L.M. and N.A.&#39;s work supported by the Penn State Center for Nanoscale Sciences, an NSF MRSEC under the grant number DMR-2011839 (2020 - 2026). D.M. was supported by ORNL&#39;s Laboratory Directed Research and Development (LDRD) Program, which is managed by UT-Battelle, LLC, for the U.S. Department of Energy (DOE). A.C. and N.A. acknowledge the Air Force Office of Scientific Research (AFOSR) program FA9550-18-1-0277 as well as GAME MURI, 10059059-PENN for support.

NOTE: The flow chart in Figure 1 shows the general procedure of the atomic position quantification.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/62164/62164fig01.jpg" /> 
Figure 1: The workflow of the atomic position quantification and structural measurement. <a href="https://www.jove.com/files/ftp_upload/62164/62164fig01large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
1. STEM image drift-correction and denoising
<ol>
	<li>Acquire high-quality annular dark-field (ADF)/annular bright-field (ABF) STEM images. 
	NOTE: The quality of the input data is key to ensuring the accuracy of data analysis, so we start the protocol with a few tips for acquiring good image data.
	<ol>
		<li>Ensure a high-quality TEM sample. The sample quality is extremely crucial. Use thin and clean TEM samples with no beam damage for imaging. Avoid touching the sample during handling and loading as this can cause sample contamination.</li>
		<li>Clean the sample before insertion (if possible). Clean the sample by using plasma cleaner, baking in a vacuum, or irradiating the region of interest in the sample at low magnifications by spreading the electron beam after sample insertion into the microscope (&#39;beam shower&#39;). Avoid damaged or contaminated areas when imaging.</li>
		<li>Align the microscope and tune the aberration correctors to minimize the lens aberrations as much as possible. Test the resolution by acquiring a few STEM images on a standard sample to confirm that the spatial resolution can resolve the specific crystal structures and further fine-tune the aberrations in the image.</li>
		<li>Tilt the sample until the optical axis is aligned with the specific zone axis of the crystal. For certain crystals, make observations from a required zone axis. For instance, align the viewing axis with the planes of the domain walls in ferroelectric crystals for the measurement.</li>
		<li>Optimize the electron dose while limiting electron beam damage and the sample drift during imaging. If the sample is stable under the electron beam and does not show drift or damage during the acquisition, it may be possible to try a higher electron dose or acquire multiple images of the same region to boost the signal-to-noise ratio. The goal here is to have a higher signal-to-noise ratio without beam damage or image artifacts.</li>
		<li>Acquire STEM images with different scanning directions to correct for potential drift during acquisition. First, acquire an image and then take the second one from the same region immediately after rotating the scan direction by 90&#176;.
		<ol>
			<li>Take images using the same imaging condition except for the scan directions. The purpose of this step is to feed the rotated images to the drift correction algorithm developed recently17. 
			NOTE: One can also input more than two images with more varying scanning directions (with arbitrary angles) into the algorithm. However, successive scanning of the same region may lead to lattice damage or drift in that area. Additionally, it is recommended that the scan direction and the low index lattice planes not maintain parallel or perpendicular directions with each other and instead maintain oblique angles. If the scan direction coincides with certain horizontal or vertical features (lattice planes, interfaces, etc.), the drift along the direction of the strong vertically/laterally varying features may cause artifacts during image registration.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Perform drift-correction with a non-linear correction algorithm. 
	NOTE: The non-linear drift correction algorithm was proposed and constructed by C. Ophus et al.17, and the open-source Matlab code can be found in the paper. Two or more images with different scanning directions are fed into the correction algorithm, and the algorithm will output the drift corrected STEM images. The downloaded code package includes a detailed yet simple procedure for the implementation. A more detailed algorithm and description of the process can be found in the original paper.</li>
	<li>Apply various image denoising techniques. 
	&#8203;NOTE: After the drift correction, perform image denoising to enhance the accuracy of future analysis. Some of the common denoising techniques are listed here. Furthermore, we introduce a free interactive Matlab app named EASY-STEM with a graphical user interface to help with the analysis. The interface is shown in Figure 2, with all the steps labeled on the corresponding buttons.</li>
</ol>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/62164/62164fig2v2.jpg" /> 
Figure 2: The graphical user interface (GUI) of the Matlab app EASY-STEM. All steps described in the protocol section are labeled accordingly. <a href="https://www.jove.com/files/ftp_upload/62164/62164fig2v2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<ol>
	<li>Apply the Gaussian filtering. In the EASY-STEM app, find a tab called Gaussian on the bottom left. Use the slider to select how many nearby pixels to average. Move the slider to apply the Gaussian filter to the image.</li>
</ol>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/62164/62164fig03.jpg" /> 
