Structural Characterization of Nucleic Acid Nanoparticles Using SAXS and SAXS-Driven MD

Abstract

Structural characterization of nucleic acid nanoparticles (NANPs) in solution is critical for validation of correct assembly and for quantifying the size, shape, and flexibility of the construct. Small-angle X-ray scattering (SAXS) is a well-established method to obtain structural information of particles in solution. Here, we present a procedure for the preparation of NANPs for SAXS. This procedure outlines the steps for a successful SAXS experiment and the use of SAXS-driven molecular dynamics to generate an ensemble of structures that best explain the data observed in solution. We use an RNA NANP as an example, so the reader can prepare the sample for data collection, analyze the results, and perform SAXS-driven MD on similar NANPs.

1. Introduction

1.1 Nucleic acid nanoparticles (NANPs) are a highly versatile class of nanomaterials with significant biomedical potential [1-3]. Through canonical and noncanonical Watson-Crick base pairing and naturally occurring RNA motif’s, NANPs can be rationally designed to adopt any number of architectures and carry multiple functional moieties in stoichiometric ratios [4-6]. One of the key translational challenges, which is preventing the progression of NANPs from research to the clinical space, lies in their interactions with the innate immune system [1, 2, 7-9]. Two of the main factors that determine the immunostimulatory properties of NANPs are their physicochemical properties (geometry, composition, size, stabilities, etc.) and functionalization [10, 11]. Owing to this unique structure-function relationship, a thorough understanding of NANP’s structure in solution, including examining factors such as their flexibility where functional moieties have been added, is of the utmost importance to their translation to clinical settings. Structural characterization of functional biopolymers, such as proteins and nucleic acids in solution, is critical to elucidate the full behavior of the sample. Solution studies provide further insight into how biological samples behave in vivo and compliment high-resolution methods, such as X-ray crystallography and single-particle cryoEM [12]. Although the latter methods provide atomistic details, these methods are not necessarily optimal for capturing the dynamics ofa system or, for example, concentration-dependent effects on oligomeric states [13]. Therefore, to obtain the best structural characterization of NANPs, solution-based methods should complement high-resolution structural methods.

The use of small-angle X-ray scattering (SAXS), in combination with wide-angle X-ray scattering (WAXS), is a method that provides information about the overall shape, size, maximal dimension, and flexibility of a particle in solution [10, 14, 15]. It is inherently a low-resolution technique, whereby the scattering contribution from all conformations tumbling in solution are rotationally averaged resulting in isotropic scattering, and thus, 3D (high resolution) structural information is lost. The small angles (SAXS) are most sensitive to overall properties of the particle, such as size and maximal dimensions, while the WAXS region can provide information about intramolecular structure. The resulting merged SAXS/WAXS dataset is a 1D profile of scattering intensity (I) as a function of q (scattering vector), defined as q = 4πsinθ/λ, where θ is half the scattering angle and λ is the incident X-ray wavelength.

A high-quality SAXS experiment can inform about particle size from the radius of gyration (Rg) value, distribution of scattering pairs via the pair distribution function P(r), and degree of flexibility from the Kratky analysis. There are several excellent reviews that provide an in-depth discussion of SAXS theory and practical applications [16-20]. To obtain meaningful results, one must properly prepare the samples and correctly analyze the results. Here, we present the procedure for preparing NANP components, particularly an RNA monomer construct that when combined with cognate partners can form planar RNA nanorings [3, 21-25], for solution scattering measurements, with an emphasis on preparation for the most common mode of operation, mail-in measurements. The advantage of mail-in measurements, and rapid access to LIX, is the reduction in turnaround of solution measurements and to lower the barrier for users to access beamlines. While the preparation steps are general for SAXS experiments collected at any facility, data analysis and modeling from data collected at LIX at NSLSII within Brookhaven National Laboratory is emphasized. For details about LIX, please refer to the following references [26-28]. Furthermore, we outline the procedures of SAXS-driven MD simulations to demonstrate the complementarity of SAXS and MD to derive meaningful results about the ensemble of structures that explain the RNA SAXS data.

1.2 SAXS-driven MD is a new methodology developed to refine the solution state structure of the biomolecule based on molecular dynamic simulations and experimental SAXS data. An extended version of commonly used molecular dynamics software, GROMACS, known as GROMACS-SWAXS, developed by Jochen Hub’s group at Saarland University in Germany, provides functionalities for the user to incorporate experimental SAXS data into the MD simulation by converting the I(q) versus q data into SAXS potentials. This method also utilizes an explicit solvent simulation to subtract background/solvent intensity and hence accurately calculate the scattering profile for the solute in solvent.

Since the process involves utilizing both SAXS intensities as potentials as well as molecular forcefields, the method is used to identify the best possible ensemble structures of the solute in solution state, where the SAXS potentials drive the biomolecules to attain a conformation, which best describes the experimental data. This method provides a way to characterize flexibility in the biomolecules, which might exist in solution state and are often difficult to identify in other state of the art methods, such as X-ray crystallography and cryo-electron microscopy. SAXS-driven MD has been used to identify large domain conformational changes in proteins [29] and recently to refine the solution state structure of RNA molecules [30].

In Subheading 3.7, 3.8, 3.9 and 3.10, we describe how to use the SAXS-driven MD functionality from GROMACS-SWAXS software to refine the RNA model structure such that it best fits the experimental SAXS data. To explore the conformational space for the RNA molecule, one must compute the free MD simulation trajectory and perform its downstream analysis.

1.3 SAXS-driven MD simulation methodology is an amalgamation of forcefield-based MD simulations as well as experimental SAXS data. Both these methods independently have their advantages and short comings, which are, to some extent, addressed through this hybrid approach. While MD simulations are sufficient to identify the conformational space of any biomolecule under the influence of the specific forcefield, not all conformations identified are physically plausible. Introduction of experimental SAXS data in terms of potentials drive the simulations toward a more realistic conformational ensemble. The difference between the conformational space traversed by the RNA molecule in this study can be identified by comparing the RMSD changes during the free MD versus the SAXS-driven MD. The RMSD changes during the SAXS-driven MD are smaller than those observed during the free-MD, hence guiding the conformational space to attain a solution, which best represents the experimental data. The ensemble structure obtained from this method can improve the overall fit of the biomolecular structure into the bead model derived from the SAXS experiment. The analysis of the ensembles and associated trajectories can also help identify the flexible regions in the biomolecule. Thus, utilizing the strengths of both these methods through this hybrid approach might pave a path for identifying functional conformations of biomolecules in the solution state.

