Possible explanations for the tooth loss and cardiovascular disease relationship

Dynamics of proteins and membranes are usually investigated by red-edge excitation spectra and fluorescence anisotropy. In a viscous or rigid medium, the fluorescence maximum position changes with the excitation wavelength upon red-edge excitation. In addition to the shift in the emission maximum on red edge excitation, fluorescence anisotropy is also known to be dependent on the excitation and emission wavelengths in viscous media. However, this dependence has always been explained by the fact that the fluorophore is rigid, i.e. it does not display any residual motions. The aim of the present work was to check the validity of this latest assumption and to explain the possible origin of the dependence of the anisotropy on both the excitation and emission wavelengths. Therefore, we compared the results obtained from the fluorescence of the Trp residues of two alpha 1-acid glycoproteins (orosomucoid). One protein was purified by chromatographic methods (orosomucoid(c)) and the other was obtained with ammonium sulfate precipitation (orosomucoid(s)). Trp residues of orosomucoidc display free motions while those of orosomucoids are rigid. The general qualitative feature of the excitation anisotropy spectra recorded on both types of preparation is identical and resembles that obtained for other proteins containing tryptophan residue in protein. The fluorescence anisotropy measured across the emission spectra decreases for both preparations, indicating that this phenomenon is characteristic for fluorophores surrounded by a rigid microenvironment or by a microenvironment that displays motions. The fluorescence anisotropy variation across the emission and the excitation spectra is more important when the fluorophore possesses constrained motions than when it displays a high degree of freedom. Our results clearly demonstrate that the tertiary structure of the protein and the structure and dynamics of the microenvironments of the Trp residues are the origin of the dependence of anisotropy on the excitation and emission wavelengths.     

Protein rotational dynamics investigated with a dual EPR/optical molecular probe. Spin-labeled eosin

An acyl spin-label derivative of 5-aminoeosin (5-SLE) was chemically synthesized and employed in studies of rotational dynamics of the free probe and of the probe when bound noncovalently to bovine serum albumin using the spectroscopic techniques of fluorescence anisotropy decay and electron paramagnetic resonance (EPR) and their long-lifetime counterparts phosphorescence anisotropy decay and saturation transfer EPR. Previous work (Beth, A. H., Cobb, C. E., and J. M. Beechem, 1992. Synthesis and characterization of a combined fluorescence, phosphorescence, and electron paramagnetic resonance probe. Society of Photo-Optical Instrumentation Engineers. Time-Resolved Laser Spectroscopy III. 504-512) has shown that the spin-label moiety only slightly altered the fluorescence and phosphorescence lifetimes and quantum yields of 5-SLE when compared with 5-SLE whose nitroxide had been reduced with ascorbate and with the diamagnetic homolog 5-acetyleosin. In the present work, we have utilized time-resolved fluorescence anisotropy decay and linear EPR spectroscopies to observe and quantitate the psec motions of 5-SLE in solution and the nsec motions of the 5-SLE-bovine serum albumin complex. Time-resolved phosphorescence anisotropy decay and saturation transfer EPR studies have been carried out to observe and quantitate the microseconds motions of the 5-SLE-albumin complex in glycerol/buffer solutions of varying viscosity. These latter studies have enabled a rigorous comparison of rotational correlation times obtained from these complementary techniques to be made with a single probe. The studies described demonstrate that it is possible to employ a single molecular probe to carry out the full range of fluorescence, phosphorescence, EPR, and saturation transfer EPR studies. It is anticipated that "dual" molecular probes of this general type will significantly enhance capabilities for extracting dynamics and structural information from macromolecules and their functional assemblies.     

Anisotropic molecular rotational diffusion in 15N spin relaxation studies of protein mobility

The backbone dynamics of the uniformly 15N-labeled N-terminal 63-residue DNA-binding domain of the 434 repressor has been characterized by measurements of the individual 15N longitudinal relaxation times, T1, transverse relaxation times, T2, and heteronuclear 15N[1H]-NOEs at 1H resonance frequencies of 400 and 750 MHz. The dependence of an apparent spherical top correlation time, tauR, on the orientation of the N-H bond vector with respect to the principal axes of the global diffusion tensor of the protein was used to establish the fact that the degree of anisotropy of the global molecular tumbling amounts to 1.2, which is in good agreement with the values obtained from model calculations of the hydrodynamic properties. A model-free analysis showed that even this small anisotropy leads to the implication of artifactual slow internal motions for at least two residues when the assumption of isotropic global motion is used. Additional residues may actually undergo internal motions on the same time scale as the global rotational diffusion, in which case the model-free approach would, however, be inappropriate for quantifying the correlation times and order parameters. Overall, the experiments with 434(1-63) demonstrate that the assumption of isotropic rotational reorientation may result in artifacts of model-free interpretations of spin relaxation data even for proteins with small deviations from spherical shape.     

