Journal of Biomolecular NMR

, Volume 53, Issue 2, pp 139–148 | Cite as

4D Non-uniformly sampled HCBCACON and 1J(NCα)-selective HCBCANCO experiments for the sequential assignment and chemical shift analysis of intrinsically disordered proteins

  • Jiří Nováček
  • Noam Y. Haba
  • Jordan H. Chill
  • Lukáš Žídek
  • Vladimír Sklenář
Article

Abstract

A pair of 4D NMR experiments for the backbone assignment of disordered proteins is presented. The experiments exploit 13C direct detection and non-uniform sampling of the indirectly detected dimensions, and provide correlations of the aliphatic proton (Hα, and Hβ) and carbon (Cα, Cβ) resonance frequencies to the protein backbone. Thus, all the chemical shifts regularly used to map the transient secondary structure motifs in the intrinsically disordered proteins (Hα, Cα, Cβ, C′, and N) can be extracted from each spectrum. Compared to the commonly used assignment strategy based on matching the Cα and Cβ chemical shifts, inclusion of the Hα and Hβ provides up to three extra resonance frequencies that decrease the chance of ambiguous assignment. The experiments were successfully applied to the original assignment of a 12.8 kDa intrinsically disordered protein having a high content of proline residues (26 %) in the sequence.

Keywords

Intrinsically disordered proteins Non-uniform sampling 13C detection Chemical shifts Residual secondary structure Prolines assignment 

Introduction

Intrinsically disordered proteins (IDPs) characterized by polypeptide chains lacking a stable and well defined tertiary structure in an isolated state have been under increased interest of biochemists and structural biologists for the past decade. IDPs comprise considerable part of the eukaryotic proteome and take part in a number of important processes (Dunker et al. 2000; Ward et al. 2004; Billadeau et al. 2006). Besides, it has been recognized that a non-negligible portion of the IDPs is related to serious human diseases (Bussell and Eliezer 2001; Dyson and Wright 2005; Fink 2005; Dunker et al. 2008).

The unusual structural state of IDPs can be characterized by an array of techniques, ranging from simple indirect methods describing their chemical and physical properties, over the techniques providing information on the size or diffusion behavior to spectroscopic methods supplying both structural and dynamic residue level information. Due to its exceptional capacity to describe structural properties at the atomic resolution, multi-dimensional NMR has become a leading tool to study structure-function relationship of IDPs (Dyson and Wright 2004; Eliezer 2007, 2009). Due to the lack of a rigid structure, the strategy applied to the NMR characterization of the IDP architecture differs significantly from the one utilized for the well ordered systems. The chemical shifts obtained in the process of sequential assignment provide the first important insight into the presence of the residual secondary structure motifs along the amino acid sequence. Due to the increased dynamics of unstructured polypeptide chains, 1H–1H NOE data no longer furnish sufficient information, and the structural studies have to rely on other NMR observables. Among them, measurement of the residual dipolar couplings (RDCs), data supplied by relaxation experiments and by measurements exploiting the attached paramagnetic labels have proven to provide crucial information to map the conformational space of the IDPs (Ganguly et al. 2009; Mukrasch et al. 2009; Salmon et al 2010).

Various strategies for the backbone assignment of the IDPs have been proposed over the past decade. First, approaches originally developed to assign the well ordered systems have been applied (Peti 2001; Yao et al. 2001; Pannetier 2007; Mukrasch et al. 2009; Motáčková et al. 2009); in particular, a combination of several triple resonance experiments that allow the sequential walk by comparing the chemical shifts of the 15N atoms (Panchal 2001; Zweckstetter et al. 2001; Frueh et al. 2006; Sun et al. 2005) or by matching the resonance frequencies of Cα and Cβ, or C′ atoms (Sattler et al. 1999; Rovnyak 2004; Pannetier 2007). However, in case of IDPs where the resonance frequencies exhibit only very low dispersion, the application of the classical approach frequently fails. As demonstrated recently, NMR experiments with higher dimensionality (m > 3), correlating nearly all resonances of a single amino acid or stretching over several amino acids, represent an efficient alternative. The acquisition of mD NMR spectra allows to resolve peaks even in the cases of overlap of resonance frequencies in conventional 2D/3D spectra (Atreya et al. 2005; Hiller et al. 2007; Narayanan et al. 2010; Kazimierczuk et al. 2010; Motáčková et al. 2010b; Wen et al. 2011; Nováček et al. 2011).