Figure 3:&#160;Example results of atomic position tracking.&#160;(i) An example of the position refining with the mp-fit algorithm. The results of regular 2D-Gaussian fitting and mpfit algorithm are shown with red and green circles respectively. The yellow arrows highlight the failure of regular 2D-Gaussian fitting due to the intensity from neighboring atoms.&#160;(a) The drift-corrected ADF-STEM image showing a typical unit cell of the ABO3 Perovskite. (b) The 3D plot of the intensity in (a). (c) The same image denoised with a Gaussian filter. (d) The 3D plot of the intensity in (c). (e) The contour plot of the intensity in (c) with the initial atomic positions (yellow circles) overlaid. (f) An example of the unit cell vector indexing system showing the index of the atomic positions in the image. (g) The contour plot of the intensity in (c) with the initial atomic positions (yellow circles) and refined atomic positions (red circles) overlaid, and (h) the 3D plot of the intensity with initial and refined atomic positions shown with yellow and red circles. <a href="https://www.jove.com/files/ftp_upload/62164/62164fig03large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
&#8203;NOTE: This technique uses a filter that averages the intensity of the nearby pixels in the images. The effect of the Gaussian filtering is presented in Figure 3a-d.
<ol start="2">
	<li>Apply Fourier filtering. In the EASY-STEM app, find a tab called FFT on the bottom left. There is a slider to restrict the spatial frequency to reduce high-frequency noise. Move the slider to apply the Fourier filter to the image. 
	NOTE: This technique limits the spatial frequency of the image to remove the high-frequency noise in the image.</li>
	<li>Apply the Richardson-Lucy deconvolution. In the EASY-STEM app, find a tab called Deconvolution on the bottom left, where there are two input boxes for the iterations of blind deconvolution and Richardson-Lucy deconvolution, respectively. Change the value and apply this denoising algorithm by clicking the button. 
	&#8203;NOTE: This technique is a deconvolution algorithm for effectively removing the noise in the image by calculating the point spread function.</li>
</ol>
2. Finding and refining the atom position
<ol>
	<li>Find the initial atomic positions. 
	NOTE: After the post-acquisition image processing, the initial atomic positions can be simply extracted as the local intensity maximum or minimum for the ADF or ABF STEM images respectively. A minimum distance between the neighboring atomic columns needs to be defined to remove the extra positions.
	<ol>
		<li>Define the minimum distance (in pixels) by changing the value in the input box that determines the distance between the neighboring peaks.</li>
		<li>Click the Find Initial Positions button in the EASY-STEM app. The result is shown in Figure 3e. 
		NOTE: Frequently, extra positions or missing positions are observed with a simple local max/min finding algorithm. Thus, a manual correction mode is created in the EASY-STEM app to further refine the atomic positions (Add Missing/Remove Extra Points buttons). This feature enables the addition and removal of the initial positions by using the mouse cursor.</li>
	</ol>
	</li>
	<li>Index the initial atomic positions with a unit-cell vector-based system.
	<ol>
		<li>Define an origin point in the image. In the EASY-STEM app, click on the Find Origin button. After clicking the button, drag the pointer to one of the initial atomic positions to define it as the origin.</li>
		<li>Define the 2D unit cell u and v vectors and the unit cell fractions.
		<ol>
			<li>Click the Find U/V button and drag the pointer to the end of the unit cells.</li>
			<li>Define the lattice fraction value by changing the value in the Lat Frac U and Lat Frac V input boxes. 
			NOTE: This value determines the lattice fraction value along the unit cell vector. For example, in the ABO3 perovskite unit cell, the unit cell can be divided equally into two halves along the two perpendicular unit cell vector directions. Consequently, there are two fractions along each unit cell vector direction, so the unit cell fraction values are 2 and 2 for u and v directions, respectively. The example result of the indexing and the corresponding u and v unit cell vectors are demonstrated in Figure 3f. For example, in Figure 3f, we will index the atoms on the corners as (0, 0), (1, 0), (0, 1), (1, 1); and we will index the atom in the center as (1/2, 1/2). This indexing system helps with information extraction in the following steps.</li>
			<li>Click on the Calculate Lattice button to index all the atoms.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Click on the Refine Positions button in the EASY-STEM app to refine atomic positions with 2D-Gaussian fitting. 
	NOTE: After obtaining the initial atomic positions and indexing the atoms in the image, a 2D-Gaussian fitting around each atomic column needs to be applied to achieve the sub-pixel level precision in the analysis. With this algorithm, it is possible to first crop an area in the image around each initial atomic position in the image and then fit a 2D-Gaussian peak in the cropped image. We then use the centers of the fitted 2D-Gaussian peaks as the refined atomic positions. This algorithm fits the 2D-Gaussian function to each atomic column in the image and the center of the fitted peak will be plotted after fitting. The result of the 2D-Gaussian fitting is shown in Figure 3g,h.</li>
	<li>(Optional) Click the mpfit Overlaps button in EASY-STEM to refine atomic positions with 2D-Gaussian multi-peak fitting (mp-fit). 
	NOTE: Refine the atomic positions using the mp-fit algorithm when the intensities from adjacent atomic columns are overlapping with each other. The mp-fit algorithm and its effectiveness are discussed in detail by D. Mukherjee et al.21. The EASY-STEM app has incorporated this algorithm and can be used to separate neighboring atoms with overlapping intensities. The result of mp-fit is shown in Figure 3i.</li>
	<li>Save the results by clicking the Save Atomic positions button. 
	NOTE: The app will prompt the user for location saving and file name. All saved results are included in the variable called &#34;atom_pos&#34;.</li>
</ol>
3. Physical information extraction
<ol>
	<li>Measure the atomic displacements based on the unit cell vector indexing and atomic positions.
	<ol>
