Restoring the 3D dynamics of organic molecular self-assembly via deep-learning-assisted LP-TEM

Abstract

The three-dimensional (3D) evolution of organic nanostructures is fundamental to understanding the non-equilibrium mechanisms of molecular self-assembly and hierarchical organization. While liquid-phase transmission electron microscopy (LP-TEM) enables real-time observation in native environments, its inherent 2D projection of volumetric information leads to significant kinetic misinterpretation by obscuring z-axis degrees of freedom. This limitation is particularly critical for organic materials, where low intrinsic contrast and extreme electron-beam sensitivity preclude the use of conventional dose-intensive 3D techniques, such as tomography or defocus series. Consequently, complex 3D behaviors, such as the coalescence of polymer nanoparticles, dynamic structural rearrangements of soft assemblies, and interfacial interactions during self-organization, are often erroneously analyzed as restricted 2D movements, masking the true stochastic nature of the assembly process. To address these challenges, we present a Depth-from-Defocus (DFD) Transformer framework designed to reconstruct high-fidelity 3D trajectories from single-view LP-TEM sequences with sub-nanometer axial precision. By employing a PSF-aware "Real-to-Sim" pipeline that explicitly incorporates instrument-specific point spread functions (PSF) and contrast transfer functions (CTF), our model achieves simultaneous denoising and quantitative depth estimation from low-dose datasets. The reliability of the inferred z-positions was rigorously validated through correlation with physical image sharpness, confirming a significant Pearson correlation between predicted depth and experimental contrast. Applying this framework to the dynamic molecular self-assembly into various nanostructures, we successfully restored 3D trajectories that reveal instantaneous isotropy, a hallmark of true Brownian motion. This finding corrects a fundamental misunderstanding in conventional 2D LP-TEM observations, where projection artifacts often misidentify 3D Brownian motion as sub-diffusive behavior. By bridging the gap between 2D observations and 3D stochastic dynamics/isotropic displacement, our work establishes a high-fidelity 4D analytical platform, transforming LP-TEM from a qualitative imaging tool into a quantitative framework for characterizing the structural evolution of beam-sensitive organic systems. Electron beam sensitivity further complicates depth inference. Traditional approaches such as defocus series or tomography require high cumulated doses, while noise reduction through time- or frame-averaging cannot distinguish thermal motion from beam-induced effects. As a result, direct quantification of 3D particle dynamics in liquid remain challenging. In this research, we introduce a real-to-sim deep learning workflow that incorporates focus conditions, contrast transfer function (CTF), and experimental noise characteristics. The trained model reconstructs 3D trajectories from single LP-TEM time-series by simultaneously determining in-plane positions and depth displacements. The reliability of the inferred z-positions was validated through correlation with CTF-dependent image sharpness variations, confirming significant Pearson correlation between predicted depth and experimental contrast. The reconstructed trajectories reveal isotropic particle displacements consistent with Brownian motion in 3D space, even under strong confinement by cell thickness. This approach extends LP-TEM beyond simple observation into a quantitative spatio-temporal framework.