Analysis of fluorescence anisotropy decays by a least square method

A method of fluorescence anisotropy decay analysis is described in this work. The transient anisotropy r(ex)(t) measured in a photocounting pulsefluorimeter is fitted by a non linear least square procedure to the ratio of convolutions of the apparatus response function g(t) by sums of appropriate exponential functions. This method takes rigorously into account the apparatus response function and is applicable to any shape of the later as well as to any values of fluorescence decay times and correlation times. The performances of the method have been tested with data simulated from measured response functions corresponding to an air lamp and a high pressure nitrogen lamp. The statistical standard errors of the anisotropy deca parameters have been found to be smaller than the standard errors previously calculated for the moment method. A systematic error delta in the fluorescence decay time entailed an error deltatheta in the correlation time such as Deltatheta/theta < deltatau/tau. By this method, good fitting of experimental data have been achieved very conveniently and accurately.     

Analysis of nonexponential fluorescence decay data by a method of moments.

A method of moments is presented for the analysis of convoluted fluorescence decay data when the impulse response function is given by f(t) = alpha exp (-At - Bt1/2). Examples of this method are given using both simulated and measured fluorescence decays. It is also shown that this method, used with moment index displacements, will correct for light-scatter leakage, zero-point time shifts, and slow lamp drift.     

Robust estimation in pulse fluorometry. A study of the method of moments and least squares.

Most laboratories use least-squares iterative reconvolution (LSIR) as a routine method for estimating decay parameters in pulse fluorometric data. It is shown here, however, that LSIR is very sensitive to small amounts of error in the data whenever two decays become too close to one another, or whenever analyses of three decays are attempted. In such cases, inferior methods of estimating integrals, small zero point shifts, or small errors in the measured exciting light will result in failures of least squares, where the method of moments, with moment index displacement and lambda invariance testing, will succeed. The method of moments is therefore robust with respect to such errors while least squares is not.     

Analysis of fluorescence lifetime curves. A new method for correcting raw fluorescence lifetime curves for the parallel contribution of scattered light.

A method is described for estimating the fractional contribution of light scattered from the excitation lamp to the normalized raw fluorescence lifetime curve. The method depends on the ratio of the slope of the normalized light scatter spectrum to the slope of the normalized raw fluorescence spectrum in the vicinity of the intersection of the two spectra. The correction for scattered light is made prior to deconvolution, and hence, has the advantage of being independent of the method selected to calculate the true fluorescence life-time spectrum. It is simple and does not require a computer. Tested against curves synthesized from known additions of scattered light to fluorescence spectra exhibiting mono-, bi-, or triexponential decay, it yielded small absolute errors.     

Analysis of fluorescence decay curves by means of the Laplace transformation.

A computational procedure is described for the analysis of fluorescence decay data convolved with a lamp flash of finite width. The computer program calculates the ratio of the Laplace transforms of the decay and the lamp flash for different values of s to give the transforms of the impulse response for each value of s. These are set equal to the analytical Laplace transforms of the decay law involved. Solution of the nonlinear simultaneous equations yields the desired decay parameters. The method can be modified to analyze data that contains a component due to scattered light and can also provide essential information regarding transit time changes of the photomultiplier with changes in emission wavelength. The method was tested by the analysis of real and simulated data. The accuracy of the analysis depends on the degree of correlation among the parameters.     

Dynamics of reorganization of instrumental food getting behavior of monkey under conditions of reinforcement delay

Six adult monkeys (Macaca fascicularis) were trained to switch on a lamp by pressing the lever, to hold the lever for not less than 1 s (the lamp being switched on), and get a portion of food. After reaching a learning criterion, the delay between the lever pressing and food reinforcement was increased to 2.5 s. The experimental procedure was repeated in three experimental sessions with 2-month between-session intervals. It was shown that the retraining process after the uneven change in the delay duration developed in three stages: (1) stage of emotional hyperreactivity that reflected a mismatch between the cation and absence of the expected result; (2) stage of intermediate stabilization, when the percent of efficient attempts was the same as under conditions of 1-s delay; (3) stage of purposive instrumental lever holding till the moment of reinforcement presentation.     

