Structural Dynamics of the Potassium Channel ... - ACS Publications

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Structural Dynamics of the Potassium Channel Blocker ShK: SRLS Analysis of 15N Relaxation Eva Meirovitch,*,† Oren Tchaicheeyan,† Inbal Sher,‡ Raymond S. Norton,§ and Jordan H. Chill‡ †

The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan 52900, Israel Chemistry Department, Bar-Ilan University, Ramat-Gan 52900, Israel § Medicinal Chemistry, Monash Institute of Pharmaceutical Sciences, Monash University, Parkville, Victoria 3052, Australia ‡

S Supporting Information *

ABSTRACT: The 35-residue ShK peptide binds with high affinity to voltage-gated potassium channels. The dynamics of the binding surface was studied recently with (microsecond to millisecond) 15N relaxation dispersion and (picosecond to nanosecond) 15N spin relaxation of the N−H bonds. Relaxation dispersion revealed microsecond conformationalexchange-mediated exposure of the functionally important Y23 side chain to the peptide surface. The spin relaxation parameters acquired at 14.1 and 16.45 T have been subjected to model-free (MF) analysis, which yielded a squared generalized order parameter, S2, of approximately 0.85 for virtually all of the N−H bonds. Only a “rigid backbone” evaluation could be inferred. We ascribe this limited information to the simplicity of MF in the context of challenging data. To improve the analysis, we apply the slowly relaxing local structure (SRLS) approach, which is a generalization of MF. SRLS describes N−H bond dynamics in ShK in terms of a local potential, u, ranging from 10 to 18.5 kBT, and a local diffusion rate, D2, ranging from 4.2 × 108 to 2.4 × 1010 s−1. This analysis shows that u is outstandingly strong for Y23 and relatively weak for K22, whereas D2 is slow for Y23 and fast for K22. These observations are relevant functionally because of the key role of the K22−Y23 dyad in ShK binding to potassium channels. The disulfide-bond network exhibits a medium-strength potential and an alternating wave-like D2 pattern. This is indicative of moderate structural restraints and motional plasticity, in support of, although not directly correlated with, the microsecond binding-related conformational exchange process detected previously. Thus, new information on functionally important residues in ShK and its overall conformational stability emerged from the SRLS analysis, as compared with the previous MF-based estimate of backbone dynamics as backbone rigidity.

1. INTRODUCTION The potassium channel blocker ShK, isolated from the sea anemone Stichodactyla helianthus, is a 35-residue peptide (Mr 4.06 kDa) stabilized by three disulfide bonds.1 ShK is of great pharmaceutical interest, as it blocks voltage-gated channels with picomolar Kd values. The Kv1.3 channel is of particular interest, being upregulated during the activation of effector memory Tcells. The latter are important in autoimmune diseases such as multiple sclerosis, rheumatoid arthritis, and type I diabetes.2 ShK analogues, designed to block selectively the Kv1.3 channel over the Kv1.1 channel, are currently being evaluated as therapeutics for these diseases.3,4 In a 33-residue segment spanning the peptide binding sites on these channels only six residues are different, with only four being nonconservatively substituted. Thus, Kv1.3 selectivity over Kv1.1 must be associated with subtle differences between the interaction patterns of ShK with Kv1.3 and Kv1.1. Quite a few studies have addressed the binding properties of ShK with Kv1.3 and Kv1.1. This has been pursued from the perspective of the channel interface,5−7 the peptide-channel complex,8 and ShK itself.9−12 Here we focus on the ShK © 2015 American Chemical Society

peptide employing NMR spin relaxation, and the slowly relaxing local structure (SRLS) approach13 as a theoretical model for treating structural dynamics. As shown below, this approach has the potential to provide important information that could not be revealed previously. Although ShK comprises only 35 residues it represents a stable folded domain. Its 3D structure, determined previously by both X-ray crystallography9 and NMR,10 is stabilized by the three disulfide bonds, linking residues 3−35, 12−28, and 17− 32. The ShK backbone adopts an extended conformation from residue 3 to residue 8, connected through a pair of interlocking turns to the relatively short α-helical segments 14−19 and 21−24. The latter are separated by a distinct bend at residue 20. The region 25−30 is unstructured and the C-terminal residues 31−34 form a turn−turn motif capped by the C-terminal residue C35, which forms a disulfide bond with residue 3 of the extended N-terminal segment. Figure 1 shows a ribbon diagram Received: August 13, 2015 Revised: November 8, 2015 Published: November 9, 2015 15130

