Band Sedimentation Experiment in Analytical Ultracentrifugation

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The Band Sedimentation experiment in Analytical Ultracentrifugation revisited Cornelia Marion Schneider, Dirk Haffke, and Helmut Cölfen Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b02768 • Publication Date (Web): 30 Aug 2018 Downloaded from http://pubs.acs.org on August 30, 2018

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Analytical Chemistry

The Band Sedimentation experiment in Analytical Ultracentrifugation revisited Cornelia M. Schneider, Dirk Haffke, Helmut Cölfen* Physical Chemistry, University of Konstanz, Universitätsstrasse 10, D-78457 Konstanz, Germany, E-mail: [email protected] ABSTRACT: The Band sedimentation experiment in Analytical Ultracentrifugation (AUC) allows for the performance of a chemical reaction inside the AUC and also offers separation of individual pure components in a sedimentation velocity experiment. Although this experiment offers exciting possibilities for application, it is barely used. This is related to the bad definition of the initial conditions. Both the duration and the time of the solution overlay during rotor acceleration are not known. In this study, we investigate these conditions under the variation of the overlay volume using recording of interference patterns in a continuous mode during the acceleration of the rotor. It was found that the overlay occurs at rotor speeds between 770 and 2000 RPM, which is very low compared to typical experimental rotor speeds from 3 000 to 60 000 RPM and therefore elucidates that the generated reaction products resp. overlaid species are subject to the centrifugal force almost from the beginning. Also, the duration of the overlay is less than 1.2 s, which is very fast compared to hours of centrifugation time for an experiment and we demonstrated that the overlay compartment is completely emptied during overlay allowing for the precise calculation of the meniscus using the known sample sector geometry. Our results show, that the initial conditions of the experiment are defined and should make an adapted analysis possible if the inter-diffusion of the two solvents is taken into account, which lead to a dynamic density gradient.

Analytical ultracentrifugation (AUC) is a standard analysis method for the determination of particle size distributions and has a very high size resolution up to the Ångström range.1-3 It can be used to characterize a variety of samples as metal or semiconductor particles4, polymers, biological macromolecules5,6 and also to analyze complex mixtures. In an AUC experiment, particles are separated in a centrifugal field according to their size / mass, density and frictional properties. The sedimentation boundaries are detected by absorbance, interference or fluorescence optics. The received sedimentation data are then analyzed using programs like ULTRASCAN7, SEDANAL8 or SEDFIT9, which finally give the particle size distributions. Although AUC provides a broad spectrum of possible experiments10,11, sedimentation velocity (SV) is the most used method. Nevertheless, the Band Sedimentation experiment offers potential for different applications, which exceed the possibilities of a simple SV experiment. The Band sedimentation experiment was first presented by Vinograd et al.12-14, and has also been applied in Active Enzyme Centrifugation15-17 and Synthetic boundary crystallization experiments18,19. This experiment allows for the formation of a sedimenting band3,20 as well as the performance of a chemical reaction inside the AUC18,19 at the beginning of the experiment. A small reservoir, connected with the sample sector via thin capillaries, can hold another solute separate from the solution in the sample sector, as shown in Figure S5. Upon speeding up the rotor, the solute is overlaid onto the sector solution, which needs to have a slightly higher density, dependent on the sample down to 0.001 g/ml18, for a proper overlay. This small density difference between the solutions provides the formation of a sharp boundary (Scheme 1).

The method can be applied for different experiment types in the field of chemical reactions as well as for biological systems. One of the first examples is the use for the characterization of an active enzyme-substrate complex by the overlay of an enzyme onto a substrate solution15,17,21, with the advantage, that the enzyme does not need to be purified and it can be analyzed in its active state. Also, another experiment type that can be performed is the overlay of a concentrated sample on the solvent, which was applied for the characterization of viruses and macromolecules12-14. The advantage is the separation into different boundaries of pure species providing higher resolution as shown for the separation of several species in a polydisperse mixture.3 Another feature offered by this experiment type is the investigation of nucleation processes. The earliest species in particle formation are captured, as the reaction is quenched when the particles sediment out of the reaction boundary. This was used for the characterization of CdS species during nucleation18,19, where the formation of the species in the cell is based on the supersaturation of the respective ions in solution. Clusters can also be created by the overlay of a reducing agent onto a metal ion solution.22 This method is already known for a long time,23 but is nowadays barely used, especially compared to the SV experiment, as there are some yet unknown variables concerning the initial boundary conditions associated with it. This hinders evaluation using direct boundary modeling approaches like the boundary modeling of Lamm equation solutions.24 It is not known when the overlay happens and how long it takes and how this influences the sample under investigation.