The correction of reaction rates in continuous fluorometric assays of enzymes

The kinetic data obtained from the action of a cathepsin D-like enzyme from Biomphalaria glabrata hepatopancreas (digestive gland) on MOCAc-Gly-Lys-Pro-Ile-Leu-Phe-Phe-Arg-Leu-Lys(DNp)-D-Arg-NH(2), was studied as a data prototype, generated by means of a fluorogenic substrate. An initial fluorescence, due to incomplete energy transfer, of about 8% of the values attained after complete substrate hydrolysis; a non-linear standard curve even at microM concentrations and an exponential decay of the steady state fluorescence of reaction product of the order of 10(-4) x s(-1) were the main analytical problems encountered. The standard curves for fluorescence of the substrate reaction product after 48 h of hydrolysis, and the reference compound MOCAc-Pro-Leu-Gly-NH(2), were fitted by polynomial approximation and the point derivates used as calibration factors. Time dependence of the calibration factor for the reaction product was -2.96 x 10(-4) a.u microM(-1) x s(-1) that is, in the same order of observed enzymic reaction rates. A mathematical treatment was devised for obtaining rates corrected for errors derived from the three analytical problems indicated. The method is of general application in continuous fluorometric assays, irrespective of the particular enzyme used, but of special value for substrates that present significant initial fluorescence. The reaction rates were 11% higher; as calculated by means of the calibration factor [substrate]/(final-initial fluorescence intensities), which is the prevalent procedure in the literature; leading to underestimation of K(m) and overestimation of V(max).     

时间分辨荧光光谱测量结果的一种数据处理改进方法

在综合矩方法和拉普拉斯变换方法原理的基础上,本文报道一种时间相关单光子计数测出的荧光衰变动力学曲线的数据处理的改进方法.此方法使我们能在花费时间较少的条件下得出和用最小二乘法拟合相比拟的准确分析结果.这一方法的优点已被用于分析香豆素102+DCM和香豆素102+PBBO激光染料乙醇溶液的双指数荧光衰变过程的结果所证实,此外,本文也讨论了仪器时间漂移校正及拉普拉斯变换的数据截取问题.     

On Method of Moments Estimation in Linear Mixed Effects Models with Measurement Error on Covariates and Response with Application to a Longitudinal Study of Gene-Environment Interaction

We study a linear mixed effects model for longitudinal data, where the response variable and covariates with fixed effects are subject to measurement error. We propose a method of moment estimation that does not require any assumption on the functional forms of the distributions of random effects and other random errors in the model. For a classical measurement error model we apply the instrumental variable approach to ensure identifiability of the parameters. Our methodology, without instrumental variables, can be applied to Berkson measurement errors. Using simulation studies, we investigate the finite sample performances of the estimators and show the impact of measurement error on the covariates and the response on the estimation procedure. The results show that our method performs quite satisfactory, especially for the fixed effects with measurement error (even under misspecification of measurement error model). This method is applied to a real data example of a large birth and child cohort study.     

A new method for decay-associated fluorescence spectroscopy. Application to the tryptophan zwitterion

We describe a new method for decay associated fluorescence spectroscopy using synchrotron radiation as the excitation pulse and a photon counting technique. This method is based on the determination of the difference between the barycenters of the exciting pulse and of the fluorescence response at several wavelengths. It is applicable to the case where individual decay times are independent of emission wavelength. Coupled to the analysis of the decay curve at only one emission wavelength, this method reduces the time devoted to the numerical analysis and avoids the spectral distortion due to the lamp profile. The results obtained by this method on indole, the tryptophan zwitterion, and N-acetyl-tryptophan are presented. Results are compared to those obtained by two other methods: Determination of the fluorescence decay parameters by deconvolution analysis at several emission wavelengths. Photon counting of the fluorescence spectrum emitted during a selected time window after the excitation pulse.     

