Rotational Brownian Motion and Polarization of the Fluorescence of Solutions

Rotational Brownian Motion and Polarization of the Fluorescence of Solutions BY GREGORIO WEBER 8ir William Dunn Institute of Biochemistry, University of Cambridge, England*

CONTENTS

Page Introduction. . . . . . , . , . . .......... . .. . . . . . . . . . . . . . 416 I. Rotational Brownian Mo ......... . . . . . . . . . . . . . . . . . . 419 1. Fundamental Assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , 419 2. Elementary Rotations and Translations.. . . . . . . . . . . . . . . . . , . . , . . . . , 420 3. Addition of Elementary Ro 4. Rotational Relaxation Time.. . . . . . . . . . . . . . . , . . . . , , . . . . . , . . , . , . . . , 424 5. Relaxation Times of Ellipsoids of Revolution . . . . . . . . . . . . . 425 of the Ellipsoid 426 6. Mean Cosine and Cosine Square Determined 7. Limitations of the Classical 11. Fluorescence Polarization. . . . . 1. Introduction ,

,

, ,

,

3. Depolarization Due to Brownian Rotations. Isotropic and Nonisotropic

Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4. Depolarization by Isotropic Rotations. Perrin’s Law of Depolariaation. . 5. Significance of p , 6. Experimental Proof of Perrin’s Theory of Depolarization . . . . . . . . . . . . , , 7. Determination of r 0 by Polarization Measurements. . . , . . . . , . . . . . . . , . , 8. Depolarization Due to Rotation of Ellipsoids of Revolution. . . . . . . . . . . . 9. Effect of Intramolecular Rotations on the Depolarization.. . , . . . . . . . . , .

111. Fluorescence of Proteins and Protein Conjugates. . . . . . . . . . . 1. Visible Fluorescence of Proteins.. . . . . . . , , . . . . . , . . . . . . . . . , . . . . , . . . . . 2. Ultraviolet Fluorescence of Proteins. . . . , . . . . . , . . . . . . . . . . . . . . . . . . . . , 3. Fluorescence of Natural Conjugated Proteins. , , . . . . . . . . . . . . . . . . . , , 4. Artificial Fluorescent Conjugates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Absorption and Fluorescence Spectra of the Conjugates.. . . . . . . . . . . . . . IV. Polarization Studies of Conjugates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Variations in Lifetime of the Excited State. . . , , . . . . . . . . , , . , . . . . . . . , . 2. Variations in Limiting Polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . , 3. Rotational Relaxation Times of Protein Conjugates 4. Reversible Combination of Fluorescent Molecules w 5. Determination of Microscopic Viscosities References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

* Present

431 432 434 435 435 437 440 442 443 443 443 445 445 445 447

457

address: Department of Biochemistry. The University, Shefield 10, England. 415

416

OREQORIO WEBER

INTRODUCTION

It is possible to learn something of the size and shape of protein molecules by studying their Brownian motion. Such motion involves not only the translation of the molecules but also their rotational movements. Except in the case of visible particles the Brownian motion itself is not observed but can be inferred from a study of the physical properties of the solution. When the dissolved molecules are fluorescent, a study of the polarization of the emitted radiation can give important information about rotational motion. In the following pages we shall first consider qualitatively the relation between the polarization of fluorescence and molecular size and shape. These considerations will then be developed in quantitative fashion.

I b)

FIQ.1.

Imagine first of all a set of protein molecules in solution and suppose that a given direction is rigidly bound to the molecules. At any instant, all possible directions are equally represented, and the molecules are thus randomly disposed, as in Fig. la. If now a t any given time we restrict our attention t o those molecules where the given direction happens to coincide (Fig. lb) and observe these molecules alone, then within a very short time they will have become randomly disposed; but if the time interval is short enough they may be observed in a state represented by Fig. l c where randomization is not yet complete. We need first to define accurately the state (c) which differs from (b) by the fact that a certain disorientation has been introduced. If the angle defined by the original direction in (b) and the new direction in (c) is called 8, the mean value of its cosine Cose can be used as a measure of the orientation. S e is in fact unity a t the initial instant when there is perfect orientation and reaches zero value when the orientation is random once more. A certain degree of disorienta-

