Supporting Information

Transcription

1 Supporting Information Band Sedimentation Experiment in Analytical Ultracentrifugation Revisited Cornelia M. Schneider, Dirk Haffke, Helmut Cölfen* Physical Chemistry, University of Konstanz, Universitätsstrasse 10, D Konstanz, Germany, * Table of contents 1. Materials 2. Instrument 3. Experiment 4. Data acquisition 5. Rotor speed at the overlay 6. Thickness and volume of the overlay solution layer 7. Calculation of the run time integral ω 2 t for different rotor speeds and comparison of the values 8. Overlay of H 2O onto D 2O 9. Comparison of different speed profiles 10. Comparison of different centerpieces 11. Overlay of a solution with higher density and viscosity 12. References S1

2 1. Materials For all measurements water of Milli-Q quality was used, sourced from a Milli-Q Synthesis A10 system equipped with a Quantum EX Ultrapure Organex cartridge (Millipore). D 2O was purchased from Aldrich and used as received. 2. Instrument The experiment was performed on a UV-vis multiwavelength analytical ultracentrifuge (AUC). The general setup has been described in literature. 1-3 Additionally, it was equipped with a custom built Advanced Interference Detection Array (AIDA) 4, which offers improvements to the standard Rayleigh interference optics of the Beckman Coulter Optima XL-I. The CCDchip used for detection is provided by the camera Canon EOS 6D. There are also different speed profiles accessible on the control board, as used for the speed ramp 2 and HDR Multifit analysis 5. The linear speed profiles used are shown in Figure S3. Data acquisition is handled by the system design software LabVIEW 2016 (32bit) from National Instruments. The rotor speed is measured by a reflection light gate, which provides the correct trigger handled by a trigger box. The trigger starts at 600 rpm. The trigger signal is furthermore used to calculate the runtime integral ω 2 t-value, which is necessary for evaluation. 3. Experiment The measurements were performed at 25 C, using the slowest speed profile 8 or speed profile 7 (see Figure S3) and spinning up to 3000 rpm for every standard run. The slowest speed profile (profile 8) for acceleration is preferred, as this leads to a higher resolution for taking pictures during the increase of the rotor speed. The number of pictures needed for the overlay gives its duration, as the picture record time is known. The correlation of a picture to the actual rotor speed gives the speed at which the overlay is happening, as the rotor speed is recorded simultaneously. For the overlay of H 2O on D 2O (movie in SI section 8), the rotor was spun up to rpm. A 12 mm charcoal filled Epon Beckman Band forming centerpiece of the Vinograd type was used to conduct the experiments. 6 This provides a small (15 µl) reservoir, which is connected with the sample sector via a thin capillary. The centrifugal force is used to overlay the solution from the reservoir onto the other. By allocating a small density difference in between the solutions, a sharp boundary is built up. For testing the system, different volumes between 1 µl and 15 µl of water were filled into the reservoir and overlaid onto 295 µl of water in the sample sector. 340 µl water were filled in the reference sector. For the overlay of a 7:3 mixture of H 2O:D 2O, 5 µl of the mixture were filled into the reservoir and overlaid onto 295 µl of H 2O in the sample sector. The density and viscosity of the mixture were determined using the density meter DMA 5000 M and microviscosimeter Lovis 2000 ME from Anton Paar. For the H 2O/D 2O experiment in the movie, 5 µl water were filled into the reservoir and overlaid onto 295 µl of D 2O in the sample sector. All measurements were repeated two times for the statistical factor. One single experiment for comparison was performed using a band forming centerpiece from Spin Analytical. 4. Data acquisition The LabVIEW program was designed that way that with the beginning of the triggering of the laser at 600 rpm, the camera starts to take pictures in continuous mode with a shutter speed of 1/6 s and an ISO value of 1250 with auto adjusting the laser delay and duration. The average picture recording time was 388 ms during the acceleration of the rotor. It may be necessary to turn off the imbalance sensor of the AUC using the slowest acceleration profile. All the pictures are saved to the implemented SD card on the camera. The speed profile is recorded by the program with start of the experiment. As the first picture is taken at the same time as the speed profile record starts, the pictures can be correlated to the actual speed of the rotor. S2

