Myosin cross-bridge orientation in rigor and in the presence of nucleotide studied by electron spin resonance.

The tilt series electron spin resonance (ESR) spectrum from muscle fibers decorated with spin labeled myosin subfragment 1 (S1) was measured from fibers in rigor and in the presence of MgADP. ESR spectra were measured at low amplitude modulation of the static magnetic field to insure that a minimum of spectral lineshape distortion occurs. Ten tilt series ESR data sets were fitted simultaneously by the model-independent methodology described in the accompanying paper (Burghardt, T. P., and A. R. French, 1989. Biophys. J. 56:525-534). By this method the average and standard error in the mean of order parameters for the probe angular distribution were calculated for the two states of the fiber investigated. The average order parameters were used to reconstruct the probe angular distribution in two dimensions, one angular dimension corresponding to a polar angle measured relative to the fiber axis, and the other a torsional angular degree of freedom of the probe. We find that the probe angular distributions for the rigor and MgADP states of the fiber differ such that the rigor distribution is broader and shifted relative to the distribution in the presence of MgADP. The shape of the rigor distribution suggests the presence of two probe orientations, one similar to that in the presence of MgADP, and another at a different orientation. The shape of the distribution in the presence of MgADP suggests that the binding of the nucleotide to the rigor cross-bridge shifts the spin population into a more homogeneous one by causing a cross-bridge rotation.     

Orientation of spin-labeled light chain-2 exchanged onto myosin cross-bridges in glycerinated muscle fibers.

Electron paramagnetic resonance (EPR) spectroscopy has been used to study the angular distribution of a spin label attached to rabbit skeletal muscle myosin light chain 2. A cysteine reactive spin label, 3-(5-fluoro-2,4-dinitroanilino)-2,2,5,5- tetramethyl-1-pyrrolidinyloxy (FDNA-SL) was bound to purified LC2. The labeled LC2 was exchanged into glycerinated muscle fibers and into myosin and its subfragments. Analysis of the spectra of labeled fibers in rigor showed that the probe was oriented with respect to the fiber axis, but that it was also undergoing restricted rotations. The motion of the probe could be modeled assuming rapid rotational diffusion (rotational correlation time faster than 5 ns) within a "cone" whose full width was 70 degrees. Very different spectra of rigor fibers were obtained with the fiber oriented parallel and perpendicular to the magnetic field, showing that the centroid of each cone had the same orientation for all myosin heads, making an angle of approximately 74 degrees to the fiber axis. Binding of light chains or labeled myosin subfragment-1 to ion exchange heads immobilized the probes, showing that most of the motion of the probe arose from protein mobility and not from mobility of the probe relative to the protein. Relaxed labeled fibers produced EPR spectra with a highly disordered angular distribution, consistent with myosin heads being detached from the thin filament and undergoing large angular motions. Addition of pyrophosphate, ADP, or an ATP analogue (AMPPNP), in low ionic strength buffer where these ligands do not dissociate cross-bridges from actin, failed to perturb the rigor spectrum. Applying static strains as high as 0.16 N/mm2 to the labeled rigor fibers also failed to change the orientation of the spin label. Labeled light chain was exchanged into myosin subfragment-1 (S1) and the labeled S1 was diffused into fibers. EPR spectra of these fibers had a component similar to that seen in the spectra of fibers into which labeled LC2 had been exchanged directly. However, the fraction of disordered probes was greater than seen in fibers. In summary, the above data indicate that the region of the myosin head proximal to the thick filament is ordered in rigor, and disordered in relaxation.     

Orientation of spin-labeled myosin heads in glycerinated muscle fibers.

