A multifrequency phase fluorometer using the harmonic content of a mode-locked laser

ABSTRACT We describe the construction and operation of a cross-correlation phase and modulation fluorometer which uses the harmonic content of a high repetition rate mode-locked laser as the excitation source. A mode-locked argon ion laser is used to synchronously pump a dye laser. The pulse train output from the dye laser is amplitude modulated by an acousto-optic modulator and then frequency doubled with an angle tuned frequency doubler. With the particular dye utilized in these studies, the ultraviolet light obtained was continuously tunable over the range 280-310 nm. In the frequency domain the high repetition rate pulsed source gives a large series of equally spaced harmonic frequencies. The frequency spacing of the harmonics is determined by the repetition frequency of the laser. Amplitude modulation of the pulse train permits variation of the frequency quasi-continuously from a few hertz to gigahertz. Use of cross-correlation techniques permits precise isolation of individual frequencies. The cross...


INTRODUCTION
In recent years there has been a marked interest in the use of fluorescence spectroscopy for the study of dynamics of macromolecules. The natural time window of fluorescence is suitable to resolve events occurring in the nanosecond-subnanosecond time domain. In particular,•the intrinsic fluorescence of proteins, due primarily to the tryptophan and tyrosine residues, have been extensively investigated as probes of dynamic processes. Even proteins containing a single tryptophan or tyrosine emitter, however, may demonstrate complex decay schemes, i.e., heterogeneity may exist in the lifetime as well as rotational modes of the fluorophore.
The practical utility of fluorescence methods is thus still limited by the availability of instrumentation capable of measuring such events accurately and resolving the heterogeneity. Our particular interest has been the development of multifrequency phase fluorometry and especially its application to the study of subnanosecond raacromolecular dynamics using intrinsic fluorescence probes such as tryptophan and tyrosine residues.
A multifrequency phase and modulation fluorometer capable of picosecond resolution has been described and operational in our laboratory for a number of years. This Instrument performs well using the visible and UV lines from a CW laser source (either argon-ion or heliura-cadmiura) and a Pockels cell for modulation.
However, the poor performance of Pockels cells in the UV, their limited frequency response and the lack of convenient CW UV sources motivated the present work.
In this paper we present (1)  In the time domain the response to the delta function excitation of an emitting system comprising N exponentially decaying components is given by the following equation, In the frequency domain the time variation of the excitation light intensity is described by E(t) = E 0 (l + H e sin ut) (2) where E o and M e are the average value of the intensity and the modulation of the excitation respectively. The overall fluorescence response of the system to the sinusoidal excitation can be written in the form Where F Q and Mj are the average value of the intensity and the modulation of the fluorescence, respectively. For linear systems the emitted fluorescence has the same modulation frequency but is demodulated and phase-shifted with respect to the exciting light.
The phase delay and modulation ratio between the excitation and the emission constitute the two independent measurable quantities in phase fluorometry. The following equations relate these parameters to the case of the pulse response, Ip(t), to excitation by a delta function at excitation frequency, u, e where S = /^I F (t)sin ut dt (6) G = /" I p (t)cos ut dt (7) N = £l F (t) dt.
Knowledge of 4 > and M is equivalent to knowledge of the functions S and G which correspond to the sine and cosine fourier transforms of the ideal pulse response Ip(t). Consequently the measurement of phase and modulation as a function of the frequency is equivalent to determining the time evolution of the emitting system to delta pulse excitation. In phase-modulation fluorometry, however, deconvolution for the finite width of the excitation pulse and the time response of the detection system is unnecessary since the ideal pulse response is obtained.
If the fluorescence decay is monoexponential then tan ( j > = UT (9) and M (i + i A 2 r 1 / 2 . do) Another advantage of phase-modulation fluorometry is that it allows direct differential measurements. The general equations related to differential phase fluorometry have been given by Weber and are applicable to a number of cases such as rotational studies and excited state reactions. As an example we discuss here its application to the determination of the time decay of the anisotropy.
In the time domain the anisotropy (r) is given by the following expressions, where I and I represent intensities observed through polarizers oriented parallel and perpendicular, respectively, to the polarization plane of the exciting light (which is typically vertical).
The function r(t) can also be expressed as a sum of expo- We should note that the modulation ratio involves only the ratio of the AC components and not the ratio of the complete modulation terras.

DESCRIPTION OF THE INSTRUMENT
The present instrument is a modified version of the phase and modulation fluorometer described previously.       The measured lifetimes are given in table I and the results of the   heterogeneity analysis are shown in table II. B.

ROTATION ANALYSIS
The differential tangent and modulation ratio for a solution of tryptophan at pH 6 was measured. The non-linear least-squares analysis in terms of a single isotropic rotator gives a rotational rate of 86 ps. The results are shown in figure 9. It is clear from our measurements that such a fast rotation can be accurately determined with our apparatus. We report also in figure 10 the measurements for the rotations of lysozyme in phosphate buffer.
In this later case the rotational motion appears more complex.
Work is in progress to determine the nature of the rotational motions in proteins.