, we used TDA to analyze the intricate movement patterns of the bees.
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Experimental Setup and Phases of Behavior
Our lead investigator, Golnar Gharooni-Fard, conducted experiments in which she gave one bee some food, introduced it into a group of unfed bees, and filmed the subsequent behavior. The collected data reveal intriguing "phase changes." These phases include a sparse phase, where the bees are uniformly spread out, and a dense phase, characterized by cohesive clusters, and sometimes even mixed phases, which exhibit combinations of dense and sparse clusters.
Applying TDA and Dimension Reduction
To make sense of the complex data and pave the way for further analysis, we characterize each frame of the movie using topology, apply dimensionality reduction to simplify the topological signature, and use clustering or change-point algorithms to look for when important changes happen during the course of the experiment.
Validation and Exciting Discoveries
To validate our approach,we tested it on synthetic data derived from an agent-based model of honeybee trophallaxis behavior. This initial experiment successfully revealed two distinct phases: a dispersed phase preceding food introduction and a food-exchange phase where aggregations formed. The real excitement ensued when we applied the same approach to the experimental data, which proved to be much noisier. Despite the challenges, we found the two previously observed phases and even identified a potential third phase, suggesting another dispersed phase after food exchange.
Implications and Future Directions
By employing TDA and dimension reduction techniques, we successfully uncovered distinct phases in trophallaxis behavior. This work not only expands our understanding of honeybees but offers up a data pipeline that holds potential for a wide range of application areas. If you're interested in exploring TDA's applicability to other contexts, I welcome discussions.