As the measurement of high resolution spectra with higher dimensionality using the standard techniques would impose extremely long, and in practice unattainable measurement times, special approaches utilizing a sparse sampling are required. Those include reduced dimensionality experiments (Szyperski et al. 1993) rooted in the concept of the “accordion” spectroscopy (Bodenhausen and Ernst 1981, 1982), methods based on projections of multi-dimensional spectra (Ding and Gronenborn 2002; Kim and Szyperski 2003; Kupče and Freeman 2003; Hiller et al. 2005), and experiments exploiting true random sampling in the indirect dimensions (Barna et al. 1987; Barna and Laue 1987; Schmieder et al. 1994; Orekhov et al. 2001; Stern et al. 2002; Malmodin et al. 2005; Marion 2006; Kazimierczuk et al. 2006; Coggins and Zhou 2007). Compared to the standard processing protocols of multi-dimensional NMR data based on the Fast Fourier Transform, special processing procedures are needed to calculate the spectra from the incomplete, sparsely sampled data sets (Coggins and Zhou 2007, 2008; Kupče and Freeman 2008; Mobli and Hoch 2008; Kazimierczuk et al. 2010; Orekhov and Jaravine 2011).

In general, the strategies based on the detection of amide protons fall short to provide sequential assignment of polypeptide chains where two or more consecutive prolines are present. However, recent advances in the design of cryogenically cooled probeheads and developments of the assignment methods utilizing the direct detection of 13C nuclei (Bermel et al. 2005, 2006a, b) to study deuterated and intrinsically disordered proteins (Bermel et al. 2006c, 2009a) paved the way for development of experiments capable to overcome this problem.

Here we present two complementary triple resonance experiments, which improve the sensitivity and extend the originally proposed three-dimensional 13C detected (H)CBCACON and (H)CBCANCO (Bermel et al. 2009a) measurements to the fourth proton dimension. As demonstrated, the measured Hα, Hβ2, and Hβ3 chemical shifts greatly facilitate resolution of the carbon atoms in polyproline stretches. The experiments provide the sequential assignment even for IDPs with very high degeneracy of the Cα and Cβ chemical shifts. Each experiment yields all the chemical shifts commonly used to probe for (partial) secondary structure characteristics. The experiments were successfully applied to the original assignment of a 12.8 kDa intrinsically disordered protein having high degeneracy in the amino acid sequence.

Materials and methods

Sample preparation

The 13C, 15N-uniformly labeled sample of WIPc has been prepared as follows. The sequence of the residues 407V–503R of the human WIP protein together with N-terminal and C′-terminal poly histidine tags (for the primary sequence of the WIPc construct see Fig. 2) was cloned into a pET28 vector and transformed into BL21 cells. Typically, cells were grown in a 1.5 L culture of enriched M9 medium (Cai et al. 1998), expression was induced with 1 mM IPTG, and purification utilized immobilized metal ion affinity chromatography which provided sufficiently pure WIPc for NMR sample preparation. The final samples used for the NMR measurements consisted of 1.0–1.2 mM WIPc in 10 mM phosphate buffer, pH 5.0, 20 mM NaCl, 10 mM β-mercaptoethanol, and 7 % D2O.
Fig. 1

Graphical representation of 900 indirectly detected time domain points generated using the Poisson disc algorithm used for the acquisition of the 4D HCBCACON (a), and of 2,000 indirect points used for the measurement of the 4D 1J(NCα)-selective HCBCANCO data (b)

Fig. 2

Primary structure of the WIPc construct. The sequence corresponding to the residues 407V–503R of the human WIP protein is depicted in red, while the sequence of the N-terminal and C′-terminal poly histidine tags is depicted in gray

