Short Column Sedimentation Equilibrium Analysis Enables Rapid and Reliable Characterization of Macromolecules in Solution

When researchers require fast and reliable characterization of the solution properties of macromolecules, short column sedimentation equilibrium analysis can be used as it provides a number of benefits.

This article describes examples where short column techniques are a suitable choice, presents a brief theoretical treatment and gives an overview of short column sedimentation techniques, including ones diagnostic for nonideality and self-association.

The distinguishing characteristics of short column techniques are:

• The two rows of larger (2.4 mm) holes used to fill the cell
• The parallel rows of four, small (1.2 mm diameter) sample viewing holes are 4 mm apart
• The connecting groove between the sample viewing holes and the fill hole

Figure 1. Eight-channel, short column centerpiece that allows the viewing of four solution-solvent pairs. Direction of the gravitational field is toward the keyway. The small holes are observation channels and the large holes are filling reservoirs. Image credt: Beckman Coulter

In Figure 1, the holes on the left half hold only the solvent and the holes on the right half hold the solvent with macromolecule.

On acceleration, the contents of a filling reservoir drain via the groove into the corresponding observation channel. The filling reservoir holes are tapered so that they completely empty.

Although short column sedimentation equilibrium techniques were developed early, they were not popular among early users of sedimentation equilibrium for the following reasons:

• Higher concentrations of material were required
• Manual data acquisition from short columns required almost the same amount of time as from longer columns and did not produce as much information for each data set
• They could not be used with the photoelectric scanner of the Model E
• A separate experiment was often required to determine the concentration of the sample

However, during the intervening years, a lot has changed and all of these problems have been resolved.

In the early 1960s, data acquisition could take days, whereas now it takes only seconds. Therefore, the fast equilibration available with short columns offers a clear benefit by providing a 20-fold increase in the number of samples that can be examined in a given time period.

Aside from a few exceptions, the amount of data acquired from short columns exceeds that from the longer columns. Also, short column centerpieces can be used with the Proteomelab XL-A analytical ultracentrifuge’s photoelectric scanner, meaning lower concentrations can be used and determination of a separate concentration is not needed.

In addition, owing to better data analysis, the data acquired from a number of short column experiments can be combined to assess target molecular parameters.

These programs also eliminate the need to determine the separate concentrations for interference optics, therefore saving time and material. These developments make short columns the first- choice method for many routine analyses.

Short column centerpieces offer the following benefits:

• Only a small volume (15 μL vs. 100 μL) is needed at moderate concentrations (0.1 OD)
• Short equilibration times are required (60 to 90 min versus 16 to 18 h for majority of molecules)
• Many samples can be studied simultaneously
• Radial redistribution of solutes is minimal

The first point is an obvious advantage when only small amounts of material are available for examination. Even more appealing is the idea that a lot of the sample volume (75 to 90%) can be recovered following analysis.

The first three benefits are of interest to users who would like to assess a sample across a broad range of buffer conditions. The final point is particularly beneficial when titrations need to be carried out or when an association between different macromolecules (heteroassociation) needs to be characterized.

These benefits are so compelling that it would be useful to outline when it is better to use the 3 mm column centerpieces.

It is better to use these longer columns when:

• Assessing low molecular weight materials
• Assessing heterogeneous samples
• When the only samples available are very dilute
• When the sticking of sample to centerpiece walls makes it desirable to use the lower surface area-to-volume ratio of the column centerpieces

Methods

Sample Preparation

No special sample preparations are required for short column sedimentation equilibrium. The optical density should be between 0.1 and 1.5 at the wavelength of interest for samples that are being used for absorbance detection.

Samples used for Rayleigh interference detection should have a greater than 0.2 fringe (60 μg/mL) initial concentration.

We have found that this technique is just as thorough as exhaustive dialysis and, aside from cases where sample is lost by binding to the gel matrix or its use is prohibited by slow kinetics, it is the preferred technique.

Cell assembly is as shown in the manual for the Proteomelab XL-A analytical ultracentrifuge, except that the top window is not placed into the cell housing until after filling the centerpiece. The dialysate is used for making serial dilutions. Samples should be rotated in Eppendorf tubes for about 5 minutes to remove any dust.

Cell Handling

A centerpiece made from material that does not interact with the target macromolecules is selected and short column centerpieces are made of Kel-F, which is the least likely to absorb water or bind materials from the solution.