2. Materials

2.1. SAXS Sample Preparation and Data Collection

1. CredoCube Series 4 L from Pelican BioThermal or similar.

2. Microdialysis chambers with an appropriate nominal molecular weight cutoff for the sample.

3. Sterile 0.2 μm filters for both microcentrifuge tubes and for larger containers (e.g., 50 mL conical tubes, bottles, etc.).

2.2. SAXS-Driven Molecular Dynamics Simulations

1. SAXS experimental data (I versus q data).

2. Model structure of the RNA molecule.

3. GROMACS-SWAXS software installation on a GPU-enabled machine for faster performance. A modified version of GROMACS was developed by Jochen Hub’s group at Saaraland University, Germany, which is available for download at https://gitlab.com/cbjh/gromacs-swaxs [31]. This software has all the same functionalities as the original GROMACS program with some additional functions, specifically designed for carrying out SAXS-driven MD simulations. MD simulations largely depend on the approximation of forcefields utilized for the biomolecule under study. Additionally, the SAXS-driven MD program depends on the calculation of Cromer-Mann parameters for all chemical/biochemical elements and ions for the forcefield being utilized for simulation. Most of the commonly used forcefields files contain the Cromer-Mann parameters in this version of the software (see Note 1).

4. Structure visualization software ChimeraX [32] or VMD [33].

5. Xmgrace for plotting graphs [34].

3. Methods

3.1. Preparation of Samples for Measurement at Beamline

1. Determine the type of question you seek to answer as outlined in Fig. 1 (see Note 2).

2. Determine the quality of sample.

3. Utilize non-denaturing gel electrophoresis, DLS, or other methods to determine sample stability and monodispersity (see Note 2).

4. Depending on the results from step 2, if the sample is stable and monodisperse, choose high-throughput static SAXS (HT-SAXS). If there are oligomeric assemblies present in the sample, choose SEC-SAXS.

Fig. 1.

Flowchart outlining the phases of a SAXS experiment. To get the most out of your data, asking the right questions is critical

3.2. For SEC-SAXS Measurement Preparation Skip to Subheading 3.3. For HT-SAXS:

1. Determine the number of unique samples and prepare ≥60 μl of pure, monodisperse sample.

2. Samples and buffers should minimize the use of organic solvents.

3. Concentration to obtain good signal-to-noise ratio depends on the size of the sample. A general rule of thumb for good signal at LIX is mg/mL = 50/MW, where MW is in kiloDaltons.

4. Prepare a concentration series around the value determined in step 3. This will be helpful to determine if Rg values are concentration-dependent. This can be performed manually by the researchers before shipping the samples or using the OT2 sample handling robot at the LIX beamline (see Note 3).

5. Prepare a matching buffer for each unique set of samples. This is critical for a proper subtraction; without a proper sample-matched buffer, there is no data (see Note 4). The highest-quality matched buffer is obtained by performing dialysis and using the dialysate as your matched buffer. Other options include the use of the flow-through from the final sample concentration step (e.g., spin concentrator flow-through) or collecting buffer from the SEC run during the polishing step of sample purification. At LIX, each buffer is classified as a sample and requires at least 60 μL. Each buffer, matched to a particular sample, should be repeated at least 2X (see Note 5).

6. To ensure there is no particulate contamination in the samples or buffer matches, filter each sample with 0.2 μm filters. By using filters designed to fit in microcentrifuge tubes, minimal sample loss from retention within the filter can be achieved.

7. Place samples in 96-well plates and prepare for shipping (step 7). For LIX-specific details about sending samples, refer to [26, 27]. In general, however, the plate should be sealed with a film that does not have adhesive over each sample well and the plate lid secured on top to protect the sealing film.

3.3. Preparing SEC-SAXS Samples

1. Determine expected chromatogram before sending samples for measurement. The type of column utilized will determine the volume and concentration needed. For well-polished samples, columns, such as the Superdex Increase 200 5/150 from Cytiva or Biozen dSec2 from Phenomenex or similar, should be employed due to reduced dilution and fast sample run time (typically 12 min/sample). The typical injection volumes are ≥60 μL, and dilution factors range from four- to sevenfold. Remember that the final concentration should be close to that determined in step 3 in Subheading 3.2.

2. Preparation of buffer. Columns must be equilibrated in at least two column volumes of buffer (or until UV 280 nm and refractive index is stable). Prepare a 5X or 10X stock to be diluted at the beamline, enough for ≥250 ml. It is important to send a pure, 0.2 μm degassed buffer. Particulates will clog and ruin column. Any bubbles that enter the system could potentially enter the X-ray flow cell and ruin the scattering experiment (see Note 6).

3. When measuring nucleic acids, particularly RNA, prepare the beamline staff, if sending samples, to work in an RNAse-free environment. Proper sterile tips, cleaning procedures for pipettes, and the working area at the beamline will be needed.

4. Shipping samples. It is best to avoid freeze thaw cycles. Ideally, send at 4 °C on ice. Always prepare for possible shipping delays, and add extra ice or utilize a reusable cooler, such as the CredoCube Series 4 L or larger from Pelican BioThermal. Ensure a next-day delivery service.

3.4. SAXS/WAXS Data Processing for High-Throughput Static Experiments

1. At LIX, all data will be shared in a standard HDF5 format. In addition, an HTML style report will be generated that will summarize the results for all your static samples (Fig. 2).

2. Examine the report for a linear Guinier region, good P(r) fit to the data, and evaluate the degree of compaction or flexibility from the Kratky plot. Figure 2a demonstrates a report from a high-quality sample. The left plot shows a linear Guinier region of high quality in blue, the experimental data (orange), and the fit of P(r) to the data (blue overlay on orange). The P(r) function behaves well, and the Kratky plot demonstrates some degree of flexibility within the system (center plot) (see Note 7). Proceed to step 8 to export data in DAT format.

3. If your report looks like Fig. 2b, there are significant issues with the measurement that resulted in a failure to perform basic analysis, such as Guinier; therefore, a closer examination of the data is required. The next steps will demonstrate the use of LIXtools to find the reason for the poor result in Fig. 2b [27].

4. At LIX, a central Jupyter Hub is available such that these next steps do not have to be performed on your local machine (see Note 8). This requires access to the LIX beamline and is setup for you by the beamline staff and is not covered here. Step 5 will assume that you have access to your data on the Jupyter Hub.