NMR experiments and data handling

The 4D HCBCACON experiment correlates the resonances of the backbone N of the ith amino acid with the Hα, Hβ, Cα, Cβ, and C′ of the (i − 1)-th amino acid (Fig. 4). The data were measured with the spectral widths set to 6,010 (aq) × 2,000 (N) × 10,000 (Cα/β) × 3,125 (Hα/β) Hz. The maximal acquisition times in the individual indirectly detected dimensions were adjusted to 8 ms for Hα/β, 7 ms for Cα/β, and 40 ms for N dimension. The experiment was acquired with 1,024 complex points in the acquisition dimension and 900 hypercomplex points were randomly distributed (vide infra) over the three indirectly detected dimensions. The experiment was acquired based on the parameter set for the standard 2D CON with 8 scans per collected FID. The interscan delay was set to 0.75 s. The data were collected within 31 h which is 0.6 % of the time needed for acquisition of the linearly sample experiment with a similar resolution (25 × 70 × 80 points for Hα/β, Cα/β, N, respectively). The 1J(NCα)-selective HCBCANCO experiment (further denoted as HCBCANCO) correlates the resonance frequency of C′ of the (i − 1)th amino acid with the Hα, Hβ, Cα, Cβ, and N resonances of the ith amino acid (Fig. 4). The experimental data were measured with the spectral widths set to 6,010 (aq) × 2,000 (N) × 10,000 (Cα/β) × 3,125 (Hα/β) Hz. The maximum acquisition times in the individual indirectly detected dimensions were adjusted to 8 ms for Hα/β, 7 ms for Cα/β, and 30 ms for N dimension. The experiment was measured with 1,024 complex points in the directly detected dimension and 2,000 hypercomplex points were randomly distributed in the indirectly detected dimensions. The data were acquired using the parameter set for the standard 2D CON experiment with 8 scans per collected FID and the recovery delay set to 0.75 s. The data were acquired within 69 h, which is equivalent to 1.9 % of the time needed for conventional experiment providing similar resolution (25 × 70 × 60 points for Hα/β, Cα/β, N, respectively). The auxiliary 2D (HCBCA)CON experiment was measured using the pulse code of the 4D HCBCACON, excluding the evolution of the chemical shift in the Hα/β and Cα/β dimension. The spectral widths were set to 6,010 (aq) × 2,000 (N) Hz. The total number of 1,024 complex points was measured in the acquisition dimension and 512 complex points in the indirect dimension. The experiment was measured with 8 scans per FID and with the interscan delay of 0.75 s. The non-uniformly sampled HNCACB experiment (Sattler et al. 1999) was measured with spectral widths set to 8,400 (aq) × 2,500 (N) × 10,000 (Cα/β) Hz and the maximal acquisition times 10 ms for Cα/β and 22 ms for N indirect dimension. The experiment was acquired with 1,024 complex points in the directly detected dimension and 1,300 hypercomplex points in the indirectly detected dimensions. The data were collected with the single scan recovery delay set to 1.15 s and 8 scans per FID. The data were acquired within 17 h, which is equivalent to 23 % of the time needed for conventional experiment providing similar resolution (55 × 100 points for N, Cα/β, respectively). The non-uniformly sampled HNCO experiment (Sattler et al. 1999) was measured with spectral widths set to 8,400 (aq) × 2,000 (N) × 2,000 (C′) Hz. The maximal acquisition times in the individual indirect dimensions were adjusted to 80 ms for N and 50 ms for C′. The experiment was acquired with 2,048 complex points in the directly detected dimension and 500 hypercomplex points in the indirectly detected dimensions. The data were collected with the single scan recovery delay set to 1.0 s and 4 scans per FID. The data were collected within 3 h which is 3 % of the time needed for acquisition of the linearly sample experiment with a similar resolution (160 × 100 points for N, C′, respectively). All data were acquired on a 600 MHz Bruker Avance II spectrometer equipped with the Bruker 1H/13C/15N TCI cryogenic probehead with the z-axis gradients at 25°C.
Fig. 3

The central regions of 1H,15N-HSQC (a) and 13C-detected 2D CON (b) spectra of the WIPc construct measured on the 600 MHz spectrometer. The spectral widths in the direct dimension were chosen so that the average signal widths (21 Hz for amide protons and 17 Hz for carbonyl 13C, defined as FWHH) appear identical in both plots. Amide proton signals spread over 600 Hz, while the carbonyl signals cover the range of 1,200 Hz in the 1H,15N–HSQC and 2D CON spectrum, respectively

Fig. 4

Magnetization transfer pathways within 4D HCBCACON experiment (blue arrows) and 4D 1J(NCα)-selective HCBCANCO experiment (green arrows). The arrows indicate individual coherence transfer steps via scalar couplings. Transfer via the 2J(NCα) coupling (gray arrow) is actively suppressed within the HCBCANCO experiment

The 4D HCBCACON and HCBCANCO experiments were acquired with the non-uniform sampling of the indirectly detected dimension. The Poisson disc algorithm was used to generate the time schedule (Kazimierczuk et al. 2008). The algorithm contains a criterion that defines minimal distances between the time points and generates an off-grid sampling scheme. The minimal distance can be represented by an ellipsoid drawn around each time point with the individual radii defined as
$$ a_{k}=\frac{\alpha}{\root 3\of{4N\sqrt{2}}}\sqrt{\frac{{\rm SW}_{l} \cdot t_{l}^{\rm max} \cdot {\rm SW}_{m} \cdot t_{m}^{\rm max}}{ {({{\rm SW}_{k} \cdot t_{k}^{\rm max})^{2}}}}}, $$
(1)
where α, N, SWk,l,m, and tk,l,mmax are: factor regulating the discrepancy of generated points (α = 0.8), total number of generated time points, spectral width, and maximal evolution time for indirect dimensions, respectively. Symbols klm loop over individual indirectly detected dimensions (k ≠ l ≠ m). At the end, the density of the time points was changed to correspond to the Gaussian distribution (σ = 0.5). The graphical representation of the sampling schedules used in the present application is shown in Fig. 1.

