Accessibility of Nitroxide Side Chains: Absolute Heisenberg Exchange Rates from Power Saturation EPR

Abstract

In site-directed spin labeling, the relative solvent accessibility of spin-labeled side chains is taken to be proportional to the Heisenberg exchange rate (W_ex) of the nitroxide with a paramagnetic reagent in solution. In turn, relative values of W_ex are determined by continuous wave power saturation methods and expressed as a proportional and dimensionless parameter Π. In the experiments presented here, NiEDDA is characterized as a paramagnetic reagent for solvent accessibility studies, and it is shown that absolute values of W_ex can be determined from Π, and that the proportionality constant relating them is independent of the paramagnetic reagent and mobility of the nitroxide. Based on absolute exchange rates, an accessibility factor is defined (0 < ρ < 1) that serves as a quantitative measure of side-chain solvent accessibility. The accessibility factors for a nitroxide side chain at 14 different sites in T4 lysozyme are shown to correlate with a structure-based accessibility parameter derived from the crystal structure of the protein. These results provide a useful means for relating crystallographic and site-directed spin labeling data, and hence comparing crystal and solution structures.

INTRODUCTION

SDSL has become a powerful tool for probing structure and dynamics of both water-soluble and membrane proteins of arbitrary molecular weight (1–8). The basic strategy of SDSL involves the substitution of a native residue (or residues) for cysteine, followed by modification of the reactive SH group with a selective nitroxide reagent. The most commonly employed reagent is the methanethiosulfonate derivative that generates the disulfide-linked nitroxide side chain, designated R1 (Fig. 1).

FIGURE 1.

The reaction of the spin label with a cysteine to generate the nitroxide side chain R1.

The primary features determined from the EPR spectrum of R1 in a protein are the side-chain motion (9), the Heisenberg exchange rate with paramagnetic reagents in solution (10), and, for proteins containing two paramagnetic centers, the interspin distance (11–14). The Heisenberg exchange rate with suitable paramagnetic reagents has been interpreted in terms of side-chain solvent accessibility, one of the most informative features of the protein fold. For example, the periodic dependence of solvent accessibility with sequence position serves as an independent means of mapping regular secondary structure, and comparison of solvent accessibilities determined by SDSL and computed from crystal structures provide a direct means of comparing solution and crystal structures of a protein (5,15).

Heisenberg exchange between a nitroxide and an “exchange reagent” R requires a direct contact interaction in an encounter complex, and the exchange rate, W_ex, is taken to be a measure of the exposure of the nitroxide to the solvent containing the reagent. For measurement of solvent accessibility, the reagent should have high water solubility, have limited accessibility to the interior of a well-packed protein, should be electrically neutral, and should be on the order of the size of the nitroxide itself. It is also important that the exchange between the nitroxide and R be in the strong exchange limit, where the rate is determined only by the rate of diffusional encounter and not on details of the encounter complex (16). Finally, it is important that the only manifestation of the reagent/nitroxide interaction is Heisenberg exchange, with little contribution from distance-dependent magnetic dipolar interactions. Otherwise, an interaction could occur through space providing an overestimate of solvent accessibility. This is insured for reagents with T_1R < τ_c, where T_1R is the longitudinal relaxation time for the reagent and τ_c is the encounter complex lifetime. In this work, it is shown that the complex NiEDDA meets the above criteria as an ideal exchange reagent for determining solvent accessibility.

Heisenberg exchange rates for nitroxide side chains in proteins are most commonly measured using CW power saturation. With some assumptions, the saturation behavior of the nitroxide can be analyzed to provide a widely used “accessibility parameter”, Π, which is directly proportional to W_ex (17,18):

One of the key results of the present study is the determination of the constant α, thus allowing the calculation of absolute exchange rates from experimental values of Π. The values of W_ex thus determined for R1 residues in T4L are shown to agree closely with corresponding values measured directly with saturation recovery EPR and reported in a companion paper (19). The correspondence holds for a wide range of spectral lineshapes for R1, thus validating the CW saturation method for determining absolute exchange rate. Collectively, the results are in agreement with the theoretical conclusions of Haas et al. (20) that CW saturation curves should provide a quantitative measure of T_1e in nitroxides, even with inhomogeneously broadened lines. Finally, a structure-based measure of R1 solvent accessibility in proteins is introduced that correlates with W_ex and a related accessibility factor (ρ) for both NiEDDA and oxygen as exchange reagents.