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Scheme 1: Band forming centerpiece (left) and scheme of the mechanism after overlay of the reactant solution (right). The centerpiece provides a small reservoir, which can contain another solution. With the acceleration of the AUC rotor, the solute is overlaid onto the sample solution and therefore forms a boundary, where the sedimentation of the sample starts. In contrast to the SV method, the meniscus position is not known from the beginning of the experiment, which is an important boundary condition. Therefore, the Band Sedimentation experiment cannot benefit from the broad variety of powerful analysis tools, which are available for the SV experiment. There are just a few suitable analysis tools, which do not take these variables into account thus compromising the quality of the evaluation. However, since the Band Sedimentation experiment is the only one allowing to perform a chemical reaction inside the AUC cell with subsequent observation of all formed and fractionated reaction products, this technique is potentially very powerful. It can therefore open up a plethora of new applications in the field of AUC, especially in hot fields like nucleation. Therefore, we aim to address the problem of the unspecified initial conditions in this study to enable future analyses of these experiments.

sector shaped sample compartment. This precisely known and experimentally confirmed meniscus position is an important initial condition for subsequent evaluation.

RESULTS AND DISCUSSION Overlay duration and speed. Upon speeding up the rotor of the AUC, the solution in the reservoir is overlaid on the solution in the sector, which leads to a slight shift of the meniscus of the solution towards the top of the cell. This can be observed by constantly taking pictures during acceleration and thereby grabbing the moment of the overlay. Normally, a small density difference between the solvents should be provided for obtaining a sharp boundary at the interface. This can be maintained by using mixtures of H2O and D2O or dissolving salts or detergent. Here, water was just overlaid onto water, as the use of D2O caused optical artefacts, as also mentioned in more detail in the SI 8. The measurements were performed on an AUC equipped with an Advanced Interference Detection System, which allows the fast acquisition of pictures during acceleration of the rotor using a speed profile (see SI 2-4).25 The materials, the experiment, the instrument and data acquisition is also described in the SI 1-4. The Interference raw data for the overlay of 5 µl are shown in Figure 1. The shift of the meniscus over the two scans the overlay took is clearly visible as a shift of the right end of the meniscus by 183 +/- 17 µm (calculated: 185 µm for an overlay of 5 µl, see Table 2). This also demonstrates that the reservoir is completely emptied during overlay, so that the meniscus position can be calculated from the solution volumes after overlay with the known dimensions of the

Figure 1: Interference raw data at the moment of the overlay. The overlay was performed with 5 µl H2O in the reservoir onto H2O and took 2 pictures (Scan 2 + Scan 3). Scan 1 is the meniscus before the overlay. Scan interval is 388 ms. The overlay volumes were varied between 1 µl and 15 µl. This should show if duration times vary as well, if and how the overlay rotor speed changes and if there is a correlation between those variables. For comparison, also theoretical values using the hydrostatic pressure p = ρ ω2r h upon overlay were calculated with ω = angular velocity, ρ = density, r = radial distance from rotor axis and h = column height. As the column height cannot be determined exactly but was estimated from geometry, this value might just be in the correct range and not exact. At a specific pressure p the capillary pressure does not resist anymore and the solution flows through the capillary (Table 1 and Figure S1 in SI). The higher the overlay volume, the earlier it is overlaid, which corresponds to a lower rotor speed (Figure S1 and SI 5). This is also in agreement with the critical hydrostatic pressures for overlay of different volumes, which are low and rather constant in the range of 0.9 – 1.9 kPa. The time point of 2


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Analytical Chemistry the overlay is in the range between 750 and 2050 RPM, which is very early compared to the rotor speed standard Runs are normally conducted, which is between 3000 RPM and 60 000 RPM. We like to point out that a maximal overlay duration of 1.2 s is very short compared to 180 s the machine takes for spinning up to 60 000 RPM and also compared to the scanning time in UV/Vis absorption, which is about 49.5 s at 60 000 RPM for two cells and even higher at lower speeds (up to 59.5 s at 10 000 RPM).