Due to the high surface-area-to-volume ratio, it is important to clean the centerpiece thoroughly to prevent contamination of the sample. While cleaning, the surfaces of the centerpiece should not be scratched.

A nonabrasive detergent should be used to scrub the surface and holes using nonabrasive scrubbers. The faces of the centerpieces can be wiped with nonwoven polyester and cellulose cleanroom wipes, while the holes can be cleaned with microswabs.

The centerpiece should be thoroughly rinsed with deionized distilled water. Special cleaning steps such as soaking in protease inhibitors and rinsing with EDTA can be included, provided that no chemical reaction with the centerpiece materials occurs and the reagents can be removed without any residue being left. After using the centerpieces, they should be cleaned, dried and stored wrapped in non-shedding paper.

Cell Assembly and Filling

A clean centerpiece and complete bottom window are introduced into the cell housing and pressed down using a lint-free tissue until the window is at the bottom of the housing. Before inserting the centerpiece and, again, before filling, a jet of dry nitrogen gas can be used to remove dust on the window.

The cell housing is positioned with the keyway facing towards the user, with the filling grooves forming a “V” (Figure 1A). The bigger holes are filled, with the holes on the right side for solution and those on the left side for solvent.

The pairs of solvent and solution are labeled A-D, going from those nearest to the center of rotation to those closest to the edge of the rotor. 20μL of solvent is put in the solvent holes.

The solution holes are first filled with 5μL of FC-43 fluorocarbon (as a base fluid) and 14μL of sample, with the most concentrated sample in position A and the most dilute sample in position D.

Cell assembly is then completed in the usual way, except that there is no need for filling-hole screws. Filling and assembly need to be rapid to minimize the effects of evaporation.

FC-43 provides a clear, “square” bottom and does not create as much reflection at the interface as other base fluids do because its refractive index is near to that of water.

FC-43 is extremely inert, but contamination with hydrocarbons can result in interactions with solution components. If this happens, then concentrated H2SO4 can be used to extract the FC-43, followed by exhaustive rinsing with deionized, distilled water.

Short Column Operation

The rotor is loaded and the cells are aligned as shown in the Proteomelab XL-A manual. The samples will transfer to the viewing holes at approximately 5000 rpm. The rotor speeds are selected as for a longer column equilibrium run such that the predicted value of σ falls between 2 and 10:

Equation 1

andrefers to the solute’s partial specific volume, ρ the solution density, R= 8.3144 x 107, and T is the temperature in K. Here, only a rough estimation is needed, so that for σ = 3, an initial choice of speed can be estimated from:

Equation 2

where the approximation is valid for aqueous buffer ρ ≈ 1, at near 25°C temperatures and for materials having close to 0.7mL/g. If M(1-ρ) is not known, the redistribution of the solute at a number of rotor speeds will need to be observed, starting at around 2500 rpm.

However, to make sure sample transfer is complete, the rotor should be brought to 8000 rpm for a couple of minutes before dropping the rotor speed back to 2500 rpm.

When using 14μL of the solution, the height of the column should be 700 to 800 μm. The cell should be scanned immediately after reaching speed so as to ensure sample transfer and to test for any leakage.

Estimating the Equilibration Time

One of the main benefits of short columns is the rapid achievement of equilibrium, which, since the time to equilibrium is relative to the square of the column height, is approximately 16 times faster than for 3 mm columns.

The time taken to reach equilibrium can be estimated from the formulas given by van Holde and Baldwin or can be determined empirically by performing successive overlay scans 10 minutes apart, looking for any additional movement of the concentration gradient.

For the majority of 10–200 kDa proteins, equilibrium was typically tested for following 45 minutes at speed. Very large molecules will take longer and viscous solvents will slow down equilibrium by an amount directly proportional to the viscosity.

Small molecules and non-ideal solutes, on the other hand, are likely to reach equilibrium more quickly than may be expected.

Data Acquisition

It is important to ensure that the point density is as high as possible, meaning that, for the Proteomelab XL-A absorbance system, a step scan should be used with 0.001 cm step size and with four repetitions for each step.

Only those parts of the cell where light is visible should be scanned in order to save time. The ending and starting radii for channels A through D can be acquired from the initial scan and, once established, recorded for use in later experiments.