Analysis of isomeric mixtures using blackbody infrared radiative dissociation: determining isomeric purity and obtaining individual tandem mass spectra simultaneously

A new method that makes possible, for the first time, simultaneous acquisition of individual dissociation mass spectra of isomeric ions in mixtures is presented. This method exploits the exquisite sensitivity of blackbody infrared radiative dissociation kinetics to minor differences in ion structure. Instead of separating precursor ions based on mass (isomers have identical mass), fragment ions are related to their original precursor ions on the basis of rate constants for dissociation. Mixtures of the peptide isomers des-R1 and des-R9 bradykinin are dissociated simultaneously at several temperatures. By fitting the kinetic data to double-exponential functions, the dissociation rate constant and abundance of each isomer in the mixture are obtained. To overcome the difficulty of fitting double-exponential functions, a novel global analysis method is used in which several dissociation data sets collected at different temperatures are simultaneously fit. The kinetic data measured at multiple temperatures are modeled with the preexponentials (corresponding to the abundance of each isomer) as "global" parameters which are constant for all data sets and the exponentials (rate constants) as "local" variables which differ for each data set. The use of global parameters significantly improves the accuracy with which abundances and dissociation rate constants of each individual compound can be obtained from the mixture data. Fragment ions produced from a mixture of these two isomers are related back to their respective precursor ions from the kinetic data. Thus, not only can the composition of the isomeric mixture be determined but an individual tandem mass spectrum of each component in the mixture can be obtained.     

Fluorescence depolarization studies on the flexibility of myosin rod

The single photon counting method has been used to measure the decay of fluorescence polarization anisotropy of myosin rods labeled with extrinsic fluorophores. Rods labeled with 8-anilino-1-naphthalenesulfonate (ANS) or 5-dimethylaminoaphthalene-1-sulfonyl chloride (DNS-Cl) exhibit negative rotational correlation times; the anisotropy increases with time. Possible artifactual causes for the negative decay times are ruled out. It is shown that such curves are to be expected for rigid rods when the fluorophore is bound so that the absorption and emission dipoles each make a small angle with the long axis of the molecule and lie on opposite sides of the rod. At pH 4 and below, rapid decay of the anisotropy (positive correlation times) indicates the presence of a freely bending region in the rod. This is probably the proteolytically sensitive region between light meromyosin and heavy meromyosin subfragment 2. At pH 8, no such free bending is observed, even at temperatures as high as 50 degrees C. From this observation and other physical properties of the rod, we conclude that, at pH 8, the hinge region has considerable resistance to bending. It is more like a spring than a free hinge. The rotational diffusion about the rod axis is faster than would be predicted for a rigid, smooth molecule.     

Quantitation of fluorescence energy transfer between cell surface proteins via fluorescence donor photobleaching kinetics

We describe practical aspects of photobleaching fluorescence energy transfer measurements on individual living cells. The method introduced by T. M. Jovin and co-workers (see, most recently, Kubitscheck et al. 1993. Biophys. J. 64:110) is based on the reduced rate of irreversible photobleaching of donor fluorophores when acceptor fluorophores are present. Measuring differences in donor photobleaching rates on cells labeled with donor only (fluorescein isothiocyanate-conjugated proteins) and with both donor and acceptor (tetramethylrhodamine-conjugated proteins) allows calculation of the fluorescence energy transfer efficiency. We assess possible methods of data analysis in light of the underlying processes of photobleaching and energy transfer and suggest optimum strategies for this purpose. Single murine B lymphocytes binding various ratios of donor and acceptor conjugates of tetravalent concanavalin A (Con A) and divalent succinyl Con A were examined for interlectin energy transfer by these methods. For Con A, a maximum transfer efficiency of 0.49 +/- 0.02 was observed. Under similar conditions flow cytometric measurements of donor quenching yielded a value of 0.54 +/- 0.03. For succinyl Con A, the maximum transfer efficiency was 0.36. To provide concrete examples of quantities arising in such energy transfer determinations, we present examples of individual cell data and kinetic analyses, population rate constant distributions, and error estimates for the various quantities involved.     

