Expression and localization of protein kinase C theta isoform in mouse testis.

Protein kinase C (PKC) is encoded by a complex of a gene family, and its multiple isoforms are expressed in various mammalian tissues. The objective of this study was to investigate the expression and localization of a PKC theta isoform in mouse testis. PKC theta displays the highest homology to PKC delta, lacks the Ca2+-binding C2 domain and, thus, belongs to the subfamily of Ca2+-independent PKC enzymes which also includes the delta, epsilon, zeta and eta isoforms. We analyzed the PKC theta mRNA and protein by Northern blotting, in situ hybridization, and immunohistochemistry. In testes of normal mice, signals of PKC theta isoform expression were detected specifically in the interstitial cells of testes. The expression of PKC theta isoform was also detected in testes of germ cell-deficient W/W(v) mice. These results suggest that PKC theta isoform has the specific biological functions in the interstitial cells of testis.     

A new member of the protein kinase C family, nPKC theta, predominantly expressed in skeletal muscle.

A new protein kinase C (PKC)-related cDNA with unique tissue distribution has been isolated and characterized. This cDNA encodes a protein, nPKC theta, which consists of 707 amino acid residues and showed the highest sequence similarity to nPKC delta (67.0% in total). nPKC theta has a zinc-finger-like cysteine-rich sequence (C1 region) and a protein kinase domain sequence (C3 region), both of which are common in all PKC family members. However, nPKC theta lacks a putative Ca2+ binding region (C2 region) that is seen only in the conventional PKC subfamily (cPKC alpha, -beta I, -beta II, and -gamma) but not in the novel PKC subfamily (nPKC delta, -epsilon, -zeta, and -eta). Northern (RNA) blot analyses revealed that the mRNA for nPKC theta is expressed predominantly in skeletal muscle. Furthermore, nPKC theta mRNA is the most abundantly expressed PKC isoform in skeletal muscle among the nine PKC family members. nPKC theta expressed in COS1 cells serves as a phorbol ester receptor. By the use of an antipeptide antibody specific to the D2-D3 region of the nPKC theta sequence, nPKC theta was recognized as a 79-kDa protein upon sodium dodecyl sulfate-polyacrylamide gel electrophoresis in mouse skeletal muscle extract and also in an extract from COS1 cells transfected with an nPKC theta cDNA expression plasmid. Autophosphorylation of immunoprecipitated nPKC theta was observed; it was enhanced by phosphatidylserine and 12-O-tetradecanoylphorbol-13-acetate but attenuated by the addition of Ca2+. These results clearly demonstrate that nPKC theta should be considered a member of the PKC family of proteins that play crucial roles in the signal transduction pathway.     

Sigma factor is not released during transcription in Bacillus subtilis.

The relationship between sigma (sigma) and delta (delta) factors of Bacillus subtilis RNA polymerase has been analyzed during initiation of RNA synthesis. When core enzyme (E) containing delta factor (E delta) binds to DNA, the delta factor is released with the formation of an E-DNA complex. The addition of sigma to the E-DNA complex results in the formation of a stable E sigma-DNA complex which can synthesize RNA upon addition of nucleoside triphosphates. Sigma factor, significantly, is not released from the core during RNA synthesis. These results suggest that delta and sigma factors can act sequentially during initiation of RNA synthesis with delta acting as a DNA recognition factor and sigma acting as an initiation factor. The results do not preclude the possibility that E sigma can initiate RNA synthesis correctly since E sigma alone can bind to DNA and initiate RNA synthesis.     