The uniformly sampled 2D (HCBCA)CON experiment was processed using the spectral processing and analysis system NMRPipe/NMRDraw 3.0 (Delaglio et al. 1995). The non-uniformly sampled 4D HCBCACON and HCBCANCO data were processed using the Sparse Multidimensional Fourier Transform (SMFT) algorithm (Kazimierczuk et al. 2010). The number of spectral points was set to 1,024 in ω1 (Hα/β) and ω2 (Cα/β) dimensions for both experiments. All the spectra were analyzed in the graphical NMR assignment and integration software Sparky 3.115 (T. D. Goddard and D. G. Kneller, University of California, San Francisco, USA).

Results and discussion

The interaction between two proteins found exclusively in human T-cells, Wiskott-Aldrich syndrome protein (WASP) and its binding partner WASP-inhibiting protein (WIP) plays a central role in the cytoskeletal changes, particularly actin polymerization, which accompanies T-cell activation (Billadeau et al. 2006). Mutations which perturb formation of the WIP/WASP are responsible for the Wiskott-Aldrich syndrome (WAS) and X-linked thrombocytopenia (XLT), hereditary immunodeficiencies characterized by impaired cytoskeleton formation and an increased incidence of autoimmune diseases and malignancies (Derry et al. 1994). WIP stabilizes WASP by shielding it from the cellular degradation systems and also conveys it to areas of active actin assembly following antigen-receptor and chemokine receptor signaling (Sasahara et al. 2002; de la Fuente et al. 2007). The WIP interaction epitope has been localized to a 35-residues segment at its C-terminal, which has been determined to wrap around the N-terminal WASP EVH1 domain in forming the complex between them (Volkman et al. 2002; Peterson et al. 2007). WIP is predicted to be disordered in solution, and characteristically contains several candidate epitopes which may interact with additional proteins. Thus the unbound state of WIP, yet to be structurally investigated, is biologically relevant.

We have successfully expressed and purified a polypeptide corresponding to residues 407–503 of WIP, henceforth referred to as WIPc (Fig. 2). This region includes a proline-rich domain (residues 413–433, PRD1), the central verprolin conserved region (residues 448–478, VCR), the PKC\(\Uptheta\) consensus sequence (residues 485–490) and a C-terminal second proline-rich domain (residues 495–503, PRD2). VCR is common to the verprolin family (60–65 % homology among WIP, WIP-related protein and CR16) and contains the previously established three WASP-binding epitopes (Peterson et al. 2007). Due to its unfolded nature, WIPc cannot be studied using crystallographic methods. Therefore, the multidimensional NMR provides an ultimate tool to characterize the WIPc protein at the atomic resolution. As in the case of other IDPs, the proton dimension of a fingerprint 1H–15N HSQC spectrum (Fig. 3a) exhibits only a very low resolution. To overcome this obstacle and to offset a high occurrence of the proline residues (26 %), experiments relying on the direct 13C detection of carbonyl atoms were used to obtain the sequential assignment of WIPc. In contrast to the 1H–15N HSQC, the 13C detected 2D CON experiment (Bermel et al. 2005) provided a well resolved spectrum exhibiting 92 of the expected 97 correlation peaks. The comparison of resolution in the 1H and 13C detected spectra, with the ranges of the \(\hbox{C}^{\prime}\) and HN resonance and their average line-widths taken into account, showed a 2.4 times higher resolution gained by employing the 13C direct detection of carbonyl resonances (Fig. 3b). Hence, the assignment was first attempted using a standard set of 3D CANCO, CBCACON, and CBCANCO spectra (Bermel et al. 2006c, 2009a, b). These data provide correlations of each \(13\hbox{C}^{\prime}_{i}, \hbox{N}_{i+1}\) moiety to its four neighboring (i) and (i + 1) 13Cα/13 Cβ nuclei. However, as a consequence of the highly repetitive amino acid sequence, this approach allowed assignments of less than 50 % of the observed resonances despite the favorable resolution in the 2D CON spectra. A close inspection of the primary structure (Fig. 2) shows that WIPc contains 26 % Pro and 15 % Ser in its 97 residues. Besides, WIPc is rich in amino acids with almost identical chemicals shifts of the 13Cα/13Cβ nuclei, such as Arg, Glu, and His (18 % in total, including the two His-tags) and Asp and Leu (9 %). Such a high content of the amino acids of the same type increases the probability of the signal overlap in the spectra.