Between 50 and 100 data points should be obtained for each channel. Optimum results are achieved by using a value between 1.65° and 1.75° as the spacing between the holes. The method described in the Proteomelab XL-A operating manual can be used to establish the best timing.

Data Editing

Data from the meniscus and base regions may have to be removed from analysis due to the inevitable refractive effects at the top and bottom of the cell. It would be best if data are removed symmetrically about the channel’s midpoint if it is desirable to establish average molecular weights with reference to the loading concentration. If not, only points that are clearly affected by the discontinuities at the menisci should be removed.

Methods for Specific Applications

Aside from rapid surveys and cases where material is limited, short columns are particularly useful for quickly determining the association state of an oligomer, examining the effects of small ligands on macromolecular associations and analyzing heteroassociations.

This suitability stems from the fact that short radial distance limits component fractionation. There are some further suggestions for applying short columns in these applications.

Determination of the Stoichiometry of an Oligomer

This is established simply by determining the molecular weight of the molecule under native conditions and comparing it to the molecular weight established under fully denaturing conditions.

The native material’s molecular weight is established at four different loading concentrations, one for each of the channels of a short column centerpiece. The concentration in channel A is usually close to 1 OD for the absorbance system or 1 mg/mL for the Rayleigh system, with channels B to D containing a 1:2 dilution of the channel A concentration.

The dilutions are made using just 35 μL of the solution, with 14 μL for each channel and 16 μL for the serial dilution, with it assumed that 2 to 3 μL are lost to the walls. On running the solutions, the solute redistribution will make the absorbance ranges in the different channels overlap and span an absorbance range between near zero to 2 OD, depending on the speed of the rotor.

Several different methods can be used to find out the molecular weight of the denatured material. If only one type of monomer makes up the oligomer, a second cell should be prepared that contains the same sample under complete denaturing conditions.

6M guanidine HCl and 8 urea are the two most commonly used denaturants for sedimentation analysis of proteins. Guanidine has been better characterized for use in sedimentation and has minimal effect on at 6M.

6M guanidine buffer is used to make serial dilutions and the second cell loaded as described above. If non-identical chains make up the oligomer, they should be isolated and examined under denaturing conditions. The cells should be balanced and loaded into the rotor as shown in the manual.

The initial speed of the rotor should be selected as described above, using an estimate of M for the native material. If the initial speed of the rotor is too high, the run should be stopped and the cells shaken to redistribute the contents.

Just reducing the rotor speed will result in an undue wait for re-equilibration. Following data acquisition at the lowest rotor speed, the speed should be increased until the ratio of the square of the rotor speeds is 1.4 or more.

Finally, it is helpful to analyze the solution at a rotor speed sufficiently high that the ratio of the square of this speed to the first is 3 or more. Using multiple speeds will provide data that can be used diagnostically and will help make sure that appropriate gradients will be developed in all channels being analyzed.

Titrations with Small Ligands

One of two methods can be used to make titrations. The first and preferred titration technique is to dialyze a sample against different concentrations of ligand. This can be most conveniently achieved using centrifugal gel filtration.

Dialysis establishes the concentration of free ligand equal to the ligand concentration in the dialysate. The second technique is simply introducing the ligand directly to the sample.

Only the total concentration of ligand is known in this method and there is a possibility of systematic errors in the determination of ligand affinities. If only qualitative results are required, this method is adequate, is much faster and uses less material.

Both methods work since small ligands simply do not form significant gradients over the length of a short column. The ligand’s concentration gradient due to sedimentation can be estimated using:

Equation 3

where C0 is ligand concentration and σ is its reduced molecular weight (Equation 1). If C0 and σ are kept sufficiently low, it can be seen that even relatively large ligands can be used.

Examination of Heteroassociations

The lack of solute fractionation in short columns is advantageous when there is a need to examine the interactions between dissimilar macromolecules. Each of the macromolecules should be equilibrated with the solvent, as described above, and each component analyzed so that the behavior of the mixtures can be properly interpreted.

It is best to analyze heteroassociating systems at various rotor speeds using a number of different loading concentrations and, if possible, spanning a range of mole ratios of components.

Overview of Data Analysis

There are three levels of analysis of short column sedimentation data. The first is qualitative evaluation of the macromolecular behavior using diagnostic graphs. The questions are more general at this level, addressing whether nonideality is important, whether the system is homogenous and whether a mass action association is taking place.