Phenotypes of Bacillus subtilis mutants altered in the precursor-specific region of sigma E.

sigma E is a sporulation-specific sigma factor of Bacillus subtilis that is synthesized from an inactive precursor protein (P31). The structural gene (sigE) for P31 was reengineered by oligonucleotide-directed mutagenesis to encode sigma E directly. The sequence specifying the first amino acid of sigma E (GGC) was placed immediately downstream of the initiating codon (ATG) of P31. The resulting sigE allele (sigE delta 84) encodes a sigma E-like protein which differs from the "processed product" by a single Met residue at its amino terminus. B. subtilis strains which carried this allele were Spo- and contained no detectable sigma E. The sigE delta 84 allele generated a product in Escherichia coli which, by quantitative Western immunoblot analysis, was present at 10 to 20% of the level of product (P31) obtained from a wild-type allele. A sigma E-like product was also not detected in two B. subtilis strains with missense mutations in the sequence encoding the processed region of P31. These results suggest that sigma E is a highly labile protein that is stabilized during its synthesis by an element of the precursor sequence. A mutant allele (sigE delta 48) which made an active sigma E-like protein in B. subtilis was isolated. This gene specified a product in which five amino acids, not derived from the P31 processed region, were joined to P31 at a position eight amino acids upstream of the processing site. The sigE delta 48 product was not processed, but it activated the sigma E -dependent spoIID promoter in vivo. The sigE delta 48 product therefore lost both an essential target for processing and a region which inhibited sigma sigma E activity. Cells which carried sig E delta 48 were Spo-. The basis of the sigE delta 48-dependent defect in sporulation is unknown, but the sigma E delta 48 activity appeared to persist beyond the time in development (4 h after onset sporulation) when wild-type sigma E activity declines. Thus, it may interfere with the proper regulation of late sporulation genes.     

Osmotic flow equations for leaky porous membranes

A basic set of equations describing the flows of volume (Jv) and solute (Js) across a leaky porous membrane, coupled to the differences of osmotic and hydrostatic pressures d pi and dP has been derived by using general frictional theory. Denoting the mean pore concentration of solute by c*s and the hydraulic and diffusive conductances by Lp and Ps/RT the equations take the form Jv = LpdP + sigma sLp d pi Js = c*s(1 - sigma f)Jv + Ps d pi/RT sigma s = theta (1 - DsVs/DwVw - Ds/Dos) sigma f = 1 - theta DsVs/DwVw - Ds/Dos in which Dw and Ds are the diffusion coefficients for water and solute in the pore and Dos that for free solution. The relation between the reflection coefficients sigma s and sigma f for osmosis and ultrafiltration is then given by sigma s = sigma f - (1- theta)(1 - Ds/Dos), where theta is the diffusive-driven:pressure-driven flow ratio. These equations follow from the fact that in leaky pores osmosis occurs by diffusion alone and that there cannot be any Onsager symmetry leading to sigma s = sigma f. Symmetry holds in the limits where either the pore is small, when sigma s = sigma f = 1, or where the pore is large when sigma s = sigma f = 0.     

Photo-oxygenation sensitized by dyes

This paper discusses the mechanism of photooxygenation reactions sensitized by dyes, such as: rose bengal, methylene blue, tetraphenylporphin and chlorophyll a. First it is shown more particularly that: the quantum yields of singlet oxygen O2(1 delta g) production gamma delta, and of intersystem crossing singlet S1-triplet T1, gamma is, are not always equal and that the possibilities gamma delta greater than or less than gamma is may occur or are observed; the processes S1 + O2(3 sigma)----T1 + O2(3 sigma) and T1 + O2(3 sigma)----S0 + O2(1 delta g) are mainly if not fully responsible for the quenching of the singlet and triplet excited states of the sensitizer by oxygen. Thereafter, clear indication is given of the considerable complication of the photooxygenation which may arise from particular properties of the investigated substrate A (or of other compounds present in the reaction medium) and which may result in a decrease of the oxygenation quantum yield phi O2. It is shown that this lowering of phi O2 is due to that of gamma delta and/or of phi A, (the probability that O2(1 delta g) yields an oxygenation product AO2) since phi O2 = gamma delta phi A. The latter effect can be induced by the quenching of singlet oxygen by the dye, a process which is quite general and which must be always taken into account in kinetic studies.     

