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J. Phys. Chem. B 2004, 108, 9390-9396
ARTICLES Location of EPR-Active Spins Buried in Proteins from the Simulation of the Spin-Lattice Relaxation Enhancement Caused by Dy(III) Complexes† Ryan MacArthur and Gary W. Brudvig* Department of Chemistry, Yale UniVersity, New HaVen, Connecticut 06511 ReceiVed: June 4, 2003; In Final Form: September 24, 2003
A computational method is described that simulates the EPR microwave power saturation characteristics of a protein sample containing an EPR signal from a buried free radical in a frozen solution containing paramagnetic spin-lattice relaxation-enhancement agents such as [Dy(III)HEDTA], where HEDTA is N-hydroxyethylenediaminetriacetate. The specific experiment modeled in this work is the EPR progressive power saturation experiment, where a series of spectra are recorded with increasing microwave power incident on the sample. A fit of the data series yields a characteristic power at half saturation, or P1/2, that is proportional to the spin-lattice relaxation rate of the signal observed in the sample. The addition of DyHEDTA to the protein solution increases P1/2 through dipole-dipole coupling to the buried free radical by an amount strongly dependent on the distance r from the fast-relaxing DyHEDTA to the slow-relaxing radical. The measured value of P1/2 reflects an ensemble of protein molecules in which each buried spin interacts with a specific distribution of DyHEDTA molecules. To simulate the effect of DyHEDTA on the P1/2 of the buried radical spin, we have created a Monte Carlo-type method that models the power-saturation characteristics of the bulk sample by creating saturation profiles of individual, randomly oriented spin ensembles. These individual spin ensembles incorporate arbitrary structural data for the protein as a region where the individual molecules of DyHEDTA are spatially excluded from the calculation, as opposed to previous methods where simple geometric models were employed. The calculation method is validated mathematically and is used to simulate experimental data from the heme-nitric oxide-containing protein systems myoglobin and horseradish peroxidase to demonstrate the effectiveness of the new simulation method.
1. Introduction A goal of many spectroscopic methods applied to biological macromolecules is the elucidation of local or global structural information relative to a particular point of interest within the macromolecule. Such a point of interest could be a chromophore in an energy transduction pathway,1,2 a residue in a protein sequence implicated in intramolecular recognition,3,4 or an enzymatic reaction center.5,6 For the EPR spectroscopist, paramagnetic metal centers, radicals, or spin labels are specific centers that can be studied. The accessibility of such buried spins to the aqueous phase can be determined by measuring the spin-lattice relaxation enhancement induced by exogenous paramagnetic agents.7 Dy(III)-chelates are particularly effective because the large magnetic moment of Dy(III) can provide longrange relaxation enhancement. In the dysprosium spin-probe experiment, a series of samples are made containing a protein with an EPR signal of interest, with increasing concentrations of the Dy(III) complex present in frozen solution.8-10 The EPR signals in this series of samples will have proportionally larger spin-lattice relaxation enhancements provided by the dipole-dipole coupling to the fastrelaxing Dy(III) ions. The Dy(III) line shape is featureless in †
Part of the special issue “Jack H. Freed Festschrift”. * Corresponding author. E-mail:
[email protected].
