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A quantitative, diffusion NMR based analytical tool to distinguish folded, disordered and denatured biomolecules Erika F. Dudás, and Andrea Bodor Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b05617 • Publication Date (Web): 11 Feb 2019 Downloaded from http://pubs.acs.org on February 12, 2019
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A quantitative, diffusion NMR based analytical tool to distinguish folded, disordered and denatured biomolecules Erika F. Dudás, Andrea Bodor* Eötvös Loránd University, Institute of Chemistry, Laboratory of Structural Chemistry and Biology Pázmány Péter sétány 1/a, Budapest 1117, Hungary Key questions in folding studies are the protein dimensions and the degree of folding. These properties are best characterized by the self-diffusion coefficients D determining the hydrodynamic dimensions. In our present study we derive empirical variations of D as a function of molecular mass M that distinguish folded, intrinsically disordered and urea-denatured biomolecules. Reliable D values are obtained from diffusion NMR measurements performed under identical conditions using a representative set of proteins/peptides with diverse amino acid sequence and length. The established relations are easy to use analytical tools for molecular mass analysis and aggregation studies as well. Deriving equations under denaturing conditions has several pitfalls and here we provide a simple quantitative method for estimating the debated end point of denaturation, while already the 1D 1H spectrum gives a qualitative picture of the collapsed, denatured structure. Data indicate that the intrinsically disordered proteins have similar behavior as synthetic polymers and urea-denatured proteins.
A central question in the characterization of proteins is the determination of folding. The structures of folded and disordered proteins differ per se. Globular systems possess a well-defined 3D structure, they are more compact, adopting spherical, oblate or prolate shapes. Disordered proteins bear a resemblance towards synthetic polymers and can be described as wormlike chains close to a „random coil” state, eventually comprising residual dynamic structuring. Fully denatured globular proteins are structurally associated with the description of intrinsically disordered proteins (IDPs), but how similar are these structures?1 Hydrodynamic parameters for the different shapes differ significantly and provide a valuable tool for a quantitative description of folding. However, it is difficult to establish empirical formulae that allow distinction between the differently folded proteins, or to give estimation for the degree of denaturation, which is instrumental for understanding protein folding/misfolding. These are goals we tried to reach in our present study. In the literature several techniques are applied for deriving such equations.2-9 Small-angle X-ray scattering (SAXS) is a good method to probe the conformation and structure of biomolecules. Despite the fact that scattering profiles are applied in increasingly sophisticated analyses, there is currently no widely accepted and tested model for the errors obtained during the fitting, and the radius of gyration rG obtained from the Guinier analysis can inherently lead to high errors.10,11 Hydrodynamic parameters derived from the elution volumes of SEC analysis12 can also carry high errors. An unambiguous parameter that globally characterizes the protein conformational state is the hydrodynamic radius derived from translational self-diffusion coefficient D. Available measurement methods are DLS and NMR spectroscopy. DLS has a higher error for small molecules.13 We focus our studies
to small and medium-sized proteins, where NMR methods are advantageous and reliable. A correlation between D and the molecular mass M is established via the Stokes-Einstein relation, assuming a hard sphere with radius rH is moving through a continuum fluid and further, the occupied hydrodynamic volume is correlated with the mass according to Equation 1: 1
kB ∙ T
D = 6∙π∙η∙𝑟
𝐻
kB ∙ T
∙F
= 6∙π∙η∙F ∙
(
4 ∙ π ∙ ρ ∙ NA 3
) ∙M 3
1
―3
(1)