		<li>Define a unit cell center. 
		NOTE: For example, for an ABO3 perovskite unit cell looking from its [100] axis, the unit cell centers can be defined as the average position of the four A-site atoms. In the first unit cell, those A-site atoms have been previously indexed as (0, 0), (1, 0), (0, 1), (1, 1).</li>
		<li>Find the position of the displaced atoms. 
		NOTE: In the case of the ABO3 perovskite unit cell, the displaced atom is the B-site atom, which was previously labeled as (1/2, 1/2).</li>
		<li>Iteratively find the position of the reference unit cell centers and displacement atoms for all the complete unit cells in the image. 
		NOTE: Unit cells may be incomplete near the edge of the TEM image. The atomic positions in those unit cells are discarded.</li>
		<li>Measure the displacement vector by entering the following command: 
		d = pos(B) - mean(pos(A))</li>
	</ol>
	</li>
	<li>Quantify the lattice strain.
	<ol>
		<li>Extract the unit cell vectors from each unit cell based on the atomic positions. 
		NOTE: Extract vector matrix &#34;C&#34;, which is a 2x2 matrix consisting of u-vector and v-vector for each unit cell in x and y directions.</li>
		<li>Define a reference vector, &#34;C0&#34;. 
		NOTE: C0 can be defined as the average unit cell vectors from the part of the image (recommended) or the theoretically calculated unit cell vector value.</li>
		<li>Calculate the 2x2 transformation matrix &#34;T&#34; using the following equation: 
		<img alt="Equation 1" src="/files/ftp_upload/62164/62164eq01.jpg" /> or <img alt="Equation 2" src="/files/ftp_upload/62164/62164eq02.jpg" /> (1)</li>
		<li>Calculate the distortion matrix &#34;D&#34;: 
		D = T - I (2) 
		where the &#34;I&#34; is the identity matrix.</li>
		<li>Decompose the distortion &#34;D&#34; to symmetric strain matrix &#34;&#949;&#34; and anti-symmetric rotation matrix &#34;&#969;&#34;: 
		<img alt="Equation 3" src="/files/ftp_upload/62164/62164eq03.jpg" /> (3) 
		NOTE: Strain matrix &#34;&#949;&#34; and rotation matrix &#34;&#969;&#34; can be extracted by using the equations: 
		&#949; = <img alt="Equation 4" src="/files/ftp_upload/62164/62164eq04.jpg" />&#160;(4) And &#969; = <img alt="Equation 5" src="/files/ftp_upload/62164/62164eq05.jpg" /> (5).</li>
		<li>Iteratively calculate strains for all unit cells.</li>
		<li>In the EASY-STEM app, click on the Calculate Strain based on the atomic positions button under the Quantify tab on the top-left of the interface. 
		&#8203;NOTE: The users can customize the displayed range of the strain map by changing the value within the Strain Upper/Lower limit input box.</li>
	</ol>
	</li>
</ol>
4. Data Visualization
<ol>
	<li>Create colored line maps. 
	NOTE: Colored line mapping of the atomic bonds is a straightforward way to present the distance between nearby atoms. In Matlab, the command to draw a line between two points is: Line([x1 x2],[y1 y2],&#39;Color&#39;,[r g b]). The inputs [x1 x2]and [y1 y2] are the coordinate values of the first and the second position. The distance variation can be presented with varying colors in the line map, which is defined by the [r g b] value. The [r g b] values stand for the red, green, and blue color values, each ranging from 0 to 1. Then&#160;iteratively connect all nearby atoms with colored lines.
	<ol>
		<li>Generate colored line maps in the EASY-STEM app. 
		NOTE: In the EASY-STEM app, line maps can be generated by a simple button clicking, which is under the Quantity tab on the top right of the interface.
		<ol>
			<li>Adjust the value (in pm) in the Mean Distance input box and Measurement Range input box in EASY-STEM. These two values define the average distance of the projected atom distance and the distance range of the measurement.</li>
			<li>In the EASY-STEM app, click on the Calculate Bond Length Based on Near Neighbor button. 
			NOTE: The line maps will be generated automatically. The users can adjust the colormap, line style, and line width for better visualization.</li>
		</ol>
		</li>
	</ol>
	</li>
	<li>Create vector maps. 
	NOTE: Vector maps can present atomic displacements in an area of the crystal. Since the displacement analysis is unique to individual systems, we have not integrated the code into the EASY-STEM app, but instead, here, we will introduce the Matlab commands for such analysis based on the standard ABO3 perovskite unit cells.
	<ol>
		<li>Calculate the reference position for displacement measurement. 
		NOTE: In the example of ABO3 perovskite, we have indexed the atoms on the corners (A-site) as (0, 0), (1, 0), (0, 1), (1, 1), and the atom in the center (B-site) as (1/2, 1/2). To compute the displacement with respect to the unit cell center, we first calculate the reference position as the averaged position of the corner (A-site) atoms. The Matlab command for this calculation is: 
		ref_center=(positionA1+positionA2+positionA3+ 
		PostionA4)/4</li>
		<li>Calculate the displacement by entering the command: 
		[displace_x displace_y] = PositionB - ref_center</li>
		<li>Implement the vector map: 
		quiver(x,y,displace_x,displace_y) 
		NOTE: The input x and y are the positions of the displaced atom. The variables displace_x and displace_y are the displacement magnitudes in x and y directions. The vector maps can be uniformly colored (e.g., yellow, white, red&#8230;) or shaded based on the displacement magnitude.</li>
	</ol>
	</li>
	<li>Create false-colored maps.
	<ol>
		<li>Generate the false-colored maps by upsampling to estimate the measured value (displacement, strain, etc.) for each pixel in the image: 
		ImageSize = Size(Image); 
		[xi,yi] = meshgrid(1:1:ImageSize(1),1:1:ImageSize(2)); 
		Upsampled_Data = griddata(x,y,YourData,xi,yi,&#39;v4&#39;); 
		NOTE: The &#34;griddata&#34; function upsamples the data at position (x,y) to estimate the value for each pixel in the entire image. The inputs xi and yi are the grid coordinates, and the &#39;v4&#39; is the bicubic upsampling method.</li>
		<li>Plot the upsampled data using user-defined color scale.</li>
	</ol>
	</li>
</ol>