FLUORESCENCE POLARIZATION OF SOLUTIONS

417

tion like that shown in ( c ) is clearly defined by stating the corresponding value of cos 0 . For reasons that willbecome clear later it will be convenient to define state (c) by choosing cos 6 = l / e = 0.365 * . The time necessary to pass from state (b) to state (c) is then called the relaxation time of the system. This has a meaning only for stated values of temperature and viscosity. In the case of visible particles the states (b) and (c) can be determined by following the movements under the microscope. I n the case of particles of submicroscopic dimensions, such states can be revealed by the changes in the physical properties of the solution due to the preferential orientation of the molecules. Thus state (b) may be realized by the application of an electric field which results in the orientation of a small fraction of the molecules. The subsequent disorientation may be followed by observing the disappearance of the optical anisotropy (Kerr effect) due to the oriented molecules (Benoit, 1950), or by the response to an electric field of opposite direction (Oncley, 1941). If the molecules are fluorescent, the disorientation caused by the Brownian rotation may be determined by an elegant method due to Perrin. Suppose that the solution is illuminated with a beam of plane polarized light vibrating in the plane of the paper YOZ, the fluorescent molecules being placed at 0 and the radiation emitted observed along the direction O X . It is known that the absorption and emission of light by organic molecules is connected with fixed directions of the molecules, the so-called oscillators of absorption and emission, and that the molecules will have a good chance of absorbing the exciting light only if the direction of their absorption oscillator is parallel, or nearly so to the plane of vibration of the exciting wave. Thus the excited molecules form nearly a state like (b), because from the randomly oriented molecules of the liquid the excitation has selected those oriented around a particular direction. Each molecule emits a plane polarized wave parallel t o its emission oscillator, and if all molecular orientations are equally probable the fluorescent light will be unpolarized. If, however, the orientation that prevailed a t the time of the excitation is partially preserved, the fluorescent light will show partial polarization. The partial polarization of the fluorescence depends only on two factors, the interval between excitation and emission and the speed of rotation, measured by the relaxation time of the fluorescent molecules. It is known that r, the interval between excitation and emission, is for many molecules in water solution of the order of sec., while their rotational relaxation time is considerably shorter. It may be expected that by the time the emission takes place, random orientation of the excited molecules will be regained and the fluorescence will be unpolarized. A large molecule such as a protein, however, will have undergone on the average only a relatively small rotation due t o its Brownian movement

-

418

G R E G O R I O WEHER

during a time interval of the order of sec. Consequently the fluorescent light which it emits will be partially polarized. The higher the viscosity of the medium, and the lower the temperature, the less will be the amount of rotary Brownian movement and the greater the polarization. Thus the study of the polarization of fluorescent light in media of varying temperature or viscosity, or both, permits an estimate of the intensity of the rotary Brownian movement, and hence of the rotary diffusion constant of the molecule or of its relaxation time. These quwtities in turn give important information concerning molecular size and shape. Similar information has been derived from measurements of dispersion of the dielectric constant (Oncley, 1940, 1942, 1943) and double refraction of flow (Cerf and Scheraga, 1952). Fluorescence polarization measurements, however, can be used t o provide information about many systems which are inacessible t o study by either of the other measurements. Dielectric dispersion measurements can be carried out only on solutions of relatively low conductivity. Therefore, the pH of the protein solution studied must be fairly close to its isoelectric point and the concentration of added electrolytes must be very low. Neither of these limitations applies to fluorescence polarization measurements. Proteins can be studied by this method over a very wide range of pH and of salt concentrations. The method of double refraction of flow is also applicable over a wide range of p H and salt concentrations but is limited t o molecules which are relatively large arid asymmetric. The fluorescence polarization technique, on the other hand, has been applied successfully t o quite small and symmetric protein molecules. Some counterbalancing disadvantages must be noted in the method. Very few proteins are naturally fluorescent. Most proteins if they are t o be studied by this method must be converted into fluorescent derivatives by attaching to them suitable fluorescent groups, and this must be done in such a way as not to denature the protein, or to alter its size or shape appreciably. Moreover the observed polarization measurements are a function both of the time interval T and of the relaxation time of the protein. The values of r for fluorescent protein molecules have not yet been directly measured and this fact, therefore, places some limitations on the conclusions which can a t present be drawn from the method. However, methods are available for the independent determination of r. This source of ambiguity is, therefore, capable of being eliminated in the future. As yet few investigations by this method have been reported. The present review is, therefore, largely concerned with the discussion of the general underlying principles, An attempt is also made to give some indication of the possible range of the future applications of the method.

