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Solution NMR is a crucial tool for structural biology, allowing for atomic-level determination of structure and dynamics of biomolecules. The recent advances in theoretical background (Hu et al. 2011; Loening et al. 2012; Bjerring et al. 2012; Nielsen et al. 2012) and in the sample preparation (Lewandowski et al. 2011a; Akbey et al. 2012) have brought solid state NMR to compete with state-of-the-art solution NMR for the determination of structure (Bertini et al. 2010a; Knight et al. 2011; Luchinat et al. 2012; Huber et al. 2012) and dynamics (Lewandowski et al. 2010, 2011b) for micro-to nanocrystalline systems, and even in the case of systems lacking long-range order like fibrils (Petkova et al. 2002; Tycko and Ishii 2003; Debelouchina et al. 2010; Bertini et al. 2011a; Lewandowski et al. 2011c; Bayro et al. 2011; Parthasarathy et al. 2011) or insoluble aggregates (Sun et al. 2009; Loquet et al. 2010).

Anyway, there is a wealth of systems that result inaccessible to these techniques for a number of reasons that are summarized in the following paragraphs.

Very large biomolecular assemblies have long rotational correlation times, resulting in broadening of the solution NMR lines beyond detection (Wider 2005; Fernández and Wider 2003; Riek et al. 1999; Fiaux et al. 2002; Guo et al. 2008; Tugarinov et al. 2006, 2005a, b; Bermel et al. 2007, 2008, 2010). To solve this problem, specific sample preparation and labelling schemes were proposed (Tugarinov et al. 2006; Matzapetakis et al. 2007). In many cases, solid state NMR requires the sample to be crystalline, with defined levels of hydration to achieve good resolution (Martin and Zilm 2003). The crystal contacts can perturb the native structure of the protein (Barbato et al. 1992; Fischer et al. 1999; Skrynnikov et al. 2000; Chou et al. 2001; Poon et al. 2007; Bertini et al. 2008, 2009). Finally, the larger the system, the more difficult the crystallization becomes.

Manipulation of the sample (i.e. precipitation, freezing or lyophilisation) is known to deteriorate the quality of the spectra (Martin and Zilm 2003; Linden et al. 2011; Pauli et al. 2000).

In this scenario, sedimented solute NMR (SedNMR) (Bertini et al. 2011b, 2012; Polenova 2011) can be regarded as a simple way to select the best of both worlds: the sample can be kept in the buffer that is used for the solution studies and the possible addition of interaction partners can be followed like in a common NMR titration; the system is always hydrated enough and its size turns from foe to friend.

Anyway the method suffers from the intrinsic sensitivity limitation that comes from having a solution (although concentrated) sealed in the volume (2–50 μl) of a solid state NMR rotor. The concentration can optimistically arrive to 60 % of the corresponding crystal in highly soluble proteins such as BSA (Lundh 1980, 1985; Andersson and Hovmoller 2000).

In addition to the volume limitation, the 1.3 rotor, that can be used to achieve high resolution spectra (Bertini et al. 2010b; Knight et al. 2011; Webber et al. 2012) and site-specific dynamics information (Lewandowski et al. 2010; 2011b), suffers from its smaller internal radius that requires higher molecular weights for sedimentation as compared to the other rotors (Bertini et al. 2012).

We thus proposed (Bertini et al. 2012) the use of ultracentrifugal devices like the one described by Böckmann et al. (2009) to increase the amount of sample in the rotor. This approach was later used by Gardiennet et al. (2012) for sedimenting a 59 kDa dodecameric helicase (total molecular weight 708 kDa).

The scheme for the design of devices of this type is the following:

  • A reservoir for increasing the amount of solution, thus allowing for more diluted solutions to be used;

  • A funnel to convey the pellet into the rotor;

  • A tight junction based on o-ring for sealing;

  • A jacket made in delrin® or vespel® to prevent rotor shattering during the ultracentrifugation;

  • A housing for the rotor that is as close to the bottom of the tube as possible.

The position of the bottom of the rotor (b4 in Fig. 2) and of the top of the solution (b0 in Fig. 2) will determine the effective clearing factor of the ultracentrifugation, i.e. the time efficiency of the process, according to Eq. 4).

