Mathematical aspects of molecular replacement. III. Properties of space groups preferred by proteins in the Protein Data Bank.

The main goal of molecular replacement in macromolecular crystallography is to find the appropriate rigid-body transformations that situate identical copies of model proteins in the crystallographic unit cell. The search for such transformations can be thought of as taking place in the coset space Γ\G where Γ is the Sohncke group of the macromolecular crystal and G is the continuous group of rigid-body motions in Euclidean space. This paper, the third in a series, is concerned with viewing nonsymmorphic Γ in a new way. These space groups, rather than symmorphic ones, are the most common ones for protein crystals. Moreover, their properties impact the structure of the space Γ\G. In particular, nonsymmorphic space groups contain both Bieberbach subgroups and symmorphic subgroups. A number of new theorems focusing on these subgroups are proven, and it is shown that these concepts are related to the preferences that proteins have for crystallizing in different space groups, as observed in the Protein Data Bank.

The identification of tryptophan residues responsible for ATP-induced increase in intrinsic fluorescence of myosin subfragment 1.

ATP binding to myosin subfragment 1 (S1) induces an increase in tryptophan fluorescence. Chymotryptic rabbit skeletal S1 has 5 tryptophan residues (Trp113, 131, 440, 510 and 595), and therefore the identification of tryptophan residues perturbed by ATP is quite complex. To solve this problem we resolved the complex fluorescence spectra into log-normal and decay-associated components, and carried out the structural analysis of the microenvironment of each tryptophan in S1. The decomposition of fluorescence spectra of S1 and S1-ATP complex revealed 3 components with maxima at ca. 318, 331 and 339-342 nm. The comparison of structural parameters of microenvironment of 5 tryptophan residues with the same parameters of single-tryptophan-containing proteins with well identified fluorescence properties applying statistical method of cluster analysis, enabled us to assign Trp595 to 318 nm, Trp440 to 331 nm, and Trp 13, 131 and 510 to 342 nm spectral components. ATP induced an almost equal increase in the intensities of the intermediate (331 nm) and long-wavelength (342 nm) components, and a small decrease in the short component (318 nm). The increase in the intermediate component fluorescence most likely results from an immobilization of some quenching groups (Met437, Met441 and/or Arg444) in the environment of Trp440. The increase in the intensity and a blue shift of the long component might be associated with conformational changes in the vicinity of Trp510. However, these conclusions can not be extended directly to the other types of myosins due to the diversity in the tryptophan content and their microenvironments.

A nanosecond fluorescence study of the simultaneous influx of Ca2+ and Cd2+ into liposomes.

Nanosecond fluorescence decay characteristics of the calcium-binding probe Quin2 and two of its cation complexes were examined by time-resolved fluorescence spectroscopy. Binding of Ca2+ and Cd2+ resulted in fluorescence lifetime enhancements as compared to that of free Quin2 ('tau' = 0.9 ns). The Quin2-Ca2+ complex displays a monoexponential decay of tau = 7.4 ns, while the cadmium complex gives an average decay time of ca. 4 ns. Lifetime measurements made on heterogeneous cationic solutions demonstrate that decay times for individual complexes can be retrieved. Time-resolved measurements were used to monitor the kinetics of ionomycin-mediated calcium and cadmium transport across artificial membranes. Fluorescence decays, collected on the time-scale of second, were sufficient to measure individual ion fluxes or those of mixtures into liposomes. The combination of steady-state and time-resolved fluorescence techniques offers the unique advantage of simultaneously detecting other cations in the presence of calcium.

The tryptophan fluorescence of Tetracarbidium conophorum agglutinin II and a solution-based assay for the binding of a biantennary glycopeptide.

The plant lectin Tetracarbidium conophorum agglutinin II binds to glycoproteins and glycopeptides in a structurally specific manner [Animashaun et al., (1994) Glycoconjugate J. 11, 299-303]. We have characterized the steady-state and time-resolved fluorescence of the tryptophan residues of this lectin. The fluorescence (lambda[ex] = 295 nm, lambda[em] = 350 nm) decay is complex and can be described by four decay times with the following values: tau1 = 7.4 nsec, alpha1 = 0.22; tau2 = 2.9 nsec, alpha2 = 0.25: tau3 = 1.0 nsec, alpha3 = 0.34, tau4 = 0.2 nsec, alpha4 = 0.18. The addition of a biantennary glycopeptide (carbohydrate sequence [see text]) to the lectin results in a quench and an 8 nm blue shift of the emission spectrum. The effect is saturable, and is described by an association constant of 1.8 x 10(5) M(-1). The tryptophan fluorescence of Tetracarbidium conophorum agglutinin II may therefore be utilized to characterize thermodynamically the binding interactions between this lectin and complex glycoprotein.

Fluorescence study of the multiple binding equilibria of the galactose repressor.