We have used electron paramagnetic resonance (EPR) spectra to study spin labels selectively and rigidly attached to myosin heads in glycerinated rabbit psoas muscle fibers. Because the angle between the magnetic field and the principal axis of the probe determines the position of the EPR absorption line, spectra from labeled fibers oriented parallel to the magnetic field yielded directly the distribution of spin label orientations relative to the fiber axis. Two spin labels, having reactivities resembling iodoacetamide (IASL) and maleimide (MSL), were used. In rigor fibers with complete filament overlap, both labels displayed a narrow angular distribution, full width at half maximum approximately 15 degrees, centered at angles of 68 degrees (IASL) and 82 degrees (MSL). Myosin subfragments (heavy meromyosin and subfragment-1) were labeled and allowed to diffuse into fibers. The resulting spectra showed the same sharp angular distribution that was found for the labeled fibers. Thus is appears that virtually all myosin heads in a rigor fiber have the same orientation relative to the fiber axis, and this orientation is determined by the actomyosin bond. Experiments with stretched fibers indicated that the spin labels on the fraction of heads not interacting with actin filaments had a broad angular distribution. Addition of ATP to unstretched fibers under relaxing conditions produced orientational disorder, resulting in a spectrum almost indistinguishable from that of an isotropic distribution of probes. Addition of either an ATP analog (AMPPNP) or pyrophosphate produced partial disorder. That is a fraction of the probes remained sharply oriented as in rigor while a second fraction was in a disordered distribution similar to that of relaxed fibers.     

Mapping global angular transitions of proteins in assemblies using multiple extrinsic reporter groups.

The fluorescence polarization intensities from fluorescent probes and the electron paramagnetic resonance spectra from spin probes, specifically modifying elements of a biological assembly such as myosin sulfhydryl 1 (SH1) in muscle fibers, are interpreted in terms of probe order parameters using a model-independent method. The probe order parameters are related to each other by an Euler rotation of coordinates. We use this relationship to link the sets of order parameters from the different probes and in so doing create a system of equations that can be solved using only the information available from the experimental data. The solution yields the Euler angles relating the different probe coordinate frames and a larger set of probe order parameters than can be directly detected experimentally. The Euler angles are used to display the relative orientation of the probe molecular frames. The order parameters give rise to probe angular distributions that are at the theoretical limit of resolution. We demonstrate the utility of this analytical method by investigating the rotation of myosin SH1 from its orientation in rigor upon the binding of the nucleotide MgADP to the myosin cross-bridge. Our findings, discussed in the accompanying paper, suggest that the rigor-to-MgADP cross-bridge angular transition consists predominantly of a rotation about the hydrodynamic axis of symmetry of the cross-bridge, i.e., its torsional degree of freedom [Ajtai, K., Ringler, A., & Burghardt, T. P. (1992) Biochemistry (following paper in this issue)].     

Probing cross-bridge angular transitions using multiple extrinsic reporter groups.

15N- and 2H-substituted maleimido-TEMPO spin label ([15N,2H]MTSL) and the fluorescent label 1,5-IAEDANS were used to specifically modify sulfhydryl 1 of myosin to study the orientation of myosin cross-bridges in skeletal muscle fibers. The electron paramagnetic resonance (EPR) spectrum from muscle fibers decorated with labeled myosin subfragment 1 ([15N,2H]MTSL-S1) or the fluorescence polarization spectrum from fibers directly labeled with 1,5-IAEDANS was measured from fibers in various physiological conditions. The EPR spectra from fibers with the fiber axis oriented at 90 degrees to the Zeeman field show a clear spectral shift from the rigor spectrum when the myosin cross-bridge binds MgADP. This shift is attributable to a change in the torsion angle of the spin probe from cross-bridge rotation and is observable due mainly to the improved angular resolution of the substituted probe. The EPR data from [15N,2H]MTSL-S1 decorating fibers are combined with the fluorescence polarization data from the 1,5-IAEDANS-labeled fibers to map the global angular transition of the labeled cross-bridges due to nucleotide binding by an analytical method described in the accompanying paper [Burghardt, T. P., & Ajtai, K. (1992) Biochemistry (preceding paper in this issue)]. We find that the spin and fluorescent probes are quantitatively consistent in the finding that the actin-bound cross-bridge rotates through a large angle upon binding MgADP. We also find that, if the shape of the cross-bridge is described as an ellipsoid with two equivalent minor axes, then cross-bridge rotation takes place mainly about an axis parallel to the major axis of the ellipsoid. This type of rotation may imitate the rotation motion of cross-bridges during force generation.     

A multifrequency electron spin resonance study of T4 lysozyme dynamics.