DOI: 10.1021/acs.jpcb.5b07875 J. Phys. Chem. B 2015, 119, 15130−15137

Article

The Journal of Physical Chemistry B

circumstances imply limited field dependence of both R1 and R2, imposing stringent demands on the accuracy of the experimental measurements. Based on this it is reasonable to proceed by replacing the simple MF method with an enhanced theoretical approach. We developed in recent years the two-body coupled-rotator slowly relaxing local structure (SRLS) approach23−25 for the analysis of NMR relaxation in proteins.13,26−28 The two bodies are in this case the globally reorienting protein and the locally reorienting probe. SRLS is a generalization of MF, yielding the latter in simple limits. The major enhancements are: (1) In SRLS the physical parameters are represented in terms of their tensorial properties, whereas in MF they assume their simplest (scalar) form; this generalization is always important. (2) SRLS accounts rigorously for dynamical coupling between the motion of the protein and the motion of the probe, whereas in MF mode-coupling is ignored; this feature is important when the time scale separation between the two motions is small. Here we have applied SRLS to the 15N relaxation data of ShK and find that N−H bond dynamics can be characterized by a local potential, u, exerted by the immediate (internal) protein surroundings at the site of the motion of the N−H bond, and a local diffusion rate, D2, describing the local motion of the N−H bond. The potential, u, is found to range from 10 to 18.5 kBT, whereas D2 is found to range from 4.2 × 108 to 2.4 × 1010 s−1. Among the residues not involved in microsecond conformational exchange, K22 is associated with relatively weak local potential and the fastest local motion, whereas Y23 is associated with the strongest local potential and the slowest local motion. These results are of interest because of the role ascribed to the K22−Y23 dyad in the ShK/channel binding process. The disulfide-bond network exhibits medium-strength potential and an alternating wave-like D2 pattern. This is consistent with moderate structural restraints combined with motional plasticity in support of, although not directly correlated with, recently revealed12 microsecond conformational exchange.

of the ShK backbone based on the solution structure (PDB accession code 1ROO).10

Figure 1. Structure of ShK. Top, ribbon model (blue) of the ShK structure based upon PDB entry 1ROO10 showing the three crosslinking disulfide bonds (yellow). Bottom, ShK amino acid sequence showing the linked Cys residues. The helical segments are shown as blue cylinders above the sequence.

The K-channel binding site on ShK is well characterized.5−8 Residues K22 and Y23 are key elements, with R11, H19, S20, and R29 also being important. K22 is ascribed the role of consolidating electrostatic interactions in the ion conduction pathway,14,15 whereas Y23 mediates hydrophobic interactions with aromatic residues on the channel.14−16 However, from a structural point of view, Y23 is quite sequestered from the channel-interacting surface of the peptide. Important information in this regard was provided by a recent 15N relaxation dispersion study, where it was found that the major ShK conformer is involved in microsecond conformational exchange with a minor conformer.12 Assuming that in the latter the side chain of Y23 is surface-exposed, conformational-selection in the binding process via equilibrium-shift toward the minor conformer was suggested.12 The picture delineated above warrants further detailed investigation of the dynamic structure of ShK. A powerful method in this context is NMR spin relaxation, associated inherently with picosecond to nanosecond dynamics and in a broad scope with local structure and geometry.13,17−19 In the previous study,12 experimental 15N R1 = 1/T1, R2 = 1/T2 (where T1 denotes the longitudinal 15N relaxation time and T2 the transverse 15N relaxation time) and 15N−{1H} NOE data were acquired at magnetic fields of 14.1 and 16.45 T, and the simple model-free (MF) method20,21 was used to analyze these data. MF yielded a virtually constant profile of the squared generalized order parameter, S2, on the order of 0.85. Only a “rigid backbone” evaluation could be inferred from this analysis. Allowing for conformational/chemical-exchange-related contributions to the NMR line width, residues K9, K18, H19, M21, L25, T31, G33, and T34 were associated with conformational exchange.12 The MF results presented above are based on separate analyses of the 14.1 and 16.45 T data. The combined two-field data yielded problematic statistics, which is quite unusual, as MF analyses of two-field19 (and even three-field)22 data can typically be accomplished with good statistics. This led us to assume that the difficulties encountered stem for the simple nature of MF combined with the fact that the main R1 component, which is also a dominant R2 component, is near its maximum at both magnetic fields (see below). These