Real-time enzyme kinetics monitored by dual-color fluorescence cross-correlation spectroscopy

A method for sensitively monitoring enzyme kinetics and activities by using dual-color fluorescence cross-correlation spectroscopy is described. This universal method enables the development of highly sensitive and precise assays for real-time kinetic analyses of any catalyzed cleavage or addition reaction, where a chemical linkage is formed or cleaved through an enzyme's action between two fluorophores that can be discriminated spectrally. In this work, a homogeneous assay with restriction endonuclease EcoRI and a 66-bp double-stranded DNA containing the GAATTC recognition site and fluorophores at each 5' end is described. The enzyme activity can be quantified down to the low picomolar range (>1.6 pM) where the rate constants are linearly dependent on the enzyme concentrations over two orders of magnitude. Furthermore, the reactions were monitored on-line at various initial substrate concentrations in the nanomolar range, and the reaction rates were clearly represented by the Michaelis-Menten equation with a KM of 14 +/- 1 nM and a kcat of 4.6 +/- 0.2 min-1. In addition to kinetic studies and activity determinations, it is proposed that enzyme assays based on the dual-color fluorescence cross-correlation spectroscopy will be very useful for high-throughput screening and evolutionary biotechnology.     

The shape of self-motion perception--I. Equivalence classification for sustained motions

Two completely different motions of a subject relative to the earth can induce exactly the same stimuli to the vestibular, somatosensory and visual systems. When this happens, the subject may experience disorientation and misperception of self-motion. We have identified large classes of motions that are perceptually equivalent, i.e. indistinguishable by the subject, under three sets of conditions: no vision, with vision and earth-fixed visual surround, and with vision during possible movement of the visual surround. For each of these sets of conditions, we have developed a classification of all sustained motions according to their perceptual equivalences. The result is a complete list of the possible misperceptions of sustained motion due to equivalence of the forces and other direct stimuli to the sensors under the given conditions. This research expands the range of possible experiments by including all components of linear and angular velocity and acceleration. Many of the predictions in this paper can be tested experimentally. In addition, the equivalence classes developed here predict perceptual phenomena in unusual motion environments that are difficult or impossible to investigate in the laboratory.     

The art of exploring predictor-criterion relationships.

Describes a general data-analysis strategy for analyzing relationships among multiple data sets. This strategy may be employed in an exploratory mode, in a hypothesis-testing mode, or in some combination of the two. Furthermore, one may focus on the original variables or summarize these variables by a small number of principal components. For the case of two data sets, the output includes (a) the complete multiple correlation analysis of each variable (component) in one set regressed on all variates of the other set, (b) a canonical correlation solution, and (c) a final transformation to enhance substantive interpretation of the data. Emphasis is placed on examining information available at each stage of the analysis. The final solution allows the data matrix to be partitioned into elements due to interset factors, battery-specific factors, and an error component. (28 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effect of serum proteins and osteoblasts on the surface transformation of a calcium phosphate coating: a physicochemical and ultrastructural study

We describe a practical method for the analysis of multiple analytes in a single sample. The vehicle for each separate measurement consists of a set of microspheres identifiable by characteristic fluorophores embedded in the particles. The use of robust, bench-top flow cytometers (flow microfluorimeters) for the analysis of the multiple sets of microspheres is facilitated by hardware and software, which acquire the data from the cytometer, classify the microspheres according to sets, and collate measurement information from each microsphere set in real time. This measurement system can analyze up to 64 analytes in a single sample. The advantages of multiplexed assays using flow cytometry include robust measurements, because each microsphere set is measured repeatedly. The advantage of the assay's is consistent with simultaneous measurement of many parameters as well as the speed with which the flow microfluorimeter (cytometer) makes measurements (many hundreds per second). Here, we describe the properties of the microspheres, the calibration of the cytometer, and the influence of the properties of the microspheres on the sensitivity of measurements.     