FLUORESCENCE POLARIZATION O F SOLUTIONS

419

I. ROTATIONAL BROWNIAN MOTION 1. Fundamental Assumptions

The classical theory of the Brownian motion rests on two fundamental assumptions: (a) that equipartition of energy exists among the degrees of freedom of the molecule, so that the average translational or rotational energy of a rigid molecule is always equal to 3.jlcT, independent of its size and shape ( b ) that the molecules moving in the liquid are considered to experience resistance from the latter in the way ascribed by hydrodynamics to macroscopic bodies of the same shape. If a body moves in a viscous medium under a constant force a final constant velocity is reached. T o derive the laws of Brownian motion it is assumed that though the velocity of the particle is constantly changing in magnitude and direction, its average displacements can be described as the effect of a constant force (corresponding to the average kinetic energy for that mode of motion) acting on a particle that experiences friction according to the laws of hydrodynamics. The elementary displacements which accumulate t o yield displacements of observable magnitude are connected with an important constant of the motion: the damping constant of the rotation or of the translation. If a particle of mass m in a viscous medium subjected to no forces, has at zero time velocity vo, its velocity decays with time t according to the law: v = voexp(-it)

where f t is the frictional coefficient of the translation. For the rotation a similar expression obtains for the angular velocity w

fr is the frictional coefficient of the rotation and I the moment of inertia which in the rotation plays a part equivalent to that of the mass in the translation. The quantities m/fi and I / f r are respectively the damping coefficients of the translation and rotation. The total linear displace1 Several authors (e.g., Chandrasekhar, 1943) call m/ft the relaxation time of the translation. To be consistent Z/f, would be the relaxation time of the rotation, but in fact the latter name is mare properly reserved for another quantity of a different order of magnitude (Debye, 1929) which is discussed later on in this article. It is therefore convenient, following Perrin (1934), to call na/fr and Z/fi the damping coefficients of the motions.

420

OREOORIO WEBER

ment Az, or angular displacement A a observed from time 0 till the particle comes t o rest is:

and similarly,

woz

Aa =

= fr

If the particle has at time zero the average kinetic energy k T / 2 per degree of freedom then

vo =

dkm;

wo =

dkT/I

The elementary displacements for spheres are easily obtained since j t = 6nqr, and jr= 8nqr3, according t o the well-known equations of Stokes and Kirchhoff, respectively, in which r is the radius of the sphere and q the coefficient of viscosity of the solvent. For a sphere of molecular weight lo6 and density do = 4.5,in water at 20°, for which 1 = lod2cgs units we obtain,

57 7 kTrdo = 2.5

Aa =

Iq dh k?&m-

=

10-%crn.

5.10-3 rad.

N

0.5 degree

2. Elementary Rotations and Translations

Suppose a molecule of irregular shape is immersed in a liquid and subjected to collisions from the solvent molecules. We may calculate the magnitude of the small displacements by the use of Eq. (lb). Squaring both sides and multiplying by Z/2 we have

where Et and Eo are respectively the kinetic energy of the particle at times t and 0. The average kinetic energy lost by the particle between time zero and 6t is

B

=

f

It

E , dt

=

EoZ [l - exp (-2fr6t/Z)] 2fdt

If 6 t is at least a few times the value of 2 j r / I , the displacement is practically the same as if the particle had come to rest and

B

= EoZ/2fV6t

(4)

FLUORESCENCE POLARIZATION OF SOLUTIONS

42 1

On the other hand, the angle turned in time 6t is by Eq. (2b), Aa =

,(" w dt = (woI/fr)[l - exp -(frijt/I)]

and if 6t equals a few times j r / I ,

eliminating Eo from Eqs. (4)and (5), if a large number of molecules is considered, l? becomes the average kinetic energy for the mode of motion considered. For translational diffusion one finds similarly, = 4BSt/ft (6b)

z?

These equations express a fundamental feature of the Brownian motion, namely that the average small rotation or translation is proportional to the square root of the time. The laws giving the probability of rotations of any amplitude may be obtained by superposing rotations of magnitude given by Eq. (6a) about an instantaneous axis which changes in a random fashion. For the translations the equivalent problem is very simple, since Eq. (6b) remains valid for translations of any magnitude. For the rotations the problem was first solved by Perrin (1926, 1928), for the case of a spherical molecule. Perrin found that calling a the angle which an arbitrary direction of the sphere at time t makes with its direction at time 0: cos2 a

=

f

Q exp (-6kl't/f,) ;

= exp

(-2kTt/f,)

(7)

More recently other demonstrations have been given by Gans (1928) and by Soleillet (1929). Soleillet's demonstration besides being very simple has the advantage of stressing the discontinuous character of the motion; we shall repeat it here with but little change. 3. Addition of Elementary Rotations for Spheres

6/-.