Table 1: Correlation of the overlay volume with the overlay duration, the current rotor speed at which the overlay occurs and the corresponding hydrostatic pressure calculated by p = ρ ω2r h

comparison with the calculated theoretical data, the real layer thickness was read out from the collected interference data. They are graphed in Figure S2 and described in SI 6. Real values agree with theoretically calculated values and therefore conclude a quantitative overlay. Comparison of ω2t values. Another point to consider in this experiment type is the ω2t value. This is used for the correct analysis of the sample. Normally it applies to the sample from time zero, but in the Band Sedimentation experiment, it can only be taken from the point when the overlay occurs. Comparison of these values shows that this deviation is in negligible range compared to the final ω2t values in the experiment (SI 7 and Table S1). Steps during the overlay.

V [µl]

t [s]

n [RPM]

σ n [RPM]

p [kPa]

1

0.39

2004

23

0.87

2

0.50

1990

184

1.71

3

0.78

1456

99

1.37

4

0.78

1220

118

1.29

5

0.78

1047

14

1.18

7

0.89

889

10

1.19

10

1.01

805

16

1.40

15

1.01

767

5

1.90

Mean values are given for three repetitions. V = volume, t = duration, n = mean rotor speed, σ n = standard deviation of the rotor speed, p = corresponding hydrostatic pressure (calibrated with the value of 5 µl). The accuracy of this measurement is limited by the time resolution, which is given by the picture recording time of 388 ms. Therefore, duration can only be given as a multiple of that value.

Thickness of the overlay solution layer. Another point of criticism of this experiment type is that by the shifting meniscus upon overlay the starting point of sedimentation is shifted and therefore scans should be corrected for that. Hence it is useful to know how much the meniscus actually shifts. This can be determined, as the exact dimensions of a sector of the AUC centerpiece are known and also the loading volume. Using this, the thickness of the layer created by the overlay of the reactant solution in the reservoir onto the sample solution was calculated and the results are shown in Table 2.

Table 2: The values for the layer thickness of the reservoir volume in the sample sector after overlay depending on the reservoir volume Volume [µl]

Layer thickness [µm]

1

37

2

74

3

111

4

148

5

185

7

259

10

370

15

556

As the radial resolution practically used in UV/Vis Absorption is 50 µm, overlay volumes below 3 µl are hardly detected as a shift in the meniscus. The resolution can be set to values of 10 µm, but this causes elongated scanning times and is therefore not practical. For the interference optics, radial resolution is 5 µm. In these cases, the shift of the meniscus needs to be considered for analysis. For checking if the full volume of the solution from the reservoir is overlaid and for

The presented results reveal that the mechanism of overlay in this method can be divided into different steps. First, at a very low rotor speed (750-2050 RPM), the solution contained in the reservoir hole is overlaid onto the solution in the sample sector within a brief time frame (0.39-1.01s). This happens in about a second, as shown above, before significant diffusion of the sample can take place smearing the initial boundary conditions needed for a proper analysis. Thus, the diffusion of the overlaid H2O onto the D2o (general less dense and dense solvent) needs to be taken into account. Diffusion happens on a rather slow time scale of minutes, as also shown in the SI 8 and the video in SI 8, and therefore will have an influence onto the sedimentation of the overlaid sample itself. Influence of a dynamic density gradient. Upon overlay of the less dense water layer onto the denser D2O layer, a dynamic density gradient is forming right at the boundary. 26,27 This is relevant because inter-diffusion of the solvents causes sample redistribution and smearing of the originally sharp boundary.26,27 This is outlined in the SI 8, where a video of the overlay of water onto D2O shows slow diffusion of the solvent on a much larger time scale than the overlay and its duration. Ideally, to ensure defined initial boundary conditions for the evaluation of the Band Sedimentation experiments, such density gradients need to be avoided to the largest possible extent, although the density difference between overlaid and supporting solution can only be minimized to 0.001 g/ml and it turned out for many samples that indeed H2O needs to be layered onto D2O to form a stable sedimenting band creating a dynamic density gradient. However, it has been demonstrated that the time and spatially dependent solvent density and viscosity can be calculated via the integrated form of Ficks 2nd law and can thus be precisely taken into account in the evaluation.28 Other variations. To assure that the results obtained for the slow speed profile used so far also apply to faster speed profiles (see different speed profiles in Figure S4), one experiment was performed for comparison at higher acceleration rate. This is shown and described in the SI 10 and shows good agreement and therefore transferability of the drawn conclusions. In addition, we conducted an experiment with a Spin Analytical centerpiece to compare to the Beckman centerpiece used so far. The values can be found in SI 11. Although the overlay speed is slightly higher and duration slightly longer, the values show a general transferability. Normally, a highly concentrated macromolecular or reactant solution is contained in the reservoir in contrast to pure H2O used in this study. This provides a higher density and viscosity and therefore we investigated the influence this will have on the 3