3 5. Rotor speed at the overlay The graph in Figure S1 shows a clear correlation between overlay volume and rotor speed at the overlay and is also in good agreement with theoretically calculated values based on a constant hydrostatic pressure. Figure S1: Graph of the correlation between the overlay volume and the current rotor speed, at which the overlay onto the solution in the sample sector happens (continuous line) and for comparison theoretically calculated values (dotted line) based on a constant hydrostatic pressure according to p = r h with = angular velocity, = density, r = radial distance from rotor axis and h = column height. The value at 5 µl was taken as reference for the column height. 6. Thickness and volume of the overlay solution layer In Figure S2 the layer thickness of the overlay is graphed versus the overlay volume. Both data from theoretical calculations based on the geometry of the cell sector and values from the data collected from the interference pattern are shown. These data are averages over 3 measurements. Theoretically calculated and real data values are in good agreement. This also shows that the full volume put into the reservoir is overlaid onto the sector solution without mass loss. S3

4 Figure S2: Comparison of the calculated layer thickness from dimensions of the cell (dotted line) and real values received from the raw data and correlating the meniscus shift to a layer thickness (continuous line). 7. Calculation of the run time integral ω 2 t for different rotor speeds and comparison of the values Another interesting value to compare is the run time integral ω 2 t, which is an important variable for analysis. The range of the ω 2 t values between the lowest and highest rotor speed for overlay (767 rpm 2004 rpm) is s s -1. For typical rotor speeds during a band sedimentation experiment between and rpm, the range for the ω 2 t value is s s -1, and for a typical run at rpm for 4 hours s -1, as also shown in Table S1. These values are in the range of 3 6 orders of magnitude higher than the values for the overlay. Therefore, the difference in ω 2 t due to the overlay, which the sample experiences is almost negligible and therefore does not significantly influence the analysis. This shows a well-defined initial boundary. Table S1: Correlating ω 2 t values after reaching different rotor speeds and after 4h of spinning at rpm rotor speed [rpm] ω 2 t [s -1 ] (4h) Overlay of H 2O onto D 2O One may notice that for a real band sedimentation experiment a slight density difference must be provided between the solutions of reservoir and sector. This was not the case in these examinations of the experiment, as water was layered onto water. This is due to the strong optical issues caused by the additional meniscus at the beginning of the experiment between H 2O and D 2O if D 2O is used as a sample solution. The meniscus bends the light, which is used for the creation of the Rayleigh interference pattern, out of the optical path and therefore the exact duration of the overlay is barely visible. 7 As the use of water does not cause that effect and serves the same purpose, this was used instead. Still, the observation of the overlay, the formation of the second meniscus and the slow mix of the two solutions can be very interesting to observe. A movie of a single run of this with the correlating rotor speed is linked below. First, this shows that the overlay speed using D 2O instead of H 2O does not have a significant influence, the rotor speed at the overlay is at 1105 rpm, which supports the assumption made that a change to H 2O would not really affect the validity of the measurements. Secondly, the development of the boundary, as well as the final mix of the reactant solutions, can be observed. This also shows that the diffusion of these solutions into each other and therefore formation of the density gradient is much slower than the overlay itself and the reaction time. This was already seen in the investigation by Mächtle. 8 The movie of the overlay of 5 µl H 2O onto D 2O can be found under the following link: 9. Comparison of different speed profiles One could raise the argument that the presented results are just valid for the applied slow speed profile, and are not transferable to faster profiles, especially the speed profile of maximum acceleration before a run, which is used in every standard sedimentation velocity experiment. This slow speed profile was used, as this provides better resolution for observing the overlay phenomenon. But we also performed an experiment with a faster speed profile 7 to address this argument. The S4