Specific association of bromocresol purple anions with a magnesium complex of a phosphorylated intermediate during steady-state hydrolysis of ATP by the Mg2+ + Ca2+-dependent ATPase of sarcoplasmic reticulum

The mechanism of dimeric binding of bromocresol purple (BCP) anions to Mg2+ + Ca2+-ATPase of the sarcoplasmic reticulum (SR) and the resulting partial inhibition of the ATPase activity were studied. BCP anions in three states, free monomer, bound monomer, and bound dimer, were spectrophotometrically calculated by solving simultaneous equations, delta A lambda 1-lambda 2 = sigma delta ai (epsilon i lambda 1-epsilon i lambda 2), and concentration changes of these states were analyzed. The addition of ATP caused an increase in the bound dimer and a decrease in the free monomer, but the change of the bound monomer was slight. The decrease in delta A (decrease phase) on the addition of ATP on dual-wavelength spectrophotometry at 585-610 nm was related to an increase in the amount of dimer bound to the SR membranes. The magnitude of the decrease phase increased with an increase in Mg2+ concentration and decreased with an increase in the concentration of Ca2+. BCP anions at the probe concentration partially inhibited the ATPase activity, and brought about a decrease in the ADP-sensitive E-P (E1P) and an increase in the ADP-insensitive E-P (E2P), though BCP anions did not affect the amount of total E-P. On elimination of Mg2+ at the steady-state E-P level both E2P and E2P . (BCP)2 were decomposed, suggesting that the enzyme form binding the BCP dimer was Mg . E-P. An increase in Mg2+ concentration increased E2P but an increase in Ca2+ concentration decreased E2P. Decomposition of E2P to P1 was inhibited by BCP anions. The following simple scheme was suggested to explain the partial inhibition of the ATPase activity, (Formula: see text). Application of BCP anions was discussed for use as a probe for Mg . E-P in the steady-state ATP hydrolysis.     

Myocardial material mechanics: characteristic variation of the circumferential and longitudinal systolic moduli in left ventricular dysfunction

Active systolic moduli for the circumferential (E theta) and longitudinal (E phi) axes of the left ventricle were determined along with circumferential and longitudinal contractile filament stress (sigma theta and sigma phi) and circumferential and longitudinal fiber strain (epsilon theta and epsilon phi). These material property parameters were determined at four points during cardiac systole. Thirty-nine patients comprising five clinical groups were evaluated using pressure and volume data acquired from single-plane cineangiography. The results indicate that the active moduli exponentially decrease during cardiac systole. Characteristic variations from normal differentiated the various pathological groups. With compensated volume overload, E theta was significantly reduced during the latter half of systole (p less than 0.25). With decompensated volume overload, both E theta and E phi were not significantly different from the normal group throughout cardiac systole. With compensated pressure overload, both E theta and E phi were significantly lower than the normal group at end-systole (p less than 0.005; p less than 0.005). With congestive cardiomyopathy, both E theta and E phi were significantly greater during the latter half of systole compared to the normal group (p less than 0.05 and p less than or equal to 0.025).     

Overexpression of nPKC theta is permissive for myogenic differentiation

Although protein kinase C (PKC) has been shown to participate in skeletal myogenic differentiation, the functions of individual isoforms of PKC in myogenesis have not been completely elucidated. These studies focused on the role of nPKC straight theta, an isoform of the PKC family whose expression has been shown to be regulated by commitment to the myogenic lineage, myogenic differentiation and innervation. We used the myogenic cell line C(2)C(12) as a tissue culture model system to explore the role of nPKC straight theta in the formation of multinucleated myotubes. We examined endogenous levels of nPKC straight theta in C(2)C(12) cells and showed that it is expressed at low levels in myoblasts compared to mouse skeletal muscle and that expression is maintained in myotubes. We overexpressed nPKC straight theta in C(2)C(12) myoblasts and examined the ability of overexpressing cells to differentiate into myotubes. Using an nPKC straight theta - green fluorescent protein (GFP) chimera to detect transfected myoblasts, we showed that overexpressed nPKC straight theta-GFP translocates to the plasma membrane in response to phorbol ester treatment of myoblast cultures in situ. nPKC straight theta-GFP was found to be completely extracted into the detergent-soluble fraction of cell lysates and was stably expressed throughout the extent of differentiation into myotubes. No difference was seen in the ability of myoblasts either overexpressing nPKC straight theta - GFP or GFP alone to form myotubes. These studies demonstrate that overexpression of nPKC straight theta does not interfere with fusion of myoblasts into myotubes suggesting that nPKC straight theta activity is not inhibitory for myogenesis. These studies also demonstrate a method for transfecting myoblasts and identifying differentiated cells that overexpress nPKC straight theta-GFP for investigating the function of nPKC straight theta in living myotubes.     