MATERIALS AND METHODS

T4L mutants and EPR spectroscopy

T4 lysozyme mutants containing the R1 side chain were previously reported (21). NiEDDA was synthesized according to Oh et al. (18). EPR spectra were recorded on a Varian E-109 spectrometer fitted with a two-loop-one-gap resonator (22) over a field range of 100 G. Samples were contained in gas permeable TPX capillaries and equilibrated with either air for Heisenberg exchange measurements with oxygen, or equilibrated with nitrogen in all other cases. For CW power saturation measurements, the central line was recorded as a function of microwave power and the peak to peak first derivative amplitude analyzed as described to obtain the accessibility parameter Π (18).

To measure the Lorentzian line broadening in EPR spectra, the broadened first-derivative spectrum was fitted as a convolution of the first-derivative spectrum in the absence of R and a Lorentzian broadening function, using a Levenberg Marquardt fitting procedure written in LabVIEW (National Instruments, Austin, TX). The three adjustable parameters were the: 1), Lorentzian width at half-height (ΔH_1/2); 2), field position offset; and 3), area of the Lorentzian. Because the two spectra are well aligned and contain a similar number of spins, the position offset was always close to zero and the area close to 1 as expected. The best fit width is directly related to the additional broadening caused by Heisenberg exchange according to W_ex = 0.5γΔH_1/2 (see below). A similar method was used by Smirnov et al. (23) to measure oxygen broadening. In this case, measurements in the absence and presence of oxygen can be done on the same sample under identical settings with only dH_1/2 as an adjustable parameter. In the case of NiEDDA, two different samples are required and the additional area and shift parameters are required to account for small dilution and field offsets errors.

Estimation of nitroxide side-chain solvent accessibility from a crystal structure

The fractional solvent-exposed surface area (f_SA) for the native amino acid at each sequence position was calculated from the crystal structure using the program Molmol (24). A structure-based accessibility parameter f_V (fractional volume) characteristic of a given site without the side chain, was calculated from the crystal structure using InsightII software (Accelrys, San Diego, CA). First, the amino acid was replaced by glycine. A spherical volume centered at the α-carbon with radius 8 Å was filled with water, and all water molecules that overlap with the protein structure removed. The number of remaining water molecules was divided by their original count, yielding an estimate of the free fractional volume near the site of interest that is potentially accessible to the R1 side chain.

THEORY

Heisenberg exchange rates and nitroxide side-chain accessibility

For a bimolecular encounter between a small nitroxide (N) in solution and an exchange reagent R, the Heisenberg exchange frequency, W_ex, experienced by a particular nitroxide is given by

(1)

where k_ex is the exchange rate constant and C_R is the concentration of R. In the strong exchange limit, where Heisenberg exchange is diffusion controlled, k_ex is given by (cgs units)

(2)

where P_max is the maximum exchange efficiency, f is the “steric factor”, k_D = 4π(N_A/1000) (D_N + D_R) r_c is the diffusion-controlled rate constant, and D_N and D_R are the diffusion constants for the nitroxide and reagent, respectively. The collision radius, r_c, is r_N + r_R, where r_N and r_R are the effective radii of the nitroxide and reagent, respectively. The dimensionless steric factor is necessary to account for exchange between molecules where particular relative orientations are required for exchange. When the encounters are in the strong exchange limit and T_1R < τ_c, P_max = 1 (16). This is apparently the case for O₂ (25) and, as discussed below, for NiEDDA.

For a nitroxide tethered to a protein, it is assumed that the nitroxide translational diffusion coefficient becomes that of the protein itself, comparatively very small, and thus D_N + D_R ≈ D_R. However, the nitroxide retains rotational degrees of freedom about the bonds of the tether. The definition of the collision radius, r_c, is retained, because R and the nitroxide (rather than the protein to which it is attached) are still viewed as the colliding species. The local protein environment, and interactions of the nitroxide with the protein, may reduce the number of effective collisions below that characteristic of the nitroxide in solution, and all such effects are collectively accounted for by a factor ρ, the “accessibility factor”. Thus, for a protein-associated nitroxide, in the strong exchange limit is

(3)

For a small, electrically neutral but polar exchange reagent, ρ varies from 0 for a nitroxide buried in the protein interior to a limiting value of unity for a nitroxide at a completely exposed site on the protein surface. With Eqs. 1 and 3, ρ can be expressed as the ratio of the exchange rate constant for the nitroxide in the protein to that in solution, scaled by a ratio of diffusion constants:

(4)

where k_ex = W_ex/C_R, and and C_R are the concentrations of R at which the corresponding exchange rates apply. As discussed below, Eq. 4 may be employed together with experimental values of exchange rates and relative values of D_R and D_N to determine ρ for a nitroxide at any site.