To overcome the problem with the high 13Cα/13Cβ chemical shift degeneracy, we have developed two complementary 4D experiments, HCBCACON and HCBCANCO, that employ the evolution of the chemical shifts of the Hα and Hβ and provide up to three extra resonance frequencies that significantly reduce the chance of ambiguous sequential assignments. The experiments are particularly useful when (1) the matching 13Cα and 13Cβ frequencies are difficult to find due to a high content of amino acids with very similar 13Cα and 13Cβ chemical shifts, (2) high content of prolines further increases the number of frequencies that can be employed in the sequential assignment, as the 1Hβ2 and 1Hβ3 resonances are well resolved, and (3) the polypeptide chain is flexible and the inherently lower sensitivity of the 13C-detected experiments is partly retrieved by a slower transverse relaxation. The correlation and pulse schemes of the 4D HCBCACON and 1J(NCα)-selective HCBCANCO experiments are shown in Figs. 4 and 5, respectively. Both experiments start with the excitation and chemical shift evolution of 1Hα/1Hβ protons followed by the \(^{1}\hbox{H}^{\alpha}/^{1}\hbox{H}^{\beta}\rightarrow ^{13}\hbox{C}^{\alpha}/^{13}\hbox{C}^{\beta}\) polarization transfer. Optimization of the proton longitudinal relaxation to speed up the acquisition (Pervushin 2002) is achieved by application of a refocused INEPT transfer step referred to as the “H-flip” where an additional 90° pulse is used to return all protons to the equilibrium state (Bermel et al. 2009b). In our implementation, the 180° high power pulse, refocusing the evolution of the 1H–15N scalar interaction during the 15N–\(^{13}\hbox{C}^{\prime}\) evolution, is paired with another 180° pulse with the opposite phase to achieve a net zero effect on the proton magnetizations. This optimization of the proton longitudinal relaxation allowed us to reduce the recycling delay by a factor of 1.7 compared to the experiment without the “H-flip” where a continuous proton decoupling was applied for the same purpose.
Fig. 5

Pulse sequence scheme of the 4D HCBCACON (a) and 4D 1J(NCα)-selective HCBCANCO (b) experiments. The carrier frequencies were placed at 3.0 ppm for 1H, at 44.0 ppm for 13Cα/β, at 123.9 ppm for 15N, and at 175.0 ppm for \(^{13}\hbox{C}^{\prime}\). The switching of the carrier frequency on the 13C channel is indicated by the vertical arrows. The narrow and wide rectangular shapes stand for 90° and 180° high power pulses. The narrow and wide filled round symbols represent selective 320 μs 90° Q5 (or time-reversed Q5) and 256 μs 180° Q3 used for \(^{13}\hbox{C}^{\prime}\) or 13Cα/β excitation resp. inversion on the 600 MHz spectrometer. The open round symbols stand for 256 μs 180° Q3 pulses applied at the center of the 13Cα resonance frequency region (58.0 ppm). The round symbol marked with asterisk represents an 500 μs adiabatic Chirp pulse used for a simultaneous inversion \(^{13}\hbox{C}^{\prime}\) and 13Cα. BSP denotes pulses for compensation of the off-resonance effects. All the pulses were applied with the x phase unless noted differently. The IPAP acquisition scheme was implemented to avoid signal splitting in the directly detected dimension due to the 13Cα-\(^{13}\hbox{C}^{\prime}\) coupling. The line denoted with G stands for pulsed field gradients applied along the z-axis. The sine-bell shaped gradients were applied with the following duration and strength: G1: 1,000 μs, 18 G/cm; G2: 1,000 μs, 5.4 G/cm, G3: 1,000 μs, 18 G/cm; G4: 1,000 μs, 11.4 G/cm. The GARP4 pulse train was employed during the acquisition for 15N decoupling. The following phase cycling was used: ϕ2 = x,  − x; ϕ3 = 2(x), 2(− x); ϕ4 = 4(x), 4(− x); ϕ5 = 4(− y), 4(y); ϕ6 = x, 2(− x), x,  − x, 2(x), x; ϕ8 = y,  − y; ϕ9 = 2(x), 2(− x). The pulse denoted with ω was applied with −x phase and power of the high power pulses for ϕ17) = x or with zero power when the ϕ17) phases were incremented. The initial lengths of the delays were: \(\Updelta=3.75\) ms, \(\Updelta_{1}=1.1\) ms, \(\Updelta_{2}=3.4\) ms, \(\Updelta_{3}=4.5\) ms, \(\Updelta_{4}=12.5\) ms, \(\Updelta_{5}=15.3\) ms, \(\Updelta_{6}=11.0\) ms, \(\Updelta_{7}=16.0\) ms,t1a = 1.8 ms, t1b = 0.0 ms, t1c = 1.8 ms. The evolution of the chemical shift of the 1Hα/β was performed in the semi-constant time manner incrementing t1at1bt1c delays as follows: \(\Updelta t_{1}^{\rm a} = {1 / 2{\rm SW}}, \Updelta t_{1}^{\rm c} = -{t_{1}^{\rm c}(0) / {\rm TD}}, \Updelta t_{1}^{\rm b}=\Updelta t_{1}^{\rm a}+\Updelta t_{1}^{\rm c}\), where SW and TD denote spectral width and number of complex points acquired in the indirect dimension, respectively. The detection of the individual quadrature components of the signal was achieved by incrementation of ϕ1, ϕ2, ϕ3 or ϕ7, ϕ8, ϕ9 in the States manner, respectively