Effects of Mutation on Selection Limits in Finite Populations with Multiple Alleles

The ultimate response to directional selection (i.e., the selection limit) under recurrent mutation is analyzed by a diffusion approximation for a population in which there are k possible alleles at a locus. The limit mainly depends on two scaled parameters S (= 4Ns sigma a) and theta (= 4Nu) and k, the number of alleles, where N is the effective population size, u is the mutation rate, s is the selection coefficient, and sigma 2a is the variance of allelic effects. When the selection pressure is weak (S less than or equal to 0.5), the limit is given approximately by 2S sigma a[1 - (1 + c2)/k]/(theta + 1) for additive effects of alleles, where c is the coefficient of variation of the mutation rates among alleles. For strong selection, other approximations are devised to analyze the limit in different parameter regions. The effect of mutation on selection limits largely relies on the potential of mutation to introduce new and better alleles into the population. This effect is, however, bounded under the present model. Unequal mutation rates among alleles tend to reduce the selection limit, and can have a substantial effect only for small numbers of alleles and weak selection. The selection limit decreases as the mutation rate increases.     

Activity of novel protein kinase C and distribution of protein kinase C theta in subcellular fractions of normal and Duchenne muscular dystrophic muscle

Phospholipid-dependent, Ca(2+)-independent isoenzymes termed novel protein kinase C or nPKC, include PKC delta, epsilon, eta, theta and mu. Status and role of nPKC and PKC theta in Duchenne muscular dystrophic (DMD) condition is unknown. In the present study, we have shown that most of the nPKC isoforms are translocated to the membrane fraction of DMD tissue specimen. It is well established that translocation plays a key role in signal transduction by individual PKC isoforms. In our experiment, the increased association of nPKC isoform PKC theta to membrane was further confirmed by Western blot. Increased expression of PKC theta mRNA was identified by dot blot analysis. The above results suggest that, the alterations in nPKC location and increased expression of PKC theta observed is a result of modification of PKC-mediated signal transduction and cell function.     

Osmotic reflection coefficient for total plasma protein in lung microvessels

The osmotic reflection coefficient (sigma) for total plasma proteins was estimated in 11 isolated blood-perfused canine lungs. Sigma's were determined by first measuring the capillary filtration coefficient (Kf,C in ml X min-1 X 100g-1 X cmH2O-1) using increased hydrostatic pressures and time 0 extrapolation of the slope of the weight gain curve. Kf,C averaged 0.19 +/- 0.05 (mean +/- SD) for 14 separate determinations in the 11 lungs. Following a Kf,C determination, the isogravimetric capillary pressure (Pc,i) was determined and averaged 9.9 +/- 0.5 cmH2O for all controls reported in this study. Then the blood colloids in the perfusate were either diluted or concentrated. The lung either gained or lost weight, respectively, and an initial slope of the weight gain curve (delta W/delta t)0 was estimated. The change in plasma protein colloid osmotic pressure (delta IIP) was measured using a membrane osmometer. The measured delta IIP was related to the effective colloid osmotic pressure (delta IIM) by delta IIM = (delta W/delta t)0/Kf,C = sigma delta IIP. Using this relationship, sigma averaged 0.65 +/- 0.06, and the least-squares linear regression equation relating Pc,i and the measured IIP was Pc,i = -3.1 + 0.67 IIP. The mean estimate of sigma (0.65) for total plasma proteins is similar to that reported for dog lung using lymphatic protein flux analyses, although lower than estimates made in skeletal muscle using the present methods (approximately 0.95).     