5. Figure 3a is the interactive GUI used to examine each of the samples in your HDF5 file(s). Figure 3a, Section 1 (red) contains a drop-down menu, next to “Sample:”, to display the raw 1D scattering profile of each sample and buffer measured. Select the buffer, in this case b20, to look for quality, i.e., a water peak at 2.0 Å⁻¹, and a smoothly decaying intensity without any aberrant spikes. Figure 3b shows an example of a good scattering profile from buffer.

6. Figure 3b displays the I(q) vs q profile. Here, ten frames were collected with a 0.5 s exposure time. Note the colored lines fit the dashed lines (average of all selected frames) well and are of high quality. Some frames are missing due to poor quality (see Note 9).

7. To see the missing frames or to exclude any frames that may deviate from the average, select the frames to exclude/include using the frame window shown in Fig. 3a, Section 1 (red box).

   Included frames will be highlighted gray. Then, click the update plot button (Fig. 3a, Section 2, purple box) to display the 1D, I(q) vs q scattering profiles with the updates.

8. Perform step 7 on each of the samples in the sample drop-down menu to ensure quality. If necessary, the raw, unsubtracted 1D profiles can be exported by clicking the Export button shown in Fig. 3a, Section 2. This will place a .DAT file in a “processed” directory of the format: sample_name.dat (see Note 10).

9. Select a sample (not buffer) in the drop-down menu and check the “show subtracted” button (Fig. 3a, Section 2). The subtracted data will be displayed as shown in Figs. 3c, d.

10. Figure 3c shows the high-quality data observed from the report (Fig. 2a). Note the blue line is subtracted data, orange is scattering from sample + buffer, and green is scattering from the buffer alone.

11. Adjust the scaling factor shown in Fig. 3a, Section 1, by clicking on the box or using the slider. A proper subtraction is shown in the window labeled “buf subtraction” in Fig. 3c. Details are described in [26].

12. The Guinier panel shows a linear fit, and an Rg value will be displayed (~20 for the RNA monomer). For large NANPs, one might have to adjust the Guinier q-start (selecting the Guinier fit qs window) to include more points at low q.

13. To export these data, click the export subtracted button (Subheading 2) and click the export button. A subtracted. DAT file (appended suffix with an s) can then be found in the processed directory.

14. For the example in Fig. 3d, note the noisy, low-intensity subtracted signal. Here, the concentration of the sample was not high enough, and no meaningful data could be obtained. See Note 11 for an NANP example.

15. Click the ATSAS report button to export a GNOM output file (*.out) in the processed directory.

Fig. 2.

Example output of the HTML style summary reports from static SAXS data. (a) Example output from a high-quality dataset. The left plot shows Guinier region (blue) and the merged SAXS/WAXS scaled data (orange). The middle plot shows Kratky analysis to assess the degree of flexibility. This sample shows a plateau in the Kratky analysis, suggesting a degree of flexibility within the sample. The right most plot is the P(r) or pair distance distribution function. The fit of P(r) to the scattering data is shown in the left plot as a blue line over the orange dots. All analysis were performed by using DATtools from the ATSAS suite of software. (b) An example of a report from a poor sample. No Guinier region was able to be determined

Fig. 3.

Example Jupyter Notebook GUI utilizing LIXtools software to visualize and analyze data from static SAXS experiments. (a) Section 1 (red box) is the region to select samples, sample frames, adjusting scaling factor, Guinier start region, and Rg value for a particular sample. Section 2 (purple box) allows for export of data (unsubtracted or subtracted) in DAT format and the ability to run the ATSAS report to generate the Kratky and pair distance distribution plots. (b) Unsubtracted raw I(q) vs q 1D scattering profile for ten frames. Each frame is separated by a scaling factor for visualization purposes. Note the presence of a water peak at 2.0 Å⁻¹ and smooth fit of each colored profile to the average (gray dashed lines). Four frames were discarded and not used for the analysis (gray dots). (c) Scattering profile for high-quality data. Left I(q) vs qplot shows the subtracted data in blue, the scattering from sample + buffer in orange and buffer alone in green. Note the good signal-to-noise ratio and flat shape at low q. The “buf subtraction” window is a zoom in of the subtracted profile around the water peak at 2.0 Å⁻¹ and is helpful for choosing the proper scaling factor. Finally, the Guinier region is displayed, showing a nice linear fit to the data. (d) Same as C, but for a sample that was too low in concentration and did not scatter strongly, resulting in no useful information

3.5. SAXS/WAXS Data Processing for Size-Exclusion Chromatography Coupled with SAXS (SEC-SAXS)

1. If polydispersity is detected after a static SAXS measurement, as shown in Fig. 4 (red diamonds), SEC-SAXS may be an appropriate alternative to improve these data. Data analysis is more involved than high-throughput static SAXS processing, as a buffer region must be manually chosen from the chromatography run (see Note 12).

2. Figure 5a shows the typical Jupyter Notebook GUI used at LIX to process SEC-SAXS data (see Note 13). There are two main types of control, one for the chromatograms (red box) and the other for subtraction (yellow box).

3. Under the chromatograms section, select the X-ray region of interest (ROI) desired, to view data. This is the q range that will be displayed. The default is 0.02, 0.03 Å⁻¹; however, up to three different ROI’s can be overlaid. This can be useful to compare how the background is changing within certain q regions.

4. Under the subtraction box, you can select normal or SVD from the drop-down menu (see Note 14).

5. If using SVD, as determined from Note 14, select the number of background components (Nc) and the polynomial order (polyN) to fit the background under the peak, until the eigenvalues and eigenvectors stabilize.

6. Adjust the scaling factor so the heat map shows a reduced water peak (Fig. 5b, right panel). Check the 1D profile to confirm that there is no over- or under-subtraction (see Note 15).

7. Select the frames under the peak to export (see Note 16). These frames will be averaged and saved as a subtracted DAT file in the processed directory.

8. Click the ATSAS report and confirm high-quality data as shown in Fig. 5c. The q range used for the ATSAS report can be adjusted using the skip and q-cutoff boxes (see Note 17).

Fig. 4.

Comparison of SAXS data collected via the static or SEC-SAXS methods on the RNA monomer NANP. The static method (red diamonds) shows an upward trend at low q indicating polydispersity within the sample. Running SEC-SAXS on the RNA monomer (blue spades) improved the data quality drastically

Fig. 5.

