Machine-learning-powered extraction of molecular diffusivity from single-molecule images for super-resolution mapping

Abstract

While critical to biological processes, molecular diffusion is difficult to quantify, and spatial mapping of local diffusivity is even more challenging. Here we report a machine-learning-enabled approach, pixels-to-diffusivity (Pix2D), to directly extract the diffusion coefficient D from single-molecule images, and consequently enable super-resolved D spatial mapping. Working with single-molecule images recorded at a fixed framerate under typical single-molecule localization microscopy (SMLM) conditions, Pix2D exploits the often undesired yet evident motion blur, i.e., the convolution of single-molecule motion trajectory during the frame recording time with the diffraction-limited point spread function (PSF) of the microscope. Whereas the stochastic nature of diffusion imprints diverse diffusion trajectories to different molecules diffusing at the same given D, we construct a convolutional neural network (CNN) model that takes a stack of single-molecule images as the input and evaluates a D-value as the output. We thus validate robust D evaluation and spatial mapping with simulated data, and with experimental data successfully characterize D differences for supported lipid bilayers of different compositions and resolve gel and fluidic phases at the nanoscale.

Deep learning reduces data requirements and allows real-time measurements in imaging FCS

“…A recent review ( 23 ) points toward the use of CNNs in addressing the challenges of FCS analysis. Furthermore, CNNs have also been applied to determine D maps from lipid bilayers using point spread function (PSF) mapping of single-particle images ( 24 ). However, it has limitations as it is a single-particle method.…”

AI analysis of super-resolution microscopy: Biological discovery in the absence of ground truth

“…SRM-based image-level class labels of endoplasmic reticulum (ER) were used to train a deep learning model to distinguish between Zika-infected and non-infected cells and showed that discriminating regions correspond to tubular matrix ER morphology ( Long et al, 2020 ). Using a convolutional neural network model, SMLM image stacks are inputted to directly measure molecular diffusion in supported lipid bilayers ( Park et al, 2023 ). Neural network extraction of features from nearest-neighbor distance-derived data identified cluster segmentation in SMLM point cloud space of C-terminal src kinase (CSK) or the associated PAG protein clustering on the cell membrane of T-cells ( Williamson et al, 2020 ).…”

Spatially Resolving Size Effects on Diffusivity in Nanoporous Extracellular Matrix-like Materials with Fluorescence Correlation Spectroscopy Super-Resolution Optical Fluctuation Imaging

“…These challenges can result in a limited capability to detect and track particles moving at very high speeds for multiple consecutive frames or in complex matrices. 32,33 Finally, other optical techniques designed to measure the diffusion coefficients, such as fluorescence recovery after photobleaching (FRAP), require much larger length scales (∼10−100 μm 2 ) for accurate imaging. 34−36 Moreover, FRAP extracts an average diffusion coefficient over the entire area, but provides no local diffusion information.…”

“…Single particle tracking (SPT) has been extensively applied to extract high-spatiotemporal information of molecular diffusion. − However, SPT measurements can be limited by the capabilities of tracking software analyses used to analyze the data that can include challenges of emitters that cross paths, photoblink, or have low signal. These challenges can result in a limited capability to detect and track particles moving at very high speeds for multiple consecutive frames or in complex matrices. , Finally, other optical techniques designed to measure the diffusion coefficients, such as fluorescence recovery after photobleaching (FRAP), require much larger length scales (∼10–100 μm 2 ) for accurate imaging. − Moreover, FRAP extracts an average diffusion coefficient over the entire area, but provides no local diffusion information.…”