Molecular dynamics of the anti-fluorescein 4-4-20 antigen-binding fragment. 2. Time-resolved fluorescence spectroscopy

Time-resolved fluorescence experiments were performed to investigate the dynamic aspects of the antigen-binding fragment (Fab) of a high-affinity monoclonal antibody (4-4-20) which binds the fluorescent hapten fluorescein. Both the unliganded Fab and a complex of the Fab with a nonfluorescent analog of fluorescein (fluoresceinamine, FLM) were examined. A fluorescence polarization probe [5-[[2-[(iodoacetyl)amino]ethyl]amino]naphthalene-1-sulfonic acid, AEDANS] was covalently attached to the C-terminus of the Fab. Experiments were performed at three different temperatures (10, 25, and 35 degrees C), and phase-modulation data sets were collected for five different molar ratios of FLM to Fab at each temperature. Global analyses were then used to extract values for fluorescence lifetime and rotational correlation time from these data. In the lifetime analysis the best fit was obtained when the emission of AEDANS was described by a Lorentzian distribution of lifetimes (tau = 15.6 ns, distribution width = 3.4 ns, both at 25 degrees C), which suggested that the probe experienced a heterogeneous environment. Anisotropy analyses suggested that two different rotational components were present. The first was attributed to the global motion of the Fab and exhibited a rotational correlation time (theta 1) of ca. 33 ns at 25 degrees C. This component was relatively unaffected by antigen binding. The second rotational component was attributed to the local or segmental motion within the Fab and exhibited a rotational correlation time (theta 2) of 1.1 ns at 25 degrees C. This value increased by more than 50% upon antigen binding, a result which was consistent with molecular dynamics simulations of the same Fab--fluorescein system [Lim & Herron (1995) Biochemistry 34, 6962-6974]. Furthermore, statistical analysis showed that this increase was significant at the 95% confidence level.     

Time-resolved fluorescence studies of dityrosine in the outer layer of intact yeast ascospores

The (time-resolved) fluorescence properties of dityrosine in the outermost layer of the spore wall of Saccharomyces cerevisiae were investigated. Steady-state spectra revealed an emission maximum at 404 nm and a corresponding excitation maximum at 326 nm. The relative fluorescence quantum yield decreased with increasing proton concentration. The fluorescence decay of yeast spores was found to be nonexponential and differed pronouncedly from that of unbound dityrosine in water. Analysis of the spore decay recorded at lambda ex = 323 nm and lambda em = 404 nm by an exponential series (ESM) algorithm revealed a bimodal lifetime distribution with maxima centered at tau 1C = 0.5 ns and tau 2C = 2.6 ns. The relative amplitudes of the two distributions are shown to depend on the emission wavelength, indicating contributions from spectrally different dityrosine chromophores. On quenching the spore fluorescence with acrylamide, a downward curvature of the Stern-Volmer plot was obtained. A multitude of chromophores more or less shielded from solvent in the spore wall is proposed to account for the nonlinear quenching of the total spore fluorescence. Analysis of the fluorescence anisotropy decay revealed two rotational correlation times (phi 1 = 0.9 ns and phi 2 = 30.6 ns) or a bimodal distribution of rotational correlation times (centers at 0.7 ns and 40 ns) when the data were analyzed by the maximum entropy method (MEM). We present a model that accounts for the differences between unbound (aqueous) and bound (incorporated in the spore wall) dityrosine fluorescence. The main feature of the photophysical model for yeast spores is the presence of at least two species of dityrosine chromophores differing in their chemical environments. A hypothetical photobiological role of these fluorophores in the spore wall is discussed: the protection of the spore genome from mutagenic UV light.     

Deriving reaction mechanisms from kinetic spectroscopy. Application to late rhodopsin intermediates

A general algebraic approach to the kinetic analysis of time-dependent absorption data is presented that allows the calculation of possible kinetic schemes. The kinetic matrices of all possible reaction mechanisms are calculated from experimental eigenvalues and eigenvectors derived from the decay constants and amplitude spectra (b-spectra) of the global exponential fit to the time-dependence of the absorption data. The eigenvalues are directly related to the decay constants, and the eigenvectors are obtained by decomposing the b-spectra into spectral components representing the intermediates. The analysis method is applied to the late intermediates (lumi, meta I, meta I-380, and meta II) of the rhodopsin photoreaction. The b-spectra are decomposed into lumi, meta I, meta-380, and rhodopsin spectra. The meta-380 component is partitioned into isospectral meta I-380 and meta II components based on physical criteria. The calculated kinetic matrices yield a number of reaction mechanisms (linear scheme with back reactions, branched schemes with equilibrium steps, and a variety of square models) consistent with the photolysis data at 25 degrees C. The problems associated with isospectral intermediates (meta I-380 and meta II) are treated successfully with this method.     