Measurement of Heisenberg exchange rate

In general, for exchange reagents with T_1R < τ_c, T_1e Heisenberg exchange leads to equal changes in T_1e and T_2e of the nitroxide, and

(5)

Thus, methods based on measurement of either T_2e or T_1e may be employed for experimental determination of W_ex. Methods based on T_2e rely on the fact that Heisenberg exchange leads to Lorentzian line broadening. As described in Materials and Methods, the broadening can be determined as the width at half height of the Lorentizian line (ΔH_1/2) that, when convoluted with the spectrum in the absence of collision, yields the interacting spectrum. Alternatively the broadening can be directly measured as the increase in peak-to-peak central linewidth of the first derivative EPR spectrum (ΔΔH_pp). Note that ΔH_1/2 = 3^1/2ΔΔH_pp. W_ex is obtained from either method according to:

(6)

where g is the g factor of the nitroxide. Simplicity of measurement and direct determination of absolute exchange frequency are the advantages of this approach. In the experiments presented below, ΔH_1/2 determined by convolution and ΔΔH_pp are both employed to measure W_ex. In general, the convolution approach is more accurate, especially for noisy spectra and small broadening, because the entire lineshape is used to obtain the result. Determination of ΔΔH_pp requires two independent ΔH_pp measurements, each relatively inaccurate in the usual case of significant spectral noise.

Two T_1e-based methods for measurement of W_ex due to fast-relaxing exchange reagents are in common use: CW saturation and saturation recovery. SR provides a direct determination of the nitroxide T_1e, and is the subject of a companion paper (19). For CW saturation, the amplitude (A) of the first derivative central (m_I = 0) resonance line is measured as a function of microwave power (P), and the data fit to the function

(7)

with I, P_1/2, and ɛ as adjustable parameters. This function describes the saturation of a first derivative EPR signal of arbitrary homogeneity (18). Parameter I is a scaling factor, P_1/2 is the incident microwave power where the first derivative amplitude is reduced to half of its unsaturated value, and ɛ is a measure of homogeneity of the saturation. For the homogeneous and inhomogeneous saturation limits, ɛ = 1.5 and 0.5, respectively. Generally, the saturation of the R1 side chain in proteins in the absence of collision reagent is found to be homogeneous as judged by ɛ. For a homogeneous Lorentzian,

(8)

where Λ = H₁/P^1/2 is the resonator efficiency (26) and γ = gβ2π/h. For the common case where W_ex ≪ 1/T_2e, T_2e may be taken as a constant, and

(9)

where P_1/2 and are in the presence and absence of R, respectively, and T_1e and are the corresponding relaxation times. Although ΔP_1/2 is proportional to W_ex, it depends on the motion of the nitroxide through T_2e and on properties of the resonator through Λ. To reduce or eliminate these dependencies, the dimensionless quantity Π was defined (17,18) as

(10)

Division of ΔP_1/2 by the nitroxide central linewidth, ΔH_pp, normalizes for the nitroxide T_2e, and division by the quantity [P_1/2/ΔH]_reference normalizes for variations in resonator efficiency. In published literature to date, a dilute DPPH powder in KCl was selected as the reference, and the reported Π values depend on this choice. In this study, α was determined using Eqs. 6 and 10 and a comparison of data from line broadening with that from CW saturation for R1 at a solvent exposed site in T4L. Values of W_ex calculated from experimental values of Π and α are shown to agree well with those determined from SR reported in a companion article (19).