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<li>De Backer, A., vanden Bos, K. H. W., Vanden Broek, W., Sijbers, J., Van Aert, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((StatSTEM%3A+An+efficient+approach+for+accurate+and+precise+model-based+quantification+of+atomic+resolution+electron+microscopy+images%5BTitle%5D)+AND+%22Ultramicroscopy%22%5BJournal%5D)">StatSTEM: An efficient approach for accurate and precise model-based quantification of atomic resolution electron microscopy images.</a> Ultramicroscopy. 171, 104-116 (2016).</li>
<li>Yankovich, A. B., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/pubmed?term=((Picometre-precision+analysis+of+scanning+transmission+electron+microscopy+images+of+platinum+nanocatalysts%5BTitle%5D)+AND+%22Nature+Communications%22%5BJournal%5D)">Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts.</a> Nature Communications. , (2014).</li>
</ol>

The authors have nothing to disclose.

When working on the post-acquisition processing, some caution needs to be taken as well. To start with, during the image drift-correction, the algorithm assumes that the 0&#176; image has the horizontal fast scanning direction, so double-check the direction before the calculation. If the scanning direction is not correctly set, the drift-correction algorithm will fail and may even introduce artifacts in the output17. Then during the imaging denoising, certain methods may introduce an artifact; for example, the Fourier filtering may create atom column contrast at the vacancy sites or remove fine features in the images, if the spatial resolution is not limited properly. As a result, it is vitally important to verify if the denoised images closely resemble the original raw input images.
Next, when determining the initial atomic positions based on local maximum/minimum, try to adjust the restriction minimum distance between peaks to avoid creating redundant positions between atomic columns. These redundant positions are artifacts generated due to the algorithm mistakenly recognizing the local maxima/minima in the image as atomic columns. Additionally, one can adjust the threshold value to find most of the positions if there are large contrast differences between various atomic species in the image (e.g., in ADF-STEM images of WS2). After obtaining most of the initial atomic positions in the image, try to manually add missing ones or remove extra ones with best effort. Moreover, the method for the indexing of the atoms is the most effective when there are not large interruptions in the periodicities within the image. When there are interruptions such as grain boundaries or phase boundaries presented in the image, the indexing may fail. The solution to this problem is to define the areas of interest in the image (by clicking the Define Area of Interest button in EASY-STEM app), and then indexing and refining the positions within each area separately. Afterward, one can easily combine datasets of different areas in the same image into one set of data and work on the analysis.
Finally, after applying 2D-Gaussian peak fittings, scatter the refined positions points onto the input image to verify the fitting results to see if the refined positions deviate from the atomic columns. The accuracy provided by the single Gaussian fitting algorithm is sufficient in most of the STEM experiments; however, if the position deviates due to the intensity from a neighboring atom, use the multi-peak fitting (mpfit) algorithm instead to isolate the intensity from adjacent atomic columns21. Otherwise, if the position deviates due to the image quality issue or the low intensity from the specific atom columns, it is suggested to discard the fitted position at that location.
There are several existing and specialized algorithms for the atomic position measurement, for example, the oxygen octahedra picker software22, Atomap python package23, and StatSTEM Matlab package24. However, these algorithms have some limitations in certain aspects. For instance, the oxygen octahedra picker requires the input of STEM images to contain only clearly resolved atomic columns and thus failed to address the issue in the images with atomic columns overlapping intensities21. On the other hand, although Atomap can calculate the positions of &#34;dumbbell-like&#34; atomic columns, the process is not very straightforward. Additionally, the StatSTEM is a great algorithm for quantifying the overlapping intensities, but its iterative model-based fitting process is computationally expensive21. In contrast, our approach, introduced in this work along with the Matlab app EASY-STEM, which is integrated with the advanced mpfit algorithm, can address the problem of the overlapping intensity and is less computationally expensive than StatSTEM, while offering competitive measurement precision. Furthermore, the analysis from Atomap and the oxygen octahedra picker software packages are designed and specialized for analyzing the data from ABO3 perovskite crystals, while the indexing system shown in this work is much more flexible about different materials systems. With the method in this work, users can fully design and customize the data analysis for their unique material systems based on the output results that contain both refined atomic positions and the unit cell vector indexing.
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/62164/62164fig06.jpg" /> 
Figure 6:&#160;Statistical quantification of the atomic position finding. (a) The distribution of the perovskite A-site to A-site distance presented in a histogram. The normal distribution fitting is plotted and overlaid as the red dashed line showing the mean of 300.5 pm and the standard deviation of 4.8 pm. (b) The statistical quantification of the perovskite unit cell vector angle measurement is presented as a histogram. The normal distribution fitting is plotted and overlaid as the red dashed line showing the mean of 90.0&#176; and the standard deviation of 1.3&#176;. (c) The statistical quantification of the polar displacement measurement in Ca3Ru2O7 (CRO) is presented as histogram. The normal distribution fitting is plotted and overlaid as the red dashed line showing the mean of 25.6 pm and the standard deviation of 7.7 pm. <a href="https://www.jove.com/files/ftp_upload/62164/62164fig06large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
The method introduced here provides picometer-level precision and simplicity for implementation. To demonstrate the measurement precision, the statistical quantification of the atomic position finding is presented in Figure 6. The measurements of cubic ABO3 perovskite A-site distance distribution and unit cell vector angle distribution are plotted using histogram in Figure 6a and Figure&#160;6b, respectively. By fitting the normal distribution curve to the distributions, the A-site distance distribution shows a mean of 300.5 pm and standard deviation of 4.8 pm and unit cell vector angle distribution shows a mean of 90.0&#176; and standard deviation of 1.3&#176;. The statistical quantification indicates the method proposed here enables picometer-level precision and can greatly alleviate the distortion due to drift during imaging. This result suggests that this measurement is trustworthy when the physical information to be measured is greater or equal to roughly 10 pm. For example, in the case of aforementioned CRO crystals, the measurement of the magnitude of the polar displacement is presented in Figure 6c. The measurement shows a mean of 25.6 pm, a standard deviation of 7.7 pm, and it shows that the polar displacement measurement in CRO STEM images is solid. Additionally, more caution needs to be taken in case of experimental limitations such as low signal-to-noise ratio when imaging beam-sensitive samples. In those cases, the measured atomic positions need to be closely examined against the raw images to ensure the validity of the measurement. Consequently, the analysis method introduced here has limitations to the measurement precision when compared to more recent and advanced algorithms. Our method is insufficient when the precision is required at the sub-picometer level, so a more advanced analysis routine is necessary if the feature to be extracted in the image is below a certain threshold. For example, the non-rigid registration algorithm has shown sub-picometer precision measurement on silicon and it enables accurate measurement of bond length variation on a single Pt nanoparticle25. Most recently, the deep learning algorithm was employed to identify various types of point defects in 2-D transition metal dichalcogenides monolayers from a huge amount of STEM image data. Later, the measurement was conducted on the averaged image of different types of defects and this method also demonstrated sub-picometer level precision on the distortion around those defects18. Consequently, as a future plan for increasing the analysis capacity, we are in the progress of developing and implementing more advanced algorithms such as deep learning. We will also try to integrate them into the future data analysis tool updates.