Reversal of multidrug resistance phenotype by surfactants: relationship to membrane lipid fluidity

Previous studies have suggested that multidrug resistance (MDR) reversal by polyoxyethylene surfactants involves alterations in plasma membrane lipid physical state of resistant cells as one of the possible mechanism(s). To date, however, a detailed and critical examination of the relationship between membrane lipid fluidity and MDR reversal by these surfactants has not been performed. In the present studies, therefore, a series of experiments were conducted to critically examine the role of membrane lipid physical state in MDR reversal by employing a unique class of clinically important nontoxic lipophilic surfactants and the KB-8-5-11 drug-resistant cell line. MDR reversal was assessed by rhodamine-123 uptake. The effect of surfactants on plasma membrane lipid fluidity of these cells was assessed utilizing a fluorescence polarization technique with fluorophores DPH, TMA. DPH, 2-AS, and 12-AS. Our studies demonstrated that: (i) in vitro addition of active MDR-reversing surfactants (Solutol HS-15, Tween 40, and Cremophor EL, 10 micrograms/ml each) decreased lipid fluidity of isolated crude plasma membranes of resistant cells; (ii) the inactive surfactants (octylglucoside, hecameg) failed to influence membrane lipid fluidity; (iii) cells grown in the presence of active surfactants also exhibited a decreased plasma membrane lipid fluidity as measured with intact cells utilizing the probe TMA.DPH; and (iv) active surfactants did not influence lifetimes of the excited state of the fluorophores. These findings demonstrate that decrease of the plasma membrane lipid fluidity of KB 8-5-11 resistant cells may be one of the important mechanism(s) of MDR reversal by polyoxyethylene surfactants.     

Ionization, partitioning, and dynamics of tryptophan octyl ester: implications for membrane-bound tryptophan residues

The presence of tryptophan residues as intrinsic fluorophores in most proteins makes them an obvious choice for fluorescence spectroscopic analyses of such proteins. Membrane proteins have been reported to have a significantly higher tryptophan content than soluble proteins. The role of tryptophan residues in the structure and function of membrane proteins has attracted a lot of attention. Tryptophan residues in membrane proteins and peptides are believed to be distributed asymmetrically toward the interfacial region. Tryptophan octyl ester (TOE) is an important model for membrane-bound tryptophan residues. We have characterized this molecule as a fluorescent membrane probe in terms of its ionization, partitioning, and motional characteristics in unilamellar vesicles of dioleoylphosphatidylcholine. The ionization property of this molecule in model membranes has been studied by utilizing its pH-dependent fluorescence characteristics. Analysis of pH-dependent fluorescence intensity and emission maximum shows that deprotonation of the alpha-amino group of TOE occurs with an apparent pKa of approximately 7.5 in the membrane. The fluorescence lifetime of membrane-bound TOE also shows pH dependence. The fluorescence lifetimes of TOE have been interpreted by using the rotamer model for the fluorescence decay of tryptophan. Membrane/water partition coefficients of TOE were measured in both its protonated and deprotonated forms. No appreciable difference was found in its partitioning behavior with ionization. Analysis of fluorescence polarization of TOE as a function of pH showed that there is a decrease in polarization with increasing pH, implying more rotational freedom on deprotonation. This is further supported by pH-dependent red edge excitation shift and the apparent rotational correlation time of membrane-bound TOE. TOE should prove useful in monitoring the organization and dynamics of tryptophan residues incorporated into membranes.     

A tale of two tails.

Comments on A. Feingold's (see record 1995-15953-001) claim that one cannot have an accurate image of group comparisons by looking only at mean difference and effect size, d. This is because, if the comparison groups have differenct variances, the differences in the left and right tails are not symmetrical and must be calculated separately using the variances of each distribution to estimate the relative tail weights at any given z. Feingold is commended for recognizing that tail differences must be examined separatetly, however, there is an assumption that it is possible to establish a standard formula for all comparisons. Although Feingold's contribution is not without merit, it hs the double flaw of resting on a questionable assumption of normality, and of, remaining insenstive to important aspects of data. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Nature of interaction between basic fibroblast growth factor and the antiangiogenic drug 7,7-(Carbonyl-bis[imino-N-methyl-4, 2-pyrrolecarbonylimino[N-methyl-4,2-pyrrole]-carbonylimino] )bis-(1, 3-naphthalene disulfonate)