A fluorescence assay has been developed to study the multiple linked equilibria which function in regulation of the Escherichia coli galactose operon. Fluorescein 5-isothiocyanate was attached to Amino-Modifier C6dT at different positions in an oligonucleotide containing the sequence for the OE site of the galactose operon. These fluorescently labeled oligonucleotides were used to study OEDNA-GalR-d-galactose interactions. The data were analyzed and fit to various models including the classical competitive binding model as well as models involving the formation of a ternary DNA-repressor-inducer complex. Examination of the reduced chi-square of the various fits and comparison of fitted parameters with those obtained in independent experiments were used to distinguish different models. Since the ternary complex is likely to exist under physiological conditions, our results suggest that obligatory dissociation of GalR from DNA may not be required for induction of the gal operon. Rather, induction may involve the formation of a ternary complex of OEDNA with GalR and D-galactose with a different conformation than the GalR-OEDNA binary repressor complex.

Characterization of fluorescence quenching in bifluorophoric protease substrates.

NorFES is a relatively rigid, bent undecapeptide which contains an amino acid sequence that is recognized by the serine protease elastase (AspAlaIleProNle downward arrow SerIleProLysGlyTyr ( downward arrow indicates the primary cleavage site)). Covalent attachment of a fluorophore on each side of NorFES's elastase cleavage site enables one to use a change of fluorescence intensity as a measure of enzymatic activity. In this study two bichromophoric NorFES derivatives, D-NorFES-A and D-NorFES-D, were prepared in which D (donor) was tetramethylrhodamine and A (acceptor) was rhodamine-X, two chromophores with characteristics suitable for energy transfer. Absorption and fluorescence spectra were obtained with both the intact and cleaved homodoubly, heterodoubly and singly labeled derivatives. It was found that both the homo and hetero doubly-labeled derivatives form ground-state complexes which exhibit exciton bands. The hetero labeled derivative exhibits little or no resonance energy transfer. Spectral measurements were also done in urea, which partially disrupts ground-state dimers.

Steady-state and time-resolved fluorescence measurements for studying molecular interactions: interaction of a calcium-binding probe with proteins.

The binding of 2-[(2-bis-[carboxymethyl]amino-5-methylphenoxy)-methyl] 6-methoxy-8-bis[carboxymethyl] aminoquinoline, the fluorescent calcium probe Quin2, to serum albumin and several other proteins has been investigated. Changes in fluorescence emission spectra and fluorescence anisotropy revealed interactions between Quin2 and several proteins including human serum albumin, bovine serum albumin, aldolase, phosphoglucose isomerase, glyceraldehyde-3-phosphate dehydrogenase, and alkaline phosphatase. Protein-probe interactions were inhibited by the presence of calcium. Binding was also measured by resonance energy transfer and gel permeation chromatography. Equilibrium binding constants for Quin2 were quantitated by the application of the recently-developed "SPECTRABIND' program to spectroscopic data (D. Toptygin and L. Brand, Anal. Biochem., 224 (1995) 330-338). Binding of Quin2 to human serum albumin is discussed in terms of the published X-ray crystal structure of human serum albumin (X.M. He and D.C. Carter, Nature, 358 (1992) 209-215).

Profluorescent protease substrates: intramolecular dimers described by the exciton model.

Xanthene dyes are known to form dimers with spectral characteristics that have been interpreted in terms of exciton theory. A unique aspect of H-type dimers is the fluorescence quenching that accompanies their formation. Using the principles of exciton theory as a guide, a series of protease substrates was synthesized with a xanthene dye on each side of the cleavage site. To bring the attached dyes into spatial proximity to form a dimer, the molecular design included structure determinant regions in the amino acid sequence. In addition, chromophores were chosen such that changes in absorption spectra indicative of exciton splitting were anticipated. Cleavage of the peptides by a protease resulted in disruption of the dimers and indeed significant absorption spectral changes were observed. Furthermore, substrate cleavage was accompanied by at least an order of magnitude increase in fluorescence intensity. This has allowed determination of intracellular elastase activity using a fluorescence microscope equipped with standard optics.

Analysis of equilibrium binding data obtained by linear-response spectroscopic techniques.

A new computational approach for the analysis of equilibrium binding data obtained by spectroscopic methods is described. The approach is aimed at systems involving multiple interactions, where the changes in the spectroscopic signal cannot be attributed to a single interaction. A family of absorption or fluorescence spectra or decay curves obtained in a course of multiple titrations can be decomposed into basic components in an infinite variety of different ways. Model equilibrium equations are used as constraints to determine the basic components associated with the actual chemical species and the concentrations of these species. No assumption is made regarding the parametric form of the component spectra or decays. Binding constants are evaluated simultaneously with the resolved spectra and/or decays in a nonlinear least-square procedure. A key benefit of the method presented is the reduction in the number of fitting parameters. The conditions necessary and sufficient for the existence of a unique solution are considered. The application of the method is demonstrated with experimental data involving titrations of horse liver alcohol dehydrogenase with NADH and isobutyramide.