the g ) 2.0 region of the EPR spectrum, so it does not interfere with signals arising from free radicals, a class of slow-relaxing EPR signals commonly observed in biological systems. It should also be noted that the EPR experiment in a frozen solution is different than relaxation enhancement in the liquid phase,11-13 in that the former uses cumulative long-range dipole-dipole interactions and the latter relies on collisions between spin centers (close-range, individual interactions) for relief from saturation. The spin-lattice relaxation enhancement provided by Dy(III) to the spin of interest can be observed directly by a decrease in the spin-lattice relaxation time, T1, with an experiment such as EPR saturation recovery. However, the spin-relaxation enhancement is more commonly measured as an increase in the power at half saturation, P1/2, a quantity proportional to 1/T1. P1/2 is obtained through an EPR progressive power-saturation experiment, which is popular due to the range of relaxation times that can be extracted from the data, the fact that it does not require the use of specialized instrumentation, and its relative ease of execution.14-17 Interpreting the experimental data is not as straightforward as the execution of the experiment, however. The problem is how to model the relaxation enhancement provided by different concentrations of relaxation agent in frozen solution on an ensemble of observed spin centers buried in their respective
10.1021/jp0355713 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/20/2004
Dysprosium Spin-Probe EPR Experiment Simulation macromolecules. Individual relaxation-agent molecules will be excluded from a discrete volume occupied by the protein structure that surrounds any spin of interest. For example, the cumulative effects of the spin-lattice relaxation enhancement provided by the relaxation agent will be greater in systems where the spin of interest is closer to the macromolecular surface or where the protein surrounding the spin of interest is small. To simulate the results of these cumulative spin-lattice relaxation-enhancement effects, geometric models have previously been employed to approximate the protein structure surrounding a spin of interest. Innes et al. modeled the globular protein myoglobin as an ellipsoidal exclusion volume, with the spin of interest offset along its major and minor axes, and also modeled the membrane protein complexes photosystem II and photosynthetic bacterial reaction center as an infinite planar slab and an infinite planar slab with an associated hemisphere, respectively.18 To treat the cumulative effects of the relaxation agent surrounding the respective protein models, the 1/r6dependent dipole-dipole relaxation-enhancement interaction was integrated over all space not excluded by the protein. The resulting model is for a single buried spin in a solution of relaxation agent that is homogeneous over all space. This provides a model for an average spin in the observed system. In an effort to simplify the simulation of the dysprosium spinprobe experiment such as those proposed by Innes and Brudvig, Oliver and Hales modeled globular proteins as spheres with spins offset from their centers.19 In this way, using an empirical equation and the known molecular weight of a protein to calculate the approximate radius of the spherical protein, a single distance could be extracted from the experiment. Again, this represents a single spin in a homogeneous relaxation-enhancement field, so the model reflects an averaged environment. Both mathematical approximations work well for the systems studied in their respective works and for systems in which no structural information is available. However, neither method can incorporate structural information on the system of interest, address complicated structures, or address conformational changes of the protein relative to a spin of interest. Nor can they address the distribution in the magnitudes of individual spin ensemble relaxation rates that occurs because each spin “sees” a unique collection of Dy(III) complexes. In this work, we will describe and validate a new computational method to simulate saturation data from the dysprosium spin-probe experiment. By repeatedly summing simulated experimental data for an individual spin buried in a protein structure in the presence of a finite number of randomly oriented relaxation-agent molecules within a discrete volume, we can effectively simulate the paramagnetic interactions that create the spin-lattice relaxation enhancement observed in a dysprosium spin-probe EPR sample. This method addresses the variability of spinlattice relaxation enhancement provided to each spin of interest depending on the configuration of the surrounding relaxation agent and incorporates arbitrary structural information for the protein surrounding the interrogated spins. 2. Experimental Details 2.1. EPR Sample Preparation. Myglobin nitroxide (MbNO) and horseradish peroxidase nitroxide (hrpNO) were prepared using previously reported techniques.18,20,21 To prepare stock solutions of MbNO, 18.5 mg of horse skeletal myoglobin (Sigma) was dissolved in 1 mL of pH 7.4, 40 mM HEPES buffer containing 150 mM NaCl and 35% v/v glycerol (buffer A). Myoglobin was reduced with 1 mg of sodium dithionite (Aldrich) in an anaerobic atmosphere chamber (Sheldon Manu-