Example of how LIXtools can be used in Jupyter Notebook GUI to analyze -SEC-SAXS data of the RNA monomer NANP. (a) Commands to run and display the GUI. Red box shows the controls for chromatograms, such as choosing a q-ROI (region of interest) and subtraction controls (yellow box), where the mode of subtraction can be chosen from a drop-down menu (normal or SVD), scaling factor, and subtracted frames to be exported. Note that upon the selection of normal mode, excluded frames becomes buffer frames, and these can be chosen manually. (b) Results of scattering of RNA monomer using Superdex Increase 200 5/150 GL column at a flow rate of 0.5 ml/min with 55 μl injection volume. The top part of both panels displays the X-ray scattering intensity (blue dots) for each frame. Each frame is a 2-second exposure for a 12-minute run; a total of 360 frames. The heat map on the bottom shows the q range (y-axis), frame # (horizontal axis), and intensity (colored) for the unsubtracted (left side) and SVD subtracted (right side). Note the intense band at 2.0 Å⁻¹, which represents scattering from water. (c) Atsas output after selecting frames 131–145 to be averaged. Kratky plot shows some degree of flexibility

3.6. SAXS-Driven Molecular Dynamics

The free MD simulation of the RNA is performed using the following steps (Fig. 6):

Fig. 6.

Flowchart outlining the steps required for performing SAXS-driven molecular dynamics to generate ensemble structure

1. Define the forcefield parameters: At this step, the appropriate forcefield is selected along with the recommended water model forcefield. Since only a few forcefields have defined parameters for RNA molecule, we used amber03 along with TiP3 water model for this simulation:

   $gmx pdb2gmx -f rna.pdb -o processed.gro -ff amber03 -water tip3p
   

2. Define a solvation box for the RNA: The size of the solvation box is defined using the parameter “d,” which is the distance from the surface of the biomolecule used to construct a box having user-defined geometry. In this case, we selected a dodecahedron geometry with a distance parameter of 3 nm. The box was then solvated with water (see Note 18).

   $gmx editconf -f processed.gro -o newbox.gro -c -d 3.0 -bt dodecahedron
      $gmx solvate -cp newbox.gro -cs spc216.gro -o solv.gro -p topol.top
   

3. Add appropriate ions to the system: Any biomolecule will have some amount to inherent charge on it, which should be neutralized before performing the MD simulation.

   $gmx grompp -f ions.mdp -c solv.gro -p topol.top -o ions.tpr
   $echo SOL \gmx genion -s ions.tpr -o solv_ions.gro -p topol.top -pname NA -nname CL-neutral
   

   If the experimental sample has additional salts/ions present, those ions should also be accounted for in the solvent box before performing MD simulation. For example, in this case, RNA was purified in 50 mM of KCl; hence, K and Cl ions were added, such that their concentration in the system is 0.05 M.

   $echo SOL \gmx genion -s ions.tpr -o solv_ions.gro -p topol.top -pname K -pq 1 -nname CL -nq – 1 -conc 0.05 -neutral
   

   Option “SOL” is used to replace water molecules with the appropriate number ofions to neutralize the system. The RNA molecule had a total charge of −43, which was neutralized by adding 84 K and 41 CL ions to the system.

4. Energy minimization of the modeled structure: The RNA molecule in the solvent with ions environment is energy minimized to ensure the system exhibits appropriate geometry and is free of any steric clashes.

   $gmx grompp -f minim.mdp -c solv_ions.gro -p topol.top -o em.tpr
   $gmx mdrun -v -deffnm em
   

   The convergence of the system in terms of energy is assessed by plotting the potential energy of the system (Fig. 7a).

   $gmx energy -f em.edr -o potential.xvg (Select 10 0)
   

5. Equilibration MD: To equilibrate the solvent and ion molecules around the solute, it is important to calibrate the system at a standard temperature and pressure. Hence, a 100 ps each of equilibration of the system is conducted at standard temperature (nvt) and pressure (npt).

   $gmx grompp -f nvt.mdp -c em.gro -r em.gro -p topol.top -o nvt.tpr
   $gmx mdrun -deffnm nvt
   $gmx grompp -f npt.mdp -c nvt.gro -r nvt.gro -t nvt.cpt -p topol.top -o npt.tpr
   $gmx mdrun -deffnm npt
   

   To check if the system is well equilibrated, temperature and pressure values throughout the 100 ps simulation are analyzed (Figs. 7b, c).

   $gmx energy -f nvt.edr -o temperature.xvg (select 16 0)
   $gmx energy -f npt.edr -o pressure.xvg (Select 18 0))
   

6. Production MD: Once the system is equilibrated, a 30 ns free MD simulation of the RNA in solvent system is performed.

   $gmx grompp -f md.mdp -c npt.gro -t npt.cpt -p topol.top -o md_0_1.tpr
   $gmx mdrun -deffnm md_0_1
   

7. Analysis of MD convergence: MD simulation of a system is considered to have converged when it no longer shows variation in the root mean square deviation (RMSD) values across the simulation trajectory. Along with RMSD, it is important to check the radius of gyration (Rg) across all axes to determine if the molecule is not unfolding and is maintaining its compactness during the simulation. Both RMSD and Rg are calculated after removing the periodic boundary conditions and making the solute whole (Figs. 7d, e).

   $gmx trjconv -s md_0_1.tpr -f md_0_1. xtc -o md_0_1_noPBC.xtc -pbc mol -center
   $gmx rms -s md_0_1.tpr -f md_0_1_noPBC.xtc -o rmsd.xvg -tu ns
   $gmx gyrate -s md_0_1.tpr -f md_0_1_noPBC.xtc -o gyrate.xvg
   

8. Analysis of the conformational space for the RNA: To identify the different conformations, present for the RNA molecule throughout the simulated trajectory, clustering analysis of the trajectory is performed based on RMSD values. Depending upon the basal level of RMSD in the molecule during the simulation, a cutoff value is determined. A lower cutoff value or the default value of 0.1 nm can sometimes lead to numerous clusters, which might not depict different conformations but only marginal backbone shifts. Here, for the RNA molecule, an RMSD cutoff value of 0.175 nm was used to identify a total of 4 clusters in the 30 ns simulation.

   $gmx cluster -f md_0_1_noPBC.xtc -s md_0_1.tpr -av yes -cutoff 0.175
   

   An average structure, representative of each of the cluster was captured and compared to the starting model structure (Fig. 8). A representative structure from each of these clusters is further analyzed to determine the starting conformation for SAXS-driven MD. The .mdp files for free MD simulations were adopted from http://www.mdtutorials.com/gmx/lysozyme/index.html.