The transfer of polarization during the 4D HCBCANCO experiment (Figs. 4b, 5b) has to be confined within a single residue to provide solely intra-residual correlations, reduce the number of correlation peaks, and maximize the sensitivity. This can be achieved by inserting an extra element to eliminate or largely suppress transfer of the magnetization via two-bond 2J(Ni+1Ciα) scalar interactions (Fig. 5b between the points denoted “a” and “d”). Although conceptually identical to the previously proposed solutions for intra-residual 3D HNCA and COHNCA experiments (Permi 2002; Brutscher 2002; Nietlispach et al. 2002), the practical arrangement in the current implementation using the 13C detection of carbonyl atoms differs as only one-directional magnetization transfer \({\rm H}^{\alpha/\beta} \rightarrow {\rm C}^{\alpha/\beta} \rightarrow \hbox{N} \rightarrow \hbox{C}^{\prime}\) is desired.

The Cartesian product operators (Sørensen et al. 1984) at the point denoted with “a” (Fig. 5b) for the magnetizations originated from the 1Hα, 13Cα (transfer amplitude α) and 1Hβ, 13Cβ (transfer amplitude β) are given by:
$$ \begin{aligned} &\alpha: {\rm A}_{i}^{y}\,{\rm cos}\,(\pi \cdot J({\rm C}^{\alpha}{\rm C}^{\beta})\cdot 2\Updelta) \\ &\beta: 2{\rm A}_{i}^{x}{\rm B}_{i}^{z}\,{\rm sin}\,(\pi \cdot J({\rm C}^{\alpha}{\rm C}^{\beta})\cdot 2\Updelta),\\ \end{aligned} $$
where Ai and Bi denote the carbon α and carbon β operators of the ith residue, respectively. The operators evolve under the 1J(NCα), 2J(NCα), and J(CαCβ) scalar couplings for the whole period confined by the labels “a” and “d”. Further, the J(\(\hbox{C}^{\prime}\hbox{C}^{\alpha}\)) coupling is active between the time period “a”–“b” and “c”–“d”. In the time point “b”, a multiple quantum coherence is created by the 90° pulse on \(\hbox{C}^{\prime}\), and the system is allowed to evolve under the J(\(\hbox{NC}^{\prime}\)) coupling. The magnetization is returned to the single quantum state in the time point “c” (see Supporting Information for the cartesian product operators at the points denoted with “b” and “c”). The amplitudes for the desired transfers of magnetizations at the end of the building block (time point “d”) are given by
$$ \begin{aligned} \alpha&: 2{\rm A}_{i}^{z}{\rm N}_{i}^{z} \cos (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot2\Updelta)\cdot \cos (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot T)\cdot \\ & \quad \cdot \sin (\pi \cdot ^{1}J({\rm NC^{\alpha}})\cdot T)\cdot \sin (\pi \cdot ^{2}J({\rm NC^{\alpha}})\cdot T)\\ \beta&: 2{\rm A}_{i}^{z}{\rm N}_{i}^{z} \sin (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot2\Updelta)\cdot \sin (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot T)\cdot\\ & \quad\cdot \sin (\pi \cdot ^{1}J({\rm NC^{\alpha}})\cdot T)\cdot \sin (\pi \cdot ^{2}J({\rm NC^{\alpha}})\cdot T)\\ \end{aligned} $$
whereas the amplitudes of the undesired magnetization transfers are
$$ \begin{aligned} \alpha&: 2{\rm A}_{i}^{z}{\rm N}_{i+1}^{z} \cos (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot2\Updelta)\cdot \cos (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot T)\cdot\\ &\quad\cdot \cos (\pi \cdot ^{1}J({\rm NC^{\alpha}})\cdot T)\cdot \cos (\pi \cdot ^{2}J({\rm NC^{\alpha}})\cdot T) \\ \beta&: 2{\rm A}_{i}^{z}{\rm N}_{i+1}^{z} \sin (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot2\Updelta)\cdot \sin (\pi \cdot J({\rm C^{\alpha}C^{\beta}})\cdot T)\cdot\\ &\quad \cdot \cos (\pi \cdot ^{1}J({\rm NC^{\alpha}})\cdot T)\cdot \cos (\pi \cdot ^{2}J({\rm NC^{\alpha}})\cdot T).\\ \end{aligned} $$
Next, the 2AiαNiz operators are converted to the −2AizNiy (or 2AizNix created to achieve quadrature detection in States manner) term which is labeled by the 15N chemical shift during the constant time period \(2\Updelta_{7}=32\) ms incorporating the appropriate time domain incrementation (t3). Simultaneously, the anti-phase terms −2AiαNiy (2AizNix) with the amplitudes α and β are refocused with respect to the 1J(NCα) coupling and the NC′ anti-phase magnetizations are allowed to built up for the subsequent N \(\rightarrow \hbox{C}^{\prime}\) transfer. The value of T = 48.6 ms for the duration of the whole building block (time points “a”–“d”) was found to be optimal for the promotion of the desired transfer. The transfer efficiencies for particular pathways are plotted as functions of the evolution time in Fig. 6a. A comparison of the CiαNi transfer amplitudes of the originally designed 3D CBCANCO experiment (Bermel et al. 2006c, 2009a) with the 4D 1J(NCα)-selective HCBCANCO experiment presented here is depicted in Fig. 6b. Neglecting relaxation, the graphs reveal 1.7 times higher efficiency of the transfer amplitude when the two-bond coupling 2J(Ni+1 Ciα) coherence pathway is suppressed. When the relaxation is considered, the longer evolution imposed by the proposed suppression element lowers this gain and provides improvement of sensitivity only for proteins with T2eff ≥ 50.0 ms.
Fig. 6