RESULTS

NiEDDA-nitroxide encounters in solution

To be useful in estimating nitroxide solvent accessibility, a nitroxide-exchange reagent encounter should be in the strong exchange (diffusion-controlled) limit. To examine this point for NiEDDA, the exchange rate with a small nitroxide in solution was investigated as a function of solution viscosity. According to Eqs. 1 and 2, the exchange rate is given by

(11)

where the substitutions D = kT/6πηr, r_c = r_N + r_R have been made, and k is the Boltzmann constant. Thus, in the strong exchange limit, W_ex is a linear function of 1/η. Fig. 2 shows a plot of experimental values of W_ex vs. 1/η for the small nitroxide 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl in the presence of NiEDDA at a fixed concentration of 3 mM. In this case, line broadening was measured as ΔΔH_pp and W_ex computed from Eq. 6. The linearity of the plot confirms that exchange is diffusion controlled, i.e., in the strong exchange limit. In addition, ΔΔH_pp → 0 as 1/η → 0 (η → ∞), showing that there is no dipolar contribution to the line broadening. This result implies that T_1R < τ_c for NiEDDA, supporting the assignment of P_max = 1 (see Eq. 2 and related discussion).

FIGURE 2.

Line broadening of 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl in solution by 3 mM NiEDDA as a function of viscosity. Line broadening at constant ambient temperature was measured directly as ΔΔH_pp from the first-derivative EPR spectra, and viscosity was varied by addition of glycerol.

Fig. 3 A shows the EPR spectra of 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl in aqueous solution at a fixed viscosity (η = 1 cP) as a function of NiEDDA concentration (gray trace). In this study, line broadening was determined by the Lorentzian convolution method. The Lorentzian used to obtain the best fit to the experimental spectrum is shown superimposed on the data, along with the best-fit spectrum (black trace). W_ex was computed from the width of the Lorentzian (ΔH_1/2) and Eq. 6, and plotted as a function of concentration in Fig. 3 B. As predicted for the strong exchange limit by Eq. 11, the relationship is linear with a slope of 1.21 ± 0.02 MHz/mM, the exchange rate constant for the nitroxide-NiEDDA encounter.

FIGURE 3.

(A) Lorentzian broadening of 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl due to Heisenberg exchange at different concentrations of NiEDDA. The EPR spectrum is shown in gray. Each spectrum was fitted to a convolution of the spectrum in the absence of NiEDDA and a single Lorentzian line as described in Materials and Methods. The best fit is shown in black and the corresponding Lorentzian as a dotted line. (B) The exchange frequency is calculated directly from the best-fit Lorentzian in panels A and C, and plotted versus the concentration of NiEDDA. (C) Lorentzian broadening of T4L 44R1 due to NiEDDA. The EPR spectrum is shown in gray. Each spectrum was fitted to a convolution of the spectrum in the absence of NiEDDA and a single Lorentzian line as described in Materials and Methods. The best fit is shown in black and the corresponding Lorentzian as a dotted line.

The steric factor, f, for the NiEDDA-nitroxide encounter may now be estimated from Eq. 2 as f = k_ex/k_D. From the definition of the diffusion-controlled exchange constant k_D,

(12)

where the substitution D = kT/6πηr has been made for the two diffusion constants, assuming that the encounter partners can be approximated as spherical in shape. For a nitroxide and reagent of the same size, (r_N + r_R)²/r_Nr_R = 4, and

(13)

This remarkable result shows that the diffusion-controlled rate constant is independent of size, as long as the two species are the same size. To a good approximation, Eq. 13 holds for reagents and nitroxides of similar size. For example, if one radius is off by a factor of two, the error incurred is only ∼10%. Thus, Eq. 13 should apply reasonably well for NiEDDA (mol wt = 232) and a nitroxide such as 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl (mol wt = 165), avoiding the necessity of estimating the hydrodynamic radii of the species involved. According to Eq. 13, k_D ≈ 6.5 Mhz/mM, Thus, the steric factor, f = k_ex/k_D ≈ 0.20.

NiEDDA and O₂ encounters with the R1 side chain in T4L

Fig. 4 shows the locations of the T4L sites investigated in this study. Residues 128–135 lie in a short α-helix (two turns), where the side chains span the full range of solvent accessibility, from completely buried to solvent exposed. These are the same sites investigated by SR in a companion article (19). Other sites were selected to represent additional solvent-exposed helix surface sites (residues 44, 65, 72), a partially solvent-exposed site (residue 74), and C-terminal helix sites (residues 81, 89). The EPR spectra for R1 at each of the sites in Fig. 4 are shown in Fig. 5 for T4L in buffer. Spectra for R1 at these sites have been previously published (21), but in that study they were recorded in 30% sucrose to reduce the rotational diffusion of the protein. Even with a contribution from protein rotation present, it is easy to identify the buried sites 129 and 133 by the broad spectral line shapes corresponding to slow motion. Collision studies should preferably be done without sucrose, because it would reduce the translational diffusion of the agents, lowering the observed collision rate.