where kB is the Boltzmann-constant, T the temperature, η the viscosity of the medium, F a form factor, ρ the effective density and NA the Avogadro number. The F value incorporates several contributions: the deviation from the spherical shape; the different hydration properties and solvent effects. The influence of the solvent on factor F was evaluated in different media.9,14 For biomolecules in aqueous solution - according to the Gierer and Wirtz formula - 15 this contribution can be neglected as the solvent water molecules are much smaller than the solute molecules. Effects of molecular crowding can be checked by measuring D of water in the presence and absence of protein. In the general case of 1mM protein our measurements showed identical D values. In addition, we determined the diffusion activation energy by measuring the temperature dependence of the diffusion coefficient. The slope of the corresponding linearized Arrhenius relation gives a 20.6 kJ/mol value in full accordance with the value obtained for the diffusion of water molecules (20 kJ/mol).16 Thus, for typical protein/peptide samples no disturbance occurs from molecular crowdedness and also the continuum model is viable. One has to note that if the biomolecule is prone to aggregation then it is necessary to test whether the system is monomeric or not. In our examples working in the µM-mM concentration range the monomeric
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2 condition was fulfilled. On selected proteins we checked the concentration dependence and found that the variation of the resulting diffusion coefficient was within error limit. Determination of D via diffusion NMR methods is routinely applied for small molecules and molecule mixtures9,14,17,18 for the calculation and distribution of molecular weight of synthetic polymers19 and dextranes20. For biomolecules Danielsson et al. determined a D(M) correlation for sequentially similar disordered Aβ fragments.2 Groves et al. used five protein molecular weight standards in D2O media.3 Even though the primarily determined parameter is the D value, several empirical formulas were established describing the variation of rH with the residue number N 4-8 (see Table S1). All these relations carry some inconsistencies: either they are based on literature data determined by different techniques, or data were not always obtained under the same experimental conditions. In this study we performed a systematic study using a representative selection of already characterized folded, intrinsically disordered, and denatured proteins under highly controlled conditions for deriving a sound and reliable empirical model for the degree of folding. We use one experimental method: pulsed field NMR spectroscopy optimizing the same pulse sequence for each sample under constant measurement conditions. Experimental Section NMR spectra were recorded on a 16.4 T Bruker Avance III spectrometer equipped with a 5mm inverse TCI probe-head with z-gradient. Experiments were performed at 287.0 K. Temperature calibration was done with methanol-d4, and the standard ’doped water’ sample was used for gradient calibration. The original PFG spin echo measurement and data analysis developed by Stejskal-Tanner is not suitable for biomolecules that have short T2 relaxation times.21 Therefore, we applied the PFG-STE stimulated echo approach with bipolar pulses with and without water suppression when necessary.22 The lengths of diffusion delays and pulses were optimized for each sample. The strength of the diffusion gradient was linearly incremented in 32 equal steps, varying between 5% and 95% of its maximum value. The number of scans was adjusted for each sample to obtain reliable S/N ratios. Each measurement was repeated at least two times to allow the measurement error to be estimated. Data evaluation was done by the T1/T2 package of the TopSpin program. Signals were chosen from several regions in the 0.0-3.0 ppm aliphatic proton range and the decay was fitted to a single Gaussian. The resulting D values were averaged. Results and Discussion The chosen disordered and folded proteins with varying size and charge-distributions were analyzed at 287K (sequence, conditions, characterization is given in Tables S2, S3, Figure S1). Already the qualitative analysis of the 1D 1H spectra can distinguish between folded and disordered molecules. While proteins with well-defined structure have considerable signal dispersion, the IDPs possessing similar environments will present a more collapsed spectrum (Figure 1). The translational diffusion measurements lead to calculated D values. Representation of these coefficients as a function of molecular mass shows a rapid decay (Figure 2) up to ca. 20000 g/mol, and above this threshold no significant variation occurs. The phenomenon can be explained by the cooperative effect of weak molecular interactions, and is consistent with the earlier
observation that the maximum size of protein domains approaches 200 residues.23,24
Figure 1. 1D 1H NMR spectra of a folded protein (red) and an IDP (blue)
A clear discrepancy is observable between the behavior of folded proteins and IDPs, and fitting of the decays lead to the following empirical formulas: 𝐷(folded) = 3.16 ∙ 10 ―9(𝑀[g/mol]) ―0.381 (m2s-1) (2) 𝐷(IDP) = 6.78 ∙ 10 ―9(𝑀[g/mol]) ―0.507(m2s-1)
(3)
Figure 2. Variation of the translational diffusion coefficients with molecular weight for folded proteins (red circles) and IDPs (blue squares).