We here report the design of two centrifugal devices with different geometries (Fig. 1a, b). Both of them can be used in SW32Ti rotor for Optima type floor preparative ultracentrifuge (Beckman Coulter) at the maximum speed (32,000 rpm).

Fig. 1
figure 1

a View of the components of device 1; b view of the components of device 2

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Device 1 (Bruker Karlsruhe) has a light polycarbonate funnel fitted into an outer aluminium funnel. This device has an internal volume of 20 ml, allowing for the use of less concentrated solutions. The polycarbonate funnel must be cut to the proper level in order to avoid crushing during the centrifugation.

Device 2 (Experimental Physics Workshop, University of Florence) is made in delrin® acetal resin. The device does not have a soft funnel so it does not require any manipulation, and delrin is resistant to corrosion as opposed to aluminium, so that the device can be cleaned through acids and bases, as required for some toxic proteins. Anyway, the internal volume is 1.38 ml, thus the device can only be used for concentrated solutions.

The amount of the macromolecule that will get into the pellet is given by the Eq. 1 (Bertini et al. 2012):

$$ c(h) = \frac{{c_{l} }}{{Ae^{{ - kh^{2} }} + 1}} $$
(1)

where h is the distance from the rotation axis, c l the limiting concentration of the macromolecule [experimentally found to be approximately 700 mg/ml for proteins (Lundh 1980, 1985)], k is given by:

$$ k = \frac{{M\left( {1 - \rho_{solvent} /\rho_{biomolecule} } \right)\omega^{2} }}{2RT} $$
(2)

and A is an integration constant that needs to be determined according to the law of concentration of mass:

$$ \pi r_{1}^{2} \int\limits_{{b_{0} }}^{{b_{1} }} {c(h)dh} + \pi \int\limits_{{b_{1} }}^{{b_{2} }} {\left( {\frac{{h_{p} - h + b_{1} }}{{h_{p} }}r_{1} } \right)^{2} {c(h)dh} + } \pi r_{2}^{2} \int\limits_{{b_{2} }}^{{b_{3} }} {c(h)dh} + \pi r_{3}^{2} \int\limits_{{b_{3} }}^{{b_{4} }} {c(h)dh} = c_{0} V_{device} $$
(3)

where the meaning of the parameters r1, r2, r3 and hp and of the integration limits is shown in Fig. 2.

Fig. 2
figure 2

Schematics of the relevant parameters for the device geometry

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The integrals in Eq. 3 cannot be evaluated analytically for the geometry of the device and therefore they must be evaluated numerically. This task can be accomplished through the annotated Mathematica® notebook provided as supporting material.

Following this approach we can estimate that almost any protein above 20 kDa can pellet from a solution at concentration c0 = 2 mmol/dm−3 at a centrifugation rate of 32,000 rpm.

On the basis of these numbers we can clearly understand that any protein can be sedimented. What makes then the real difference is the time required for completing the sedimentation. To calculate it, one should only know the sedimentation coefficient s of the biomolecule (easily attainable by analytical ultracentrifugation and usually quite well documented in the literature) and resort to the integrated Svedberg equation:

$$ t = 2.533 \times 10^{11} \frac{{\ln \left( {b_{4} /b_{0} } \right)}}{{sf^{2} }} $$
(4)

where f is the rotation rate in rpm, as it is commonly done in the preparative ultracentrifugation.

It is important to remark that selective sedimentation of the desired solute from a mixture of solutes with different molecular weights can be attained by the classical differential centrifugation approach.

Overall, sample preparation for an experiment of sedimented solute NMR by means of an ultracentrifugal device can be summarized as follows:

  • Choose the concentration and volume that will allow for sedimentation (Eqs. 1–3) and will provide enough material to fill the rotor;

  • Choose the experimental time according to Eq. 4;

  • Add the solution to the ultracentrifugal device and, if needed, cut the funnel to avoid crushing;

  • Run the ultracentrifugation;

  • Seal the rotor through CRAMPS insert (4 mm), silicon plugs (3.2 mm) or marker ink on the caps (1.3 mm). This is necessary to avoid spilling of the solution and possible probe damage.