FIGURE 4.

Ribbon model of T4L showing the location of the sites investigated as spheres on the corresponding α-carbon.

FIGURE 5.

EPR spectra of T4L mutants containing the R1 nitroxide side chain at the designated position. All spectra are recorded in buffer at ambient temperature.

For each of these sites, Π was determined for NiEDDA at 3 mM and for O₂ at ∼0.27 mM, the concentration in buffer at equilibrium with air. The values are given in the first two columns of Table 1, normalized by the concentration of reagent (k_ex = Π/C_R). At all sites, k_ex(O₂) is significantly greater than k_ex(NiEDDA), due in part to the larger diffusion coefficient of O₂. In previous work, native residues have been classified as “solvent accessible”, “partially solvent accessible”, or “buried” based on the fractional solvent accessibility (f_sa) computed from the crystal structure by the method of Lee and Richards (15). The fractional solvent accessibility for the native residue at each site is also given in Table 1. For R1 at solvent-accessible sites (f_sa > 0.25) the ratio k_ex(O₂) / k_ex(NiEDDA) is roughly constant (Table 1, column 3). However, for R1 at partially solvent-accessible (0.05 < f_sa < 0.25) or buried (f_sa < 0.05) sites, the ratio increases dramatically.

TABLE 1.

Parameters characterizing Heisenberg exchange rates for R1 in T4L

Residue	kex(NiEDDA)*	kex(O2)	kex(O2)/kex(NiEDDA)	fsa†	fV‡	ρ
44	0.213	1.89	8.85	0.80	0.42	0.64
65	0.173	1.52	8.76	0.74	0.36	0.52
72	0.140	1.67	11.90	0.55	0.38	0.42
74	0.040	0.70	17.59	0.10	0.07	0.12
81	0.197	1.59	8.10	0.17	0.18	0.59
89	0.290	2.00	6.90	0.57	0.41	0.87
128	0.290	2.00	6.90	0.55	0.49	0.87
129	0.037	0.70	19.19	0.00	0.10	0.11
130	0.173	1.44	8.33	0.12	0.15	0.52
131	0.233	2.07	8.89	0.68	0.44	0.70
132	0.300	1.78	5.93	0.31	0.27	0.90
133	0.003	0.19	55.56	0.01	0.06	0.01
134	0.147	1.52	10.35	0.30	0.22	0.44
135	0.333	2.04	6.11	0.80	0.44	1.00

^*k_ex = Π/C_R, where C_R is the concentration of reagent corresponding to Π.

^†f_sa is the fractional surface area accessibility of the native side chain calculated according to Lee and Richards (31).

^‡f_V is the fractional volume accessibility computed as described in Materials and Methods.

For R1 at the solvent-exposed sites 44 and 65 and at the partially solvent-exposed site 74, Π was determined as a function of NiEDDA concentration. As shown in Fig. 6, the relationship is linear and the slopes, which reflect the relative solvent accessibilities of the R1 side chain, are 0.24, 0.17, and 0.04 mM⁻¹, respectively (corresponding to the values for k_ex in Table 1). NiEDDA concentrations above ∼10 mM could not be used in Π determination of 44R1 and 65R1 because of line broadening effects, which were not apparent up to 30 mM in the less accessible 74R1.

FIGURE 6.

The accessibility parameter Π versus concentration of NiEDDA for residues 44R1, 65R1, and 74R1.

The R1 side chain at the solvent-accessible position 44 in T4L was selected as an ideal site for comparison of Π and and for determination of the proportionality constant α of Eq. 10. Because of the high accessibility (Table 1; Fig. 6) and relatively narrow linewidth (Fig. 5) of R1 at this site, measurable line broadening was produced by NiEDDA in the range of 10–100 mM, providing an absolute determination of via Eq. 6. Fig. 3 C shows the NiEDDA-induced Lorentzian line broadening for 44R1 analogous to the experiment with the free nitroxide shown in Fig. 3 A. Fig. 3 B shows the derived as a function of NiEDDA concentration. The exchange rate constant determined from the slope is 0.44 ± 0.02 MHz/mM for 44R1 over the concentration range 10–100 mM. Two factors contribute to the lower value compared to the result with the free nitroxide (k_ex = 1.21 MHz/mM). The translational diffusion rate of the spin label attached to the protein is negligible compared to the free label, while the NiEDDA diffusion is the same. Because NiEDDA and the nitroxide are of similar size this will cause an ∼50% reduction in collision rate. The remainder of the difference is due to the presence of the protein structure. Accounting for the diffusion effect, the presence of the protein causes only a 30% reduction in collisions for such an exposed site.

