[Paper Review] Physics-informed deep learning characterizes morphodynamics of Asian soybean rust disease

Endres, R, Cavanagh, H+3 more|arXiv (Cornell University)|Nov 29, 2021

Wheat and Barley Genetics and Pathology41 references16 citations

TL;DR

This paper introduces a physics-informed deep learning framework that characterizes the morphodynamics of *Phakopsora pachyrhizi*, the Asian soybean rust pathogen, by learning a 2D morphospace from high-throughput image data. Using a physics-informed neural network (PINN) to infer Waddington-type landscapes and approximate Bayesian computation (ABC-SMC) to fit a persistent random walk model of tip growth, the study reveals condition-dependent morphological transitions and identifies fungicide-induced disruptions in growth zone stability, such as barriers, plateaus, and canalized pathways.

ABSTRACT

Medicines and agricultural biocides are often discovered using large phenotypic screens across hundreds of compounds, where visible effects of whole organisms are compared to gauge efficacy and possible modes of action. However, such analysis is often limited to human-defined and static features. Here, we introduce a novel framework that can characterize shape changes (morphodynamics) for cell-drug interactions directly from images, and use it to interpret perturbed development of Phakopsora pachyrhizi, the Asian soybean rust crop pathogen. We describe population development over a 2D space of shapes (morphospace) using two models with condition-dependent parameters: a top-down Fokker-Planck model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. We discover a variety of landscapes, describing phenotype transitions during growth, and identify possible perturbations in the tip growth machinery that cause this variation. This demonstrates a widely-applicable integration of unsupervised learning and biophysical modeling.

Motivation & Objective

• To develop a data-driven framework that captures dynamic shape changes (morphodynamics) in fungal pathogens from static images.
• To overcome limitations of static, human-defined features in phenotypic screening by enabling continuous, interpretable characterization of shape evolution.
• To integrate unsupervised deep learning with biophysical modeling to infer condition-dependent dynamics and modes of action of fungicides.
• To identify mechanistic disruptions in tip growth machinery caused by fungicides through quantitative morphodynamic analysis.

Proposed method

• An autoencoder is trained on high-throughput, fixed-image snapshots of *P. pachyrhizi* across 9 time points and 6 conditions to learn a 2D morphospace capturing salient shape features.
• A physics-informed neural network (PINN) is used to infer the potential energy landscape (U(x)) by solving the Fokker-Planck equation with condition-dependent parameters.
• A bottom-up persistent random walk model of tip growth is formulated with stochastic differential equations for curvature dynamics, incorporating a relaxation term (τ⁻¹) to model directional persistence.
• Approximate Bayesian computation with sequential Monte Carlo (ABC-SMC) is applied to infer posterior distributions of model parameters using a morphospace-derived similarity metric.
• Model selection is performed across three bending models (random walk in global angle, curvature, and persistent curvature) using ABC-SMC and data comparison via summed absolute distance.
• The framework combines unsupervised dimensionality reduction, biophysical modeling, and statistical inference to produce interpretable, condition-specific morphodynamic characterizations.

Experimental results

Research questions

• RQ1 How can morphodynamic changes in fungal germ tubes be captured as continuous, low-dimensional dynamics from high-throughput image data?
• RQ2 What biophysical landscapes underlie the transition from diffusive to deterministic morphological development in *P. pachyrhizi*?
• RQ3 How do different fungicides perturb the tip growth machinery, and what are the resulting morphological phenotypes?
• RQ4 Can physics-informed deep learning models provide interpretable, condition-dependent characterizations of pathogen development beyond static descriptors?

Key findings

• The Fokker-Planck model revealed that morphodynamics are diffusive until germ tube bending begins, after which deterministic forces dominate and drive trajectories apart.
• Fungicide treatments induced distinct morphodynamic disruptions: Compound A (carbendazim) caused barrier-like features, Compound B (PIK-75) induced plateaus, and Compound C (benzovindiflupyr) at high concentration created canalized pathways.
• Model 3, a persistent random walk with relaxation (dκ = −τ⁻¹κdt + σdW), best reproduced observed morphologies, indicating that directional persistence is a key feature of tip growth.
• The PINN analysis showed convergence to interpretable landscapes, validating the model’s physical plausibility and avoiding black-box interpretation.
• Parameter posteriors from ABC-SMC revealed condition-specific changes in germination time (tg), growth rate (α), and curvature relaxation (τ⁻¹), linking molecular targets to morphological outcomes.
• The study demonstrates that morphodynamic phenotypes can be linked to specific modes of action: microtubule disruption (Compound A), PI3K inhibition (Compound B), energy depletion (Compound C), and epigenetic modulation (Compound X).