The linearized equations are usually more favored: logD (folded) = ― 0.381logM – 8.499
(4)
(5) These relations represent easy to use analytical tools for molecular mass determination, moreover, they can be used to distinguish or estimate the degree of folding for a biomolecule. Analyzing the error, an aggregation and/or a change of 10% in molecular weight can be already determined. The formulae carry generalized shape information: the 0.381 exponent for folded proteins resembles the theoretical value from Equation 1, in accordance with a more compact spherical/distorted spherical shape. As such, a global conceptual shape factor is obtained, that is applicable to most compact proteins and individual extreme protein shapes might lead to deviations. The 0.507 exponent determined for IDPs is indicative of more elongated, loose structures. In this case a similarity to polymer solutions can be assumed as scaling parameters of 0.52-0.55 were established for poly(ethylene-oxide) (PEO) in D2O and 0.55 in H2O solutions.19 Diffusion coefficients are the starting point in the evaluation of the effective hydrodynamic radius rH (Equation 1), and to do so two literature approaches are available. The absolute method is based on direct calculation from Equation 1 and necessitates exact knowledge of solvent viscosity at the given temperature. The relative method avoids the viscosity issue by using an internal reference molecule. Traditionally dioxane is used for this purpose, presenting one resonance peak at 3.54 ppm and constant rH. The exact number is contradictory in literature: both 1.7Å25 and 2.12Å4 are used (we determine 2.16 Å). Testing lysozyme and ovalbumin we found significantly larger errors in logD (IDP) = ― 0.507logM – 8.169
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Analytical Chemistry
3 the rH values (± 2.0 and 1.4Å) for the relative method compared to the absolute method (±0.4 and 0.5Å, respectively). Peak overlap with protein resonances is another disadvantage of the relative approach. Based on these, we suggest the application of the absolute method whenever possible. Literature is more abundant in rH(N) relations (Table S1). This is a less accurate approach, as it carries the assumption of spherical molecules and does not consider the exact molecular mass. The idea originates from polymer theory,26 and considers the polypeptide chain a freely jointed chain built from N statistical segments of given dimensions. Keeping this in mind we derive residue-based correlations using Equations 1-3 for better comparison with literature data: rH(folded) = 3.405N0.382 (Å) (6) rH(IDP) = 3.128N0.492 (Å)
(7)
For the same N value the more compact folded molecules should present lower rH than the corresponding IDP. Literature data (Table S5, Figure S2) show discrepancies especially for moderate N values. Our rH values are higher than literature predictions for IDPs, a difference of 4-6Å is observed in the N = 50-200 residue range. For folded systems with low N our predicted values fall between literature data, and systematically higher rH values (7-8Å) are observed for N >100 residues. One possible explanation for this deviation might arise from the fact that literature relations are based on data collected from different methods and conditions. On the other hand the discrepancy might originate from different shape, therefore we tried to investigate shape factors using a set of folded proteins with available 3D-structures. The HYDROPRO27 program on the basis of the pdb coordinates derives a Dcalc value from the diffusion tensor, and gives the radius of gyration rG as well. The rG/rH ratio reports on molecular shape, for a hard sphere this value being 0.77.28 The higher the rG/rH ratio, the bigger is the distortion from the spherical shape (see Table 1). For values close to 1.00, the molecule will present an elongated shape, thus rH will become higher than expected (ovalbumin and BSA). Still, we believe that for analytical purposes the D(M) relations are more to be trusted. Table 1. Selected folded proteins from PDB; derived and measured diffusion coefficients; the calculated rG/rH ratio Protein/PDB code
Dcalc(m2s-1)
Dexp(m2s-1)
rG/rH
TC5b/1l2y
1.41E-10
1.76E-10
0.94
PAF/2mhv
1.21E-11
1.06E-11
0.79
ribonuclease/2e3w
8.08E-11
9.17E-11
0.83
lysozyme/1lys
9.00E-11
7.84E-11
0.65
S100A4wt/1m31
6.54E-11
6.80E-11
0.77
chymotrypsinogen/1ex3
7.61E-11
7.41E-11
0.70
ovalbumin/1ova
3.84E-11
5.10E-11
1.00
BSA/3v03
3.74E-11
4.80E-11
1.03
Another way to analyze diffusion data is by further developing Equation 1. In this way shape will be incorporated in the effective density. Small molecules can be characterized with good approximation9 by a single value (620kg/m3), but in case
of proteins the density will not be independent of the chain length, as will be influenced by shape, solvation and flexibility. The Voronoi method29 determines 1470kg/m3 average density valid for buried atoms with zero solvent accessible area. The exposed atoms will possess varying number of water neighbors; thus different inflated volumes and different densities will be obtained. As expected, the effective densities for our studied molecules show higher values for folded proteins, and no specific variation with the molecular weight can be traced. Indeed, for native globules the density is more or less independent of the chain length.30 For the more solvated IDPs the 𝜌 = 569 ∙ 𝑀 ―0.52 decay is obtained. The theoretical description for the density variation in case of macromolecules in an “ideal” solvent follows a -0.50 power of M, and apparently the IDP behavior is in agreement with this statement. Moreover, previous studies on proteins under high denaturation conditions (6M GdnHCl) describe an apparent density variation of M having -0.64 and -0.66 exponents, respectively.31 The correlations we observe indicate that IDPs behave similarly to denatured, unfolded proteins. Massive experimental efforts were directed to characterize the unfolded states under denaturing conditions.4,5,30 Yet, it is still debated when is the denaturation end-point achieved and which chaotropic agent to use. We chose the most frequently applied 8M urea media and investigated the denaturing behavior of 6 IDPs and 5 folded proteins. It is expected that under high denaturant concentrations a completely unfolded “random coil” conformation will be present, regardless what the protein initial structure has been. However, our data points are more spread on the linearized representation (see Figure S3).