The development of spherical aberration correction in the modern scanning transmission electron microscope (STEM) has enabled microscopists to probe crystals with sub-angstrom sized electron beams1,2. This has allowed imaging of individual atomic columns in a wide variety of crystals with interpretable atomic resolution images for both heavy and light elements3,4. Recent developments in pixelated direct electron detectors and data analysis algorithms have enabled phase reconstruction imaging techniques, such as ptychography, with further improvements in spatial resolution to around 30 pm5,6,7. Additionally, the recent progress in STEM tomography has even enabled three-dimensional atomic resolution reconstruction of the single nano-particle8. The electron microscope has thus become an extraordinarily powerful tool for quantifying structural properties in materials with both high precision and site-specificity.
With the ultra-high resolution STEM images as the data input, direct measurements of structural distortions were performed to extract physical information from crystals at the atomic scale9,10. For example, the defect coupling between a Mo dopant in the WS2 monolayer and a single S vacancy was directly visualized by measuring the atomic positions and then calculating projected bond lengths11. Furthermore, the measurement on crystal interfaces, such as the coalesced grain boundaries in monolayer WS2, can exhibit the local atomic arrangement12. The interfacial analysis performed on the ferroelectric domain walls in LiNbO3 revealed the domain wall to be a combination of Ising and Neel states13. Another example is the visualization of the polar vortex structures achieved in the SrTiO3-PbTiO3 superlattices, achieved through calculation of the titanium atomic column displacements with respect to the strontium and lead column positions14. Finally, the advances in computer vision algorithms, such as image denoising with non-local principle component analysis15, Richardson and Lucy deconvolution16, drift-correction with non-linear registration17, and pattern recognition with deep learning, have significantly strengthened the accuracy of the measurement to sub-picometer precision18. One such example is the alignment and image registration of multiple fast-scan cryogenic-STEM images to enhance the signal-to-noise ratio. Subsequently, the Fourier-masking technique was applied to analyze the charge density waves in crystals by directly visualizing the periodic lattice distortion19. Even though the incredible aberration-corrected STEM instrumentation is increasingly accessible to researchers around the globe, the advanced data analysis procedures and methods remain uncommon and an enormous barrier for one without experience in data analysis.
In the present work, we showcase the complete pathway for the metrology of atomic resolution STEM images. This process includes firstly acquiring the STEM images with an aberration-corrected microscope followed by performing post-acquisition denoising/drift-correction for enhanced measurement accuracy. We will then further discuss the existing methods to clearly resolve and accurately quantify the atom column positions with either 2D-Gaussian single peak fitting or multi-peak fitting routines for slightly overlapping atomic columns20,21. Lastly, this tutorial will discuss methods for the quantification of lattice distortion/strain within the crystal structures or at the defects/interfaces where the lattice periodicity is disrupted. We will also introduce a simple self-developed free MATLAB app (EASY-STEM) with a graphical user interface (GUI) that can help with the analysis of STEM images without the need for writing dedicated analysis code or software. The advanced data analysis methods presented here can be applied for the local quantification of defect relaxations, local structural distortions, local phase transformations, and non-centrosymmetry in a wide range of materials.

<table><tbody><tr><td>EASY-STEM</td><td>Nasim Alem Group, Pennsylvania State University</td><td></td><td>Matlab app for STEM image processing; Download link: https://github.com/miaoleixin1994/EASY-STEM.git</td></tr><tr><td>JoVE article example script</td><td>Nasim Alem Group, Pennsylvania State University</td><td></td><td>Example Script for sorting atoms in unit cells</td></tr><tr><td>Matlab Optimization Tool Box</td><td>MathWorks</td><td></td><td>Optimization add-on packge in Matlab</td></tr><tr><td>Matlab</td><td>MathWorks</td><td></td><td>Numerical calculation software</td></tr><tr><td>Matlab: Image Processing Tool Box</td><td>MathWorks</td><td></td><td>Image processing add-on packge in Matlab</td></tr></tbody></table>

picometer-precision atomic position tracking through electron microscopy

The modern aberration-corrected scanning transmission electron microscopes (AC-STEM) have successfully achieved direct visualization of atomic columns with sub-angstrom resolution. With this significant progress, advanced image quantification and analysis are still at the early stages. In this work, we present the complete pathway for the metrology of atomic resolution scanning transmission electron microscopy (STEM) images. This includes (1) tips for acquiring high-quality STEM images; (2) denoising and drift-correction for enhancing measurement accuracy; (3) obtaining initial atomic positions; (4) indexing the atoms based on unit cell vectors; (5) quantifying the atom column positions with either 2D-Gaussian single peak fitting or (6) multi-peak fitting routines for slightly overlapping atomic columns; (7) quantification of lattice distortion/strain within the crystal structures or at the defects/interfaces where the lattice periodicity is disrupted; and (8) some common methods to visualize and present the analysis.
Furthermore, a simple self-developed free MATLAB app (EASY-STEM) with a graphical user interface (GUI) will be presented. The GUI can assist in the analysis of STEM images without the need for writing dedicated analysis code or software. The advanced data analysis methods presented here can be applied for the local quantification of defect relaxations, local structural distortions, local phase transformations, and non-centrosymmetry in a wide range of materials.