J. Phys. Chem. B, Vol. 108, No. 27, 2004 9391 facturing; Cornelius, OR). The solution was adjusted to 10 mM in sodium nitrite (Fisher) to generate NO in situ and create the nitric oxide adduct. To prepare stock solutions of hrpNO, 60 mg of type II horseradish peroxidase (Sigma) was dissolved in 1 mL of buffer A, transferred to an anaerobic chamber, and reduced with excess dithionite prior to the addition of sodium nitrite solution. The stock solutions were then diluted into 4-mm quartz EPR tubes (Wilmad) containing varying concentrations of DyHEDTA in buffer A. Because of the paramagnetism of molecular oxygen as well as its reactivity with nitric oxide and its adducts, all samples were prepared in an anaerobic atmosphere chamber. 2.2. EPR Spectroscopy. All EPR spectra of the MbNO and hrpNO samples were recorded on a Varian E-line spectrometer using a standard TE-102 cavity interfaced to a Macintosh IIci running National Instruments’ LabView 2.2 with a Lab-NB board. The EPR spectra were collected over the available power range of the microwave bridge, about 0.01-200 mW. Instrumental parameters were identical for each sample recorded, with a 100-kHz modulation amplitude of 4 G and a microwave frequency of 9.242 GHz; the microwave frequency was calibrated with a frequency meter (General Electric). An Oxford Instruments ESR-900 cryostat with an ITC-4 temperature controller ensured data collection at a constant 20 ( 1.0 K (unless noted otherwise). The thermocouple junction in the cryostat was calibrated using a silicon diode, which was in turn referenced to liquid-helium and liquid-nitrogen temperatures. Power-saturation data presented are the result of integration over the line shape of each spectrum acquired, after a linear baseline correction to compensate for the underlying dysprosium line shape. P1/2 values from both EPR and simulated data were extracted by fitting with eq 1b. 2.3. Progressive Microwave Power Saturation. In a progressive power-saturation experiment, the microwave power incident on the cavity containing the sample is progressively increased, and the amplitude of the spectrum is recorded at each observing power P. Because the signal intensity S in the nonsaturating regime is proportional to xP, a log-log plot of S/xP versus P will have two readily apparent regimes: nonsaturating and saturating. In the nonsaturating region of this saturation curve, the plot is a straight line parallel to the power axis. As the signal becomes saturated, the plot curves down, forming another linear regime whose slope depends on the extent of inhomogeneous broadening. Historically, the intersection of these two linear regimes when extrapolated has been used to determine P1/2, the power at half saturation; more recently, this plot is fit using least-squares fitting to an equation of the form
S k ) xP (1 + (P/P1/2))(b/2)
(1a)
where k is an instrumental scaling factor and b is an inhomogeneity parameter22,23 that varies between 1.0 for an inhomogeneously broadened line and 3.0 for a homogeneous line shape.24 For free radicals buried in proteins, the powder line shape is typically inhomogeneously broadened such that b ) 1, as in eq 1b:
S k ) xP x1 + (P/P1/2)
(1b)
When a fast-relaxing paramagnet is present, the relaxation of a slow-relaxing paramagnet will be enhanced via a pairwise
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dipole-dipole interaction. The dipolar relaxation enhancement, kd, will add to the intrinsic relaxation rate, ki (eq 2).
P1/2 ∝
1 1 1 ) + ) ki + kd T1 T1i T1d
SCHEME 1: Flowchart Representing the Algorithm Used to Simulate the Dysprosium Spin-Probe EPR Experiment
(2)
The form of kd depends on the properties of the two interacting spins. (For a review, see Lakshmi and Brudvig.25) In the case when the fast-relaxing spin is Dy(III) and the slowrelaxing spin is a nitrosyl-Fe(II) adduct, the C term of the dipolar alphabet is dominant (eq 3):
kd ) (r -6)3γ2s µ2f T1f sin2 θ cos2 θ
(3)
where r is the distance between the paramagnets and γs is the magnetogyric ratio of the slow-relaxing electron. Additionally, µ2f and T1f, are the magnetic moment and spin-lattice relaxation time of the fast-relaxing paramagnet, respectively. Depending on the ratio of kd/ki, the interpretations of P1/2 and b are not straightforward. It has been found previously that for systems in which kd/ki is large eq 1a can best fit the data when b is allowed to vary below 1.0.26 It is important to note that the inhomogeneity parameter cannot physically fall below unity. Rather, it was concluded that the distribution of relaxation rates for the individual spin-packets, caused by the distribution of the spin-lattice relaxation enhancement of the observed spins, is manifested in the data as an apparent drop in b. The greater the distribution of the magnitudes of the individual relaxation rates, the lower the apparent b value. In the case of the dysprosium spin-probe