Fig. 7.

Analysis of free MD performed prior to SAXS-driven MD. (a) Energy minimization convergence plot depicting potential energy of the system. (b) Normal temperature equilibration. (c) Normal pressure equilibration. (d) RMSD with respect to the reference structure (black), moving average considering 100 ps time scale (red) during 30 ns simulation. (e) Radius of gyration (Rg:black) and moving average (Rg_x: red) during 30 ns simulation

Fig. 8.

Trajectory cluster representative structures (cyan) from free MD simulation. (a) Average structure from cluster 1 representing 0 to 17.8 ns in the trajectory. (b) Average structure from cluster 2 representing 17.8 to 17.9 ns (c) Average structure from cluster 3 representing 17.9 to 22.5 ns and (d) average structure from cluster 4 representing 22.5 to 30 ns in comparison to model RNA structure (khaki)

3.7. Free MD Calculation for Solvent-Water and Ions

1. The SAXS-driven MD simulation requires an only solvent simulation to perform the approximation for calculating the SAXS profile from the simulated trajectory. Hence, an explicit solvent free MD simulation is performed using the following steps.

2. Defining the solvent box: A solvent box containing only water is generated by increasing the box size created in step 1b by a few nanometers. In general, the box size for solvent-only simulation should be greater than the solute in solvent simulation.

   $gmx solvate -box x y z -cs spc216.gro -o solvent_box.gro
   

   The dimensions for the box in the case of RNA in a solvent system were x = 12.435, y = 12.435, and z = 12.435. The solvent-only simulation box was created by adding 2 nm in each direction, with the final box size as x = 14.435, y = 14.435, and z = 14.435.

3. Define forcefield for solvent-only box: The same forcefield as used for RNA in the solvent box (Amber03) is used in the water-only box.

   $gmx pdb2gmx -f solvent_box.gro -o processed.gro -ff amber03 -water tip3p
   

4. Add ions to the system: The ions present in the RNA in solvent system were also to be added to the solvent-only box, i.e., 50 nM of KCl.

   $gmx grompp -f ions.mdp -c processed.gro -p topol.top -o ions.tpr
   $echo SOL \ gmx genion -s ions.tpr -o solv_ions.gro -p topol.top -pname K -pq 1 -nname CL -nq – 1 -conc 0.050 -neutral
   

5. Energy minimization to production MD: Following the generation of a solvent system containing the same concentration of ions as for the solute in solvent free MD, energy minimization to production MD steps is performed for the solvent-only system using the same commands described in the section above (free MD calculations for solute-RNA molecule in solvent, 4–7). See Note 19.

3.8. SAXS-Driven MD

1. Generate index file: The first step for performing SAXS-MD is to generate an index file to define the solute in the system. If your system contains additional molecules, such as ligands, a group combining the biomolecule and ligand can be generated using the make index function of GROMACS. In this case, the solute is defined as only RNA; hence, defining additional groups is not required.

   $echo q \ gmx make_ndx -f md.gro
   

   md.gro: output file from free MD simulation for RNA in solvent

2. Calculating Cromer-Mann parameters for the solute in the system: Once the solute group is defined, a structure file (dummy.tpr) is generated to calculate the Cromer-Mann parameters for the solute group. This is one of the features specifically designed in the modified version of GROMACS (GROMACS-SWAXS).

      $touch empty.mdp
   $gmx grompp -f empty.mdp -c md.gro -p topol.top -o dummy.tpr
   $gmx genscatt -s dummy.tpr -vsites
   

   The solute group should be selected here as “RNA.” See Note 20.

   md.gro: output file from free MD simulation for RNA in solvent.

   topol.top: topology file generated from free MD simulation

   Output file: scatter_RNA_chain_A.itp

   The output file contains the scattering parameters for the solute molecule. For the program to read this scattering topology, the topol.top file is edited by adding the following lines just before the inclusion of the positional restrains. The topology.top file should read like:

   ;Include Scattering topology
   #ifdef SCATTER
   #include “scatter_RNA_chain_A.itp”
   #endif
   ;Include Position restrain file
   ....
   

3. Defining envelop boundaries for the SAXS-driven MD: For mimicking the in-solution experimental conditions, an envelope is defined around the RNA molecule to perform SAXS-MD simulation. The trajectory obtained from the free MD simulation is utilized to construct this envelope so that all possible transitions in the solvent box can be traversed. The distance “d” defined here is the distance from the surface of the RNA molecule. In general, this distance should be greater than 0.6 nm, but for systems containing ions, the distance can be up to 3 nm for better convergence of experimental data. Here, for the RNA molecule, the distance was defined as 1.5 nm, and the trajectory without periodic boundary conditions (md_noPBC.xtc) was used to ensure the RNA molecule was whole (Fig. 9).

   $gmx genenv -d 1.5 -s dummy.tpr -f md_noPBC.xtc
   

   Output files: envelope-ref.gro, envelope.dat, envelope.py (see Note 21).

   Two environment features are defined before processing SAXS-MD to read the envelope coordinates

   $export GMX_WAXS_FIT_REFFILE=/path/to/the/file/envelope-ref.gro
   $export GMX_ENVELOPE_FILE=/path/to/the/file/envelope.dat
   

   While performing the calculation for generating the envelope, a global atom number (GOOD PBC atom) is generated, which is noted to be defined in the mdp file for SAXS-driven MD.

   For example:

   ############ G O O D P B C A T O M ################################

   N.B.: Solute atom number 15 is near the center of the bounding sphere - it would make a good waxs-pbc atom (distance = 0.279619)

   Global atom number = 15 (name C5, residue G-1)

   #######################################################################

4. Generate solvent structure file from free MD solvent-only simulation: To define the Cromer-Mann parameters for the solvent system for the SAXS-driven MD, a structure file (.tpr) from the free MD solvent-only simulation is generated. This structure file and trajectory file of the solvent from free MD is used as input in the final SAXS-driven production MD step.

   $gmx grompp -c solvent.gro -f solvent.mdp -p solvent-topol.top -o solvent.tpr
   

5. Solute in solvent SAXS-driven production MD: Three input files were prepared for performing the solute in solvent SAXS-driven production MD.