Figure 3&#160;shows the example results of atomic position tracking by following steps 1 and 2 in the protocol. A raw ADF-STEM image of a unit cell of the ABO3 perovskite is shown in Figure 3a, and its intensity profile is plotted in 3-D in Figure 3b. Figure 3c shows the result after Gaussian filtering is applied to the STEM image in Figure 3a, and the intensity profile is plotted in Figure&#160;3d. The initial positions are determined by finding the local maxima in the image and the positions are indicated by yellow circles in Figure 3e. The atomic positions are indexed based on the unit cell vector and shown in Figure 3f. After the initial position is found and indexed, 2D-Gaussian fitting is applied to further refine the measurement. In Figure 3g and Figure 3h, the fitted positions are indicated as red circles, the measurement precision is improved as the refined positions are closer to the center compared to the initial positions (yellow circles). Lastly, the advantage of applying the mpfit algorithm on the overlapping intensities is showcased in an ADF-STEM image of BaMnSb2 crystal (Figure 3i). The regular 2D-Gaussian fitting (red circles) fails severely on the Mn columns as highlighted by yellow arrows, while the mpfit algorithm can determine the positions much more accurately (green circles).
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/62164/62164fig04.jpg" /> 
Figure 4: HAADF-STEM image of the Ca3Ru2O7 (CRO). (a) The magnified image of the ADF-STEM image of the Ca3Ru2O7 (CRO) crystal with the crystal structure schematic superimposed. The relative displacement of the Ca atom in the perovskite layer is highlighted with the yellow arrow. (b) Drift-corrected and denoised ADF-STEM image of CRO and (c) with overlaying refined atomic positions (red dots). (d) An example of using an indexing system to identify the upper (red), center (blue) and lower (yellow) Ca atoms in the perovskite layer. <a href="https://www.jove.com/files/ftp_upload/62164/62164fig04large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
The HAADF-STEM image of the Ca3Ru2O7 (CRO) is shown in Figure 4a and Figure 4b (with the overlaid crystal structure). CRO is a Ruddlesden-Popper phase perovskite crystal with the polar space group A21am. ADF-STEM imaging shows the contrast from the heavier elements well (Ca and Ru), but the O atoms are not visualized as lighter atoms do not scatter the beam strong enough to become visible with HAADF detectors. The non-centrosymmetry of the crystal structure is caused by the tilting of O octahedra and can be visualized in ADF-STEM images by analyzing the displacement of the Ca atom in the center of the double perovskite layer. By following the steps listed in the Protocol section, all atomic positions in this image can be located by finding the centers of the fitted 2D-Gaussian peaks, as shown in Figure 4c. Furthermore, using the indexing system, in step 3.2, each type of atom in the unit cell can be identified and used for further processing. For example, the Ca atoms at the upper, center, and lower side of the perovskite double layer can be easily identified and their positions are presented with circles filled with different colors, as shown in Figure 4d.
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/62164/62164fig05.jpg" /> 
Figure 5:&#160;Physical information. (a) An example of the implementation of the vector map showing the polarization obtained from the center Ca displacement pattern. The arrows are colored based on the orientation (red to the right, blue to the left). The vertical 90&#176; head-to-head and head-to-tail domain walls are indicated with blue arrows and a horizontal 180&#176; domain wall is indicated with a red arrow. (b) An example of the implementation of the false-colored map showing the polarization. The color indicates the magnitude in left (yellow) and right (purple) directions. Reduced magnitude results in faded color. (c) An example of implementation of the false-colored map showing the &#949;xx strain in the image. The color indicates the value of tensile (red) and compressive (blue) strain. <a href="https://www.jove.com/files/ftp_upload/62164/62164fig05large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
After positioning and indexing the atoms in the STEM images, the physical information can be extracted and visualized via various types of plots, as shown in Figure 5. The vector map that shows the polarization direction is shown in Figure 5a. The arrows point towards the projected polarization direction, and by coloring the arrows based on their orientation, a vertical head-to-head 90&#176; domain wall (labeled with blue arrows), and a horizontal 180&#176; domain wall (labeled with red arrows) are shown at the top of the image. By constructing the false-colored map as shown in Figure 5b, a decreasing polar displacement magnitude can be observed via the fading color in the center, and thus the head-to-tail domain wall can be visualized. By combining the vector map and false-color map, the T-junction formed by three domain walls is shown in the ADF-STEM image. Additionally, with the dimension of each unit cell in the image measured, an &#949;xx strain map can be constructed, as shown in Figure 5c.

Watch this Scientific Journal Video about Picometer-Precision Atomic Position Tracking through Electron Microscopy at JoVE.com

Picometer-Precision Atomic Position Tracking through Electron Microscopy

This work presents a workflow for atomic position tracking in atomic resolution transmission electron microscopy imaging. This workflow is performed using an open-source Matlab app (EASY-STEM).

The modern aberration-corrected scanning transmission electron microscopes (AC-STEM) have successfully achieved direct visualization of atomic columns ...

picometer-precision-atomic-position-tracking-through-electron

Universidad Científica del Sur

Research

JoVE Journal

Chemistry

7.2K Views.  The Pennsylvania State University. This work presents a workflow for atomic position tracking in atomic resolution transmission electron microscopy imaging. This workflow is performed using an open-source Matlab app (EASY-STEM). 

Video: Picometer-Precision Atomic Position Tracking through Electron Microscopy

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this work, we use single particle tracking of fluorescently labeled PNIPAM microgels as a showcase for tuning microgel size by a rapid non-stirred precipitation polymerization procedure. This approach is well suited for prototyping new reaction compositions and conditions or for applications that do not require large amounts of product. Microgel synthesis, particle size and structure determination by dynamic and static light scattering are detailed in the protocol. It is shown that the addition of functional comonomers can have a large influence on the particle nucleation and structure. Single particle tracking by wide-field fluorescence microscopy allows for an investigation of the diffusion of labeled tracer microgels in a concentrated matrix of non-labeled microgels, a system not easily investigated by other methods such as dynamic light scattering.

Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels

Non-stirred precipitation polymerization provides a rapid, reproducible prototyping approach to the synthesis of stimuli-sensitive poly(N-isopropylacrylamide) microgels of narrow size distribution. In this protocol synthesis, light scattering characterization and single particle fluorescence tracking of these microgels in a wide-field microscopy setup are demonstrated.

Stimuli-sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have various prospective practical applications and uses in fundamental research. In this ...

Preparation and 3D Tracking of Catalytic Swimming Devices

We report a method to prepare catalytically active Janus colloids that "swim" in fluids and describe how to determine their 3D motion using fluorescence microscopy. One commonly deployed method for catalytically active colloids to produce enhanced motion is via an asymmetrical distribution of catalyst. Here this is achieved by spin coating a dispersed layer of fluorescent polymeric colloids onto a flat planar substrate, and then using directional platinum vapor deposition to half coat the exposed colloid surface, making a two faced "Janus" structure. The Janus colloids are then re-suspended from the planar substrate into an aqueous solution containing hydrogen peroxide. Hydrogen peroxide serves as a fuel for the platinum catalyst, which is decomposed into water and oxygen, but only on one side of the colloid. The asymmetry results in gradients that produce enhanced motion, or "swimming". A fluorescence microscope, together with a video camera is used to record the motion of individual colloids. The center of the fluorescent emission is found using image analysis to provide an x and y coordinate for each frame of the video. While keeping the microscope focal position fixed, the fluorescence emission from the colloid produces a characteristic concentric ring pattern which is subject to image analysis to determine the particles relative z position. In this way 3D trajectories for the swimming colloid are obtained, allowing swimming velocity to be accurately measured, and physical phenomena such as gravitaxis, which may bias the colloids motion to be detected.

A method to prepare catalytically active Janus colloids that can "swim" in fluids and determine their 3D trajectories is presented.

We report a method to prepare catalytically active Janus colloids that "swim" in fluids and describe how to determine their 3D motion using fluorescence ...

