Izchak Z. Steinberg

On the analysis of fluorescence decay kinetics by the method of least-squares

Abstract Analysis of fluorescence decay kinetics aims at the determination of the analytic expression and the numerical values of the pertinent parameters which describe the decay process. In the well-known method of least-squares, one assumes a plausible functional form for the decay data and adjusts the values of the parameters until the statistically best fit is obtained between the data and the calculated decay function, i.e., until the sum of the weighted squares of the residuals is at a minimum. It is shown that proper weighting of the squares of the residuals may markedly improve the quality of the analysis. Such weighting requires information about the character of the experimental noise, which is often available, e.g., when the noise is due to counting error in photon-counting techniques. Furthermore, dramatic improvements in the accuracy of the analysis may often be achieved by use of auxiliary information available about the system studied. For example, the preexponents in a multiexponential fluorescence decay of a mixture of chromophores (such as tryptophan residues in a protein molecule) may sometimes be estimated independently; much higher accuracy can then be attained for the decay lifetimes by analysis of the decay kinetics. It is proposed that the shape of the autocorrelation function of the weighted residuals may serve as a convenient criterion for the quality of fit between the experimental data and the decay function obtained by analysis. The above conclusions were reached by analysis of computer-simulated experiments, and the usefulness of this approach is illustrated. The importance of stating the uncertainties in the estimated parameters inherent in the analysis of decay kinetics is stressed.

Relationship between presynaptic calcium current and postsynaptic potential in squid giant synapse

The relationship between calcium current and transmitter release was studied in squid giant synapse. It was found that the voltage-dependent calcium current triggers the release of synaptic transmitter in direct proportion to its magnitude and duration. Transmitter release occurs with a delay of approximately 200 mus after the influx of calcium. A model is presented which describes these relations formally.

The fluorescence decay of tryptophan residues in native and denatured proteins

The fluorescence decay kinetics at different ranges of the emission spectrum is reported for 17 proteins. Out of eight proteins containing a single tryptophan residue per molecule, seven proteins display multiexponential decay kinetics, suggesting that variability in protein structure may exist for most proteins. Tryptophan residues whose fluorescence spectrum is red shifted may have lifetimes longer than 7 ns. Such long lifetimes have not been detected in any of the denatured proteins studied, indicating that in native proteins the tryptophans having a red-shifted spectrum are affected by the tertiary structure of the protein. The fluorescence decay kinetics of ten denatured proteins studied obey multiexponential decay functions. It is therefore concluded that the tryptophan residues in denatured proteins can be grouped in two classes. The first characterized by a relatively long lifetime of about 4 ns and the second has a short lifetime of about 1.5 ns. The emission spectrum of the group which is characterized by the longer lifetime is red shifted relative to the emission spectrum of the group characterized by the shorter lifetime. A comparison of the decay data with the quantum yield of the proteins raises the possibility that a subgroup of the tryptophan residues is fully quenched. It is noteworthy that despite this heterogeneity in the environment of tryptophan residues in each denatured protein, almost the same decay kinetics has been obtained for all the denatured proteins studied in spite of the vastly different primary structures. It is therefore concluded that each tryptophan residue interacts in a more-or-less random manner with other groups on the polypeptide chain, and that on the average the different tryptophan residues in denatured proteins have a similar type of environment.

Resonance Rayleigh scattering of cyanine dyes in solution

Every process of light absorption is inherently associated with a resonance scattering of the incident beam regardless of the nature of the absorbing molecules. Both the real and imaginary parts of the refractive index contribute to the resonance scattering, and marked depolarization is expected to be observed as a rule in the light scattered by complex molecules. The resonance and near‐resonance Rayleigh scattering has been measured for a number of cyanine dyes: pseudocyanine, orthochrome T, 1,1′‐diethyl‐2, 2′‐pyridyl‐quinolyl cyanine, and pinacyanol chloride, in a number of solvents. In no case was the measured scattering intensity weaker than that expected theoretically, and good agreement between theory and experiment was found as a rule at the blue part of the absorption bands. In contrast, the measured scattering intensities exceeded (by up to fourfold) the theoretically expected values at the red parts of the absorption bands. Possible reasons for this discrepancy are discussed.