6. SAXS experimental data file: The experimental data obtained collected for the RNA sample is first smoothened to reduce the noise as well as improve the computational efficiency of the SAXS-driven MD. A shell script is used to smoothen and re-bin the experimental data, which is based on the DATGNOM model of the ATSAS package [35] . Smoothed and re-binned data leads to better convergence of the computationally calculated SAXS profile. The values obtained after smoothening are then converted to nm⁻¹ from Angstrom⁻¹ by multiplying the q values by 10. The data is cut off around a q value of 10 nm⁻. The lowest and highest value of q in the target dataset are noted.

   $./smooth-saxs-curve.sh -f saxs_experimental_data.dat -o target_smooth.xvg.
   

7. Parameter in the SAXS-driven.mdp file:

   • Waxs-pbc = Atom number obtained while generating envelope file (15 in this case).
   • Solute group = RNA (if ligand is present, mention the group create while defining the index file, e.g., RNA_LIG).
   • Solvent group = “Water_and_ions” in case ions are present, if not, “Water.”
   • Fc = 1–5 (for Bayesian solution, fc is defined as 1).
   • Number of q points: 30–50.
   • q start = slightly larger value than the smallest q point in the experimental data file. For example, if the first datapoint is 0.055, q start should be 0.06.
   • q end = slightly smaller than the largest q point in the experimental data file. For example, if the last datapoint is 10.15, q end should be 10.
   • Waxs-nstcalc = 250. The number of steps after which the SAXS curve is calculated. If the number of steps is given as 500, the SAXS curve is calculated after every 250 ps in the simulation. It is recommended to keep the nstcalc value as 250, i.e., calculate SAXS curve after every 125 ps, thus maintaining a 2 fs time step and avoiding any LINCS errors during simulations.
   • WAXS-tau = 250 ps. The number of frames utilized for calculating the SAXS curve. In simple terms, the SAXS curve calculated throughout the simulation takes into considerations this time window to generate an average curve. The SAXS curve obtained at the end of the SAXS-driven MD is also an approximation or on the fly curve generated by averaging the intensities in the last 250 ps of the simulation.
   • WAXS-t-target = 10,000 ps. This is the time up till which the SAXS experimentally derived potentials are introduced in the simulation. The SAXS potentials are not incorporated all together in the SAXS-driven MD; rather, the potentials are introduced slowly at each step such that the relative weight of the target curve to the calculated curve reaches 1 when the simulation reaches a time defined by Waxs-t-target. For example, if the waxs-t-target is defined as 5000 ps, the relative weight of the target to calculated curve is 0.5 at 2500 ps and 1 at 5000 ps. The .mdp file for SAXS-driven MD were obtained from https://cbjh.gitlab.io/gromacs-swaxs-docs/tutorials.html.

8. Starting conformation of the RNA molecule: Determining the starting conformation for the SAXS-driven MD is a crucial step since the conformation of the biomolecule is not intended to change much following the SAXS-driven simulation. To identify the starting conformation, the rerun module of SAXS-driven MD is utilized. Through the clustering analysis performed for RNA in solvent free MD simulation, specific trajectory windows are obtained that depict major conformational changes. The rerun module essentially utilizes the trajectory generated from free MD simulation and generates a SAXS curve for the RNA molecule as well as provides an estimate of the Rg value. In this case, four clusters were identified from the 30 ns free MD trajectory analysis: cluster 1: 0–17.8 ns; cluster 2:17.8–17.9 ns, cluster 3: 17.9–22.2 ns; and cluster 4: 22.2–30 ns. Since the number of frames in cluster 2 were less, this cluster was not utilized for the SAXS curve calculation.

   The starting and ending frames of these clusters are defined as global environment features, i.e., GMX_WAXS_BEGIN and GMX_WAXS_END, and a SAXS curve is calculated by taking a non-weighted average across the free MD frames.

   $gmx grompp -f rerun.mdp -p topol.top -c md.gro -o saxs_01.tpr
   $gmx mdrun -sw solvent.tpr -fw solvent.xtc -rerun md_noPBC.xtc -deffnm saxs_01
   

   The Rg value was calculated for each of the cluster trajectories, i.e., cluster 1: 22.5 Å, cluster 3: 23.8 Å, and cluster 4: 22.4 Å. Since the experimental value is close to 20, both cluster 1 and 4 can be utilized performing SAXS-driven MD. Hence, the first frame as well as the last frame of the free MD were considered as the starting structure of SAXS-driven MD simulation. Multiple starting conformations should be tested to reach a consensus for the experimental SAXS data.

   $gmx grompp -f SAXS-driven.mdp -p topol.top -c firstframe.gro -o saxs_driven.tpr
   -n index.ndx
   $gmx mdrun -s saxs_driven.tpr -is target_smooth.xvg -sw solvent.tpr -fw solvent.xtc -deffnm saxs_driven
   

Fig. 9.

Envelope construction for SAXS-driven MD. (a) Envelope defined before SAXS-driven MD using the distance parameter “d” (1.5 nm in this example). (b) Envelope system containing RNA, water, and ions during SAXS-driven MD derived by merging RNA in solvent and explicit solvent free MD simulation systems

3.9. Output Files and Analysis

1. The following output files are generated after the completion of SAXS-driven MD. These files are important to analyze the results and generate the average SAXS-driven MD structure.

2. Saxs_driven.gro: The structure of the RNA molecule obtained from the last frame of the SAXS-driven MD.

3. Saxs_driven.xtc: The trajectory file for the SAXS-driven MD. It can be visualized with the .gro file in software, such as ChimeraX [32] or VMD [33], to see the conformational changes the RNA molecule went through during the simulation. An analysis of the RMSD and Rg values throughout the simulation can be performed using the trajectory file in a similar way as performed for free MD simulation (Fig. 10a, b).

4. Saxs_driven.edr: The energy components of the SAXS-driven MD. This file is used to analyze the effect of SAXS potentials on the SAXS-driven MD simulation. The SAXS potentials through the simulation are calculated using the command:

   $gmx energy -f saxs_driven.xtc -o energy.xvg (Select option 16 0– X.coupl energy)
   

   The overall effect of the SAXS potentials should not be enormous and minimal toward the end of the simulation. A lower energy contribution also indicates that the appropriate structural conformation, matching the experimental data, has been achieved through the SAXS-driven simulation. This analysis is also useful in determining which starting conformation is best suited for the downstream analysis. A starting conformation leading to lower energy fluctuations through the simulation should be preferred. In this example, when the first frame from cluster 1 of free MD trajectory was used as the starting conformation, it yielded in an average energy of 50 kcal/mol (Fig. 10c). Whereas for the starting conformation as the last frame from cluster 4 of free MD, the average energy was 88 kcal/mol. Hence, the SAXS-driven MD performed using the first frame structure is best suited for further analysis, and generation of a SAXS-driven ensemble structure.