Engineering

Magnetic Tweezers for the Measurement of Twist and Torque

Single-molecule techniques make it possible to investigate the behavior of individual biological molecules in solution in real time. These techniques include so-called force spectroscopy approaches such as atomic force microscopy, optical tweezers, flow stretching, and magnetic tweezers. Amongst these approaches, magnetic tweezers have distinguished themselves by their ability to apply torque while maintaining a constant stretching force. Here, it is illustrated how such a &#8220;conventional&#8221; magnetic tweezers experimental configuration can, through a straightforward modification of its field configuration to minimize the magnitude of the transverse field, be adapted to measure the degree of twist in a biological molecule. The resulting configuration is termed the freely-orbiting magnetic tweezers. Additionally, it is shown how further modification of the field configuration can yield a transverse field with a magnitude intermediate between that of the &#8220;conventional&#8221; magnetic tweezers and the freely-orbiting magnetic tweezers, which makes it possible to directly measure the torque stored in a biological molecule. This configuration is termed the magnetic torque tweezers. The accompanying video explains in detail how the conversion of conventional magnetic tweezers into freely-orbiting magnetic tweezers and magnetic torque tweezers can be accomplished, and demonstrates the use of these techniques. These adaptations maintain all the strengths of conventional magnetic tweezers while greatly expanding the versatility of this powerful instrument.

Magnetic tweezers, a powerful single-molecule manipulation technique, can be adapted for the direct measurements of the twist (using a configuration called freely-orbiting magnetic tweezers) and torque (using a configuration termed magnetic torque tweezers) in biological macromolecules. Guidelines for performing such measurements are given, including applications to the study of DNA and associated nucleo-protein filaments.

Single-molecule techniques make it possible to investigate the behavior of individual biological molecules in solution in real time. These techniques ...

Bioengineering

3D Orbital Tracking in a Modified Two-photon Microscope: An Application to the Tracking of Intracellular Vesicles

The objective of this video protocol is to discuss how to perform and analyze a three-dimensional fluorescent orbital particle tracking experiment using a modified two-photon microscope1. As opposed to conventional approaches (raster scan or wide field based on a stack of frames), the 3D orbital tracking allows to localize and follow with a high spatial (10 nm accuracy) and temporal resolution (50 Hz frequency response) the 3D displacement of a moving fluorescent particle on length-scales of hundreds of microns2. The method is based on a feedback algorithm that controls the hardware of a two-photon laser scanning microscope in order to perform a circular orbit around the object to be tracked: the feedback mechanism will maintain the fluorescent object in the center by controlling the displacement of the scanning beam3-5. To demonstrate the advantages of this technique, we followed a fast moving organelle, the lysosome, within a living cell6,7. Cells were plated according to standard protocols, and stained using a commercially lysosome dye. We discuss briefly the hardware configuration and in more detail the control software, to perform a 3D orbital tracking experiment inside living cells. We discuss in detail the parameters required in order to control the scanning microscope and enable the motion of the beam in a closed orbit around the particle. We conclude by demonstrating how this method can be effectively used to track the fast motion of a labeled lysosome along microtubules in 3D within a live cell. Lysosomes can move with speeds in the range of 0.4-0.5 &#181;m/sec, typically displaying a directed motion along the microtubule network8.

In this video protocol we track - at high speed and in three dimensions - fluorescently labeled lysosomes within living cells, using the orbital tracking method in a modified two-photon microscope.

The objective of this video protocol is to discuss how to perform and analyze a three-dimensional fluorescent orbital particle tracking experiment using a ...

Magnetic Field Mapping using Off-Axis Electron Holography in the Transmission Electron Microscope

Off-axis electron holography is a powerful technique that involves the formation of an interference pattern in a transmission electron microscope (TEM) by overlapping two parts of an electron wave, one of which has passed through a region of interest on a specimen and the other is a reference wave. The resulting off-axis electron hologram can be analyzed digitally to recover the phase difference between the two parts of the electron wave, which can then be interpreted to provide quantitative information about local variations in electrostatic potential and magnetic induction within and around the specimen. Off-axis electron holograms can be recorded while a specimen is subjected to external stimuli such as elevated or reduced temperature, voltage, or light. The protocol that is presented here describes the practical steps that are required to record, analyze, and interpret off-axis electron holograms, with a primary focus on the measurement of magnetic fields within and around nanoscale materials and devices. Presented here are the steps involved in the recording, analysis, and processing of off-axis electron holograms, as well as the reconstruction and interpretation of phase images and visualization of the results. Also discussed are the need for optimization of the specimen geometry, the electron optical configuration of the microscope, and the electron hologram acquisition parameters, as well as the need for the use of information from multiple holograms to extract the desired magnetic contributions from the recorded signal. The steps are illustrated through a study of specimens of B20-type FeGe, which contain magnetic skyrmions and were prepared with focused ion beams (FIBs). Prospects for the future development of the technique are discussed.

Guidelines are presented for recording and interpreting off-axis electron holograms to provide quantitative images of magnetic fields in nanoscale materials and devices in the transmission electron microscope.

Off-axis electron holography is a powerful technique that involves the formation of an interference pattern in a transmission electron microscope (TEM) by ...

Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis

A novel elemental and chemical analysis scheme based on electron-channeling phenomena in crystalline materials is introduced, where the incident high-energy electron beam is rocked with the submicrometric pivot point fixed on a specimen. This method enables us to quantitatively derive the site occupancies and site-dependent chemical information of impurities or intentionally doped functional elements in a specimen, using energy-dispersive X-ray spectroscopy and electron energy-loss spectroscopy attached to a scanning transmission electron microscope, which is of significant interest to current materials science, particularly related to nanotechnologies. This scheme is applicable to any combination of elements even when the conventional Rietveld analysis by X-ray or neutron diffraction occasionally fails to provide the desired results because of limited sample sizes and close scattering factors of neighboring elements in the periodic table. In this methodological article, we demonstrate the basic experimental procedure and analysis method of the present beam-rocking microanalysis.

We provide a general outline of quantitative microanalysis methods for estimating the site occupancies of impurities and their chemical states by taking advantage of electron-channeling phenomena under incident electron beam-rocking conditions, which reliably extract information from minority species, light elements, oxygen vacancies, and other point/line/planar defects.

A novel elemental and chemical analysis scheme based on electron-channeling phenomena in crystalline materials is introduced, where the incident ...