Electron spin resonance (ESR) spectroscopy at 250 GHz and 9 GHz is utilized to study the dynamics and local structural ordering of a nitroxide-labeled enzyme, T4 lysozyme (EC 3.2.1.17), in aqueous solution from 10 degrees C to 35 degrees C. Two separate derivatives, labeled at sites 44 and 69, were analyzed. The 250-GHz ESR spectra are well described by a microscopic ordering with macroscopic disordering (MOMD) model, which includes the influence of the tether connecting the probe to the protein. In the faster "time scale" of the 250-GHz ESR experiment, the overall rotational diffusion rate of the enzyme is too slow to significantly affect the spectrum, whereas for the 9-GHz ESR spectra, the overall rotational diffusion must be accounted for in the analysis. This is accomplished by using a slowly relaxing local structure model (SRLS) for the dynamics, wherein the tether motion and the overall motion are both included. In this way a simultaneous fit is successfully obtained for both the 250-GHz and 9-GHz ESR spectra. Two distinct motional/ordering modes of the probe are found for both lysozyme derivatives, indicating that the tether exists in two distinct conformations on the ESR time scale. The probe diffuses more rapidly about an axis perpendicular to its tether, which may result from fluctuations of the peptide backbone at the point of attachment of the spin probe.     

Reliability of nitroxide spin probes in reporting membrane properties: a comparison of nitroxide- and deuterium-labeled steroids

The reliability for the study of membrane properties of the steroid nitroxide spin probe, 3-doxylcholestane, was tested by comparison of analogous data for the deuterated steroid, cholesterol-3 alpha-d. Good agreement between the two probes was found for the dependence of their order parameters on variation of temperature or cholesterol concentration in egg phosphatidylcholine bilayers. This finding is contrasted with the results of a previous study of fatty acid probes where poor agreement was found for the spectral responses of nitroxide- and deuterium-labeled species. The angular dependence of the ESR spectra of nitroxide-labeled probes in oriented multibilayer films was examined to determine if the probes were oriented in a tilted fashion in the bilayer. The 3-doxylcholestane probe and a doxylstearic acid labeled at position 14 orient with their long molecular axes perpendicular to the bilayer plane. In contrast, the stearic acid probe nitroxide labeled at position 5 does not appear to orient in such a fashion. We suggest that the behavior of the latter probe reflects the difficulty of inserting a bulky nitroxide group into a highly ordered region of the bilayer rather than an inherent tilting of the phospholipid acyl chains. On the basis of the comparisons between various types of probes, some suggestions are made concerning the choice of ESR spin probe to obtain reliable information in membrane studies.     

Effect of ADP on the orientation of spin-labeled myosin heads in muscle fibers: a high-resolution study with deuterated spin labels

We have used electron paramagnetic resonance (EPR) to determine the effects of ADP on the orientational distribution of nitroxide spin labels attached to myosin heads in skinned rabbit psoas muscle fibers. To maximize the specificity of labeling, we spin-labeled isolated myosin heads (subfragment 1) on a single reactive thiol (SH1) and diffused them into unlabeled muscle fibers. To maximize spectral and orientational resolution, we used perdeuterated spin labels, 2H-MSL and 2H-IASL, eliminating superhyperfine broadening and thus narrowing the line widths. Two different spin labels were used, with different orientation relative to the myosin head, to ensure that the results are not affected by unfavorable probe orientation. In rigor, a very narrow three-line spectrum was observed for both spin labels, indicating a narrow orientational distribution, as reported previously (Thomas & Cooke, 1980). ADP induced very slight changes in the spectrum, corresponding to very slight (but significant) changes in the orientational distribution. These changes were quantified by a digital analysis of the spectra, using a two-step simplex fitting procedure (Fajer et al., 1990). First, the magnetic tensor values and line widths were determined by fitting the spectrum of a randomly oriented sample. Then the spectrum of oriented fibers was fit to a model by assuming a Gaussian distribution of the tilt angle (theta) and twist angle (phi) of the nitroxide principal axes relative to the fiber axis. A single-Gaussian distribution resulted in inadequate fits, but a two-component model gave excellent results. ADP induces a small (less than 5 degrees) rotation of the major components for both spin labels, along with a similarly small increase of disorder about the average positions.     

Electron spin resonance of TOAC labeled peptides: folding transitions and high frequency spectroscopy

The unnatural, conformationally constrained nitroxide amino acid TOAC (2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid) stabilizes helical structure and provides a means for studying rigidly spin labeled peptides by electron spin resonance (ESR). Two new directions in TOAC research are described. The first investigates intermediates formed during alpha-helix unfolding. Double TOAC labeled alpha-helical peptides were unfolded at low temperature in aqueous solution with increasing concentrations of guanidine hydrochloride. Comparison of ESR spectra from two doubly labeled peptides suggests that 3(10)-helix emerges as an intermediate. The second research direction involves the use of high frequency ESR (140 GHz) at low temperature to assess dipolar couplings and, hence, distances between TOAC pairs in a series of 3(10)-helical peptides. Preliminary simulations suggest that high frequency ESR is able to extract correct distances between 6 and 11 A. In addition, the spectra appear to be very sensitive to the relative orientation of the TOAC labels.     

