[Paper Review] Zyxin is all you need: machine learning adherent cell mechanics

Matthew S. Schmitt, Jonathan Colen+6 more|arXiv (Cornell University)|Mar 1, 2023

Cellular Mechanics and InteractionsBiochemistry, Genetics and Molecular Biology3 citations

TL;DR

This study demonstrates that a single focal adhesion protein, zyxin, visualized via fluorescence imaging, contains sufficient information to train machine learning models that accurately predict cellular traction forces in adherent cells. Using deep neural networks and physics-informed modeling, the authors show that zyxin distribution encodes two distinct length scales governing force transmission, enabling generalization across biological conditions without requiring knowledge of other cytoskeletal components.

ABSTRACT

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.

Motivation & Objective

• To develop a data-driven approach for inferring large-scale cellular mechanical properties from limited molecular imaging data.
• To determine whether a single focal adhesion protein (zyxin) can encode sufficient information to predict complex cellular force fields.
• To construct interpretable, physics-informed continuum models of cell mechanics using only zyxin imaging data.
• To identify the underlying length scales governing force transmission in adherent cells from minimal experimental inputs.
• To demonstrate a generalizable framework for integrating machine learning with phenomenological modeling in cell biology.

Proposed method

• Trained U-Net neural networks to predict traction forces from zyxin fluorescence images, achieving high accuracy on unseen cells.
• Used Green's function neural networks (GFNN) to learn the relationship between zyxin distributions and force fields, incorporating physical constraints.
• Applied sparse regression (SINDy) to extract interpretable equations from learned Green's functions, yielding a minimal set of terms.
• Formulated force fields as linear combinations of Green's functions convolved with local zyxin gradients and scalar functions.
• Incorporated physical symmetries and conservation laws into the model architecture to improve generalization and interpretability.
• Validated models across 31 distinct adherent cells, using 15-cell test sets unseen during training.

Experimental results

Research questions

• RQ1 Can a single focal adhesion protein like zyxin encode enough information to predict the full traction force field of a cell?
• RQ2 What are the dominant length scales in the mechanical organization of adherent cells, as inferred from zyxin distribution?
• RQ3 Can physics-constrained machine learning models generalize to unseen biological conditions without explicit knowledge of other cytoskeletal components?
• RQ4 How can interpretable phenomenological models of cell mechanics be derived from deep learning without prior knowledge of microscopic mechanisms?
• RQ5 To what extent do learned force models remain accurate when applied to perturbed cellular states not seen during training?

Key findings

• Zyxin fluorescence images alone enabled neural networks to predict traction forces with high accuracy, achieving a median correlation of 0.99 between predicted and experimental force directions.
• The model generalized to 15 test cells not used in training, with mean-square error (MSE) consistently low across all test cases.
• Sparse regression revealed that cellular forces are governed by two distinct length scales encoded in zyxin distributions: one short-range and one long-range, corresponding to different Green's function decays.
• The contribution of the $ abla heta$ term in the Clebsch representation was negligible (1.1% of total force), indicating that zyxin alone suffices for accurate prediction.
• The final interpretable model contained only 10 terms, with relative error decreasing as more parameters were added, confirming improved predictive power with increasing complexity.
• The model achieved a relative error of -0.25 in the best case, indicating that adding parameters significantly improved performance over the baseline model with zero parameters.