5. Saxs_driven_final.xvg: It contains 3 SAXS curves:

   • 5.1
     The input smoothened SAXS experimental data
   • 5.2
     Maximum Likelihood target data, scaled to match the calculated SAXS profile.
   • 5.3
     On the fly SAXS curve: Obtained by averaging the last 250 ps or the memory value (waxs-tau) provided during the simulation. The on-the-fly curve might not necessarily match the experimental value, since it only considers the last few frames and also if the simulation has not converged (Fig. 11a).

6. Saxs_driven_spectra.xvg: It contains the SAXS curve calculated after every 10 ps during the simulation. This file is plotted along with the experimental SAXS curve, to understand the time frame at which the simulation converged for the RNA molecule. (Fig. 11b). The overlay of the ML target on the spectra can also help determine the minimum number of frames required to describe the ensemble structure from the SAXS profile (Fig. 11c).

7. Saxs_driven.log: Provides details about the energy calculation during the simulation and also the Guinier fit Rg value for the on-the-fly curve generated from the simulation. The Rg calculated by this module of SAXS-driven MD for the RNA molecule was 20.77 Å.

Fig. 10.

Analysis of SAXS-driven MD convergence. (a) RMSD with respect to reference starting structure (black), moving average over 100 ps (red) during the 30 ns SAXS-driven MD. (b) Radius of gyration (black) and moving average (red) during 30 ns simulation. (c) Energy contribution from SAXS potentials during 30 ns SAXS-driven MD simulation

Fig. 11.

Analysis of SAXS curves generated from SAXS-driven MD and RERUN module. Red: maximum likelihood target SAXS curve (experimental curve). Blue: calculated SAXS curve from SAXS-driven MD. (a) On the fly SAXS curve generated toward the end of SAXS-driven MD. (b) SAXS curve spectra generated from the simulation by calculating SAXS profile after every 10 ps in the 30 ns simulation (gray). (c) Trajectory frames selected from spectra analysis to depict convergence of the system (27 ns to 30 ns: gray). (d) Average SAXS curve calculated using RERUN module considering 27 ns to 30 ns of trajectory frames

3.10. Rerun SAXS-MD Module

1. Since the on-the-fly curve obtained from SAXS-driven MD only takes into consideration the last 250 ps of the simulation, it might not be the correct estimate, depending upon when the simulation converged. To assess the correct Guinier approximation of Rg, the rerun module of this package is utilized. This module reruns the trajectory obtained from SAXS-driven MD and calculates an average curve for the overall trajectory. Depending upon the analysis and visualization of the trajectory file as well as the SAXS-driven spectra, an appropriate window of the trajectory can also be selected to reduce the number of frames being used to determine the average solution structure (Fig. 11c).

2. Based on the SAXS-driven spectra analysis, the global parameters GMX_WAXS_BEGIN and GMX_WAXS_END were defined as 27 ns and 30 ns, respectively.

   $export GMX_WAXS_BEGIN=27000
   $export GMX_WAXS_END=30000
   $gmx grompp -f rerun.mdp -p topol.top -c saxs_driven.gro -o waxs.tpr
   $gmx mdrun -sw solvent.tpr -fw solvent.xtc -rerun saxs_driven.xtc
   

3. The output files obtained from this module include a spectra file as well as an average calculated SAXS curve (Fig. 11d). The Guinier fit Rg approximation is reported in the log file. The Rg from the SAXS-driven MD rerun module was calculated as 20.18 Å.

4. Fitting estimated model from SAXS-MD trajectory to SAXS envelope: Once the best fitting window is determined from the analysis performed through the rerun module, an average structure can be determined and fitted into the envelope generated from the SAXS data analysis. The average structure generated from the best fit trajectory window is superimposed on the model RNA structure for comparison (Fig. 12).

Fig. 12.

Final frame structure obtained from SAXS-driven MD (cyan) superimposed onto model RNA structure (khaki)

4. Notes

1. Note: Possible error: “No default Xray coupl. Types.” Solution: Check forcefield.itp and ions.itp files of the particular forcefield being used in the share/top folder, and add the following to forcefield.itp file: #ifdef SCATTER.

   #include "cromer-mann-defs.itp"

   #include "neutron-scatt-len-defs.itp"

   #endif

   And add the following to the ions.itp file. The following block should be added for all the ions present in the system under study:

   #ifdef SCATTER

   [ scattering_params ]

   ;i ft a1-a4, b1-b4, c

   1 1 CROMER_MANN_Cl_minus

   1 2 NEUTRON_SCATT_LEN_Cl

   #endif

2. Monodispersity of sample is critical for a successful SAXS/WAXS experiment. Interactions between the particles in your samples will show either an uptick or downturn in low q data and make it difficult to obtain a good Guinier fit. For this type of case, the use of SEC-SAXS or adjustments to buffer conditions (such as screening repulsive charges with salts) is appropriate to eliminate the effect of higher-order contaminants or to obtain SAXS data from additional oligomeric states. Moreover, upticks at low q can also indicate that one has a flexible sample, which exists in a wide range of conformations, altering the experimental approach. Therefore, understanding the behavior of your sample before sending it for SAXS measurement is critical. It may not always be optimal to run SEC-SAXS if you see an uptick at low q and have evidence of flexibility (such as an intrinsically disorder protein or IDP). One can then proceed to the SAXS-MD section. Finally, the beamline should not be used to measure partially purified samples. When discussing sample preparation with beamline scientists, be able to show chromatograms, gels, or other data to demonstrate sample stability so that an optimal experiment can be designed.

3. It can be useful to perform a concentration series starting with a wide range and narrowing the range if necessary (e.g., to focus on a structural transition around a particular concentration). For example, to ensure that you do not have concentration-dependent effects, such as aggregation, Rg values determined by Guinier analysis should be the same for changing concentration, and I(0) should increase linearly with increasing concentration. A concentration series can also be useful to observe transitions to various oligomeric states and to calculate Kd values. For an example and details, see [13]. At LIX, the Opentrons OT2 liquid handler can help to make concentration series easy to setup. A stock concentration of your sample protein is in a specific well of a 96-well plate and can be diluted with matched buffer using the OT2. This simplifies setup for both the user and beamline staff and increases sample throughput. For details, see [27].