2. THEORETICAL SUMMARY The slowly relaxing local structure approach23−25 has been applied to NMR relaxation in proteins13,26−28 as a two-body coupled-rotator approach. The globally reorienting protein represents an unrestricted rotator and the locally reorienting probe a restricted rotator. The local spatial restrictions experienced by the mobile probe are imposed by the mobile protein in the form of a coupling/ordering potential. As both rotators (protein and probe) are moving, their rotational degrees of freedom are statistically dependent (coupled).23 In the limit of large time scale separation between the two motions, one may consider these degrees of freedom to be statistically independent (decoupled).23 In the relaxation limit applicable to proteins in aqueous solution,13,26−28 the physical picture described above is substantiated in terms of a Smoluchowski operator. The corresponding Smoluchowski equation is solved. The solution consists of generic time correlation functions (TCFs) given by the spherical harmonics of rank, L, and order, K. These TCFs are subjected to Fourier transformation to yield the corresponding generic spectral densities. The real parts of the latter are linearly combined into the measurable spectral densities according to the local geometry, given in this case by the relative orientation of the local diffusion/local ordering tensor and the magnetic 15N−1H dipolar and 15N chemical shift anisotropy (CSA) tensors.29,30 15131


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Figure 2. Experimental 15N R1, 15N R2, and 15N−{1H} NOE acquired at 14.1 T (black) and 16.45 T (red), and 293 K. Taken from ref 12.

Figure 3. Best-fit values of the potential coefficient c20 (part a), the axial order parameter S20 (part b), and log(D2, s−1) (part c), as a function of residue number. The residues depicted in red in part c have been associated with microsecond conformational exchange.12 The errors are estimated at 5% for c20 and S20 and 10% for D2. In the calculations shown in this figure and all subsequent figures we used an 15N CSA value of −172 ppm, rNH = 1.015 Å, and a −17° tilt between the 15N−1H dipolar and 15N CSA tensors.13,26−28,34−37

where θ is the angle between the principal axis of the ordering tensor, S (with principal value S20 = ⟨D200(0,θ,0)⟩), and the local director frame (given in this case by the equilibrium orientation of the N−H bond). The coefficient c20 evaluates the strength of the local potential; S20 is given by

The exact potential is given by expansion in the full basis set of the spherical harmonic functions.13,26−28 This expression is clearly not practical, as it comprises an infinite number of coefficients; it has to be truncated. Here we preserve only the lowest (L = 2) axial (K = 0) term obtaining the Maier−Saupe potential: u(θ ) ≅

2 −c02D00

=

⎛1⎞ −c02⎜ ⎟[3(cos ⎝ ⎠ 2

2 ⟨D00 (0,θ ,0)⟩ =

2

θ ) − 1]

(1) 15132

∫ D002(0,θ ,0)e−u(θ) sin θ dθ ∫ e−u(θ) sin θ dθ

(2)


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Figure 4. Average values of c20 (part a) and of log(D2, s−1) (part b) for the distinct structural elements of ShK. These data have been calculated from Figure 3 after excluding the exchange-associated residues. The errors are estimated at 5% for c20 and 10% for log(D2, s−1).

16.45 T data yielded unduly large S2 values, often exceeding 0.95, also with good statistics. These results are rationalized as follows. The original MF spectral density20 can fit the 14.1 T data with no conspicuous problems. It force-fits the 16.45 T data (i.e., it leads to good statistics but unrealistic parameters). This is a consequence of the approximate treatment of the local motion, which makes a larger relative contribution at higher magnetic fields − cf. the form of the original MF spectral density. Nevertheless, when combined with the 14.1 T data, the 16.45 T data degrade the statistics but largely preserve the S2 profile. Thus, the latter, shown in Figure 3D of ref 12, properly reflects the information that can be extracted with MF from the two-field data. However, it is clear that the 16.45 T data comprise additional information. Toward extracting it, the analysis could be enhanced within the scope of model-free by using the extended MF (EMF) spectral density.21 The DYNAMICS fitting scheme used in ref 12 features eight models. The analysis starts with model 1, where only S2 is allowed to vary. If the statistics are unfavorable, then model 2, where S2 and τe are allowed to vary, will be applied, etc. Models 1−4 are associated with the MF spectral density whereas models 5−8, with the EMF spectral density. Models 5−8 are generally applicable to combined twofield (in this case, 14.1 and 16.45 T) data sets. However, as pointed out above, for the two-field data set χ2 was too large even for model 1; it was totally unacceptable for models 5−8. Utilizing an extended version of the two-parameter MF spectral density is clearly the method of choice. SRLS, as used herein, is just that. 3.2. Experimental Data. Panels a−c of Figure 2 show R1 and R2 of the 15N nucleus and 15N−{1H} NOE, acquired in ref 12 at 14.1 T (black) and 16.45 T (red). The NOEs exhibit similar and clearly distinguishable patterns at 14.1 and 16.45 T (Figure 2c). This is not the case for the patterns exhibited by 15 N R1 and R2 (Figure 2a,b). As pointed out in section 3.1, this is consistent with the fact that ShK has a global motional correlation time τ1 = 2.4 × 10−9 s (see below), which yields ωN2τ12 ∼ 1 at both magnetic fields. This sets the spectral density J(ωN) near minimum, implying limited field depend-

