SINGLE: An open-source software package to spot the atomic-resolution structure of nanocrystals

-By Nikita Vijay Biliye

Overall workflow and descriptions of each step of SINGLE are shown. SINGLE consists of two major steps: Preprocessing of the time series (orange), including (i) time-window frame averaging with anisotropic motion correction and (ii) tracking particle trajectory with using total variation (TV)–based denoising, and particle 3D reconstruction from individual particle trajectories (blue), including (i) graphene background identification and subtraction, (ii) time-restrained 2D clustering with exclusion of out-of-focus images, (iii) initial model generation, and (iv) 3D reconstruction and atomic-scale structure analysis

In the past 5-decades, there have been many changes and advancements in crystallography. These changes occurred in multidisciplinary fields like chemistry and biology.

To disclose the unique physiochemical properties of the 3D (3 Dimensional) structure of nanocrystals, scientists typically used solution-phase Transmission Electron Microscopy (TEM). To decide the structure of a protein, scientists used the single-particle 3D reconstruction method in structural biology. However, these traditional methods failed to manage other various targets like solubilized nanocrystals. 

Colloidal nanocrystals contain up to hundreds of atoms. These atoms have numerous applications in a wide range of areas. It may be catalysis, electronics, or biological sensors. The structural characteristics of these nanocrystals are estimated by a simplistic scale-down picture of corresponding bulk materials. This attempt too failed because of the unique characteristics rising at the nanoscale.

According to the recent reports, Cyril F. Reboul and a research team at the Monash University, Australia, Seoul National University, South Korea, and the Lawrence Berkeley National Laboratory U.S., developed a methodology based on the 3D reconstruction of time series high-resolution transmission (HRTEM) images. These images are obtained for individual nanocrystals undergoing Brownian-motion. They imaged ensembles of colloidal nanocrystals by making use of graphene liquid-cell transmission electron microscopy.

Project images of uniquely related nanocrystals were obtained using an electron detector. This detector is used to obtain an ensemble of 3D reconstruction. They introduced methods of computation that can be used to successfully reconstruct 3D nanocrystals at atomic resolution. The 3D reconstruction of nanocrystals was then achieved by continuously tracking individual particles. The interfering background is subtracted, during the process.

These developments were then made available through an open-source software package, known as SINGLE. This free software is now available on GitHub. It is distributed under GNU general public license. SINGLE is the only method that is developed to date, capable of resolving 3D atomic structures of heterogeneous nanocrystals, directly from the solution phase.

Overview and workflow of SINGLE

The workflow of SINGLE is divided into two steps.

  1. Pre-processing

This step operates in movie frames (each movie frame – represented by a 2D projection of random orientation of several particles) of the time series.

2. Particle 3D construction

This step operates on individual particle trajectories. Each trajectory consists of a set of differently projected views of unique nanocrystals.


● Firstly, the time window averaging over multiple frames with anisotropic motion correction is conducted. It improves the SNR versus the individual frames and leads to visible particles and an enhanced graphene signal in the power spectrum.

● Positions of the particles are identified manually in the first-time window average. These positions then inputted into the tracker

● In the next stage, graphene background subtraction is done.

● Time restrained 2D clustering and in-plane registration are applied. It will help to identify the centers of the mass of the particles. Frames corresponding to the adjacent time segments are eliminated. It is where the particle has moved out of the narrow depth of focus of the aberration-corrected TEM.

● Starting model is generated based on the expected crystallographic structure, diameter of the particle, and the constituent elements.

● In the last stage, 3D reconstructions are produced, atomic coordination is fitted, and atomic-scale structure analysis like strain mapping is performed.

The pre-processing of time series included:

Time-window averaging with anisotropic motion correction:

● In recent studies, including the isotropic motion-correction lead to improvement of Time-window averaging.

● Correlation-based frame weights were included to marginalize the flanking frame’s influence in the time window.

● To correct resolution loss that occurred due to anisotropic motion, weighted time window averaging was introduced using the elastic deformation model.

Tracking of the individual particles throughout the statistic:

● A new tracking method was introduced to overcome the previous failure rate.

● The newly introduced method is based on translational registration of time windows that are non-overlapping.

● The combined use of denoising (reducing variations in a manner that preserves edges and structural features) and time-averaging provided a strong method that enables efficient tracking of the motion of individual nanocrystal.

Particle 3D reconstruction included:

● The Automated Fourier filtration method was introduced during the recent advancement.

Graphene background subtraction:

● Graphene subtraction is repeated as follows:

  1. Obtain rotational average of the power spectrum, over its 8 nearest neighbors, that contain GLC background.
  2. Rotational-correlation of the generated spectrum with that of the theoretical graphene sheet is calculated.
  3. Mask away both sets of graphene peaks using a smooth polynomial function. This function should be zero at each determined peak position.

Time-restrained 2D clustering and in-plane registration:

● The nature of nanocrystals is characterized in the highly confined space of the GLC by mopping the angular distance of particle trajectory that was previously reconstructed.

● Greedy-algorithm is used to derive the lower bound of rational change by measuring the angular distance between the two closest projection directions.

Starting model generation:

● During the recent advancement, a Starting-model estimation procedure was developed.

● It uses the knowledge that the particles have an arrangement of approximate cubic atomic position with a bond length similar to the bulk material.

3D reconstruction:

● Critical modifications were introduced. 

● The 3D refinement method could not be applied straightforwardly to the time series data of the nanocrystals.

● The deterministic assignment of the in-plane degree of freedom was used.

● Also, to provide an initial 3D reference, Starting-model initial procedure was used.

Validating the 3D construction:

● A validation method was developed that uses time restrained 2D class averages having higher SNRs

● These are well suited for visual inspection, independent of any 3D model .

The public git repository is available at


Park J. et al. Nanoparticle imaging. 3D structure of individual nanocrystals in solution by electron microscopy. Science, 10.1126/science.aab1343

 Reboul C. F. et al. SINGLE: Atomic-resolution structure identification of nanocrystals by graphene liquid cell EM, Science AdvancesDOI: 10.1126/sciadv.abe6679

Baldi A. et al. In situ detection of hydrogen-induced phase transitions in individual palladium nanocrystals. Nature


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