Analysis of photoacoustic waveforms using the nonlinear least squares method.

Pulsed-laser photoacoustics is a technique which measures photoinduced enthalpic and volumetric changes on the nano- and microsecond timescales. Analysis of photoacoustic data generally requires deconvolution for a sum of exponentials, a procedure which has been developed extensively in the field of time-resolved fluorescence decay. Initial efforts to adapt an iterative nonlinear least squares computer program, utilizing the Marquardt algorithm, from the fluorescence field to photoacoustics indicated that significant modifications were needed. The major problem arises from the wide range of transient decay times which must be addressed by the photoacoustic technique. We describe an alternative approach to numerical convolution with exponential decays, developed to overcome the problems. Instead of using an approximation method (Simpson's rule) for evaluating the convolution integral, we construct a continuous instrumental response function by quadratic fitting of the discrete data and evaluate the convolution integral directly, without approximations. The success and limitations of this quadratic-fit convolution program are then demonstrated using simulated data. Finally, the program is applied to the analysis of experimental data to compare the resolution capabilities of two commercially available transducers. The advantages of a broadband, heavily damped transducer are shown for a standard organic photochemical system, the quenching of the triplet state of benzophenone by 2,5-dimethyl-2,4-hexadiene.     

Correlation of tryptophan fluorescence intensity decay parameters with 1H NMR-determined rotamer conformations: [tryptophan2]oxytocin.

While the fluorescence decay kinetics of tyrosine model compounds [Laws, W. R., Ross, J. B. A., Wyssbrod, H. R., Beechem, J. M., Brand, L., & Sutherland, J. C. (1986) Biochemistry 25, 599-607] and the tyrosine residue in oxytocin [Ross, J. B. A., Laws, W. R., Buku, A., Sutherland, J. C., & Wyssbrod, H. R. (1986) Biochemistry 25, 607-612] can be explained in terms of heterogeneity derived from the three ground-state chi 1 rotamers, a similar correlation has yet to be directly observed for a tryptophan residue. In addition, the asymmetric indole ring might also lead to heterogeneity from chi 2 rotations. In this paper, the time-resolved and steady-state fluorescence properties of [tryptophan2]oxytocin at pH 3 are presented and compared with 1H NMR results. According to the unrestricted analyses of individual fluorescence decay curves taken as a function of emission wavelength and a global analysis of these decay curves for common emission wavelength-independent decay constants, only three exponential terms are required. In addition, the preexponential weighting factors (amplitudes) have the same relative relationship (weights) as the 1H NMR-determined chi 1 rotamer populations of the indole side chain. 15N was used in heteronuclear coupling experiments to confirm the rotamer assignments. Inclusion of a linked function restricting the decay amplitudes to the chi 1 rotamer populations in the individual decay curve analyses and in the global analysis confirms this correlation. According to qualitative nuclear Overhauser data, there are two chi 2 populations. Depending upon the degree of correlation between chi 2 and chi 1, there may be from three to six side-chain conformations for the tryptophan residue. The combined fluorescence and NMR results are consistent with a rotamer model in which either (i) the chi 2 rotations are fast compared to the fluorescence intensity decay of the tryptophan residue, (ii) environmental factors affecting fluorescence intensity decay properties are dominated by chi 1 interactions, or (iii) the chi 2 and chi 1 rotations are highly correlated.     

Decay-associated fluorescence spectra and the heterogeneous emission of alcohol dehydrogenase