overlay speed and the band smearing. The overlay happens at a somewhat lower speed than for pure H2O, which is in agreement with the higher capillary pressure due to the higher density. The band smearing is simulated and graphed in Figure S3 and is generally less, the less the difference in density and viscosity between the solutions. The exact values for this investigation can be found in SI 9.

CONCLUSION In this study, we demonstrate results which show that in a Band Sedimentation AUC experiment the overlay happens early and very fast. The comparison of different speed profiles and centerpieces show the transferability and therefore the general validity of these findings. The important consequence is, that the times or run time integrals for the overlay process are negligible compared to the typical times/run time integrals of a typical AUC experiment or even of reaching the maximum speed. Since the overlay compartment completely empties, the shift of the meniscus due to the overlay can be precisely calculated from the sample sector geometry and known overlay solution volumes. However, a dynamic density gradient forms upon the overlay process, which needs to be taken into account, because the locally and time dependent density and viscosity gradient also changes the sample sedimentation and leads to smearing of the initially sharp band. This gradient can be calculated using the integrated form of Ficks 2nd law.28 Therefore, we can conclude that the boundary conditions of such experiments for precise evaluations are defined, since we identified the relevant parameters for sample overlay and the smearing of the initial band. Therefore, as the most important conclusion we state defined boundary conditions for Band Sedimentation experiments and point towards the necessity to take the dynamic density gradient into account in the evaluation.28 AUC Band Sedimentation experiments are therefore suitable for analyses by all modern AUC analysis approaches including boundary fitting via solutions of the Lamm equation once these algorithms are properly modified enabling to derive much more detailed information from such experiments in the future than is possible today. In addition to this, Band Sedimentation experiments can now be used to perform chemical reactions directly in the AUC cell, allowing to separate and observe all formed reaction species. This suggests these experiments for the analysis of nucleation, which is not yet understood even after decades of intense research in this area. Other reactions of similar importance in (Bio)chemistry might be equally suitable for analysis by this powerful method.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Materials, Instrument, Experiment, Data acquisition, Rotor speed at the overlay, Thickness and volume of the overlay 2 solution layer, Calculation of the run time integral ω t and comparison of the values, Overlay of H2O onto D2O, Comparison of different speed profiles and comparison of different centerpieces (PDF)

AUTHOR INFORMATION Corresponding Author * Email: [email protected]

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Author Contributions All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT We acknowledge funding by Deutsche Forschungsgemeinschaft within the NSF-DFG Materials World Network (GE 2278/6-1; CO 194/12-1).