Orientation of spin-labeled light chain 2 of myosin heads in muscle fibers

Electron paramagnetic resonance (e.p.r.) spectroscopy has been used to monitor the orientation of spin labels attached rigidly to a reactive SH residue on the light chain 2 (LC2) of myosin heads in muscle fibers. e.p.r. spectra from spin-labeled myosin subfragment-1 (S1), allowed to diffuse into unlabeled rigor (ATP-free) fibers, were roughly approximated by a narrow angular distribution of spin labels centered at 66 degrees relative to the fiber axis, indicating a uniform orientation of S1 bound to actin. On the other hand, spectra from spin-labeled heavy meromyosin (HMM) were roughly approximated by two narrow angular distributions centered at 42 degrees and 66 degrees, suggesting that the LC2 domains of the two HMM heads have different orientations. In contrast to S1 or HMM, the spectra from rigor fibers, in which LC2 of endogenous myosin heads was labeled, showed a random orientation which may be due to distortion imposed by the structure of the filament lattice and the mismatch of the helical periodicities of the thick and thin filaments. However, spectra from the fibers in the presence of ATP analog 5'-adenylyl imidodiphosphate (AMPPNP) were approximated by two narrow angular distributions similar to those obtained with HMM. Thus, AMPPNP may cause the LC2 domain to be less flexible and/or the S2 portion to be more flexible, so as to release the distortion of the LC2 domain and make it return to its natural position. At high ionic strength, AMPPNP disoriented the spin labels as ATP did under relaxing conditions, suggesting that the myosin head is detached from and/or weakly (flexibly) attached to a thin filament.     

Electron spin resonance study of human alpha 1-acid glycoprotein interaction with a spin labelled steroid.

The interaction of human alpha 1-acid glycoprotein (AAG) with a corticosteroid was studied using nitroxide labeled deoxycorticosterone and electron spin resonance (ESR) spectroscopy. The ESR spectra of the spin labeled steroid in the presence of AAG could be used to characterize the ligand-protein interaction at equilibrium without the need of a separation between bound and free species. An association constant Ka of 6.10(5) M-1 at 20 degrees C and a binding capacity of one site per mole protein were found. ESR spectra recorded at equilibrium at various temperatures allowed the calculation of enthalpy and entropy variations for the steroid-protein interaction; these thermodynamic parameters exhibited a rapid change above 45 degrees C which may be related to a protein conformational modification above this temperature, as detected by circular dichroism study. The ESR spectra width could be used to define a polar character for the spin label environment in the steroid binding site of AAG and to calculate an apparent rotational correlation time of 2.8 x 10(-8) sec for the steroid-protein complex in aqueous solution at 20 degrees C. It can be concluded that spin labeling and ESR methodology is of value in the study of steroid-protein interactions of biological significance above all because it can provide direct physico-chemical information concerning the local environment of the ligand in its binding site at equilibrium.     

Detection and imaging of superoxide in roots by an electron spin resonance spin-probe method

The detection, quantification, and imaging of short-lived reactive oxygen species, such as superoxide, in live biological specimens have always been challenging and controversial. Fluorescence-based methods are nonspecific, and electron spin resonance (ESR) spin-trapping methods require high probe concentrations and lack the capability for sufficient image resolution. In this work, a novel (to our knowledge), sensitive, small ESR imaging resonator was used together with a stable spin probe that specifically reacts with superoxide with a high reaction rate constant. This ESR spin-probe-based methodology was used to examine superoxide generated in a plant root as a result of an apical leaf injury. The results show that the spin probe rapidly permeated the plant's extracellular space. Upon injury of the plant tissue, superoxide was produced and the ESR signal decreased rapidly in the injured parts as well as in the distal part of the root. This is attributed to superoxide production and thus provides a means of quantifying the level of superoxide in the plant. The spin probe's narrow single-line ESR spectrum, together with the sensitive imaging resonator, facilitates the quantitative measurement of superoxide in small biological samples, such as the plant's root, as well as one-dimensional imaging along the length of the root. This type of methodology can be used to resolve many questions involving the production of apoplastic superoxide in plant biology.     