A procedure is described for using nanosecond time resolved fluorescence decay data to obtain decay-associated fluorescence spectra. It is demonstrated that the individual fluorescence spectra of two or more components in a mixture can be extracted without prior knowledge of their spectral shapes or degree of overlap. The procedure is also of value for eliminating scattered light artifacts in the fluorescence spectra of turbid samples. The method was used to separate the overlapping emission spectra of the two tryptophan residues in horse liver alcohol dehydrogenase. Formation of a ternary complex between the enzyme, NAD+, and pyrazole leads to a decrease in the total tryptophan fluorescence. It is shown that the emission of both tryptophan residues decreases. The buried tryptophan (residue 314) undergoes dynamic quenching with no change in the spectral distribution. Under the same conditions, the fluorescence intensity of tryptophan (residue 15) decreases without a change in decay time but with a red shift of the emission spectrum. There is also a decrease in tryptophan fluorescence intensity when the free enzyme is acid denatured (succinate buffer, pH 4.1). The denatured enzyme retains sufficient structure to provide different microenvironments for different tryptophan residues as reflected by biexponential decay and spectrally shifted emission spectra (revealed by decay association). The value of this technique for studies of microheterogeneity in biological macromolecules is discussed.     

A systems-theory approach to the analysis of multiexponential fluorescence decay.

A mathematical model of the fluorescence decay experiment based on linear systems theory is presented. The model suggests an experimental technique that increases the probability of correctly determining the decay constants of a multicomponent system. The use of moment methods for data analysis improves accuracy by combining information obtained from several discrete experiments. Examples are presented to show that the analysis of a three component system composed of known standards is improved as the number of experimental determinations is increased from one to four. The discrete measurements are made by changing the excitation and emission wavelengths.     

Refolding of ribonuclease in the presence and absence of ammonium sulfate pulses. Comparison between experiments and simulations

Experiments have been carried out on ribonuclease A in which refolding in high concentrations of guanidine hydrochloride is either preceded or not preceded by a short ammonium sulfate pulse. Application of the pulse causes the rapid formation of the nativelike intermediate, and the effect of this pulse was determined by using three different methods for monitoring the subsequent refolding reaction: direct absorbance, direct fluorescence, and a double-jump fluorescence unfolding assay which is specific for the isomerization of proline-93. The effect of the pulse is quite different depending on the method of detection. With absorbance detection, the pulse causes a large reduction in the refolding amplitude with no change in the kinetics of the decay curve, while with the fluorescence unfolding assay, the pulse causes no change in the refolding amplitude but produces a large acceleration in the decay kinetics. The results with direct fluorescence are intermediate with some reduction seen in the refolding amplitude and some acceleration in the decay kinetics. The results of these experiments are simulated by using the simple model of Lin and Brandts (1984) [Lin, L.-N., & Brandts, J. F. (1984) Biochemistry 23, 5713] in which proline-93 must be in the correct cis configuration before folding to the native or nativelike state can occur. In all cases, the simulations accurately predict the experimental results for all three methods of detection, without any adjustment of parameter values from those published earlier.(ABSTRACT TRUNCATED AT 250 WORDS)     

Study of the time-resolved tryptophan fluorescence of crystalline alpha-chymotrypsin

The tryptophan environments in crystalline alpha-chymotrypsin were investigated by fluorescence. The heterogeneous emission from this multitryptophan enzyme was resolved by time-correlated fluorescence spectroscopy. The fluorescence decays at 296-nm laser excitation and various emission wavelengths could be characterized by a triple-exponential function with decay times tau 1 = 150 +/- 50 ps, tau 2 = 1.45 +/- 0.25 ns, and tau 3 = 4.2 +/- 0.4 ns. The corresponding decay-associated emission spectra of the three components had maxima at about 325, 332, and 343 nm. The three decay components in this enzyme can be correlated with X-ray crystallographic data [Birktoft, J.J., & Blow, D.M. (1972) J. Mol. Biol. 68, 187-240]. Inter- and intramolecular tryptophan-tryptophan energy-transfer efficiencies in crystalline alpha-chymotrypsin were computed from the accurately known positions and orientations of all tryptophan residues. These calculations indicate that the three fluorescence decay components in crystalline alpha-chymotrypsin can be assigned to three distinct classes of tryptophyl residues. Because of the different proximity of tryptophan residues to neighboring internal quenching groups, the decay times of the three classes are different. Decay tau 1 can be assigned to Trp-172 and Trp-215 and tau 2 to Trp-51 and Trp-237, while the tryptophyl residues 27, 29, 141, and 207 all have decay time tau 3.     

