Dipole-spread-function engineering for simultaneously measuring the 3D orientations and 3D positions of fluorescent molecules

Abstract

Interactions between biomolecules are characterized by where they occur and how they are organized, e.g., the alignment of lipid molecules to form a membrane. However, spatial and angular information are mixed within the image of a fluorescent molecule–the microscope’s dipole-spread function (DSF). We demonstrate the pixOL algorithm to simultaneously optimize all pixels within a phase mask to produce an engineered Green’s tensor–the dipole extension of point-spread function engineering. The pixOL DSF achieves optimal precision to simultaneously measure the 3D orientation and 3D location of a single molecule, i.e., 4.1° orientation, 0.44 sr wobble angle, 23.2 nm lateral localization, and 19.5 nm axial localization precisions in simulations over a 700 nm depth range using 2500 detected photons. The pixOL microscope accurately and precisely resolves the 3D positions and 3D orientations of Nile red within a spherical supported lipid bilayer, resolving both membrane defects and differences in cholesterol concentration in six dimensions.

Deep-SMOLM: Deep Learning Resolves the 3D Orientations and 2D Positions of Overlapping Single Molecules with Optimal Nanoscale Resolution

“…Robust single-molecule imaging, especially in vivo , necessitates an estimation algorithm that can reliably detect and estimate parameters from emitters whose images overlap [41, 42]. Early algorithms for measuring simultaneously SM orientations and positions either cannot cope with image overlap [9, 11, 23], are very computationally expensive [18], or can become stuck in local minima leading to correlated orientation and position biases [14]. To facilitate Deep-SMOLM’s robustness to these imaging conditions, we train it using simulated images containing both well-separated and overlapped DSFs corrupted by Poisson shot noise (SI section 4.ii).…”

“…Here, we demonstrate a deep learning-based estimator, called Deep-SMOLM, for simultaneously estimating 3D orientations and 2D positions of single molecules from a microscope implementing an engineered dipole-spread function [14]. Compared to traditional optimization approaches, Deep-SMOLM achieves superior estimation precision for both 3D orientation and 2D position that is on average within 3% of the best-possible precision (Fig.…”

“…2); otherwise, directly estimating orientation angles [ θ, ϕ , Ω] is ill-conditioned and unstable. Importantly, for high-performance DSFs, each brightness-weighted orientational moment contributes approximately equally to the final DSF shape [12, 14]. Further, we have designed 3D orientations and 2D positions to be orthogonally encoded into the intensities and spatial positions, respectively, of Gaussian spots within Deep-SMOLM’s output images (Fig.…”

“…To remedy these issues, we use a polarization-sensitive microscope that splits fluorescence into x- and y-polarized detection channels, along with a pixOL phase mask placed at the pupil or back focal plane (Fig. 11) [14]. The resulting pixOL DSF changes dramatically for molecules oriented in various directions (Fig.…”

“…Researchers have used molecular orientations [1] to elucidate the architectures of amyloid aggregates [2][3][4], the organization of proteins in actin filaments [5,6], and changes in lipid membrane polarity and fluidity induced by cholesterol [4,7,8]. To effectively use limited photon budgets in single-molecule (SM) imaging, dipole-spread functions (DSFs), i.e., the vectorial extension of the optical microscope's point-spread function, must be engineered to encode additional information about a molecule's 3D orientation [5,[9][10][11][12][13][14][15]. However, simultaneously estimating the 3D orientation and position of an emitter is challenging because 1) it is difficult to estimate SM parameters in 5-dimensional space (3D orientation, wobble, 2D position) without getting trapped in local minima instigated by severe Poisson shot noise [4,14],…”