If two successive rotations about independent axes are considered the position of a direction rigidly bound to the sphere will be 0 successively along OA, OB, and OC, while FIG.2. the angles determined by these directions are a, p, and y as shown in Fig. 2. By an elementary equation, cos y = cos a cos p

+ sin a sin p

COB II,

422

GREGORIO WEBER

+

where is the azimuth of OC about the plane AOB. Taking averages of a large number of molecules which have undergone two successive rotations -- --cos y = cos a cos p sin a sin cos (8)

+

+

or squaring and averaging,

- -- cos2 y = cos2 a cos2 p

+ sin2 a sin3 p cos2 + + 2 ----sin a cos a sin p cos p cos + 7-

(9)

If all azimuths of OC about AOB are equally probable, Equations (8) and (9) become now:

- -= cos a cos p cos y

cos2 y

=

(10a)

--

sin2 a sin2 0 cos2 a cos2 p f 2

__.-

(lob)

The latter equation may also be written

3 cos2y 2 - 1 = ( 3 y - 1 ) ( 3 c o s ’ p2- l

)

(11)

The quantities cos cr and (3 cos2 a - 1)/2 can be considered as descriptive of the individual impulses. Addition of the effect of the impulses corresponds to multiplication of these quantities. The effect of any number of individual impulses may thus be computed and Eqs. (10) and (11) show that the order of the impulses is immaterial. Using equations (10) and (11) together with (Ba), the equations of Perrin are easily derived. As cos2 LY is always small and

cos2 a = 1 - (486t/fr) (3 C O S ~cx - 1)/2 = 1 - (6E62/f,)

The value of cos2 a at time t , which we may call cos2 at may be calculated as follows. We divide the time t into elementary intervals sufficiently large so that the particle comes to rest during each of them, i.e., we make 6t >> I / f i . On the other hand, we choose t sufficiently large so that 6 t / t << 1. Application of Eq. (11) yields then,

3 cos2 crt 2

- 1 = (1 - 6E13t/f,.)~/~~ = exp (-68t/fr)

and in the same way,

cos at

=

exp ( -2Bt/fi)

(12) (13)

FLUORESCENCE POLARIZATION O F SOLUTIONS

423

If rotations about one axis alone are considered, the value of cos # in Eqs. (8) and (9) can only be either 1 or -1, and these equations become respectively:

- - - -cos y = eos a - cos /3 & sin a sin p - - -cos2 y = cos2 a! . cos2

+ sin2a sin2p

----

2 sin a cos

cos a sin fi

(144 (14b)

On account of the double sign preceding it, the last term of each equation vanishes on taking averages so that the equivalents of Eqs. (loa) and (11) are respectively, - -cos y = cos a . C O S p (15a) 2 cos2 y - 1 = ( 2 cos2 a! - 1)(2 cos* p - 1) (15b) and consequently, cos at = exp ( -2Et/f,) 2 cos2 at - 1 = exp (-8Et/fr)

( W (16b)

For the sphere f, = 8nqr3. E is the average kinetic energy for the mode = kT/2; for the of motion considered. For rotation about one axis movement of one axis in space which requires rotations about two axes normal t o the given axis and is not affected by rotations about the third, E = kT. Thus Eqs. (12) and (13) and (16a and b) become: cos at = exp (-kTt/4nqr3) cos2 at =+++exp (-3kTt/4nqr3) cos aL = exp (-kTt/8*qr3) cos2 at = exp (- kTt/2nvr3)

Movement of one axis in space Rotation about one axis

{-

+++

(174 (17b) (184 (18b)

Equations (17) and (18) are valid for rotations of any magnitude. If in Eq. (18b) the exponential is developed and terms of order higher than the first are neglected, we have for small angles: cos2 at ‘v 1 - a2 = 1 - (kTt/4rqr3) or

-

a2 N kTt/4nqr3

(19)

