Resolving Heterogeneous Mechanical Domains via Physics-Aware Deep Clustering of Single-Molecule Force Spectroscopy Data

Abstract

Many biological processes rely on mechanical forces, with protein molecules acting as key mediators. Understanding how proteins respond to mechanical stress is essential for conditions including cardiomyopathy and muscular dystrophy. Natural proteins such as dystrophin and utrophin are composed of heterogeneous folding domains with distinct mechanical properties; deciphering domain-level behavior provides insights into disease mechanisms and informs therapeutic strategies. Single-molecule force spectroscopy (SMFS) enables probing the mechanical properties of entire proteins, yet current approaches struggle to identify heterogeneous folding domains, particularly without prior knowledge. Here, we present the first automated framework to identify heterogeneous folding domains in SMFS data, applying both existing clustering methods and a novel physics-aware deep clustering architecture, LatentUnfold. LatentUnfold learns complementary latent representations from force magnitude and the force-extension physical relationship through dual autoencoders, jointly optimized for clustering assignments. We apply our framework to experimental SMFS data collected from a synthetic two-domain protein (ddFLN4-Titin I27) as well as natural protein constructs of dystrophin and utrophin, with Monte Carlo simulated datasets serving as controlled validation. For the synthetic protein, we recover mechanical properties consistent with previously reported values for each domain. For the natural proteins, we uncover two mechanically distinct domain populations - corresponding to the N-terminal domain and spectrin-like repeats - with differences in both unfolding force and contour length increase, and reveal different unfolding order between them for the first time. This work enables domain-level biological inference, overcoming prior limitations that relied on averaging and overlooked heterogeneity, thus advancing the understanding of mechanical behavior in protein unfolding.