Transfer efficiencies for the desired (green solid and dashed curves for the α and β pathway, respectively) and undesired (red solid and dashed curves for the α and β pathway, respectively) magnetization transfer (a). The transfer amplitudes of the Cα,iNi transfer as designed in the original application (blue solid and dashed curves for the α and β pathway, respectively) (Bermel et al. 2006c, 2009a) and the application proposed here (green solid and dashed curves) (b). The amplitudes corresponding to the applied delay lengths are marked by the vertical bars. The values of 1J(NCα) = 11.0 Hz, 2J(NCα) = 7.0 Hz, J(CαCβ) = 35.0 Hz (Sattler et al. 1999) were used to plot the graphs

The implementation of the non-uniform sampling of the indirectly detected dimensions t1, t2, and t3 allowed to extend the maximal acquisition times to 8, 7, and 40 ms, respectively, without a need to increase the number of the indirectly detected points. As a result, 4D spectra with high resolution were obtained within 31 and 69 h for the HCBCACON and HCBCANCO experiments, respectively, representing thus only 0.6 and 1.9 % of the experimental time which would be needed for acquisition of the linearly sampled experiments with a similar resolution.

The non-uniformly sampled data were processed using Sparse Multidimensional Fourier Transform (SMFT) (Kazimierczuk et al. 2009). This method does not recover the full high-dimensional spectrum. Instead, a set of cross-sections with lower dimensionality is calculated at the specific positions of the high-dimensional data set (Kazimierczuk et al. 2010; Zawadzka-Kazimierczuk et al. 2010; Nováček et al. 2011). In case of the 4D HCBCACON and HCBCANCO experiments, a set of Hα/β, Cα/β 2D cross-sections (Fig. 7) was calculated for all pairs of \({\rm C}^{\prime}_{i-1}, {\rm N}_i\) resonance frequencies identified in the 2D (HCBCA)CON spectrum. Then, the peak picking was performed on the particular cross-sections and the Hiα, Ciα/β, Hi-1α/β, Ci-1α/β resonance frequencies were allocated to each \({\rm C}^{\prime}_{i-1}, {\rm N}_i\) correlation signal. Finally, the sequential assignment was performed via matching the Hα/β, Cα/β resonance frequencies using both a simple UNIX shell script and visual inspection.
Fig. 7

The examples of the 2D cross-sections from the 4D HCBCACON experiment (a) and HCBCANCO experiment (b) calculated at the position of the R422C-P423N resonance in the 2D (HCBCA)CON spectrum (δ(13C′) = 174.024 ppm, δ(15N) = 137.080 ppm)

Fourier transform of sparsely sampled NMR data leads to processing artifacts commonly termed as a sampling noise. A number of sophisticated methods have been developed to remove the sampling artifacts (Coggins and Zhou 2007, 2008; Stanek and Koźmiński 2010). None of these methods had to be utilized in the present application providing thus an evidence of a very high sensitivity which allowed us to unambiguously identify the signals in the spectra containing both the thermal and the sampling noise. It has to be noted that a significantly reduced number of correlation peaks due to the suppressed 2J(Ni+1Ciα) coherence pathway greatly reduced the amount of the sampling noise in the 4D HCBCANCO experiment.