experiment, the decrease in population of relaxation rates higher or lower than the average will result in an apparent b value close to unity. P1/2 can therefore be artificially increased by the addition of fast-relaxing paramagnets, such as complexes of Dy3+, to increase kd, but the inhomogeneity parameter was fixed at unity during analysis of all data (eq 1b). As a result of the dipoledipole interactions of Dy3+ ions with the slow-relaxing signal of interest, a series of samples with increasing concentrations of Dy3+ will show increasing rates of relaxation. From eq 2, we assign the dysprosium-induced relaxation rate to be the dipole-induced rate. Because relaxation processes are additive, we can describe the relationship between the change in the power at half saturation, ∆P1/2, induced by Dy3+ and a distance term, r:
∆P1/2 ∝
kDy-induced ∝ ∑ r-6 ∑ Dy Dy Dy
(4)
The last term in eq 4 can be thought of as sites where Dy3+ ions are not excluded by protein structure surrounding the spin of interest. Substituting the concentration of Dy3+ ions for the summation term and taking the difference between P1/2 of the spin at different concentrations of dysprosium, the experimental data will show that
∆P1/2 ∝ ∆[Dy]
(5)
When ∆P1/2 is plotted versus ∆[Dy3+], the slope of the line will reflect how buried the observed spin is in the protein. A steeper slope would indicate a more exposed spin. In a system with heterogeneous relaxation times, the saturation curve, or profile, does not reflect a single value for the power at half saturation obtained from nonlinear least-squares fitting of the data with eq 1b. As mentioned earlier, it has been previously demonstrated26 that for a system with two dipoles at a fixed distance, upon distribution of the dipole-dipole vector
over all angles relative to the applied magnetic field, the powersaturation curve is no longer described accurately by eq 1a if b, the inhomogeneity parameter, is not allowed to vary below unity. The inhomogeneity parameter can be thought of as inversely proportional to the ratio of the intrinsic spin-packet line width to the overall envelope of the resonance line shape. For a homogeneous system (such as a VK center in KCl),27 b ≈ 3, and for an inhomogeneous system (such as a buried free radical in a protein), b ≈ 1. However, in cases where the relaxation properties of the spin packets are inhomogeneous, the values of ∆P1/2, when extracted from cw EPR powersaturation curves, are not directly proportional to ∑r-6. They are instead a weighted average of the composite of P1/2 curves from individual spins with different T1 values. Therefore, the system is more effectively described as -6 kDy-induced(i) ∝ ∑∑ rDy(i) ∑i ∆P1/2(i) ∝ ∑i ∑ Dy i Dy
(6)
2.4. Computational Details of the Monte Carlo Simulation Method. To simulate the characteristics of a power-saturation curve measured in a cw EPR experiment, a composite curve was constructed from the sum of r-6 values calculated for each ensemble of dipoles using eqs 1b and 4 to calculate eq 6 explicitly. The algorithm used for the simulation of these composite curves is presented in Scheme 1.28 Fundamentally, it relies on eq 1b to simulate the saturation characteristics of a single EPR spin of interest buried in a macromolecular structure surrounded by a set number of Dy3+ ions (proportional to the concentration) randomly fixed in space. A power-saturation curve is then generated for the individual spin ensemble, and
Dysprosium Spin-Probe EPR Experiment Simulation the simulation is repeated, as described in greater detail below, with a different random orientation of Dy3+ ions. The powersaturation curves for the individual spin ensembles are summed at the end of the simulation to form the composite ∆P1/2 curve, a simulation of the experimentally observed power-saturation curve for a protein sample at a given concentration of Dy3+. In the simulation algorithm, a structural model can be introduced either geometrically or as coordinates from the Protein Data Bank (PDB).29 The structural model was offset so that the proposed location of the spin was at the origin. The geometric model or coordinate files were then subjected to the following simulation algorithm (Scheme 1): •A random 3D point is generated. •The point is tested to determine if it falls within a predefined sphere within which the calculation is being executed: a discrete volume around the protein coordinates. A spherical calculation volume was chosen because the dipole-dipole interaction equation used is spherical. In addition, such a calculation will not show artifacts from the corners of a cubic calculation volume. If the point passes the initial calculation volume screen, then it proceeds to the next step. If not, the process is repeated until a point is generated that passes the screen. •The point is then treated as a probe sphere of a specified radius and is screened for collisions against an array of “good” points that have already passed through the entire calculation and whose r-6 values have been calculated. •The point is then screened against the array of points in the PDB file (and/or other structural elements such as