﻿Analyzing the Heterogeneous Performance of Single Nanoparticles with Electrochemical Methods

Tracking Electrochemistry on Single Nanoparticles with Surface-Enhanced Raman Scattering Spectroscopy and Microscopy

Studying electrochemical reactions on single nanoparticles is important to understand the heterogeneous performance of individual nanoparticles. This nanoscale heterogeneity remains hidden during the ensemble-averaged characterization of nanoparticles. Electrochemical techniques have been developed to measure currents from single nanoparticles but do not provide information about the structure and identity of the molecules that undergo reactions at the electrode surface. Optical techniques such as surface-enhanced Raman scattering (SERS) microscopy and spectroscopy can detect electrochemical events on individual nanoparticles while simultaneously providing information on the vibrational modes of electrode surface species. In this paper, a protocol to track the electrochemical oxidation-reduction of Nile Blue (NB) on single Ag nanoparticles using SERS microscopy and spectroscopy is demonstrated. First, a detailed protocol for fabricating Ag nanoparticles on a smooth and semi-transparent Ag film is described. A dipolar plasmon mode aligned along the optical axis is formed between a single Ag nanoparticle and Ag film. The SERS emission from NB fixed between the nanoparticle and the film is coupled into the plasmon mode, and the high-angle emission is collected by a microscope objective to form a donut-shaped emission pattern. These donut-shaped SERS emission patterns allow for the unambiguous identification of single nanoparticles on the substrate, from which the SERS spectra can be collected. In this work, a method for employing the SERS substrate as a working electrode in an electrochemical cell compatible with an inverted optical microscope is provided. Finally, tracking the electrochemical oxidation-reduction of NB molecules on an individual Ag nanoparticle is shown. The setup and the protocol described here can be modified to study various electrochemical reactions on individual nanoparticles.

Author Spotlight: Tracking Electrochemistry on Single Nanoparticles with Surface-Enhanced Raman Scattering Spectroscopy and Microscopy  

The protocol describes how to monitor electrochemical events on single nanoparticles using surface-enhanced Raman scattering spectroscopy and imaging.

Studying electrochemical reactions on single nanoparticles is important to understand the heterogeneous performance of individual nanoparticles. This ...

High-Speed Magnetic Tweezers for Nanomechanical Measurements on Force-Sensitive Elements

Single-molecule magnetic tweezers (MTs) have served as powerful tools to forcefully interrogate biomolecules, such as nucleic acids and proteins, and are therefore poised to be useful in the field of mechanobiology. Since the method commonly relies on image-based tracking of magnetic beads, the speed limit in recording and analyzing images, as well as the thermal fluctuations of the beads, has long hampered its application in observing small and fast structural changes in target molecules. This article describes detailed methods for the construction and operation of a high-resolution MT setup that can resolve nanoscale, millisecond dynamics of biomolecules and their complexes. As application examples, experiments with DNA hairpins and SNARE complexes (membrane-fusion machinery) are demonstrated, focusing on how their transient states and transitions can be detected in the presence of piconewton-scale forces. We expect that high-speed MTs will continue to enable high-precision nanomechanical measurements on molecules that sense, transmit, and generate forces in cells, and thereby deepen our molecular-level understanding of mechanobiology.

Here, we describe a high-speed magnetic tweezer setup that performs nanomechanical measurements on force-sensitive biomolecules at the maximum rate of 1.2 kHz. We introduce its application to DNA hairpins and SNARE complexes as model systems, but it will be also applicable to other molecules involved in mechanobiological events.

Single-molecule magnetic tweezers (MTs) have served as powerful tools to forcefully interrogate biomolecules, such as nucleic acids and proteins, and are ...

Biochemistry

A Protocol for Real-time 3D Single Particle Tracking

Real-time three-dimensional single particle tracking (RT-3D-SPT) has the potential to shed light on fast, 3D processes in cellular systems. Although various RT-3D-SPT methods have been put forward in recent years, tracking high speed 3D diffusing particles at low photon count rates remains a challenge. Moreover, RT-3D-SPT setups are generally complex and difficult to implement, limiting their widespread application to biological problems. This protocol presents a RT-3D-SPT system named 3D Dynamic Photon Localization Tracking (3D-DyPLoT), which can track particles with high diffusive speed (up to 20 &#181;m2/s) at low photon count rates (down to 10 kHz). 3D-DyPLoT employs a 2D electro-optic deflector (2D-EOD) and a tunable acoustic gradient (TAG) lens to drive a single focused laser spot dynamically in 3D. Combined with an optimized position estimation algorithm, 3D-DyPLoT can lock onto single particles with high tracking speed and high localization precision. Owing to the single excitation and single detection path layout, 3D-DyPLoT is robust and easy to set up. This protocol discusses how to build 3D-DyPLoT step by step. First, the optical layout is described. Next, the system is calibrated and optimized by raster scanning a 190 nm fluorescent bead with the piezoelectric nanopositioner. Finally, to demonstrate real-time 3D tracking ability, 110 nm fluorescent beads are tracked in water.

This protocol details the construction and operation of a real-time 3D single particle tracking microscope capable of tracking nanoscale fluorescent probes at high diffusive speeds and low photon count rates.

Real-time three-dimensional single particle tracking (RT-3D-SPT) has the potential to shed light on fast, 3D processes in cellular systems. Although ...

Combining Single-molecule Manipulation and Imaging for the Study of Protein-DNA Interactions

The paper describes the combination of optical tweezers and single molecule fluorescence detection for the study of protein-DNA interaction. The method offers the opportunity of investigating interactions occurring in solution (thus avoiding problems due to closeby surfaces as in other single molecule methods), controlling the DNA extension and tracking interaction dynamics as a function of both mechanical parameters and DNA sequence. The methods for establishing successful optical trapping and nanometer localization of single molecules are illustrated. We illustrate the experimental conditions allowing the study of interaction of lactose repressor (lacI), labeled with Atto532, with a DNA molecule containing specific target sequences (operators) for LacI binding. The method allows the observation of specific interactions at the operators, as well as one-dimensional diffusion of the protein during the process of target search. The method is broadly applicable to the study of protein-DNA interactions but also to molecular motors, where control of the tension applied to the partner track polymer (for example actin or microtubules) is desirable.

Here we describe the instrumentation and methods for detecting single fluorescently-labeled protein molecules interacting with a single DNA molecule suspended between two optically trapped microspheres.

The paper describes the combination of optical tweezers and single molecule fluorescence detection for the study of protein-DNA interaction. The method ...