Equation (19) is the well-known Einstein equation (1906) giving the average small rotation of the sphere about an instantaneous axis during time t. This equation may also be derived from (6a) by substituting for E and f,.the appropriate values. Thus the equation for elementary displacements is also valid for small displacements for which cos2a N 1 - a2. Einstein’s equation was tested by Jean Perrin (1909) by microscopic observation of suspended spherical particles. He effectively followed the angle turned by a diameter in a meridian plane (the focal plane of the

424

GREGORIO WEBER

microscope), a case t o which Eq. (18b) may properly be applied. The mastic granules, of diameter of 13p turned on the average a t the rate of 14.5 degrees/minute. The value of E from Eq. (19) is 15.1 and by the more accurate Eq. (18b) is 14.7. The granules were observed by white light which precludes the possibility of determining their diameter with better accuracy than 0.2 p or about 1 part in 60. An accuracy not much better than one degree may be expected in the measurements of the individual angles, and the altogether excellent agreement with the theory was no doubt due to the large number of independent measurements (nearly 200) which allowed for cancellation of errors in the measured angles.

4. Rotational Relaxation Time Equations (17) and (18) show that the rotation of the sphere may be characterized in terms of a single constant p o = 4.rrqr3/kT,which has the dimensions of a time. This quantity is called the relaxation time of the rotation and may be defined in general, following Debye (1929), as the time after which a direction bound t o the rotating molecules makes on = e-l. the average a n angle e with its original direction such that The relaxation time of the rotation of a molecular direction is independent of azimuth only if the molecule is a figure of revolution about the said direction. In all other cases the rotational relaxation time of a direction may be defined by considering that all positions of the molecule obtained by rotation about the given direction enter with equal weight. Such will often be the case with molecules in solution where complete randomness of orientation prevails. The change in orientation of a molecular direction depends on rotations about two axes perpendicular t o the said direction. If the frictional coefficients of the rotation about these directions are fi and f,, the relaxation time of the k direction (normal t o i a n d j ) is given by 1 1

pk=mi73

For a sphere symmetry indicates fi = fj = fk and therefore, f

For small angular velocity (Stokes’ approximation) the f’s are linear functions of the viscosity coefficient of the solvent and then by Eq. (20) p is linear in q / T , the proportionality factor depending only on the geom-

425

FLUORESCENCE POLARIZATION OF SOLUTIONS

etry of the molecule. The rotational diffusion constants 0 of a molecule are related t o the frictional coefficients in a simple way, namely

so that

(21)

Equations (17a and b) are used in the theory of dielectric effects and in the depolarization of fluorescence of solutions. Both depend on the orientation of a molecular direction (dipolar axis or emission oscillator respectively) with respect to fixed axes. Dipoles making with the field angles a and a ?r cancel each other in their effects, so that the total effect on the field depends on On the other hand, the linear polarization of the fluorescence is the same for oscillators making angles a! and a! ?r with a given direction, the effects being therefore dependent on cos2 a.

+

z.

+

5. Relaxation Times of Ellipsoids of Revolution

In the case of an ellipsoid of revolution there are two frictional coefficients of the rotation, one for rotation around the axis of revolution (fa) and another for rotation around a direction normal to the first (ft = fc). Consequently there are two principal relaxation times :

is the relaxation time of the axis of revolution, p b , the relaxation time of the rotation of any direction normal to the first. The frictional coefficients for an ellipsoid of revolution have been calculated by Edwardes (1893). Gans (1928) arid Perriii (1934) have used these frictional coefficients to calculate p a / p o and p t / p o , the ratios of the principal relaxation times to the relaxation time of a sphere of equal volume. Perrin characterizes the ellipsoid by the ratio of the axes ( b l a ) , this ratio being smaller than 1 for prolate and greater than 1 for oblate spheroids. . equations, alGans uses the numerical eccentricity [I - ( b 2 / a 2 ) ]His though numerically equivalent to those of Perrin, are less manageable and the latter have therefore been used by most authors. Perrin’s equations show that for a prolate ellipsoid (b/a < 1) pa increases monotonically with the elongation and for large values of this it is proportional t o the cube of the major semiaxis. The relaxation time of the minor axis remains nearly equal to P O (slightly smaller in fact) up to b / a = l / d , then increases and pa