geometric shapes) for collisions. •If all of the above have not resulted in collisions, then the value of the dipole-dipole relaxation enhancement is calculated and added to the overall value. •When the final concentration of probe points has been generated and their values summed, the process is repeated. The Monte Carlo-style integration algorithm itself was verified by numerically calculating the integrals of several existing geometric models, namely, the oblate ellipsoid and planar slab with offset hemisphere mentioned above.18 The relative values from the Monte Carlo numerical integration results were then compared to the corresponding mathematical approximation and solution for the same integrals, respectively, and were found to be in good agreement with the published values. Rather than using geometric values to simulate our experimental data, we chose the proteins myoglobin and horseradish peroxidase because of their robust nitric oxide adducts and the existing structural information available from the PDB. The spin of interest was assigned to the iron atom in each of the structures. 3. Results and Discussion A graphical representation of 10 superimposed calculation sets on the horse heart myoglobin PDB file 1DWR, is shown in Figure 1 to convey visually how the simulation works. For clarity, the spherical calculation geometry illustrated here is smaller than the volume used in the simulations. The volume chosen for calculations and the number of iterations needed for a good estimation of ∆P1/2 were selected with the aid of plots such as those shown in Figure 2. At a minimum, the calculation volume must be large enough to incorporate the most distant features of the protein from the spin center. The additional contribution from relaxation agents in the volume beyond this region must also be calculated for the full treatment of the cumulative effects of the relaxation agents. However, as the volume of the calculation is increased, so is the time needed
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Figure 1. Graphical representations of calculation data from 10 calculation iterations on the protein horse skeletal myoglobin (PDB file 1DWR). Small gray spheres are calculated points, medium spheres are rejected points, and the large light-gray sphere in the center represents the spin, centered on the heme iron atom. The mass of black dots represents the individual atomic coordinates from the protein structure. For this illustration, calculation conditions that were used were 100 Å as the diameter of the sphere and 2.7 Å as the probe sphere’s radius at a concentration of 0.015 M.
for each calculation. A calculation sphere size of 300 Å was identified as the lower limit that included all of the significant interactions, as shown in Figure 2a. The spin-relaxation enhancement of a buried spin by a relaxation agent has been proposed to increase as the inverse sixth root of the distance of closest approach of the relaxation agent from the surface of the macromolecule to the buried spin.9 We observe a general trend, in both the experimental and calculated power-saturation data, that the relaxation enhancement increases as the distance of closest approach decreases. However, the distance-of-closest-approach dependence of the relaxation enhancement depends on the size and structure of the macromolecule, and the cumulative effects of more distant paramagnetic ions are significant in enhancing the spin-lattice relaxation of a buried spin. Despite these cumulative effects, it was found that calculation sphere sizes greater than 300 Å do not significantly increase the magnitude of the dipolar term (Figure 2a), so additional calculation volume is unnecessary for an accurate estimation of the dysprosium-induced spin-lattice relaxation-rate enhancement. To determine the number of iterations needed for the accurate simulation of the experiment, the average value of r-6 was output for every iteration over the course of 105 experiments. The number of iterations per calculation, or number of randomized spin ensembles modeled per calculation, was chosen to be 104 from Figure 2b. For this number of calculations, the final calculated values do not change by more than 1%. With fewer than 103 calculations, the difference between average r-6 values can be as high as 4-fold. Three calculation sets of 104 iterations, each with a different random number seed, were averaged for the final values used. The probe sphere size of 2.7 Å as a model for the radius for the DyHEDTA complex was estimated from the crystal structure of DyEDTA,30 where the dysprosium ion has a water-
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Figure 3. Effect of the modeled probe radius on the calculated dipoledipole relaxation-rate enhancement. Points represent the ratios of the calculated average rate enhancements for the nitric oxide adduct of sperm whale myoglobin (1JDO). For probe radii between 3 and 7 Å, the ratio does not vary by more than 6%. Larger probe radii result in lower ratios as the distance from the center of the probe sphere to its own surface becomes the dominant distance component of r.
