[Paper Review] Topological data analysis approaches to uncovering the timing of ring structure onset in filamentous networks

Maria-Veronica Ciocanel, Riley Juenemann+2 more|arXiv (Cornell University)|Oct 13, 2019

Topological and Geometric Data AnalysisComputer Science46 references10 citations

TL;DR

This paper proposes a topological data analysis (TDA) method using persistent homology to track the emergence and timing of ring-like structures in actin-myosin filamentous networks from time-series agent-based simulations. By sampling points along filaments and analyzing persistence diagrams over time, the method identifies significant 1D topological holes (ring channels) through a path-connected approach, demonstrating robust detection of ring formation onset across varying sampling densities and motor protein parameters.

ABSTRACT

Improvements in experimental and computational technologies have led to significant increases in data available for analysis. Topological data analysis (TDA) is an emerging area of mathematical research that can identify structures in these data sets. Here we develop a TDA method to detect physical structures in a cell that persist over time. In most cells, protein filaments (actin) interact with motor proteins (myosins) and organize into polymer networks and higher-order structures. An example of these structures are ring channels that maintain constant diameters over time and play key roles in processes such as cell division, development, and wound healing. The interactions of actin with myosin can be challenging to investigate experimentally in living systems, given limitations in filament visualization extit{in vivo}. We therefore use complex agent-based models that simulate mechanical and chemical interactions of polymer proteins in cells. To understand how filaments organize into structures, we propose a TDA method that assesses effective ring generation in data consisting of simulated actin filament positions through time. We analyze the topological structure of point clouds sampled along these actin filaments and propose an algorithm for connecting significant topological features in time. We introduce visualization tools that allow the detection of dynamic ring structure formation. This method provides a rigorous way to investigate how specific interactions and parameters may impact the timing of filamentous network organization.

Motivation & Objective

• .
• To develop a TDA method that identifies the timing of ring structure formation in dynamic filamentous networks.
• To assess the significance of topological features in persistent homology to distinguish real ring channels from noise.
• To evaluate the robustness of feature detection across varying sampling densities of actin monomer units.

Proposed method

• .
• The method samples monomer units along actin filaments at each time point to generate point clouds.
• It constructs persistence diagrams for each time point to capture 1D topological features (holes).
• A path-connected algorithm links birth-death pairs across time to trace the evolution of the most persistent topological feature.
• Significance is assessed using null models with randomized filament positions and survival function comparisons to distinguish real features from noise.
• The approach uses a 500 nm persistence threshold to identify significant topological features, validated across multiple sampling densities.

Experimental results

Research questions

• RQ1 .
• RQ2 When does a significant 1D topological hole (ring channel) first appear in the simulated actin-myosin network?
• RQ3 How does the sampling density of actin monomer units affect the detection of ring structure onset and persistence?
• RQ4 Can the method distinguish between ring formation driven by different motor protein binding parameters in simulations?
• RQ5 What is the role of noise in topological feature detection, and how can it be statistically separated from biologically meaningful features?

Key findings

• .
• The method successfully identifies the onset of a significant 1D topological hole corresponding to a ring channel, with emergence detectable across varying sampling densities.
• The survival function of persistence lengths for model-generated frames differs significantly from that of null model frames, confirming feature significance.
• A 500 nm persistence threshold reliably identifies the dominant topological feature across different sampling densities, with consistent plateau behavior observed at 300–500 nm.
• Sampling at 10% and 30% of monomer units yields similar timing of ring formation onset, though 30% sampling produces approximately four times more features due to higher point cloud density.
• The path-connected approach effectively links topological features through time, enabling clear visualization and quantification of ring structure emergence.
• The method demonstrates robustness to sampling density, with mid-range to high sampling densities producing consistent and persistent detection of the dominant ring-like feature.