5 speed profiles are shown in Figure S3, also for comparison with the maximal acceleration. For an overlay of 5 µl, a mean overlay speed of 1093 ± 40 rpm and a duration of two times the picture record time was found (0.78 s), which is still in very good agreement with the results found for the slower speed profile 8 (Table 1: 5 µl: 1047 ± 14 rpm, 0.78 s). Although the standard acceleration profile is remarkably faster, no significant difference is expected by applying the fastest speed profile. Figure S3: Different speed profiles used in this study, shown in comparison with the maximal acceleration 10. Comparison of different centerpieces The centerpiece used in these experiments was a Beckman band forming centerpiece, but there are also band forming centerpieces offered by Spin Analytical. For comparison, there was a single experiment performed using the Spin Analytical centerpiece. For an overlay volume of 5 µl H 2O, an overlay speed of 1174 rpm and a duration of 1.166s was found, which is slightly later and longer than the values found for the Beckman centerpiece (Table 1: 5 µl: 1047 ± 14 rpm, 0.78 s). Also, the hydrostatic pressure p = 1636 Pa is somewhat higher compared to 1182 Pa from the Beckman centerpiece. This could be caused by the thinner capillaries of the Spin Analytical centerpiece than the ones of the Beckman centerpiece (see Figure S4). Still, the values show a general transferability and applicability of the experiment also if performed with other centerpieces. Generally, one needs to consider the chemical resistance of the Epon centerpieces, when conducting these experiments. 9 Figure S4: Comparison between Beckman Band forming centerpiece (left) and Spin Analytical Band forming centerpiece (right) S5

6 11. Overlay of a solution with higher density and viscosity The solution contained in the reservoir may consist of a concentrated macromolecular solution or a reactant solution, dependent on the experiment type, and therefore could provide a higher density and viscosity. To test how this influences the overlay speed and duration in comparison to the results obtained by the overlay of pure water, another experiment was performed with the overlay of 5 µl of a 7:3 mixture of H 2O and D 2O onto H 2O, providing a higher density (ρ = g/ml) and higher viscosity (η = mpas) than H 2O (ρ factor 1.03, η factor 1.07). The use of a concentrated macromolecular solution caused optical artefacts and could therefore not be applied. For a 5 µl overlay, an overlay speed of 966 ± 10 rpm and an overlay duration of 0.78 s was found. This is somewhat less than the speed found for the overlay of pure water (Table 1: 5 µl: 1047 ± 14 rpm, 0.78 s), but can be explained, as a higher density causes a higher capillary pressure due to p = r h and therefore an earlier overlay. The pressure in this case is 1.04 kpa, which is still in good agreement with the other pressure values (Table 1). The smearing of the boundary was simulated for an overlay of 1 µl pure H 2O onto D 2O in literature. 10 For comparison, the same simulation was conducted using 5 µl of a 7:3 mixture of H 2O and D 2O, as used in this experiment based on the integrated form of Fick s second law. Further details on the calculation are described in literature. 10 The results are shown in Figure S5. The small volume is overlaid and the smaller the density and viscosity difference between the solutions is, the smaller are the changes in concentration of H 2O and therefore the deviation in s 20,w. Here, the deviation of s is a factor of 1.2 directly at the boundary at time zero. But this quickly decreases to 1.05 after 800 s. Figure S5: Simulation of a dynamic density gradient between H 2O and D 2O. A volume of 5 µl of a 7:3 mixture of H 2O : D 2O were overlaid onto D 2O. The simulation was performed using the integrated from of Fick s second law. In (a), the concentration of H 2O in pure D 2O is plotted against the time and the distance from the boundary. The thereby caused changes in viscosity and density influence the deviation of the calculated sedimentation coefficient s 20,w; this is shown in (b). 12. References (1) Strauss, H.; Karabudak, E.; Bhattacharyya, S.; Kretzschmar, A.; Wohlleben, W.; Cölfen, H. Colloid. Polym. Sci. 2008, 286, (2) Walter, J.; Löhr, K.; Karabudak, E.; Reis, W.; Mikhael, J.; Peukert, W.; Wohlleben, W.; Cölfen, H. ACS Nano 2014, 8, (3) Bhattacharyya, S. K.; Maciejewska, P.; Börger, L.; Stadler, M.; Gülsün, A. M.; Cicek, H. B.; Cölfen, H. Prog. Colloid Polym. Sci. 2006, 131, (4) Schilling, K.; Krause, F. PLOS ONE 2015, 10, e (5) Walter, J.; Peukert, W. Nanoscale 2016, 8, (6) Vinograd, J.; Radloff, R.; Bruner, R. Biopolymers 1965, 3, (7) Mächtle, W.; Klodwig, U. Macromol. Chem. Phys. 1979, 180, S6

7 (8) Mächtle, W. Analytical Ultracentrifugation V 1999, 1-9. (9) Beckman Coulter, I.; Online at (10) Schneider, C. M.; Cölfen, H. European Biophysics Journal 2018, DOI: /s S7