PNU145156E (7,7-(carbonyl-bis[imino-N-methyl-4, 2-pyrrolecarbonylimino[N-methyl-4,2-pyrrole]-carbonylimino]) -bis-(1, 3-naphthalene disulfonate)) is a naphthalene sulfonic distamycin A derivative that interacts with heparin-binding growth factors. Because PNU145156E inhibits tumor angiogenesis, it was selected for clinical development. Picosecond time-resolved fluorescence emission and anisotropy were used to characterize the binding of PNU145156E to the basic fibroblast growth factor (a protein associated with tumor angiogenesis). A decrease in PNU145156E fluorescence lifetime was observed as a function of human basic fibroblast growth factor (bFGF) concentration. Nonlinear least-squares fitting of the binding isotherm yielded Kd = 145 nM for a single class of binding sites. Time-resolved anisotropy gave Kd = 174 nM. Kd = 150 nM was independently verified by quantitative high-performance affinity chromatography. The displaced volume of the complex, calculated from its rotational correlation time, fitted a sphere of 1:1 stoichiometry. These results account for the formation of a tight yet reversible PNU145156E:bFGF complex. An evaluation of PNU145156E fluorescence lifetimes in various solvents has highlighted the forces involved in stabilizing the complex. These are mostly electrostatic-hydrophobic in nature, with a relatively low contribution from hydrogen bonding. Both polar and nonpolar groups are involved on the protein-binding site within a largely hydrophobic cleft. A potential binding trajectory, based on a combination of these results with site-directed chemical modification and known bFGF x-ray structure, is suggested.     

Dynamic structure of subtilisin-eglin c complex studied by normal mode analysis

Normal mode analysis of subtilisin-eglin c complex was performed to investigate the dynamics at the interface between the enzyme and the inhibitor. The internal motions of the complex calculated from the normal modes were divided into three parts: the internal motions changing the shape of each molecule, the external rigid-body motions changing their mutual dispositions, and the coupling between the internal and external motions. From the results of the analysis, the following characteristic features were found in the dynamics at the interface regions: 1) negative correlation between the internal and external motions within each molecule, and 2) positive correlation between the external motions of the two molecules. The former decreases the apparent amplitudes of motions at the interface. The latter minimizes the interference between individual motions of the two molecules. These dynamic characteristics allow the enzyme and the inhibitor to move as freely as possible. This finding suggests that the experimental evidence of the large entropy gain on binding should be attributed not only to strong hydrophobic interactions, but also to the dynamic structure of the complex, which is found to minimize an unavoidable loss of the conformational entropy on binding.     

Testing whether correlation matrices are different from each other.

Developmental psychologists use correlation matrices both as tools for summarizing the relations among sets of variables and as input to multivariate statistical procedures. This article reviews methods for testing whether 2 or more correlation matrices are different from each other. Methods are illustrated for evaluating the similarity of 2 independent correlation matrices, such as those obtained from boys and girls, and 2 dependent correlation matrices, such as those obtained in longitudinal research by using multiple measures. Applications of the models to data from the published developmental literature are provided. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Two-dimensional components and hidden dependencies provide insight into ion channel gating mechanisms

Correlations between the durations of adjacent open and shut intervals recorded from ion channels contain information about the underlying gating mechanism. This study presents an additional approach to extracting the correlation information. Detailed correlation information is obtained directly from single-channel data and quantified in a manner that can provide insight into the connections among the states underlying the gating. The information is obtained independently of any specific kinetic scheme, except for the general assumption of Markov gating. The durations of adjacent open and shut intervals are binned into two-dimensional (2-D) dwell-time distributions. The 2-D (joint) distributions are fitted with sums of 2-D exponential components to determine the number of 2-D components, their volumes, and their open and closed time constants. The dependency of each 2-D component is calculated by comparing its observed volume to the volume that would be expected if open and shut intervals paired independently. The estimated component dependencies are then used to suggest gating mechanisms and to provide a powerful means of examining whether proposed gating mechanisms have the correct connections among states. The sensitivity of the 2-D method can identify hidden components and dependencies that can go undetected by previous correlation methods.