A reasonable estimation of the monomer molecular weight can often be achieved at this level; however, quantitative determination of thermodynamic parameters is not possible.

The second level involves combining data sets from several short column experiments and fitting the ensemble to models by means of nonlinear least squares techniques.

Such analyses can enable estimates of thermodynamic parameters such as the association constants, monomer molecular weight, nonideality coefficients and association stoichiometries to be obtained.

It is also possible to determine the confidence interval for these parameters. However, the precision of the analysis depends on application of the right model to describe the system.

If only one plausible model is available and it fits the data sufficiently, then the analysis can be concluded at this second level. However, a third level of analysis is required for many systems.

This level involves testing a range of plausible models and selecting the ones that describe the data sufficiently. There is often no truly unique model, but this ambiguity is not the result of limitations of short columns nor sedimentation, but rather intrinsic to the determination of thermodynamic parameters. The rest of this article is focused on the first level of analysis.

The most rapid and simplest analysis of short column equilibrium data is the average molecular weight determination. The diagnostic graphs described below are based on the concentration and rotor speed dependence of these determinations.

It is possible to estimate the molecular weight from the slope of the graph of ln(Abs) versusr2/2 using the absorbance system. These graphs are provided in the Proteomelab XL-A user interface.

Graphs of ln(Abs) versusr2/2should be sensibly linear, unless nonideality or heterogeneity are especially severe. The slope of this line is σ (Equation 1). For the Rayleigh system, which only gives the relative concentration, σ should be established via a nonlinear least squares method. When integrated with , ρ, ω2, R and T, σ gives the molecular weight:

Equation 4

Where values for ρ and are easily estimated from sample and buffer composition. If is not known, the buoyant molecular weight Mb can be applied for the diagnostic graphs described below: Mb = M(1 - ρ) = σ/RTω2.

In cases where the solvent has an increased concentration of one or more components, the effects on of preferential hydration should be considered.

Besides graphical analysis, the concentration distribution data can be fitted to functions derived from thermodynamic first principles. For a single ideal thermodynamic species, the absorbance profile will be an exponential:

Equation 5

Abs0 is the absorbance at the reference radial position r0, and δ is the baseline offset. For a mixture of ideal species, the resultant curve is the sum of exponentials:

Equation 6

where Abs0i and σi are the reference concentration and reduced molecular weight for the ith component, respectively. When a mixture of molecules is present, but the data are treated as if there were only a single sedimenting species, then the σ determined will be an average value for the components.

Under specific conditions, the average value is well defined and can be applied in the study of a chemical system. The weight-average molecular weight is defined as:

Equation 7

where Mi is the molecular weight and Ci is the weight concentration of the ith component. It can be seen that the scanner provides absorbances and that the average molecular weight requires weight concentrations.

It is important to be aware that if the weight extinction coefficients vary for the different components, then the molecular weight is not a well-defined average.

It is best to use the Rayleigh optical system when this is the case. The same arguments as those mentioned above with respect to the determination of average molecular weights hold true, except that if a nonlinear least squares analysis program is applied to directly fit the data and includes the baseline offset δ as a parameter, then it is the z-average that is established, providing all the solution column is visible:

Equation 8

It can be seen that the z-average is influenced more strongly by high molecular weight material than is the weight-average.

Diagnostic Graphs

Two molecular weight graphs – one as a function of the rotor speed and the other as a function of the overall cell loading concentration – will serve for the initial characterization of a system. There are five possible conclusions that can be reached based on these graphs:

• The system is sensibly ideal and homogenous
• The system is non-ideal and homogenous
• The system is ideal, homogenous and shows a mass-action association
• The system is non-ideal, homogenous and shows a mass-action association
• The system is heterogeneous with respect to mass

The latter category does not exclude the possibilities of non-ideality or mass-action association. Nonetheless, although the short column technique can be applied to detect heterogeneity, it is not particularly good at resolving it.

As a result, apart from describing the graphical consequences of heterogeneity, sample homogeneity will be presumed in the remainder of this discussion.

The first diagnostic graph shows the apparent molecular weight as a function of the midpoint absorbance of each channel (Figure 2).