Determination of DPH order parameters in unoriented vesicles.

This article reviews the determination of orientational order parameters in non-macroscopically oriented membranes from the data obtained with the fluorescent probe all-trans-1,6-diphenyl-1,3,5-hexatriene (DPH). Special attention is paid to the effect of microheterogeneity in the probe environment on the recovered values of the order parameters. An effort is made to accommodate new findings in the existing picture of orientational order in membranes.

Fluorescence decay of DPH in lipid membranes: influence of the external refractive index.

The radiative decay rate of a fluorescent probe in an optically thin layer is known to depend on the orientation of the probe and on the refractive indices inside and outside the layer (W. Lukosz, Phys. Rev. B 22 (1980) 3030). Fluorescent probes in phospholipid bilayer membranes approximate such a system. The natural lifetime is expected to vary with the refractive index of the medium surrounding the bilayer. The lifetime variation with the refractive index depends on the orientation of the fluorescent probe. This can be used to retrieve the second-rank orientational order parameter, . The fluorescence decay of all-trans 1,6-diphenyl-1,3,5-hexatriene in L-alpha-dipalmitoyl-phosphatidylcholine large unilamellar vesicles (LUVs) was measured at a temperature well below that of the phase transition. The refractive index of the medium was varied by addition of glycerol or sucrose. The observed change of decay time with the refractive index followed the theoretical prediction. The value of the order parameter, , recovered is significantly lower than that obtained from fluorescence polarization data. Possible reasons for this disagreement are discussed.

Dynamic fluorescence measurements of two-state systems: applications to calcium-chelating probes.

A fluorescence technique for characterizing ligand binding is evaluated. This technique uses the combination of steady-state and time-resolved methods to recover molar concentrations and overcomes errors inherent in the use of either method alone. The technique is applicable to time-resolved measurements made either with time-domain or frequency-domain instrumentation. A straightforward single-frequency phase/modulation approach is presented to determine whether an experimental system can be described by a two-state system. The approach is based on a nonlinear transformation of the phase/modulation data that results in a linear model function. Here, the theory is applied to the fluorescent calcium-binding probes Quin-2 and Calcium Green, but is relevant to studies involving other interacting systems. The technique described is used to assess the fraction of bound ligand (Ca2+) and binding constants for these probes.

Time-resolved intrinsic fluorescence of Enzyme I. The monomer/dimer transition.

Enzyme I of the bacterial phosphotransferase system can exist in a monomer/dimer equilibrium which may have functional significance. Each monomer contains two tryptophan residues. It is demonstrated that the decay of both the monomer and the dimer can be described by a biexponential. The decay times depend on the temperature and at 6 degrees C the decay times are tau 1 = 0.4 ns and tau 2 = 3.2 ns for the monomer and tau 3 = 3.2 ns and tau 4 = 7.2 ns for the dimer form of the enzyme. The changes in the fluorescence decay parameters can be utilized to measure the equilibrium constant for the monomer/dimer transition.

Rotational relaxation rate of 1,6-diphenyl-1,3,5-hexatriene in cytoplasmic membranes of Bacillus subtilis. A new model of heterogeneous rotations.

The temperature dependence of fluorescence anisotropy, lifetime and differential tangent of 1,6-diphenyl-1,3,5-hexatriene (DPH) and its polar trimethylammonium derivative (TMA-DPH) were investigated in cytoplasmic membranes of Bacillus subtilis. The fluorescence parameters were compared in the two types of membranes prepared from bacteria cultivated at 20 and 40 degrees C. Steady-state anisotropy measurements showed that within a broad range of temperatures, membranes cultivated at 20 degrees C exhibit significantly lower values than those prepared from cells cultivated at 40 degrees C. The temperature dependence of lifetime and differential tangent measurements (differential polarized phase fluorimetry) were fully consistent with steady-state anisotropy data of both DPH and TMA-DPH. The low anisotropy values in the case of TMA-DPH could be explained by a shorter lifetime and higher temperature-induced decrease as compared with DPH. Surprisingly, the temperature dependence of rotational rate R calculated according to the model of hindered rotations (Lakowicz 1983) gave misleading results. When increasing the temperature from 5 to 25 degrees C, a marked drop of rotational relaxation rate was observed. The minimum R values were measured between 25 and 30 degrees C and further increase of temperature (up to 60 degrees C) was reflected as increase of the R values. Therefore, a new model of "heterogeneous rotations" was developed. This model assumes that even at low temperatures (approaching 0 degrees C) where the differential tangent reaches zero, a fraction of fast rotating molecules exists. The ratio between fast and slowly rotating molecules may be expressed by this model, the newly calculated rotational rates are fully consistent with anisotropy, lifetime and differential tangent measurements and represent the monotonically increasing function of temperature.