Electron paramagnetic resonance study of the interactions between steroid hormones and binding proteins]

Interaction of a spin labeled corticosteroid (desoxycorticosterone nitroxyde: DOC -NO) with three purified proteins (albumin, transcortin, progesterone binding protein: PBG) was studied by electron spin resonance (ESR) spectroscopy. DOC-NO was competitive with natural corticosteroids and therefore bound at the same site to specific binding proteins. ESR spectra in the presence of each of the proteins showed an immobilized (bound) form of the spin labeled steroid and allowed the calculation of the corresponding association constant (Ka) at equilibrium. The three binding proteins could be characterized by the ESR parameters of the DOC-NO bound form. The thermodynamic parameters (deltaH, deltaS) of the steroid-protein interactions were calculated from the ESR data obtained within a wide temperature range (3--40 degrees C). The ESR spectra width (2T) was used to evaluate the polarity of the spin label environment within the steroid binding site: a hydrophobic character was observed for transcortin whereas PBG exhibited a more hydrophilic steroid binding sits. The rotational correlation time of the three protein DOC-NO complexes at equilibrium were calculated from ESR data; the results were correlated with the protein molecular size and suggested a non spherical shape for the binding macromolecule in solution. Spin labelling of biologically active steroids thus provides a novel approach for the study of the interaction of these hormones with their binding protein. Providing a suitable spin label, the ESR parameters may allow the characterization of several types of binding sites of different biological significance for the same hormone, in biological fluids as well as in target tissues.     

A spin label that binds to myosin heads in muscle fibers with its principal axis parallel to the fiber axis.

We have used an indane-dione spin label (2-[-oxyl-2,2,5,5-tetramethyl-3-pyrrolin-3-yl)methenyl]in dane-1,3-dione), designated InVSL, to study the orientation of myosin heads in bundles of chemically skinned rabbit psoas muscle fibers, with electron paramagnetic resonance (EPR) spectroscopy. After reversible preblocking with 5,5'-dithiobis(2-nitro-benzoic acid) (DTNB), we were able to attach most of the spin label covalently and rigidly to either Cys 707 (SH1) or Cys 697 (SH2) on myosin heads. EPR spectra of labeled fibers contained substantial contributions from both oriented and disordered populations of spin labels. Similar spectra were obtained from fibers decorated with InVSL-labeled myosin heads (subfragment 1), indicating that virtually all the spin labels in labeled fibers are on the myosin head. We specifically labeled SH2 with InVSL after reversible preblocking of the SH1 sites with 1-fluoro-2,4-dinitrobenzene (FDNB), resulting in a spectrum that indicated only disordered spin labels. Therefore, the oriented and disordered populations correspond to labels on SH1 and SH2, respectively. The spectrum of SH2-bound labels was subtracted to produce a spectrum corresponding to SH1-bound labels, which was used for further analysis. For this corrected spectrum, the angle between the fiber axis and the principal axis of the spin label was fitted well by a Gaussian distribution centered at theta o = 11 +/- 1 degree, with a full width at half-maximum of delta theta = 15 +/- 2 degrees. The unique orientation of InVSL, with its principal axis almost parallel to the fiber axis, makes it complementary to spin labels previously studied in this system. This label can provide unambiguous information about axial rotations of myosin heads, since any axial rotation of the head must be reflected in the same axial rotation of the principal axis of the probe, thus changing the hyperfine splitting. Therefore, InVSL-labeled fibers have ideal properties needed for further exploration myosin head orientation and rotational motion in muscle.     

Method for the determination of myosin head orientation from EPR spectra.

The determination of the iodoacetamide spin label orientation in myosin heads (Fajer, 1994) allows us for the first time to determine directly protein orientation from EPR spectra. Computational simulations have been used to determine the sensitivity of EPR to both torsional and tilting motions of myosin heads. For rigor heads (no nucleotide), we can detect 0.2 degree changes in the tilt angle and 4 degrees in the torsion of the head. Sensitivity decreases with increasing head disorder, but even in the presence of +/- 30 degrees disorder as expected for detached heads, 10 degree changes in the center of the orientational distribution can be detected. We have combined these numerical simulations with a Simplex optimization to compare the orientation of intrinsic heads, with the orientation of labeled extrinsic heads that have been infused into unlabeled muscle fibers. The near identity (within 2 degrees) of the orientational distribution in the two instances can be attributed to myosin elasticity taking up the mechanical strain induced by the mismatch of myosin and actin filament periodicity. A similar analysis of the spectra of fibers with ADP bound to myosin revealed a small (approximately 5 degrees-10 degrees) torsional reorientation, without a substantial change of the tilt angle (< 2 degrees).     