The 2D cross-sections from the 4D HCBCACON (Fig. 7a) and 4D HCBCANCO (Fig. 7b) for signals correlating the R422 carbonyl and P423 nitrogen atoms to their Hα/β and Cα/β resonances are shown to manifest simplicity of the analysis. Figure 7b documents a particular usefulness of the proposed experiments for the assignment of proline rich sequences. The proline residues are recognized by well separated Hβ2 and Hβ3 chemical shifts even in IDPs, in contrast to most of other amino acids with two Hβ protons, where the high mobility of the IDPs causes the Hβ chemical shift averaging (R422 in Fig. 7a). Since the Hβ2 and Hβ3 chemical shifts in all prolines of WIPc are well distinguished, the full potential of five resolved resonances—Hβ2, Hβ3Cβ, Hα, and Cα—to provide sequential assignments could have been exploited. As a result, all residues in the WIPc construct containing 26 % proline residues in the primary structure were successfully identified. The analysis of the retrieved chemical shifts also revealed why the assignment using the standard 3D experiments failed. The high content of repetitive sequences in WIPc results in severe clustering of the chemical shifts. The sequential assignments in 3D experiments rely on the resolution of the Cα and Cβ chemical shifts. The combined Cα and Cβ chemical shifts of two amino acids i and j with the most similar frequencies \(\Updelta_{\rm CC} = \sqrt{({\rm C}^{\beta}_{i}-{\rm C}^{\beta}_{j})^2+({\rm C}^{\alpha}_{i}-{\rm C}^{\alpha}_{j})^2}\) were found to be less than 10 Hz for 36 amino acids residues. In contrast, when the Hα and Hβ data measured in the 4D experiments were also included in the combined chemical shift calculations, the differences \(\Updelta_{\rm HHCC} = \sqrt{({\rm C}^{\beta}_{i}-{\rm C}^{\beta}_{j})^2+({\rm C}^{\alpha}_{i}-{\rm C}^{\alpha}_{j})^2 + ({\rm H}^{\beta}_{i}-{\rm H}^{\beta}_{j})^2+({\rm H}^{\alpha}_{i}-{\rm H}^{\alpha}_{j})^2}\) smaller than 10 Hz were identified for only 5 amino acid residues.

The complete sequential assignment of the WIPc construct was achieved using 4D HCBCACON and 4D HCBCANCO with the exception of residues H402, H403, H404 from the N-terminal His-tag, which did not provide any signal in the 2D CON spectrum. In addition, the 4D HCBCANCO spectrum lacked some of the Hα/β, Cα/β resonance frequencies of residues W450-E451-S452. We attribute this to decreased backbone dynamics in this region, suggested by the fact that peaks corresponding to the 446–456 segment were considerably broadened in the 2D CON spectrum. We were able to overcome this in straightforward manner using the more sensitive proton-detected 3D HNCACB and HNCO experiments which with the benefit of the available 97 % assignment afforded the missing Cα/β chemical shifts. In contrast to somewhat less-sensitive 4D HCBCANCO, the 4D HCBCACON experiment provided all chemical shifts needed for the secondary structure determination from a single spectrum.

Conclusions

Two complementary 4D experiments (HCBCACON, HCBCANCO) for the sequential assignment of intrinsically disordered proteins have been presented. The experiments combine several approaches to minimize the time necessary to acquire the data and maximize the resolution in the spectra (\(^{13} {\rm C}^{\prime}\) direct detection, non-uniform sampling, longitudinal relaxation optimization, selective 1J(NCα) transfer). Thanks to the choice of the correlation scheme, the sequential connectivity is encoded in up to five distinct frequencies (Hiα, Hiβ3, Hiα, Ciβ, and Ciα) and the experiments are well suited for the assignment of the proline rich proteins. The fact that all the chemical shifts employed for the secondary structure estimation are obtained from a single spectrum allows to avoid the problem of systematic deviations in the resonance frequencies (e.g., due to the different sample heating) that may occur when multiple spectra are used. The application of the experiments led to a complete sequential assignment of the 12.8 kDa WIPc protein with 26 % of proline residues (BMRB 18265).

Notes

Acknowledgments

This work was supported by the project "CEITEC - Central European Institute of Technology" from European Regional Development Fund, grant number CZ.1.05/1.1.00/02.0068, (J. N., L. Z., and V. S.) and by the Czech Science Foundation, grant numbers P206/11/0758 (J. N., L. Z., and V. S.). J.H.C. acknowledges the support of a Legacy Heritage personal grant by the Israel Science Foundation. Financial support by the Access to Research Infrastructures activity in the 7th Framework Programme of the EC (Contract 228461, EAST-NMR) for conducting the research is gratefully acknowledged. The project is a part of Joint Research Activity in the 7th Framework program of the EC (BioNMR n. 261863).

Supplementary material

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Jiří Nováček
    • 1
  • Noam Y. Haba
    • 2
  • Jordan H. Chill
    • 2
  • Lukáš Žídek
    • 1
  • Vladimír Sklenář
    • 1
  1. 1.Faculty of Science, NCBR, and CEITECMasaryk UniversityBrnoCzech Republic
  2. 2.Department of ChemistryBar Ilan UniversityRamat GanIsrael

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