Time-resolved fluorescence of erythrocyte plasma membrane Ca2(+)-ATPase in different functional states.

The fluorescence decay of the plasma membrane calmodulin-activated Ca2(+)-ATPase from the erythrocyte was measured for the first time. The availability of a novel procedure for on-line blank subtraction in frequency-domain lifetime data acquisition (G.G. Reinhart, B. Feddersen, D. Jameson and E. Gratton, Biophys. J. 57 (1990) 189a) permitted the elimination of background interference from detergent-solubilized purified plasma membrane ATPase samples. The fluorescence decay of the erythrocyte Ca2(+)-ATPase was measured in the absence of Ca2+, or in the presence of Ca2+ or Ca2+ plus calmodulin. In the three different experimental conditions the fluorescence decay was very heterogeneous and could be best described by Lorentzian distributions of lifetime values. In the absence of Ca2+ the decay was described by a broad lifetime distribution centered at 4.4 ns with a width of 3.2 ns, indicating heterogeneity of tryptophan microenvironments in the ATPase. Calcium ion binding promoted an 11% increase in the center and a 27% decrease in the width of the distribution. By contrast, addition of calmodulin in the presence of Ca2+ caused a 15% decrease in the center of the distribution, revealing structural difference between calmodulin-activated and Ca2(+)-activated states of the ATPase. These results indicate the usefulness of on-line blank subtraction in frequency-domain lifetime measurements to investigate conformational changes in detergent-solubilized membrane protein samples.     

Simultaneous analysis of single-photon timing data for the one-step determination of activation energies, frequency factors and quenching rate constants. Application to tryptophan photophysics

A general global analysis of single-photon timing data is presented in which each fluorescence decay curve can be described by a different decay law. The model parameters can be held in common within one curve and/or between related curves. Any or all parameters can be kept fixed, or they may be variable to seek optimum values. This general analysis allows the determination of activation energies, frequency factors and quenching rate constants in one step. The construction of the global mapping table which relates parameters in one experiment to those in another is explained in detail. The use and performance of this general simultaneous analysis are examined using tryptophan fluorescence decays at pH 6.0 obtained at various emission wavelengths as a function of temperature and added solute quencher. The results show that tryptophan at pH 6.0 decays as a biexponential with decay times which are independent of the analysis wavelength. The decay component with the short lifetime has a deactivation rate constant of 1.4 x 10(9) s-1 independent of temperature. The decay component with the long lifetime has an activation energy of 28 kJ/mol and a frequency factor of 3 x 10(13) s-1; its temperature-independent decay rate constant equals 1 x 10(8) s-1. Recursion formulas for a computer program to estimate activation energies, frequency factors, and decay rate constants are provided.     

The emission yields of delayed and prompt fluorescence from chloroplasts.

1. The decay of delayed fluorescence from chloroplasts blocked with 3-(3,4-dichlorophenyl)-1,1-dimethylurea and uncoupled with gramicidin has been measured in the time range 0.75--45 ms by use of a laser phosphoroscope. 2. The decays have been analysed as the sum of three first-order components of approximate half-lives 0.2, 2.5 and 300 ms by a computer-assisted least-squares fit procedure. 3. The prompt fluorescence yield of the chloroplasts was manipulated by changing the cation concentration of the chloroplast-suspending medium. 4. Analysis of the concentration dependence of the components of the delayed fluorescence decay and of the prompt fluorescence inductions indicates that the emission yield of the intermediate (tau approximately 2.5 ms) component of the decay is equal to the fluorescence yield of a Photosystem II photosynthetic unit with an open trap, and that for the slow (tau approximately 300 ms) component the emission yield is equal to the total Photosystem II prompt fluorescence yield. 5. It is concluded that the delayed fluorescence yield in the time range studied is a complex function of time, which may be due to there being different mechanisms leading to delayed fluorescence production at short and long times after cessation of illumination.