In this study we assume that both rotators are isotropic. The rate for global tumbling of the peptide is D1 = 1/(6τ1), where τ1 is the correlation time for global motion. The diffusion rate for the local motion of the N−H bond is D2 = 1/(6τ2), where τ2 is the correlation time for local motion.

3. RESULTS AND DISCUSSION 3.1. Previous MF Analysis; Justification for SRLS Analysis. The theme of this article is reanalysis of 15N relaxation data from ShK with SRLS. Previous analysis was carried out in ref 12 with MF. That article focuses on conformational exchange; 15N relaxation is treated succinctly. To realize the need for reanalysis, and to justify the choice of SRLS as method, we describe below the MF analysis in further detail. For ShK, R1 is given primarily, and R2 to a large extent, by the spectral density component (τ1/(1 + ωN2τ12)) (where ωN denotes the 15N Larmor frequency). Given that ωN2τ12 is on the order of 1 for both ωN(14.1 T) and ωN(16.45 T), the experimental measurements have to be very accurate to properly distinguish between R1(14.1 T) and R1(16.45 T) on the one hand, and R2(14.1 T) and R2(16.45 T) on the other hand. Careful measurements12 yielded |R 1 (16.45 T) − R1(14.1 T)| on the order of the experimental error for many residues, and |R2(16.45 T) − R2(14.1 T)| varying from very small to quite large (Figure 2). To avoid overinterpretation of such challenging data, the authors of ref 12 utilized the simple MF spectral density.20 The latter comprises only two parameters qualifying the local motion: the squared generalized order parameter, S2, and the effective local motional correlation time, τe. As most residues have been ascribed τe = 0, the MF results consist of the S2 profile.12 The combined 14.1 and 16.45 T data yielded a nearly invariant S2 profile, with S2 on average equal to 0.85, typical of relatively rigid globular proteins. However, for many residues the statistics turned out to be unsatisfactory. In search of the underlying reasons single-field analyses were carried out. The 14.1 T data yielded a similar S2 profile with good statistics. The 15133