The slope of the versus NiEDDA concentration plot in Fig. 3 B and that for the Π versus NiEDDA plot in Fig. 6 determine the important constant α = W_ex/Π = 0.44/0.24 = 1.8 ± 0.1 MHz. With this value Π data can now be expressed directly in terms of absolute exchange rate according to W_ex (MHz) = 1.8Π, or as the concentration-independent rate constant the latter of which could be taken as a quantitative experimental measure of solvent accessibility for R1 in a protein.

An alternative to as a measure of accessibility is the more intuitive “accessibility factor” ρ given by Eq. 4. The accessibility factor ranges from 0 for a buried site to 1 for a nitroxide with accessibility equal to that of a free nitroxide in solution. To estimate the accessibility factor for any site using experimental values of and Eq. 4, the quantities [(D_N + D_R)/D_R] and k_ex are required, where D_N and k_ex refer to the small “reference” nitroxide 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl in solution. Because of the similar size of the reference nitroxide and NiEDDA, [(D_N + D_R)/D_R] ≈ 2, a choice supported by diffusion coefficients computed from the Wilke-Chang equation and molar volumes of the compounds (27). Using k_ex = 1.2 MHz/mM appropriate for the encounter of NiEDDA and the reference nitroxide, and α = 1.8 MHz/mM to convert to Π values, Eq. 4 gives

(14)

Clearly the value of ρ given in Eq. 14 depends on the choice of exchange reagent, and it is thus designated. Values for ρ(NiEDDA) for all residues investigated are given in Table 1, and will be discussed further below for particular cases.

The constant α relating W_ex and Π should be independent of the nature of the exchange reagent, as long as T_1R < T_1e, and independent of the EPR spectral lineshape (mobility). In principle, this could be checked by determining α using the method described above at sites other than 44, representing the full range of motion, and with other exchange reagents. However, line broadening due to exchange is only measurable at highly exposed, and therefore mobile, sites. As an alternative approach, absolute values of for both NiEDDA and O₂ derived from CW power saturation were compared to those from SR, which measures directly. Moreover, data were compared for R1 residues at eight sequential positions along an α-helical sequence in T4L (residues 128–135) where the nitroxide mobility and lineshape varied widely. Fig. 7 A summarizes the data as a function of sequence position. As is evident, derived from both methods and for both exchange reagents reveals the periodicity of the α-helix. For comparison, Fig. 7 A also shows ρ(NiEDDA) determined from CW saturation; as expected, it varies from 0 to 1. Of particular interest is the striking agreement between the absolute values of derived from CW saturation and SR methods for both reagents for all sites. This similarity is emphasized in the plot of Fig. 7 B that directly compares the values from the two techniques. The dashed trace is the ideal case with a slope = 1. The excellent agreement suggests that the constant α is independent of the location or mobility of the nitroxide in the protein, from highly mobile exposed sites to essentially immobilized buried sites, and independent of the exchange reagent.

FIGURE 7.

Correlation of W_ex determined by CW saturation and by saturation recovery EPR. (A) W_ex for NiEDDA (black) and O₂ (gray) determined by SR and CW saturation are plotted for R1 residues along the sequence 128–135. SR data is taken from Pyka et al. (19) and shown as dotted lines with the same color scheme. The right axis shows the same data in units of ρ. (B) W_ex determined from SR is plotted versus W_ex from CW saturation. Open gray circles are data for O₂, and solid circles for NiEDDA. The dashed line has a slope of 1, passing through the origin.

Relation of ρ(NiEDDA) to solvent accessibility computed from the crystal structure