REFERENCES (1) Cölfen, H.; Pauck, T. Colloid. Polym. Sci. 1997, 275, 175-180. (2) Cölfen, H.; Schnablegger, H.; Fischer, A.; Jentoft, F. C.; Weinberg, G.; Schlögl, R. Langmuir 2002, 18, 3500-3509. (3) Karabudak, E.; Brookes, E.; Lesnyak, V.; Gaponik, N.; Eychmüller, A.; Walter, J.; Segets, D.; Peukert, W.; Wohlleben, W.; Demeler, B.; Cölfen, H. Angew. Chem. Int. Ed. 2016, 55, 1177011774. (4) Zook, J. M.; Rastogi, V.; MacCuspie, R. I.; Keene, A. M.; Fagan, J. ACS Nano 2011, 5, 8070-8079. (5) Cölfen, H.; Völkel, A.; Eda, S.; Kobold, U.; Kaufmann, J.; Puhlmann, A.; Göltner, C.; Wachernig, H. Langmuir 2002, 18, 7623-7628. (6) Laue, T. M.; III, W. F. S. Annu. Rev. Biophys. Biomol. Struct. 1999, 28, 75-100. (7) Demeler, B. In Analytical Ultracentrifugation: Techniques and Methods, Scott, D. J.; Harding, S. E.; Rowe, A. J., Eds.; The Royal Society of Chemistry, 2005, pp 210-230. (8) Stafford, W. F.; Sherwood, P. J. Biophys. Chem. 2004, 108, 231-243. (9) Schuck, P. Biophys. J. 2000, 78, 1606-1619. (10) Mächtle, W.; Börger, L. Analytical Ultracentrifugation of Polymers and Nanoparticles; Springer Berlin Heidelberg, 2006. (11) Schuck, P.; Zhao, H.; Brautigam, C. A.; Ghirlando, R. Basic principles of analytical ultracentrifugation; CRC Press, 2016. (12) Vinograd, J.; Bruner, R. Biopolymers 1966, 4, 157-170. (13) Vinograd, J.; Bruner, R. Biopolymers 1966, 4, 131-156. (14) Vinograd, J.; Bruner, R.; Kent, R.; Weigle, J. Proceedings of the National Academy of Sciences 1963, 49, 902-910. (15) Harding, S.; Rowe, A. Enzymology LabFax. Bios Scientific, Oxford, UK 1996, 66-75. (16) Cohen, R.; Claverie, J.-M. Biopolymers 1975, 14, 1701-1716. (17) Cohen, R.; Mire, M. The FEBS Journal 1971, 23, 267-275. (18) Börger, L.; Cölfen, H.; Antonietti, M. Colloids Surf., A 2000, 163, 29-38. (19) Börger, L.; Cölfen, H. Prog. Colloid Polym. Sci. 1999, 113, 23-28. (20) Lebowitz, J.; Teale, M.; Schuck, P. W. Biochem. Soc. Trans. 1998, 26, 745-749. (21) Kemper, D. L.; Everse, J. Methods Enzymol. 1973, 27, 67-82. (22) Völkle, C.; Gebauer, D.; Cölfen, H. Faraday Discuss. 2015, 179, 59-77. (23) Vinograd, J.; Radloff, R.; Bruner, R. Biopolymers 1965, 3, 481-489. (24) Walter, J. Multidimensional Characterization of Nanoparticles by Means of Analytical Ultracentrifugation. PhD Thesis, Friedrich-Alexander Universität Erlangen-Nürnberg, Bamberg, 2017. (25) Schilling, K.; Krause, F. PLOS ONE 2015, 10, e0120820. (26) Mächtle, W. In Analytical Ultracentrifugation V, Cölfen, H., Ed.; Springer Berlin Heidelberg: Berlin, Heidelberg, 1999, pp 1-9. 4


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Analytical Chemistry (27) Mächtle, W. Colloid. Polym. Sci. 1984, 262, 270-282.

(28) Schneider, C. M.; Cölfen, H. European Biophysics Journal 2018, DOI: 10.1007/s00249-018-1315-1.

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Band forming centerpiece (left) and scheme of the mechanism after overlay of the reactant solution (right). The centerpiece provides a small reservoir, which can contain another solution. With the acceleration of the AUC rotor, the solute is overlaid onto the sample solution and therefore forms a boundary, where the sedimentation of the sample starts. 490x160mm (300 x 300 DPI)


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Analytical Chemistry

Interference raw data at the moment of the overlay. The overlay was performed with 5 µl H2O in the reservoir onto H2O and took 2 pictures (Scan 2 + Scan 3). Scan 1 is the meniscus before the overlay. Scan interval is 388 ms. 74x52mm (600 x 600 DPI)


Band Sedimentation Experiment in Analytical Ultracentrifugation

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