Figure 2. Convergence of the calculated values. (a) Change in the average calculated relaxation-rate enhancement relative to the change in calculation volume vs the calculation diameter for the nitric oxide adduct of sperm whale myoglobin (1JDO). There is no significant change in the calculated relaxation-rate enhancement with calculation diameters of 300 Å or larger. (b) Effect of the number of calculation iterations on the calculated relaxation-rate enhancement for myoglobin, 1DWR (s) and horseradish peroxidase, 7ATJ (dashed line). By 105 calculations, the values do not change by more than 0.1%. Values reported in this work are the result of the average of three different calculation sets of 104 iterations (using different random number seed values), and the errors reported are the standard deviations.
coordinated face. The 2.7-Å distance represents the distance from a hydrogen-bond-acceptor atom on the surface of a protein to the central dysprosium ion in the H2O-Dy-HEDTA complex. The relative simulated ∆P1/2 values at a given concentration of relaxation agent plots show a small but nontrivial variation depending on the radius of the probe sphere. The relative calculated values for the average dipole-dipole induced-relaxation rates, however, are relatively insensitive to the probe sphere size (Figure 3), similar to results reported by others using geometric models.19 Power-saturation curves were calculated using PDB files 1DWR31 and substructure A of 7ATJ32 for the myoglobin and peroxidase calculations, respectively. Protons were added to the structures using standard geometries (WebLabViewer Pro, Molecular Simulations, Inc.) before preprocessing to extract raw Cartesian coordinates for use by the simulation program. The
simulation, therefore, is based only on spatial interactions between probe sphere and atomic protein coordinates, although ionic charge or hydrophobic interactions could be addressed in future versions. Summation of the calculated curves (as from individual spinpackets) results in an overall composite curve containing each ensemble as a component of equal weight. The calculated curves were then fit in the same manner as the experimental data (Figure 4). For systems with a greater variance in the magnitude of the dipole-dipole interactions present (proteins with a shorter distance of closest approach to the spin center), a greater deviation from the fit to eq 1b is observed. Simulated powersaturation curves generated with the simulation program28 along with their fits to eq 1b are shown in Figure 4. There is a slight deviation between the simulated data and the fit to eq 1b that is apparent at lower relaxation-agent concentrations because of the greater distribution in relaxation rates for the individual calculated ensembles, as described earlier. The extracted ∆P1/2 values were then plotted versus the DyHEDTA concentration and fit to a straight line intersecting the origin to yield the calculated slopes for the respective protein models. Experimental data sets from the EPR microwave progressive power-saturation experiments on the corresponding nitric oxideheme protein adducts are shown in Figure 5. Again, the data are fit well by eq 1b. The ∆P1/2 values reported are the difference between the P1/2 extracted at a given concentration and the P1/2 extracted at zero concentration (the intrinsic P1/2). Treatment of experimental and simulated data in this same manner, therefore, will reproduce any artifacts, if any, from fitting the data so that the two sets can be accurately compared. Plots of experimental data using DyHEDTA as a relaxation agent are shown in Figure 6. For comparison, the linear leastsquares fit of ∆P1/2 values calculated by using the Monte Carlo method is superimposed on the respective experimental data after being scaled relative to MbNO. The calculated values for the PDB file of myoglobin were scaled to make the calculated values coincident with the experimental values. In this way,
Dysprosium Spin-Probe EPR Experiment Simulation
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Figure 4. Sample simulated power-saturation curves for (a) horse skeletal myoglobin, PDB file 1DWR (b) and horseradish peroxidase, PDB file 7ATJ. The individual symbols are the output of the simulation program, and the solid lines are fits to the simulated data using eq 1b. Sample curves are the result of 104 iterations each, using a 2.7-Å probe radius and a 300-Å diameter of the calculation sphere. P1/2 values obtained from fits using eq 1b are as follows: 0.564 ( 0.007 at 15 mM (part a, lower curve), 2.409 ( 0.008 at 50 mM (part a, upper curve), 0.305 ( 0.002 at 15 mM (part b, lower curve), and 1.119 ( 0.002 at 50 mM (part b, upper curve). The calculated P1/2 values are reported in arbitrary units and then scaled using a particular experimental system, in this case, myoglobin. The values from the calculated myoglobin curves were scaled to match experimental myoglobin data, and the scaling constant found, Cscaling, was used to scale the rest of the calculated ∆P1/2 data.