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as log(D2, s−1)). Distinction among parameters associated with different physical quantities is indicative of appropriate data fitting.13 According to ref 12, residues 9, 18, 19, 21, 25, 31, 33, and 34 are involved in microsecond conformational exchange. It can be seen that all of these residues, and only these residues, have low log(D2, s−1) values when the exchange process is not accounted for. That is, D2 “absorbs” the additional (to spin relaxation) dynamic effect. Our software allows for variable exchange contribution, Rex. However, within the scope of challenging data, such phenomenological addition to spin-relaxationassociated R2 is not recommended. Hence, we exclude the exchange-involved residues from the analysis. The remaining residues could be analyzed with 5% error in c20 and 10% error in D2. To minimize the effect of challenging 15N R1 and R2 data, we calculate average c20 and log(D2, s−1) values over the distinct structural elements. The latter include the regions 3−8 (extended segment), 9−13 (pair of interlocking turns), 14−19 (helix), 21−24 (helix), 25−30 (loop), and 31−34 (turn−turn). The results are shown in Figure 4 and discussed in detail below. The only chain segment that is not involved in disulfide bonds is the helix comprising residues 21−24. In this region the average local potential is strong ( = 15 kBT) and the average local motional rate is = 3 × 109 s−1. This is characteristic of helices in typical globular proteins.13,26−28,34−37 The bend at residue 20 has c20 = 15 kBT and D2 = 2 × 1010 s−1. The latter rate will be our benchmark for “fast” local motion. Helix 14−19 is associated with substantially weaker average local potential on the order of 11 kBT, as are all of the other chain segments associated with the disulfide-bond-network. ⟨c20⟩ ranges from 11.3 to 12.9, assuming a mean value of 12.1 ± 0.8. The error in ⟨c20⟩ is 5%; hence, the error in the mean value is ±0.6. Thus, it is appropriate to consider ⟨c20⟩ = 12.1 as representing medium-strength local potential prevailing in the entire disulfide-bond-associated network. D2 ranges from 1.6 × 109 s−1 (log(D2, s−1) = 9.2) in the chain segment 3−8 to 6.3 × 109 s−1 (log(D2, s−1) = 9.8) in the chain segment 25−30, assuming a mean value of 3.95 ± 2.35 s−1. The error in D2 is 10%; hence, the error in the mean value is ±0.4 s−1. In this case it is meaningful to distinguish among the D2 values associated with the individual structural elements. An alternating wave-like pattern in the D2 profile is clearly visible in Figure 4b. A similar observation based on residual dipolar and hydrogen-bond couplings (hence involving substantially slower local motions) has been reported for the β-sheet of an Igbinding domain of streptococcal protein G.38 That observation has been interpreted as correlated motion across the β-sheet of the protein G domain investigated. We offer tentatively a similar interpretation for the local dynamics across the disulfide-bond-associated network of ShK. It appears that we have revealed a flexible network of disulfide bonds that is not anchored by strong potentials and characterized by relatively slow correlated picosecond−nanosecond motion. The extended N-terminal region 3−8 is associated with outstandingly weak average local potential and slow average local motion. The average parameters shown in Figure 4 were obtained omitting seven residues engaged in millisecond−microsecond conformational exchange, proline at position eight, and six residues for which experimental data are not available. This kind of incompleteness is typical of analyses where collective properties are derived from localized measurements.38 Another

ence of R1 and R2, whose variation with the magnetic field is dominated by J(ωN) (note that the NOE does not depend on this spectral density). The differences between corresponding R1 values are often within experimental error (Figure 2a), and those between corresponding R2 values vary from zero to over 10 times the experimental error (Figure 2b). As noted above, these features, associated with inherent difficulties in measuring accurately very small changes in R1 and R2, render the respective data challenging. We account for the challenging nature of the experimental data by relaxing the statistical criteria and calculating averages over the distinct structural elements (Figure 4). Our data-fitting calculations feature six data-points and two adjustable parameters; they feature four degrees of freedom. The corresponding reduced χ2 for a critical value of 0.1 is 4.31 We accept χ2 values that exceed this threshold up to 3 times. To establish that allowing for larger χ2 is more appropriate than allowing for additional SRLS parameters to vary (an option discussed below), we carried out calculations where singular data points have been excluded from the data set used. This lowered χ2 but had a small effect on the emerging results, indicating that the larger-than-standard χ2 is very likely a consequence of challenging data rather than an oversimplified set of adjustable parameters. 3.3. Global Motion. In the MF-based 15N relaxation study the isotropic correlation time for global motion was estimated as 2.6 ns (the relatively small anisotropy in the global diffusion tensor, determined with hydrodynamics calculations, was found not to be important).12 We have calculated an average global motional correlation time of τ1 = 2.4 ns from the experimental ratios R2/R1 obtained at 14.1 and 16.45 T at 293 K. A previous 15 N relaxation study of the chicken villin headpiece subdomian (HP36), which comprises 36 residues, determined 2.5 ns as a correlation time for global motion at 295 K.32 As a conservative approach, we allowed τ1 to vary in the 2.4−2.6 ns range, and obtained the best results for 2.4 ns. This value has been used throughout the calculations reported below. 3.4. Local Motion. In analyzing the combined two-field data set we used 15N chemical shift anisotropy (CSA) of −172 ppm, N−H bond length of 1.015 Å, and 15N−1H dipolar/15N CSA tensor tilt of −17° (ref 13). With τ1 set equal to 2.4 ns, c20 and D2 were allowed to vary. The starting values of c20 have been taken from the 5−20 range. The starting values of D2 have been taken from the 5.0 × 108 to 5.0 × 1010 s−1 range. Note that the adjustable parameter set comprising c20 and D2 corresponds formally to model 2 in MF (cf. ref 33). As pointed out above, in principle, one might lower χ2 by allowing additional parameters to vary. To examine this option, we carried out calculations where the local ordering/local diffusion frame was allowed to be tilted from the magnetic frames, or the local diffusion tensor was allowed to be axially symmetric. Improvement of the analysis, consisting of both low χ2 and physically relevant results, was not obtained. This indicates that increasing the set of adjustable parameters within the scope of the data available is likely to imply overfitting. Figure 3 shows c20 (part a) and the logarithm of the local diffusion rate, D2 (part c) for all of the experimentally accessible N−H bonds of ShK. The order parameter, S20, is also shown (part b). Note that S20 is not an independent parameter; rather, it is calculated from c20 according to eqs 1 and 2. It can be seen that the profiles of the structure-related parameters, c20 and S20, are quite similar and differ qualitatively from the profile of the motion-related parameter, D2 (displayed 15134