The Gibbs-Donnan near-equilibrium system of heart

The gradients of the major inorganic ions across the plasma membrane of heart were examined to determine the factors controlling the extent and direction of the changes induced during injury, certain diseases, and electrolyte disturbances. The ionic environment was altered by changing only the concentration of inorganic phosphate, [sigma Pi]o, from 0 to 1.2 to 5 mM in the Krebs-Henseleit buffer perfusing working rat hearts. Raising [sigma Pi]o from 1.2 to 5 mM resulted in a decrease in total Mg2+ content and calculated free cytosolic [Mg2+] from 0.44 to 0.04 mM, conversion of 4 mmol of MgATP2- to ATP4- and a decrease in measured intracellular [Cl-]i from 41 to 16 mM. At all levels of [sigma Pi]o, both the [Na+]i and [K+]i were invariant at about 3 mM and 130 mM, respectively, as was the energy of hydrolysis of the terminal phosphate bond of sigma ATP, delta GATP Hydr, of -13.2 kcal/mol. The relationship maintained between the ions on both sides of the plasma membrane by the 3Na+/2K(+)transporting ATPase (EC 3.6.1.37) and an open K+ channel was: (formula; see text) The energy of the gradients of the other inorganic ions across the plasma membrane, delta G[ion]o/i, exhibited three distinct quanta of energy derived from the prime quantum of delta GATP Hydr of -13.2 kcal/mol. The second quantum was about one-third of delta GATP Hydr or +/- 4.4 kcal/mol and comprised the delta G[Na+]o/i, delta G[Mg2+]o/i, and delta G[HPO42-]o/i. These results indicated near-equilibrium was achieved by the reactants of the 3Na+/2K(+)-ATPase, the K+ channel, the Na(+)-Pi co-transporter, and a postulated net Mg2+/H2PO4- exchanger. The third quantum was one-third of delta G[Na+]o/i or about +/- 1.5 kcal/mol and comprised delta G[H+]o/i, delta G[HCO3-]o/i, and delta G[Cl-]o/i. The delta G[K+]o/i was 0, indicating near-equilibrium between the chemical energy of [K+]o/i and the E across the plasma membrane of -83 mV. It is concluded that the gradients of the major inorganic ions across the plasma membrane and the potential across that membrane constitute a Gibbs-Donnan equilibrium system catalyzed by transport enzymes sharing common substrates. The chemical and electrical energies of those gradients are equal in magnitude and opposite in sign to the chemical energy of ATP hydrolysis.     

Stimulus-induced phosphorylation of PKC theta at the C-terminal hydrophobic-motif in human T lymphocytes

Protein kinase C (PKC) is a family of serine/threonine kinases whose activity is controlled, in part, by phosphorylation on three conserved residues that are located on the catalytic domain of the enzyme, known as the activation-loop, the turn-motif, and the C-terminal hydrophobic-motif sites. Using a panel of phospho-specific antibodies, we have determined that PKC beta(I) and delta are constitutively phosphorylated on all three sites in unstimulated and activated T cells. Although PKC theta is constitutively phosphorylated at the activation-loop and turn-motif sites in T cells, PMA or anti-CD3/CD28 stimulation results in an increase in phosphorylation at the hydrophobic-motif (Ser695), an event that coincides with translocation of the enzyme from the cytosol/cytoskeleton to the membrane. Studies on the stimulus-induced phosphorylation of PKC theta demonstrate that an upstream kinase activity involving a conventional PKC isoform(s) and the PI3-kinase pathway, rather than autophosphorylation or the rapamycin-sensitive mTOR pathway, regulates this site in T lymphocytes. However, hydrophobic-motif phosphorylation does not appear to control membrane translocation, suggesting that this site may control other aspects of PKC theta signalling.     