Figure 5. Sample power-saturation curves at 20 K for (a) MbNO in 50 mM DyHEDTA (b) and hrpNO in 50 mM DyHEDTA with their respective cw EPR spectra (4-G modulation width, 9.24-GHz microwave frequency) (insets). The solid lines are the least-squares fits of the data using eq 1a. P1/2 fits by eq 1b are as follows: MbNO, 20 ( 1.8 mW; hrpNO, 5.8 ( 0.5 mW. These values reflect the intrinsic relaxation rates of the signals, which vary in different proteins, and the relaxation-rate enhancement afforded by dysprosium in solution.
myoglobin serves as the control protein to which all other calculated values are referenced, such that
∆P1/2(obs-MbNO) ) ∆P1/2(calcd-MbNO)Cscaling
(7)
Cscaling is then used to scale the other calculated ∆P1/2 values, predicting values expected to be observed in an EPR experiment on the corresponding system, in this case, the nitric oxide adduct of horseradish peroxidase. The scaling term can be thought of as the integration of the terms in eq 3 that are not distance-dependent. Because a relaxation process analogous to eq 3 can be induced in the slow relaxer via a spin-spin rather than a spin-lattice relaxation mechanism, for Cscaling to remain constant from one system to another the condition that changes in T2 are negligible must exist for the slow relaxer. We assume that the effect of the addition of relaxation agent on T2 is negligible such that T1 is always the dominant relaxation mechanism. Saturation-recovery EPR spectroscopy measurements of a variety of protein samples with buried heme-NO radical species in the presence of Dy(III) chelates confirms this assumption.28 However, caution should be taken if applying this method to systems where T1 changes by the relaxation agent are not dominant. Additionally, if lineshape effects are observed upon the addition of relaxation agent (i.e., broadening), then factors affecting T2 are at work, and the data cannot be modeled solely by addressing T1 effects.
Figure 6. Comparison of experimental data from MbNO (9) and hrpNO (b) measured at 20 K. The calculated values from PDB files 1DWR and 7ATJ are shown as solid lines. All calculations were run with a 300-Å calculation diameter, 104 iterations, and a 2.7-Å probe radius. The solid lines are the linear least-squares fits of calculated values using points at 0, 15, and 50 mM.
The simulation shows that the crystal structures of the respective proteins are accurate models to account for the excluded volume surrounding the heme-NO radical in each protein, within the resolution of the dysprosium spin-probe experiment. Using the Monte Carlo-type method described here, we have shown that the analysis of data from the dysprosium
9396 J. Phys. Chem. B, Vol. 108, No. 27, 2004 spin-probe experiment is no longer limited to simple geometric models. Arbitrary structural information, from geometric models to atomic resolution structural information, can be used to simulate the relaxation behavior of a buried EPR-active spin. This should prove useful for testing models of global macromolecular structure such as protein complex formation, conformational changes, and the location of intramolecular electrontransfer centers. Simultaneously, we have developed a rigorous treatment for the issue of inhomogeneous spin-relaxation intrinsic in samples used in this type of EPR experiment. The algorithm used is easily modified to simulate different relaxation mechanisms and can accommodate models such as the binding of the relaxation agent to a protein surface. Although the method described here is simple, it is applicable to a wide variety of macromolecules containing a stable spin center for which any amount of structural information is available. In general, all that is required of a macromolecule of interest is an EPR signal with a P1/2 available within the temperature range where the addition of a reasonable amount of relaxation agent can significantly increase the observed P1/2. This technique should be well suited to other proteins with buried organic free radicals, to which we are currently applying this method. Acknowledgment. This work was supported by NIH grant GM36442. References and Notes (1) Hirsh, D. J.; Brudvig, G. W. J. Phys. Chem. 1993, 33, 13216. (2) Koulougliotis, D.; Innes, J. B.; Brudvig, G. W. Biochemistry 1994, 33, 11814. (3) Gopalan, V.; Ku¨hne, H.; Biswas, R.; Li, H.; Brudvig, G. W.; Altman, S. Biochemistry 1999, 38, 1705. (4) MacArthur, R.; Sazinsky, M. H.; Ku¨hne, H.; Whittington, D. A.; Lippard, S. J.; Brudvig, G. W. J. Am. Chem. Soc. 2002, 124, 13392. (5) Galli, C.; Atta, M.; Andersson, K. K.; Gra¨slund, A.; Brudvig, G. W. J. Am. Chem. Soc. 1995, 117, 740. (6) Tang, X.-S.; Diner, B. A.; Larsen, B. S.; M. Lane Gilchrist, J.; Lorigan, G. A.; Britt, R. D. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 704.
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