A spin-label study of membrane proteins and internal microviscosity of erythrocytes in hereditary spherocytosis

Electron spin resonance (ESR) spectra of erythrocyte membranes of patients with hereditary spherocytosis (HS) and of healthy controls labeled with a maleimide spin label did not differ significantly both before and after prolonged incubation at 37 degrees C. It suggests that the different behavior of spin-labeled HS erythrocyte membranes upon incubation at a higher temperature reported previously is due indeed to structural abnormalities of HS red cell membranes and not to alterations in their proteolytic activity. Measurements of the rotational correlation time of Tempamine spin probe demonstrated a significant elevation of internal microviscosity of erythrocytes in HS, more pronounced in non-splenectomized patients.     

A comparison of spin probe ESR, 2H- and 31P-nuclear magnetic resonance for the study of hexagonal phase lipids

We have investigated the feasibility of the various possible magnetic resonance probes of lipids which form non-bilayer phases. As a model system we have used equimolar mixtures of phosphatidylethanolamine (PE) and cholesterol, which exhibit a thermotropic transition from a bilayer to a hexagonal phase. Variable temperature electron spin resonance (ESR) spin probe spectra were obtained using random dispersion and oriented lipid systems. Simultations of the ESR spectra were performed in order to aid in the interpretation of the experimental results for the oriented system. ³¹P- and ²H-nuclear magnetic resonance (NMR) studies were carried out using a deuterated PE. The ESR spin probes in the random dispersions show essentially no effect attributable to the phase transition. However, there are large, reversible effects in the temperature-dependent behaviour for the oriented system. The orientation dependence of the spectra above the transition temperature indicate that the hexagonal phase lipids may spontaneously assume a macroscopic organization on a flat surface. We find, however, that such an organization cannot be unambiguously assigned from the ESR spin probe spectra, and point out a potential difficulty in the interpretation of spin probe spectra in oriented systems. In contrast, the ²H-NMR method provides a reliable monitor of the phase transformation. Taken together, the ²H and ³¹P data indicate that the structure of the headgroup in PE is quite similar in both the bilayer and hexagonal phase. ²H-NMR should be very useful in probing the structural and dynamic characteristics of lipids in non-bilayer phases.     

Simulation of saturation transfer electron paramagnetic resonance spectra for rotational motion with restricted angular amplitude.

We have simulated both conventional (V1) and saturation transfer (V'2) electron paramagnetic resonance spectra for the case of Brownian rotational diffusion restricted in angular amplitude. Numerical solutions of the diffusion-coupled Bloch equations were obtained for an axially symmetric 14N nitroxide spin label with its principal axis rotating within a Gaussian angular distribution of full width delta theta at half maximum. Spectra were first calculated for a macroscopically oriented system with cylindrical symmetry (e.g., a bundle of muscle fibers or a stack of membrane bilayers), with the Gaussian angular distribution centered at theta 0 with respect to the magnetic field. These spectra were then summed over theta 0 to obtain the spectrum of a randomly oriented sample (e.g., a dispersion of myofibrils or membrane vesicles). The angular amplitude delta theta was varied from 0 degrees, corresponding to isotropic motion (order parameter = 0). For each value of delta theta, the rotational correlation time, tau r, was varied from 10(-7) to 10(-2) s, spanning the range from maximal to minimal saturation transfer. We provide plots that illustrate the dependence of spectral parameters on delta theta and tau r. For an oriented system, the effects of changing delta theta and tau r are easily distinguishable, and both parameters can be determined unambiguously by comparing simulated and experimental spectra. For a macroscopically disordered system, the simulated spectra are still quite sensitive to delta theta, but a decrease in tau r produces changes similar to those from an increase in delta theta. If delta theta can be determined independently, then the results of the present study can be used to determine tau r from experimental spectra. Similarly, if tau r is known, then delta theta can be determined.