The data presented above suggest that ρ(NiEDDA) may be a reasonable experimental measure of the solvent accessibility of the R1 side chain in proteins. To examine this idea, a measure of the exposure of the side chain accessible to solvent is required. As a first approximation, the solvent-accessible surface area of the original native side chain (f_SA) computed from the crystal structure might be employed. This approach was used to compare Π values with the solvent-accessible surface areas of rhodopsin (5) and annexin (15). Although a good correlation was found for many sites, native residues that had significantly different size compared to R1, and residues that were involved in specific interactions were problematic. For the sites in T4L studied here, the correlation of f_SA and ρ(NiEDDA) is poor (correlation coefficient 0.69; data not shown). A refinement would be to replace the native amino acid with an energy minimized R1 side chain, and compute the solvent accessible from the model. Unfortunately, the true conformation of the R1 side chain at the various sites is not known, and the measure must be based on properties of the environment around the site in question. For one such measure the native side chain is removed and replaced with a glycine. A sphere of radius 8 Å (approximate size of the R1 side chain) is drawn centered on Cα, and a parameter f_V is calculated as the fraction of the available spherical volume filled with water, as described in Materials and Methods. The maximum value of f_V for residues on helical surfaces is ≈0.5, because roughly half of the sphere contains backbone atoms. Fig. 8 shows a plot of W_ex (NiEDDA) and W_ex(O₂) versus f_V for all sites investigated. As is apparent, the parameters are well correlated over the full range of sites investigated here.

FIGURE 8.

Correlation between experimental measures of R1 accessibility (k_ex(Oxygen), k_ex(NiEDDA)), and the structure-based parameter f_V.

DISCUSSION

NiEDDA and oxygen as exchange reagents

Both NiEDDA and O₂ have been extensively used as paramagnetic reagents to determine nitroxide side-chain solvent accessibility, but NiEDDA has not been previously characterized with respect to exchange parameters. As shown in Fig. 2, the NiEDDA-nitroxide exchange rate in glycerol-water mixtures is proportional to η⁻¹, demonstrating a diffusion-limited mechanism consistent with a strong exchange interaction (Jτ_C > 1, where J is the exchange integral). Importantly, the line broadening becomes undetectable at high viscosity (ΔΔH_pp → 0 as η⁻¹ → 0), showing that there is little linewidth contribution from magnetic dipolar interaction between NiEDDA and the nitroxide (16). This suggests that the spin-lattice relaxation time of NiEDDA is short compared with the lifetime of the encounter complex, a circumstance that leads to high collision efficiency (16). The diffusion-controlled rate constant for exchange between NiEDDA and the small nitroxide 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl was determined to be 1.21 ± .02 MHz/mM (1.21 × 10⁹ M⁻¹s⁻¹), similar to that found for other Ni(II) complexes in aqueous solution (28). Together with the high water solubility (>200 mM) and inaccessibility to the interior of proteins (Table 1; Fig. 7 A), these properties make NiEDDA an excellent choice as a probe for solvent accessibility of nitroxide side chains in soluble proteins.

Oxygen is a very convenient reagent for accessibility measurements, because it can be readily added and removed through the use of gas permeable capillaries as EPR sample containers. The exchange rate constant for O₂ with small nitroxides in solution is 8.1 ± 0.2 MHz/mM (23), significantly larger than that for NiEDDA, and O₂ has a size more similar to H₂O than does Ni(EDDA). However, the actual concentration of oxygen in water equilibrated with a gas mixture depends on many experimental variables, such as temperature, partial pressure of oxygen, and buffer composition (29). For example, a change in temperature from 25 to 15° will cause an ∼20% increase in oxygen concentration.

Table 1 shows that the ratio k_ex(O₂)/k_ex(NiEDDA) (and the corresponding ratio of exchange rates) is relatively constant for exposed residues (f_SA > 0.25), even though the individual values vary by more than a factor of 2. Thus, W_ex(O₂) and W_ex(NiEDDA) are equivalent measures of solvent accessibility in this regime. However, for partially solvent-exposed and buried residues (f_SA < 0.25) there is a dramatic decrease in the accessibility of NiEDDA relative to O₂. This “steric exclusion” effect has been previously noted (15), and is likely due to differential penetration of the relatively small and nonpolar O₂ into the protein interior. Thus, NiEDDA has a higher contrast for mapping solvent accessibility. For the above reasons, NiEDDA is the preferred probe for determination of ρ.

Experimental measures of Heisenberg exchange

Here and in a companion article (19), three methods for measurements of Heisenberg exchange rates have been employed: SR, spectral line broadening, and CW power saturation. Each has strengths and weaknesses depending on the application. For example, in the presence of multiple spin populations SR has an advantage because it can resolve multiple components and identify differential accessibility in the presence of exchange reagents (19). CW power saturation cannot easily distinguish between two homogenously saturating components with different accessibility and a single component with inhomogeneous saturation. Direct measurement of line broadening in the presence of multiple spectral components is also difficult to analyze; direct ΔΔH_pp measurements will favor the sharpest component, which could be a minority component, and the simple convolution approach for measurement of ΔH_1/2 is not possible if two components show differential broadening.

