Authors
Gregorio Weber
Topics
Biotin and Related StudiesPhotosynthetic Processes and MechanismsClick Chemistry and ApplicationsBy G. WEBER* Biochemical Laboratory, University of Cambridge (Received 2 August 1951) According to the theory developed by Perrin (1926), the partial polarization of the fluorescent light emitted by molecules in solution depends upon the relation of their rotational relaxation time to the lifetime of the excited state of the fluorescence.The measurements of Gaviola (1927), Szymanowski (1935) and Dushinsky (1936) show that the life- time of the excited state of the fluorescence is a quantity of the order of 10-8 sec. for many dyes in water solution. As the relaxation time of the rota- tion of these molecules in water is much shorter than 10-8 sec., almost completely depolarized radiation is to be expected and is in fact observed. On the other hand, fluorescent macromolecules, e.g. proteins, should already emit partially polarized fluorescence in water solution as their relaxation times are of the required order of magnitude. Measurements of the degree of polarization of the fluorescence should in consequence afford a convenient means of determining the relaxation times of macromolecules in dilute solution under a variety of circumstances.In this paper are described the general principles which attend the application of this method to the study of macromolecules. The following paper of this series (Weber, 1952) describes experiments done with proteins rendered fluorescent by the conjuga- tion with a small fluorescent molecule. THEORY Perrin (1926, 1936) has developed the theory of the polarization of the fluorescence of solutions on the assumption that the emitting molecules carry rigidly bound linear oscillators of absorption and emission and that the molecular rotations are described by Einstein's (1906) equation. The first assumption can be considered experimentally proved (Foofflov, 1943). Although the classical experiments of J. Perrin (1909) have shown that the rotation of large, visible particles follows the Ein- stein equation, some doubt may be entertained as to its validity in the case of dissolved molecules which do not greatly differ in size from the molecules of the solvent. The protein molecules fall midway between these two extremes, and the measurements of their relaxation times by the dielectric dispersion method (Oncley, 1942) indicate that the equation of Einstein cannot seriously be at fault. However, the fact that the real shape of the particles is not known and that the measurements have been carried out over a limited range of temperatures and viscosities does not allow a decision as to how closely the theory is followed.Let us consider a system of co-ordinates O(xyz). The fluorescent solution is placed at 0 in a square cell with faces oriented normally to the co-ordinate axes. The exciting light travels in the xO direction, and unless otherwise stated we shall assume it to be completely polarized with its electric vector in the Oz direction. The fluorescent light emitted in the Oy direction, i.e. at right angles both to the direction of propagation ofthe exciting light and to the direction of the electric vector is observed. Its partial polari- zation p is defined by the equationIV -+I (1)where I is the component of the intensity emitted in the direction Oy with its direction of vibration parallel to that of the exciting light, while I, is the component normal to the former, i.e. in the Ox direction.According to Perrin (1926) the value of p for a spherical molecule is given by (2) where R is the gas constant, T the absolute temper- ature, q the viscosity of the solvent, V the molecular volume of the fluorescent molecule and x0 the life- time of the excited state of the fluorescence; po is clearly the value of p when T/ -+ 0, i.e. when no depolarization by molecular rotation takes place. In practice it differs little from the polarization observed in a medium of high viscosity like glycerol.According to the above equation, if I/p is plotted against T/I a straight line is obtained cutting the I/p axis at l/po. Experimentally, for fluorescent dyes with V -500 in glycerol-water mixtures it is found that the relation just mentioned obtains down to viscosities of 10-15 centipoises, but for viscosities below these values the polarization is lower than predicted (Perrin, 1926; Wawilow, 1936) . Several explanations have been advanced, notably that Einstein's law is not valid in these conditions (Perrin, 1936) . Whatever the explanation, if a change in molecular volume has the same effect as a corresponding change in viscosity, Perrin's law should hold accurately for molecules of V> 104 in media of viscosity of 1 centipoise.Simultaneous excitation of 8everal osciUator8 If several oscillators corresponding to one or more molecular species in solution are simultaneously excited, the observed polarization p is related to the individual polarizations pi that would obtain if each type of oscillator were the only one excited, in the following manner:1 _11 + I F =i I-i-Iij, In-lj P= li, + 1il Fi Moreover IX = Ij, and I = li i i z Fipi Therefore - II z (3)i Addition law of the polarizations of 8everal o8cilaator8 The total intensity of the radiation emitted by a point of the fluorescent source can be represented by three orthogonal components. Choosing for the directions of the components the co-ordinate axes, we have in the case of non-polarized radiation, I, =11=i, the total intensity being proportional to 3i. If the fluorescence excited by polarized light as described, becomes now partially polarized to the extent pi, while the total emitted intensity remains constant, Curie's law of symmetry (Perrin, 1929) shows that the total radiation is then proportional to This requires I* + 2I = 3i.(5) From the last equations, 4 and 5, together with 1, we have for the ith oscillator species in solution: Thus I/p3j is the harmonic mean of the quantities lrpi -i weighed according to the contribution to the total fluorescent intensity of the solution.Eqns. 4 and 5 refer to excitation with polarized light. In this case the electric vector of the exciting light is an axis of symmetry and 3i = I11 + 2I1 . Ifthe fluorescence is excited with natural light the direc- tion of propagation is now an axis of symmetry (Perrin, 1929) and the total radiation of the source is proportional to 3i = 2I, + I1 . Eqns. where the subscript n refers to the same quan- tities as before but on excitation with natural light. Perrin's law for the excitation with natural light reads 11 ~~R -Pn 1 1 1 I-i-Iij, In-lj P= li, + 1il Fi p 3 E2fL i -1 pi 3 Moreover IX = Ij, and I = li i i z Fipi Therefore - II z (3)
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PublishedMay 1, 1952
TypeArticle
Citations684
References1