Figure 2. Diagnostic graph providing a qualitative characterization of the solution behavior of macromolecules. All data were acquired at a constant temperature between 20 and 25°C. This figure shows the apparent molecular weight as a function of cell loading concentration. Image credt: Beckman Coulter

This diagnostic graph will be helpful for detecting mass-action associations and non-ideality. Three conditions may be seen:

• The molecular weight increases with increasing concentration
• The molecular weight decreases with increasing concentration
• The molecular weight is constant with variable concentration (absorbance)

If the last result is acquired, it indicates that the molecule is behaving ideally. Thermodynamic non-ideality is indicated by a downward curvature to the molecular weight with increasing concentration. This concentration dependence may provide useful data and techniques are available for studying non-ideality.

A mass-action association is indicated by increasing molecular weight with increasing concentration and will require a more thorough analysis. The reaction is often driven to an end point at high concentrations, in which case it is possible to establish the stoichiometry of the largest oligomer.

In other cases, experimental complexities may make it hard to establish an upper limit for the oligomer size or the association may not be definite. Even in the case of a limited association, it becomes difficult to determine the stoichiometry (N) as 1/N approaches the accuracy of the molecular weight estimate, which is usually 1 to 3%.

Figure 3 shows graphs of the apparent molecular weight as a function of rotor speed, which are useful for detecting heterogeneity. They are also important for establishing the reversibility of a mass-action association. For a homogenous, non-interacting sample under all conditions, the molecular weight should not depend on rotor speed.

Figure 3. Diagnostic graph providing a qualitative characterization of the solution behavior of macromolecules. All data were acquired at a constant temperature between 20 and 25°C. This figure shows the apparent molecular weight (presented as M/M0, where M0 equals the molecular weight determination at the lowest rotor speed) as a function of rotor speed for a homogeneous sample and a heterogeneous sample. Image credt: Beckman Coulter

The same principle holds true for a homogenous mass-action association, providing the concentration gradient can be tracked all the way from the meniscus to the base. On the other hand, a systematic decrease in the molecular weight with increasing rotor speed is diagnostic for sample heterogeneity.

Such heterogeneity is often accompanied by a band of material accumulating at the FC-43 layer at higher rotor speeds. Since the hydrostatic pressure formed in a short column is fairly small, even at high rotor speeds, pressure-reliant dissociation is unlikely to be the cause of decreasing molecular weight with increased rotor speed, thereby simplifying the interpretation.

If heterogeneity is suspected, the sample requires additional fractionation. For a heterogeneous mass-action association, the apparent molecular weight may display rotor-speed dependence depending on how tight the oligomerization is and whether all the reactants are present in stoichiometrically correct amounts. These graphs are not useful under such circumstances and more detailed analysis would be needed.

A few cautions should be considered. Firstly, thermodynamic nonideality and macromolecular association create opposite effects on the concentration dependence of the molecular weight. There have been cases where seemingly ideal behavior actually stems from the compensating effects of non-ideality and association.

If this is a worry, the solution can be re-examined under slightly different salt or pH conditions. Secondly, the graphs are better considered as qualitative guides and should not be applied for estimating molecular weights or association non-ideality.

Sample Recovery

One appealing feature of sedimentation analysis is that it is nondestructive to the sample and most of the sample can be recovered from a short column centerpiece. This is achieved by holding the centerpiece in place with a fill-hole screw while removing the top window.

To help remove the window, two tiny holes were drilled into the top rim of the window holder so that screws can be inserted to act as handles. As the window is lifted off, there is unavoidable loss of liquid to the window, although most stays in the holes.

As soon as the window is lifted off, a micropipette fitted with a microcapillary tip can be used to remove the samples. About 70% of the initial 14 μL is typically recovered. Since procedures for optimizing sample recovery have not yet been described, the recovery of even greater quantities is feasible.

Conclusion

The solution behavior of macromolecules can be quickly and reliably characterized using short column sedimentation equilibrium.

The small amount of material required, together with the ability to retrieve the sample undamaged, makes this an appealing molecular biology technique. Short columns are especially useful for performing quick surveys of the environmental effects on macromolecular association.

Acknowledgment

Produced from content authored by Thomas M. Laue University of New Hampshire Department of Biochemistry Durham, NH 03824. The work presented here was supported by a National Science Foundation grant DIR 90-02027.

The author thanks Daryl Lyons and Jun Liu for providing the experimental data presented here; Dr. Lawrence Rosenberg for providing articular cartilage link protein, dermatan sulfate proteoglycan core protein and GAG chains; Dr. John Little for providing Lex A; and Dr. Rachel Klevit for providing MyoD-bHLH peptide.

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