Because T₁ ≫ T₂ for R1 in proteins, the T₁-based methods of CW power saturation and SR can detect much lower exchange rates than the T₂-based line broadening methods; in general, line broadening is not attractive for characterizing partially solvent accessible sites in proteins. However, line broadening and SR have a distinct advantage in that they provide absolute values of exchange rates, while CW saturation only provides parameters such as Π that are proportional to exchange rates through a reference-dependent constant. Moreover, a number of assumptions underlie the apparent proportionality. Because of the simplicity and wide availability of the CW saturation method compared to SR, it is desirable to validate the method and determine strategies for evaluating the proportionality constant so that absolute exchange rates can be reported. In this work, the proportionality constant, α, between Π and W_ex was determined by comparing line broadening and CW saturation results for a reference sample (T4L 44R1) where data could be collected for both methods in the same concentration range of exchange reagent. The value of α thus determined depends on the choice of reference used in the saturation studies; DPPH powder in KCL in these studies. For other choices of reference, new values of α could be determined by the above procedure.

Absolute values of exchange rates for R1 side chains with either NiEDDA or O₂, calculated as αΠ, are in excellent agreement with the corresponding values determined from SR, regardless of the spectral lineshape (Fig. 7 B). This result validates the assumptions underlying the CW power saturation method, and indicates that saturation parameters are indeed valid measures of nitroxide T_1e values over a wide dynamic range. This result supports the work of Haas et al. (20) who used spectral simulations to conclude that reliable values of T_1e could be extracted from continuous wave saturation curves of nitroxides, even though the lines are inhomogeneously broadened. More recently, Nielsen et al. (30) presented the results of a study that is very similar in intent to that reported here. In that work, the R1 side chain was placed at a number of solvent-exposed sites in phospholipase A2, and Heisenberg exchange with O₂ investigated with both SR and CW power saturation. CW saturation was characterized by a parameter P₂ (rather than P_1/2 or Π), and fractional changes in P₂ were found to be correlated with fractional changes in 1/T_1e measured by SR with a correlation coefficient of 0.62. In this study, the correlation between CW-derived and SR-derived values for W_ex is much higher, with correlation coefficients of 0.99 and 0.88 for NiEDDA and O₂, respectively. This difference is most likely due to the much smaller dynamic range of accessibilities investigated in the study of Nielsen et al. (30).

Experimental measures of solvent accessibility

In previous work, the R1 side-chain solvent accessibility was measured by the accessibility parameter, Π. This parameter faithfully reflects relative solvent accessibility, and was sufficient to recognize a periodic dependence on sequence that identified secondary structure (5,15). The accessibility factor ρ introduced in this study is on an absolute scale, ranging from 0 to 1, which can be directly compared between laboratories. The accessibility factor has a simple physical meaning, namely the exchange rate constant experienced by the nitroxide in a protein () relative to that experienced by the hypothetical state of the nitroxide in solution that has the same translational diffusion coefficient it had in the protein (k_ex*). The hypothetical rate constant is k_ex* = k_ex [D_R/D_R + D_N], where k_ex is the actual exchange rate constant for the nitroxide in solution, here taken to be the reference compound 4-cyano-2,2,5,5-tetramethylpryollidine-1-oxyl. The value of ρ depends on the exchange reagent employed, just as the solvent accessibility computed from the crystal structure depends on the radius of the probe used in the calculation (31). As discussed above, NiEDDA is the preferred probe. As shown in Fig. 7 A, ρ(NiEDDA) shows a periodic variation with sequence along the 128–135 helix, and varies from essentially 0 to 1, as expected.

A primary use for an experimental solvent accessibility measure is to permit comparison of solution and crystal structures. For this purpose, it is necessary to have a structure-based measure of ρ(NiEDDA) that can be computed from a known crystal structure. As shown in Fig. 8, the parameter f_V, the factional volume accessibility, is linearly correlated with ρ(NiEDDA), and with W_ex(O₂). If this correlation holds for a larger database, it will be possible to compute estimates for f_V for any protein from experimental values of ρ(NiEDDA), and vice versa. This will permit a quantitative comparison of crystal structure data with solution structures determined by nitroxide scanning and associated ρ(NiEDDA) data.