426

GREGORIO W E B E R

reaches the limiting value of 4p0/3 as b/a -+ 0. It is clear that for a prolate ellipsoid pa depends mainly on the length, p b almost entirely on the volume of the particle. For an oblate ellipsoid both relaxation times increase monotonically as the flatness increases, never differing among themselves by more than 10%. Thus an oblate ellipsoid cannot by present methods be distinguished qualitatively from a sphere, but this distinction is possible in the case of a prolate ellipsoid. In fact the demonstration of more than one relaxation time in a monodisperse solution is equivalent to the demonstration that the individual particles are elongated. 6. Mean Cosine and Cosine Square Determined by the Axes of the Ellipsoid

For ellipsoids of revolution the equivalents of Eq. (17a) and (b) for each principal axis have been derived by Perriri (1936). They are: COS‘

aa =

cos2 bb

+ + + exp ( - 3 t / p a ) ;

=

cos uu

=

exp

1 + exp (- 2 + L) + 1 exp (3 3 Pa Pb

cos bb

=

”>

(-t/pa)

Pa

(23)

exp ( - t / p b )

Here the angle aa (or bb) is determined by the direction of axis a (or 6) at time t with respect to its direction a t time 0. Przibram (1912, 1913) observed the angle rotated by the long axis of microscopic elongated objects. These were rigid bacterial chains of different lengths obtained by heating a suspension of Bacillus subtilis in dilute formaldehyde. Few of his measurements correspond to small or medium angles to which Eq. (19) may, in agreement with Eq. (23), be apTABLEI Relaxation Times of the Rotation of the Long Axis of Cylindrical Particles From values of Przibram (1913) Relaxation time Volume of the particles Axial ratio (cm.3 X l o l l ) 2.26 2.29 2.59 2.92 3.83 4.58 4.58

7.8 8.6 9.8 10.9 14.5 16.9 16.9

Calculated (sec.) 161.6 188.9 265.4 358.7 739.2 1136 1136

Observed (sec.) 112 183 280 272 977 1250 1483

FLUORESCENCE POLARIZATION OF SOLUTIONS

427

plied. Using Eq. (19) and the data of the table of p. 1909 of Przibram’s (1913) paper, I have deduced the values of pa which are tabulated (Table I) as Pobsarved. From the volume and elongation of the particles and the equations of Perrin (1934) peal ulated of the same table is computed. I have excluded the first two measurements given in Przibram’s table because they refer to large angles, in which case Eq. (19) cannot be applied. When the sources of error of this type of observations are taken into account, together with the fact that the calculations assume the particles to be ellipsoidal, while their real shape is nearly cylindrical, it appears that the agreement is as good as may be expected and that Perrin’s theory of the rotations of the ellipsoid is a valid approximation for elongated particles.

7. Limitations of the Classical Theory of Brownian Rotations As we have seen, the hydrodynamical equations of Kirchhoff and Stokes for the frictional resistances to rotation and translation are assumed. They suppose: ( a ) that the medium is continuous and ( b ) that the viscosity coefficient appearing in the equations is the viscosity coefficient of the solvent as measured by flow. The effect of treating the medium as continuous is to neglect the existence of free space in the liquid. This free space depends on the packing of the solvent molecules around the particle under consideration, and if this latter is not much larger than the solvent molecules, there may occur larger rotations than those which according to Eq. (3) correspond to a continuous medium. As pointed out by Frenkel, in such case it will not be possible t o consider the problem of Brownian rotations as one of differential diffusion. An important difference appears here between translational and rotational diffusion. As regards the former (Frenkel, 1946)’ the relative size of the solvent molecules is of no consequence, so that the Stokes approximation remains valid even for the self-diffusion of solvent molecules. It is not simple t o determine the relative size of solute molecules at which the classical picture of the Brownian rotations breaks down. Some idea may be obtained by considering that a large rotation occurs when the Brownian particle moves to fill a hole left by one or more solvent molecules, previously in contact with it. One may expect that only rarely A a = & sin-’ r / R

where R and r are respectively the radii of the solute and solvent particles. If r = 2 A and R = 50 A the value of Aa from the last equation does not differ in magnitude from that given in Eq. (3b), so that in this case the Stokes approximation is justified. For particles of the size of protein molecules (mol. wt. greater than a few thousands) the effect of considering the medium as continuous should not introduce an appreciable error. It is pos-

428

GREGORIO WEBER

sible however that the approximation may not be valid for the rotation of individual groups or side chains attached to the protein. The introduction of the coefficient of viscosity measured by flow in the case where the particle moves in a pure liquid has been experimentally justified by Svedberg and Eriksson-Quensel (1936), who showed that the same sedimentation constant of Helix hemocyanin is obtained in mixtures of heavy and ordinary water in various proportions if corrections for density and viscosity are introduced. In the cases where the solvent is a dilute electrolyte solution, the necessity of a correction for the increased viscosity has not been completely proved. The corrections which are applied are in most cases sufficiently small to fall within the error of the determinations since for solutions of buffer below half-molar concentration the ratio Tbulfe./qaater does not exceed unity by more than 5%. That a large increase in the flow viscosity may make little difference in the microscopic viscosity is exemplified by the fact that the translational and rotational diffusion of small molecules in gels is much the same as in the pure solvent.

