Protein effective rotational correlation times from translational self-diffusion coefficients measured by PFG-NMR

https://doi.org/10.1016/j.bpc.2008.06.002Get rights and content

Abstract

Molecular rotational correlation times are of interest for many studies carried out in solution, including characterization of biomolecular structure and interactions. Here we have evaluated the estimates of protein effective rotational correlation times from their translational self-diffusion coefficients measured by pulsed-field gradient NMR against correlation times determined from both collective and residue-specific 15N relaxation analyses and those derived from 3D structure-based hydrodynamic calculations. The results show that, provided the protein diffusive behavior is coherent with the Debye–Stokes–Einstein model, translational diffusion coefficients provide rapid estimates with reasonable accuracy of their effective rotational correlation times. Effective rotational correlation times estimated from translational diffusion coefficients may be particularly beneficial in cases where i) isotopically labelled material is not available, ii) collective backbone 15N relaxation rates are difficult to interpret because of the presence of flexible termini or loops, or iii) a full relaxation analysis is practically difficult because of limited sensitivity owing to low protein concentration, high molecular mass or low temperatures.

Introduction

Knowledge of the effective rotational correlation times is of significant value in biophysical characterization of biomolecules in solution. The rotational correlation time of a protein in solution can be rigorously determined from its experimentally measured backbone relaxation parameters if its 3D structure is known [1]. An effective rotational correlation time, τc, defined by an isotropic rigid rotor, is often estimated from the ratios of backbone transverse and longitudinal 15N relaxation rates, R2/R1, of residues not experiencing slow timescale/large amplitude internal motion or chemical/conformational exchange [2], [3], [4]. In order to identify those residues with significant internal motion (i.e. residues experiencing slow timescale/large amplitude internal motion or involved in chemical/conformational exchange), and for them to be excluded from the determination of τc, residue-specific 15N R1 and R2 values need to be obtained. Alternatively, collective 15N relaxation rates of backbone amides have been used for rapid estimates of protein effective rotational correlation times [5], [6]. This kind of rapid estimation of τc is beneficial, in particular when a full relaxation analysis is practically hindered due to limited sensitivity, for example in cases of inadequate protein concentration, high molecular mass or low temperatures. However, the inevitable inclusion of residues with significant internal motion in the estimation of rotational correlation time from collective 15N relaxation rates makes the resulting τc a lower limit of the actual value, with the extent of underestimation depending on the details of internal motion of the protein [6]. Collective 15N relaxations rates may therefore result in a severe underestimation of the rotational correlation time if substantial local motion is present.

Protein translational self-diffusion coefficients, which are readily measurable by pulsed-field-gradient NMR (PFG-NMR), have been used widely to characterize protein/peptide self-association and aggregation [7], [8], amide exchange [9], folding and unfolding [10] and ligand binding [11]. Given that molecular translational and rotational diffusion are well described by the Stokes–Einstein and the Debye–Stokes–Einstein equations, experimentally measured self-diffusion coefficients have been employed previously to calculate protein hydrodynamic radius, Rh [12], as well as for the estimation of protein rotational correlation times [13], [14]. Here we have further explored the suitability of translational self-diffusion coefficients measured by PFG-NMR for rapid estimation of protein effective rotational times using a protein complex in the presence of a reference molecule. The resultant effective rotational correlation times calculated directly from translational diffusion coefficients are compared with those determined from collective and residue-specific 15N relaxation analyses, as well as those obtained from 3D structure-based hydrodynamic calculations. Our results show that a rapid estimate of rotational correlation time of a protein/protein complex, which is otherwise difficult to determine by alternative means, can be obtained exclusively from translational diffusion coefficients measured by PFG-NMR (Eq. (6)) with reasonable accuracy.

Section snippets

Experimental

Measurements were carried out primarily on a 15N-labelled 30 kDa ternary protein complex of mouse elonginB, elonginC and the SOCS box domain of SOCS3 (termed ElonBC-SB) using a Bruker DRX600 spectrometer with a 5 mm triple resonance probe (equipped with triple gradients). A detailed description of expression and purification of this ternary complex as well as a table summarizing NMR experiments performed (Table S1) are given in the Supplementary data. Dioxane, with a published hydrodynamic

Results and discussion

This three-protein complex, ElonBC-SB, was chosen as it is sufficiently stable to allow measurements over a range of temperatures and it represents a ‘real life’ situation where the presence of unstructured regions can dominate collective 15N relaxation rates and make rapid τc estimation difficult in the absence of a residue-specific relaxation analysis. SOCS box proteins form stable ternary complexes with the elonginBC. As shown in Fig. 1, ElonBC-SB is well structured in solution and retains

Conclusions

We have shown that, provided the protein diffusive behavior is coherent with the Debye–Stokes–Einstein model, translational diffusion coefficients provide a means for quick estimates of rotational correlation times with reasonable accuracy, which may be otherwise difficult to determine from alternative rapid methods, such as collective backbone 15N relaxation rates. Translational diffusion coefficients provide rapid estimates of protein rotational correlation times with the advantages that the

Acknowledgements

This work was supported in part by the Australian National Health and Medical Research Council (NHMRC) (Program grant 461219). We thank Arthur Palmer (Columbia University) for valuable comments and Mark Hinds for thoughtful discussions.

References (26)

  • L.E. Kay et al.

    Backbone dynamics of proteins as studied by 15N inverse detected heteronuclear NMR-spectroscopy — application to staphylococcal nuclease

    Biochemistry

    (1989)
  • D.S. Korchuganov et al.

    Determination of protein rotational correlation time from NMR relaxation data at various solvent viscosities

    J. Biomol. NMR

    (2004)
  • W.S. Price et al.

    Lysozyme aggregation and solution properties studied using PGSE NMR diffusion measurements

    J. Am. Chem. Soc.

    (1999)
  • Cited by (0)

    1

    These authors contributed equally to this work.

    View full text