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Figure 5. Same as Figure 3 with the exchange-associated residues excluded and the residues involved in ShK binding to the potassium channel depicted (red). The disulfide bonds (green dashed lines) and the pertinent Cys residues (green filled circles) are also depicted.

whereas the D2 [s−1] values are similar to the exception of C28 (Figure 5b). However, the picture emerging from Figure 4 with regard to the disulfide-bond network, based on average best-fit parameters, is not altered by residues C3 and C28 digressing from the mean. Let us examine the nature of these digressions. Nearly horizontal green lines in Figures 5a,b indicate that similar potential strengths and extents of local motion prevail at the N−H sites of chemically bonded cysteine residues. The C3− C35 line in Figure 5a, in particular C3, and the C12−C28 line in Figure 5b, in particular C28, are exceptions. C3 is located in the extended 3−8 chain segment, which has relatively small N−H-site-related c20 (Figure 5a); this factor dominates. C28 is located at the intersection of two interlocked loops (Figure 1). It appears that from a structural point of view rigidity, reflected by fast local fluctuations rather than slow local motion, is required at the N−H site of C28; this factor dominates. As shown in Figure 5b, as a result of this dominance log(D2, s−1) of C28 differs substantially from log(D2, s−1) of its neighbor, R29 (although in a loop, where these residues reside, such disparity is not so surprising). In summary, we find that the local motional rates exhibit an alternating pattern throughout ShK, with residue S20, located at the kink between the two helices, standing out in its increased local motional rate. We identify three degrees of local potential strength (cf. Figure 4a): (i) a weak potential in the Nterminal region, (ii) a medium-strength potential within the disulfide bond network, and (iii) a strong potential within the 21−24 helix (the only secondary structure element not involved in the disulfide-bond network). This picture, which quantitatively correlates physically well-defined parameters such as potential strength and motional rate with key elements of the ShK backbone, is to be compared with the MF picture evaluating the ShK backbone as “uniformly rigid”.12 A pictorial representation of our results appears in Figure 6, where the chain segments associated with strong, mediumstrength, and weak potentials are colored distinctively. The 3D ShK structure appears to feature a “rigid” anchor-point

issue to consider is the relation between the average values and fluctuations therein. If the same factor dominates all of the constituents of a given average, the fluctuations will be small. If different factors imposing contrasting behavior dominate different constituents, the fluctuations will be large. For ShK the latter case applies in quite a few cases, as shown below for the pairs K22/Y23 (Figure 5) and C28/R29 (Figure 5b). Figure 4 has been generated to find out whether averaging over the various factors yields collective parameters informative in a comparative sense. As shown above, the answer to this question is affirmative for ⟨D2⟩ and negative for ⟨c20⟩ of the disulfidebond-network. To avoid losing information relevant to potassium channel binding, we show in Figure 5 the best-fit c20 and log(D2, s−1) values for the individual N−H bonds, with the residues involved in binding depicted in red. Y23 exhibits the strongest potential and the slowest local motion whereas K22 exhibits medium-strength potential and the fastest local motion. K22 is believed to provide electrostatic interactions by becoming inserted into the potassium channel. To function effectively, this residue has to feature structural adaptability, which is consistent with the relatively weak local N−H potential, and fast localized (i.e., independent) N−H fluctuations. Y23, which promotes interaction with hydrophobic residues of the potassium channel, appears to be robustly backbone-anchored, as indicated by its strong local N−H potential. Y23 exhibits relatively slow local motion at its N−H site. Slow picosecond− nanosecond motions are often collective in nature.39 The observed behavior of the pair K22/Y23 is not anticipated either by the correlations strong ordering/fast motion and weak ordering/slow motion19 or by the fact that K22 and Y23 are adjacent in the 21−24 helix. The observed c20 and log(D2, s−1) values of K22 and Y23 serve well their biological role. Thus, effective biological performance overcomes in this case all of the other factors. The disulfide bonds (green dashed lines) and the pertinent Cys residues (green filled circles) are also depicted in Figure 5. The c20 values are similar to the exception of C3 (Figure 5a), 15135