Figure 3. Logarithmic representation of diffusion coefficients as function of molecular weight for folded proteins (red circles), IDPs (blue squares), viscosity corrected denatured folded proteins (open green circles) and IDPs (open green squares).
Taking separately the two classes, the variation of denatured IDPs is similar to their behavior in aqueous solution, and the two lines are almost parallel. If we want to compare the real degree of denaturation then a viscosity correction needs to be performed. The ratio between the viscosities of aqueous and 8M urea solutions is mostly temperature independent (see Table S4) and for obtaining a viscosity corrected D value this number can be applied. This viscosity ratio can be determined also experimentally measuring dioxane in the given solution and in another sample under denaturing conditions. Our results show, that corrected values for denatured IDPs fall very close to their values measured in aqueous solution (Figure 3). For folded proteins almost no variation is detected if disulphide bridges are present in the molecule (that urea will not cause unfolding). If a protein starts to denature, then the corresponding diffusion
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4 coefficient will be between the folded and IDP lines, while denatured systems will be situated along the disordered line. These experiments reveal two features: a) IDPs cannot be further denatured in 8M urea. This is supported also by the above depicted effective density variation. Moreover, comparing rH values calculated for IDPs in the present work with the values from the available literature variation for denatured proteins no significant differences are detected (Figure S4). Both IDPs and denatured proteins can present residual structures, but these inherent structural tendencies do not seem to influence the highly mobile ensembles represented by the global hydrodynamic parameters. b) The 1H 1D spectrum indicates qualitatively (Figure S5) whether the structure is collapsed, while the diffusion measurement reveals whether the final unfolded state had been achieved under the applied denaturing conditions, or if not then what was the extent of denaturation. Conclusions In the present study we provide new empirical relations that make possible to obtain reliable protein structural and compactness information, and to characterize the success of their unfolding during denaturation both qualitatively and quantitatively. The measurements are easy to carry out; irrelevant if the unlabeled or the isotopically labeled protein is used (keeping in mind the corresponding molecular mass correction in case of labeling). Complementary in situ information is obtained regarding aggregation state and shape. Applying this method for IDPs the observed anomalous behavior of higher molecular mass detected in the SDS-PAGE gels can be overcome. We show the similarity in behavior between IDPs and denatured proteins, and the resemblance of IDPs to synthetic polymer chains - features that can be exploited in potential applications. The method provides both analytically and chemically useful results, and should enhance the application of diffusion NMR experiments in the structural characterization of proteins.
ASSOCIATED CONTENT Supporting Information D(M) , rH(N) relations from literature; water and 8M urea viscosity values; characteristics of the investigated proteins; data comparison with previous relations; data evaluation for selected proteins, 1D 1H spectra of folded and intrinsically disordered proteins and calculated IDP rH values from rH(N) relations (PDF)
AUTHOR INFORMATION Corresponding Author * A. Bodor, PhD. Habil; E-mail:
[email protected] Author Contributions The manuscript was written through contributions of all authors. / All authors have given approval to the final version of the manuscript.
ACKNOWLEDGMENT Support by the ELTE Institutional Excellence Program (17833/2018/FEKUTSRAT) of the Hungarian Ministry of Human Capacities; the National Research, Development and Innovation Office, Hungary (NKFI K124900), the MedInProt Program of the HAS is acknowledged. We thank A. Perczel, Gy. Batta, K. Liliom,
L. Nyitray, A. Reményi, Á. Tantos, P. Tompa for the proteins; and L. Novák, I. Bányai for the viscosity measurements.
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