Theoretical Analysis of the Role of Diffusion in Chemical Reactions, Fluorescence Quenching, and Nonradiative Energy Transfer

The kinetics of diffusion‐controlled chemical reactions in solution are analyzed by a statistical treatment. To start with, the probability of interaction of two molecules A and B, separated by a given distance at zero time and undergoing Brownian motion subsequently, is determined. The probability of interaction of an A molecule with one of many surrounding B molecules is then deduced. Finally, the course of reaction between A and B molecules distributed at random at zero time in a system containing a large number of molecules of both species, is calculated. The treatment outlined is readily extended to systems in which factors other than random diffusion are operative, as well as to systems in which the distribution of A and B molecules is not random at zero time. A few examples are discussed in detail. The theoretical treatment presented is applied to the kinetics of quenching of electronically excited molecules by collision with quencher molecules in solution, and to the calculation of the extent of n...

Depolarized rayleigh light scattering in absorption bands measured in lycopene solution

Abstract The depolarized scattering intensity from the polyene pigment lycopene was measured in the visible absorptiion band and was found to be in good agreement with theoretical calculations at the short wavelength part of the band whereas significant deviations were observed at the red edge of this band.

Sensitive Instrument for the Study of Circular Polarization of Luminescence

A sensitive instrument is described for the measurement of the extent of circular polarization of light emitted by chiral molecules. In this instrument the intensity of the circularly polarized component of the luminescence light is selectively modulated by an electro‐optic or photoelastic light modulator, while the unpolarized component of the luminescence is unaffected. The modulated light beam is detected by a photomultiplier and the ac component of the electric signal produced is amplified by a phase‐sensitive amplifier tuned to the modulation frequency. The light used for the excitation of the sample and the luminescence light are monochromated. An accessory is described which produces controlled mixtures of unpolarized and circularly polarized light and thus permits calibration of the output of the instrument in terms of the degree of circular polarization of the light under examination. Signal to noise ratios of 20 have been readily obtained with luminescence which is circularly polarized to an extent of 10−3 to 10−4.

An improvement of nanosecond fluorimeters to overcome drift problems

For the processing of fluorescence decay data it is often necessary to obtain the time profile of the flash lamp which excites the fluorescence as well as the variation with time of the fluorescence intensity. If these intensity profiles are collected in consecutive experiments, instrumental drift may introduce serious errors. This problem is shown to be minimized by alternate collection of the data for the fluorescence and for the excitation lamp. An automatic setup for performing such experiments is outlined.

Nonradiative Energy Transfer in Systems in which Rotatory Brownian Motion is Frozen

The effect of the complete restriction of rotatory Brownian motion of donor and acceptor molecules on the extent of nonradiative energy transfer in systems containing many donors and acceptors has been investigated. It is assumed that the molecules under discussion are randomly distributed and randomly oriented in space at the moment of excitation. The number of donor molecules which retain their excitation energy at time t after excitation is found to decrease exponentially with the sum of two terms: one proportional to t and the other proportional to t1 / 2. This time dependence is similar in form to that found by Forster for systems in which donor and acceptor molecules undergo rapid rotatory diffusion. While the coefficient of −t in the exponent is the same in both cases, the coefficient of −t1 / 2 is smaller for systems in which molecular rotation is frozen than for systems in which rotatory Brownian motion is rapid.

Measurement of the depolarization ratio of Rayleigh scattering at absorption bands

Measurements of the depolarization ratio ρv of light scattered by the pigments lycopene and β‐carotene at the red part of their absorption bands yielded values which are very close to the theoretical value 1/3 of a fully anisotropic molecular polarizability, i.e., that due to an electric dipole moment. Measurements of ρv at the blue edge of the visible absorption band of pinacyanol chloride yielded a value of 0.75 at 472.2 nm, which is the maximum value that a depolarization ratio can assume, and is attained if the average molecular polarizability is zero. This is possible only if the diagonalized polarizability tensor has at least one negative element to counterbalance the positive ones. A negative refractive index at the blue edge of the absorption band is thus experimentally demonstrated.