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dynamics of residues not involved in conformational exchange has been characterized in terms of a local potential, u, and a local diffusion rate, D2. The potential varies from 10 to 18.5 kBT and D2 varies from 4.2 × 108 to 2.4 × 1010 s−1. K22 exhibits weak local N−H potential and fast local motion, whereas Y23 exhibits outstandingly strong local potential and slow local motion. These findings provide new information on the K22− Y23 dyad, which plays a key role in the channel-binding process. The disulfide-bond-associated N−H sites form a network characterized by medium-strength potential and a standing-wave-like pattern of local motional rates. This is consistent with a ShK structure capable of adapting (in terms of local structure and dynamic plasticity) to different experimental conditions. Averaging parameters over distinct structural elements is very useful when the data are inherently challenging.

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Figure 6. Schematic representation of SRLS-based local restriction and motional rates in ShK. Residues are numbered from N- to C-terminus, and disulfide bonds are depicted as yellow sticks. The polypeptide backbone is color coded with red, orange, and green indicating weak, medium-strength, and strong potentials, respectively. S20 and C35, which exhibit fast local motion, are designated with red arrows.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b07875. Summary of the slowly relaxation local structure approach for 15N relaxation in proteins is provided. Complete references 2, 4, and 8 (PDF).

comprising the largely structurally confined helix 21−24, and the rapidly fluctuating residue S20. From it extends the both structurally and dynamically not-so-“rigid” disulfide network, capped by the least “rigid” N-terminal segment. 3.5. Comparison between SRLS and MF. Let us compare in detail the SRLS-based picture with the MF-based picture. SRLS characterizes each distinct structural element of ShK in terms of a spatially restricting local potential, u, and a rate of local N−H motion, D2. MF does not distinguish among different structural elements. SRLS provides information that may be associated with the role of the K22−Y23 dyad in the potassium channel binding process, as well as the structural dynamics of the disulfide-bond-network that stabilizes the ShK structure. No such inferences can be deduced from the MF analysis. SRLS provides physically well-defined parameters. MF provides the empirical squared generalized order parameter, S2. As shown previously, S2 is a construct given by40 1 2 2 S2 = (S02) + (S22) 2 where S20 and S22 are the axial and rhombic order parameters associated with the second-rank ordering tensor, S. The physical meaning of S2 is unclear. The reasons for better performance of SRLS as compared to MF are as follows. The global motional rate is D1 = 6.94 × 107 s−1. The slowest (individual) local motional rate is D2 = 4.2 × 108; hence, the time scale separation is D1/D2 = 0.165. Modecouplingaccounted-for in SRLS and ignored in MFis important for D1/D2 > 0.01.13,26−29,34−37 SRLS accounts for the noncollinearity of the 15N CSA and 15N−{1H} dipolar tensors, whereas MF does not do so. For these reasons SRLS-based analysis of the 15N relaxation data of ShK yielded informative quantitative results whereas MF yielded only a general assessment of backbone rigidity.

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AUTHOR INFORMATION

Corresponding Author

*E. Meirovitch. E-mail: [email protected]. Phone: 972-3531-8049. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Shih Chieh Chang (Monash University, Parkville, Australia) for preparation of the 15N-labeled ShK sample. This work was supported by the Israel−U.S.A. Binational Science Foundation (Grant No. 2010185 to E.M. and Jack H. Freed), and the Israel Science Foundation (Grant No. 437/11 to E.M.). J.H.C. acknowledges support from the Christians for Israel Chair for Medical Research. R.S.N. acknowledges the award of a fellowship by the National Health and Medical Research Council of Australia.

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REFERENCES

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4. CONCLUSIONS The experimental 15N relaxation parameters of ShK are inherently challenging. By applying SRLS conservatively, we have obtained new information associated with structural and dynamic properties of this important peptide. N−H bond 15136


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