4. Scattering from your sample is relatively weak compared to that of the components of the buffer. A good buffer subtraction is critical to obtaining the scattering from your sample alone. If, for example, you are studying a system and add ligand to assess conformational changes, any unbound ligand must be removed. If there is free ligand in your sample, but not in your buffer, the scattering contributions from the buffer will be different, and the subtraction will not represent scattering from the sample alone.

5. Please refer to [26] for details about sample setup at LIX. Briefly, each protein or nucleic acid sample set should have at least two matched buffers, one before sample set measurement and immediately after, in order to verify the background does not change throughout the experiment (i.e., your sample fouls the flow cell).

6. Buffers should minimize the use of any organics or high concentrations of glycerol, sucrose, or similar viscous components (≤5%). Avoid high salt and buffer concentrations. Most SEC-SAXS runs may be performed at room temperature. Often, temperatures within the experimental hutch are higher than room temperature. At LIX, we have a temperature controlled multi-sampler, but the buffer and column must be chilled separately and thus requires advanced preparation.

7. The report is a Jupyter Notebook that employs parts of DATtools from the ATSAS suite [27, 36]. This report is a “first look” at your results and should be scrutinized. For example, the default values that are used in GNOM to calculate the P(r) fit might need adjustment. For the case of Fig. 2a, the Dmax value is slightly overestimated, and therefore, an adjustment is necessary. This can be done within GNOM or other software. Details are covered elsewhere and beyond the scope of this chapter. For NANPs, they can be very large, and estimating Dmax (if necessary) can be difficult if there are not enough data points collected in the low q range. Therefore, it is important to have some understanding of the overall size by other methods such as light scattering.

8. Data stored on Jupyter Hub (Brookhaven National Laboratory) can be downloaded to your local machine after processing to perform downstream analysis such as modeling. The details about Jupyter Hub change and, therefore, involve a conversation with beamline staff. Always check with the facility for details about data access and storage time.

9. Sometimes, not all frames are of high quality. These are thrown out if they deviate from the average intensities of the set. At least three high-quality frames are needed to obtain a confident average. Loss of frames could be a result of highly viscous samples that are difficult to load into the flow cell. Thus, planning with beamline staff before your experiment is critical to avoid such issues and explore alternative setups to accomplish your goals.

10. The DAT files are ASCII format files of your 1D data that contain three columns. Column 1 is the q range, column 2 are the associated intensities, and the last column are the error values. These files can be used for import into downstream analysis software.

11. As mentioned in Subheading 1, an RNA NANP was generated. The monomeric form of the base structure was measured at LIX, and the resulting 1D scattering profile is shown in Fig. 4 (red diamonds). The experiment was performed with a good signal-to-noise ratio, but there was a significant uptick at low q indicating sample polydispersity. Thus, we cannot accurately determine what we are measuring since multiple species are present. To improve the dataset, the RNA monomer sample was rerun using SEC-SAXS on a Superdex Increase 200 5/150GL column from Cytiva. The improved SEC-SAXS results are shown as blue spades in Fig. 4. Note the flat region in the low-q range, where an accurate Rg value could now be determined. These data were used in the downstream analysis of SAXS-driven MD.

12. SEC-SAXS data will be shared in HDF5 format from LIX, like that found in step 1 of the high-throughput static saxs processing section. The file will be much larger as it contains a series of SAXS patterns in time. The number of frames is dependent on column utilized and exposure time.

13. HDF5 files can be directly read into RAW [37] and processed outside of the Jupyter Notebook if desired [21]. Use of other software will require exporting the desired frames in DAT format from the Jupyter Notebook and importing into desired software.

14. If the background is stable, as shown in Fig. 5b, normal subtraction can be used, where individual frames will be averaged and used for buffer subtraction. It is good practice to test various frame ranges before and after the peak of interest to see if it affects the subtraction and thus the 1D scattering profile. If there are significant changes, it would be beneficial to try SVD to interpolate the scattering contribution from the buffer. See reference [26] for details about SVD. If using SVD, be sure to select the frames of interest in the excluded frames window to ensure they are not included in the SVD analysis.

15. Over- or under-subtraction can be visualized using the heat maps in Fig. 5b, right panel. The left panel shows unsubtracted data, with a strong intensity at 2.0 Å⁻¹ that corresponds to the water peak. Over/under-subtraction of the water peak by adjustment of the scaling factor can be visualized by observing this intensity decrease under the peak. A final look at the 1D scattering profile at 2.0 Å⁻¹ will confirm if the scaling factor needs further adjustment. If the plot shows a large drop (over subtraction), decrease the scaling factor. On the other hand, if there is a water peak still present (under subtraction), increase the scaling factor. This is largely empirical and takes practice to get correct.

16. Selection of the optimal frames within a peak can be difficult. It is useful to plot Rg values across each frame of the peak to determine a stable region to use as your data. It is also useful to pay attention to the Kratky plot. If the graph does not plateau (as in Fig. 5c), the sample may have flexible regions. If this is the case, the hydrodynamic radius will vary, resulting in a single peak with multiple shapes, and thus, multiple models may explain these data. See the SAXS-driven MD section.

17. It is best to utilize other software, such as ATSAS, RAW or the like, to generate the P(r) function. These software packages have more control over the parameterization of the P(r) and details can be found [36, 37]. Anote of caution: If you find you need to “skip” many datapoints at low q, there is an issue with the data, and no further downstream data interpretation should be attempted.

18. Note the dimensions of the newbox generated from this step. These dimensions will be used to generate solvent box for only solvent simulations.

19. The temperature groups (tc) were changed in the mdp files for the solvent-only simulation to “Water_and_ions” in place of “RNA; Water_and_ion.”

20. If the solute system under consideration has more than one chain, then the scattering file is generated for each chain, and these lines must be added to each topol.top or topol_chain_A.itp file.

21. The envelope generated can be visualized by reading the file envelope-ref.gro and envelope.py in pymol. The surface of the envelope should look uniform and if spikes at certain points are observed, a larger distance parameter (d) should be provided to define the envelope.

Abbreviations:

LIX

Life Sciences X-ray scattering beamline

SAXS

small-angle X-ray scattering

WAXS

wide-angle X-ray scattering

NANP

nucleic acid nanoparticle

DLS

dynamic light scattering

MW

molecular weight

HT-SAXS

high-throughput static SAXS

SEC-SAXS

size exclusion chromatography coupled with SAXS

SVD

single value decomposition

MD

molecular dynamics