Localization of conserved and variable segments in amino acid sequences of homologous proteins using a personal computer]

A set of aligned homologous protein sequences is divided into two groups consisting of the most related sequences m and k. The value of the position variability of homologous protein sequences is defined as a number of failures to coincide in the intergroup comparison of all possible k x m pairs of amino acid residues in that position divided by k x m. The position variability value plotted vs the sequence position number with a window of 10 positions gives the intergroup local variability profile. The area S of the figure included between the local variability profile and the straight line corresponding to the mean local variability value is compared with the average area S(r) for 1000 random homologous protein families. If S is greater than S(r) by more than 2 standard deviation units sigma r the local variability profile is assumed to contain peaks and hollows corresponding to significant variable and conservative regions of the sequences. The profile extrema containing the area surplus delta S = S-(S(r) + 2 sigma r) are cut off by two straight lines to locate significant regions. The numerical experiment on the family of homologous phospholipases A2 revealed the linear dependence of the values S(r) and sigma r upon the position variability standard deviation sigma v of the homologous sequences. Furthermore, it was shown for protein families of various length (rhodopsins, aspartate aminotransferases, cytochromes b, L- and M-subunits of photosynthetic bacteria photoreaction centre and alpha-subunits of Na, K-ATPase), that delta S = S - n(S'r + 2 sigma r), where S - the area of the local variability profile, n = L/l (L - the length of the given protein family and l - the length of the hypothetical protein domain). If l = 250 then S'r = -1.42 + 62.56 sigma v and sigma'r = -0.14 + 7.46 sigma v.     

Effect of residual stress and heterogeneity on circumferential stress in the arterial wall

Quantifying the stress distribution through the arterial wall is essential to studies of arterial growth and disease. Previous studies have shown that both residual stress, as measured by opening angle, and differing material properties for the media-intima and the adventitial layers affect the transmural circumferential stress (sigma theta) distribution. Because a lack of comprehensive data on a single species and artery has led to combinations from multiple sources, this study determined the sensitivity of sigma theta to published variations in both opening angle and layer thickness data. We fit material properties to previously published experimental data for pressure-diameter relations and opening angles of rabbit carotid artery, and predicted sigma theta through the arterial wall at physiologic conditions. Using a one-layer model, the ratio of sigma theta at the internal wall to the mean sigma theta decreased from 2.34 to 0.98 as the opening angle increased from 60 to 130 deg. In a two-layer model using a 95 deg opening angle, mean sigma theta in the adventitia increased (112 percent for 25 percent adventitia) and mean sigma theta in the media decreased (47 percent for 25 percent adventitia). These results suggest that both residual stress and wall layers have important effects on transmural stress distribution. Thus, experimental measurements of loading curves, opening angles, and wall composition from the same species and artery are needed to accurately predict the transmural stress distribution in the arterial wall.     

Differential regulation of T-cell receptor processing and surface expression affected by CD3 theta, an alternatively spliced product of the CD3 zeta/eta gene locus.

The T-cell receptor (TCR) is a multisubunit complex consisting of the clonotypic Ti alpha and beta (or Ti gamma and delta) subunits and the invariant CD3 gamma, CD3 delta, CD3 epsilon, CD3 zeta, and CD3 eta subunits. Herein, we describe an additional product from the CD3 zeta/eta gene locus which we have termed CD3 theta. The cDNA derives from the first seven exons common to CD3 zeta and CD3 eta, 94 base pairs (bp) of the CD3 eta-specific exon 9 and an additional exon 10 encoding the carboxyl-terminal 15 amino acids and the 3'-untranslated region. The expression of CD3 theta is equivalent to that of CD3 eta in tissue distribution and level of expression as judged by RNase protection analysis. Despite the identity of the amino-terminal 121 amino acids of CD3 zeta, CD3 eta, and CD3 theta and an additional 31 amino acids shared between CD3 eta and CD3 theta, transfection of CD3 theta into the CD3 zeta- eta- T-cell hybridoma, MA5.8, failed to restore detectable surface TCR expression in contrast to transfection with CD3 zeta or CD3 eta. Analysis of the CD3 theta protein in transfectants indicated that CD3 theta is associated with the TCR intracellularly. However, unlike with CD3 zeta, Ti alpha-beta chains remain endoglycosidase H sensitive, suggesting a role for the unique COOH-terminal segment of CD3 theta in mediating TCR retention and/or degradation in a pre-Golgi compartment.     

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.