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. 2021 Nov 5;12(1):6424.
doi: 10.1038/s41467-021-26577-1.

Physics-informed deep learning characterizes morphodynamics of Asian soybean rust disease

Henry Cavanagh  1 , Andreas Mosbach  2 , Gabriel Scalliet  2 , Rob Lind  3 , Robert G Endres  4
Affiliations

Physics-informed deep learning characterizes morphodynamics of Asian soybean rust disease

Henry Cavanagh et al. Nat Commun. .

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.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1. Morphodynamics of the Asian soybean rust pathogen, P. pachyrhizi, are characterized through condition-dependent dynamics over a global morphospace.
a P. pachyrhizi burrows into soybean leaves to extract nutrients, as sketched (top). Image sets at nine time points under six conditions (bottom) are processed to yield aligned, single-fungus images. b An autoencoder learns the biophysical degrees of freedom from the images, discovering a 2D morphospace. c Dynamics are characterized using two models: a top-down landscape (U(x)) model, where a physics-informed neural network fits the Fokker–Planck equation to the morphospace embeddings, and a bottom-up persistent random walk model of the growth zone, with parameters fitted using approximate Bayesian computation with a morphospace-derived similarity metric. These yield d interpretable, condition-dependent characterizations in the form of Waddington-type landscapes and tip growth parameter posteriors.
Fig. 2
Fig. 2. Global morphospace learned by a convolutional autoencoder.
a Human categorization of P. pachyrhizi phenotypes is time consuming and introduces human biases and unnatural discretization. b A convolutional autoencoder addresses these shortcomings by learning the manifold associated with each condition, sketched inset. Morphospace features are shown by propagating morphospace coordinates on a grid through the decoder. c 210 min embeddings for all conditions show that fungicides can induce perturbed dynamics over the morphospace, which therefore represents for an expressive space for differentiating morphodynamics upon.
Fig. 3
Fig. 3. Morphodynamic landscapes learned by the PINN.
a Morphospace embeddings are transformed into probability density functions (PDFs), p(x, t), using kernel density estimation (KDE), yielding nine snapshots per condition. b A physics-informed neural network (PINN) learns the landscapes by fitting the Fokker–Planck equation to the PDFs. For each condition, the architecture comprises a neural network to learn each of the PDF, p^(x,t), diffusivity, D^(x,t), and landscape, U^(x). The outputs of these are put through a series of differential operators that outputs the Fokker–Planck residual, N, and the architecture is trained to match the data (LPDF), minimize the magnitude of the residual (LPDE), satisfy the boundary conditions (LBC), and learn a normalized PDF (Lnorm). c The architecture is trained over a series of mini-batches, with lower-frequency solutions explored first. d Landscapes with simulated particles, from 90 min (pink) to 210 min (blue) after mixing with compounds, are shown, colored by the gradient magnitude, ∥F∥ (in terms of morphospace units, m.u.). These are analogous to Waddington’s epigenetic landscape, as sketched in the inset. The black outlines show the contour where the PDF learned by the PINN is 10−3 for DMSO and each condition. The inner region therefore highlights areas with high data density, with the remaining areas shown to facilitate connection with the morphospace and outer tendencies. Contour lines are plotted along equal landscape values, with spacings of 0.11, 0.08, 0.07, and 0.09 m.u.2 min−1 for the landscapes from left to right. Morphodynamics are diffusion-dominated until the germ tube begins to bend, at which point deterministic forces begin to drive trajectories apart. Fungicide-induced deformations including barriers, plateaus, and canalized pathways. This susceptibility to deformation, combined with the generality of the model, make the Fokker–Planck model well-suited for system characterization.
Fig. 4
Fig. 4. A persistent random walk model of the growth zone is fitted to image data.
a Tip growth is described with variables for length, L, linearly increasing in time, and path curvature, κ, which undergoes a persistent random walk, with relaxation to straight growth (i.e., a central growth zone). Dynamics of κ may be the result of a diffusing growth zone, shown with angular location θtip, which causes a changing direction of growth, described by θglobal in the lab frame. b All parameters were fitted using approximate Bayesian computation with sequential Monte Carlo (ABC-SMC). Lengthening parameters were fitted using length (L) histograms at nine equally spaced time points (three of the nine DMSO snapshots are shown here, with data in gray and simulations in black), between 90 and 210 min after mixing with solution. c Bending parameters were fitted by comparing morphospace embeddings of the 210 min snapshot data with those of images simulated with MAP lengthening parameters, as shown here for DMSO. d MAP germination time cumulative density functions (CDFs) and growth rate probability density functions (PDFs) show typical perturbations include premature germination, reduced germination frequency, and reduced maximum and mean growth rates. e Bending parameter posteriors (for stochasticity, σ, and relaxation to straight growth, τ−1) show final morphologies depend primarily on the ratio of the two bending parameters and fungicides can both increase and decrease this ratio. Accepted parameters of the final ABC-SMC population are plotted in white, with MAP values in red. Source data are provided for d, e.
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