11. FLUORESCENCE POLARIZATION 1. Introduction The absorption of light by a molecule results in the appearance of an electronically excited state. If undisturbed the molecule returns t o the ground state with emission of a photon of the absorbed frequency after a time of the order of sec. In atoms in the gas phase this behavior is commonly observed as resonance radiation (e.g., Herzberg, 1944). In molecules the ground and excited states have multiple vibrational levels (Fig. 3) and accordingly emission of a broad band rather than a line takes place. Not every absorbed photon is reemitted as fluorescence. In molecules in particular several processes compete for the absorbed energy, Dissociation with appearance of radicals or other photochemical reactions may dissipate the energy in some cases, while in others radiationless transitions to the ground state take place. The latter involve internal conversion processes whereby the electronic energy is converted into vibrational energy within the same molecule (Franck and Livingstone, 1941), and in many cases transitions to the triplet state where the long lifetime, of the order of a second, favors the dissipation of the absorbed energy by the medium. This process has been discussed by Kasha '(1947), McClure (1949), and Karyakin and Terenin (1949). The molecules in the ground state are practically all in. the zero vibrational level at room temperature. On absorption they may pass t o the different vibrational levels of El. There in a time short compared to T ~the ,

FLUORESCENCE POLARIZATION OF SOLUTIONS

429

lifetime of the excited state, the excited molecules reach thermal equilibrium with their surroundings as regards their vibrational energy, that is, they find themselves mainly (at room temperature) or exchsively (at 0" K.) in the zero level of El.From these levels the emission takes place, and as a result the fluorescent spectrum is independent of the exciting wavelength, there is little overlap of emission and absorption bands, and the former is of lower frequency than the latter (Stokes rule).

FIG. 3. Energy levels of a molecule. G ground state, El first electronic state, Ei upper electronic state. TI first triplet state. Small numbers indicate the first few

vibrationai levels of each electronic state. G-El and G-E2are the transitions in absorption. Ez-E~radiationless transition that precedes fluorescence. El-G transitions in fluorescence. G-TI absorption transition to the first triplet. TI-G transition from the first triplet state to the ground state, believed to be responsible for the low temperature phosphorescence. Allowed transitions in full line. Forbidden transitions are dotted.

It is usually assumed, following Perrin (1926),that the rate of emission is correctly described by the expression nL/no= exp - ( t / 7 0 ) where nt and no denote the number of excited molecules a t times t and 0, respectively, after the excitation. This expression does not take into account that the emitting molecules reach the zero level of El from upper levels, either by radiationless transitions or vibrational exchange with their surroundings, so that the population of the zero level first increases rapidly and then decreases slowly after the excitation. This situation is correctly described by a probability of emission of the form, well known in the theory of radioactive decay:

430

GREGORIO WEBER

where 71 is a function of the exciting wavelength and represents the lifetime of the transition that carries the molecule from the level reached on excitation t o the lower levels of El. For values of t a few times 71 or greater, the emission rate is practically described by the expression

ntlnc

=

exp ( - t / d

so that in many applications the latter is a sufficient approximation. However, the more exact Eq. (24) may prove necessary in the theory of quenching and depolarization. 2. Polarization Due to Dipole Oscillators

The state of linear polarization of the light emitted by dipole oscillators is easily calculated when, as in fluorescence, there are no permanent relations of phase between the emitted waves, i.e., when the radiation is

z

FIG.4.

incoherent. I n such a case it will only be necessary t o add the components of the emitted intensity along two directions. Thus the polarization of the light emitted in the Oy direction is given by

I , and I , are the result of adding the intensity components along the 2 and y directions, both normal to Oy. The quantity p is completely defined by the orientation of the emitting dipole oscillators in space. The intensity, lifetime of the excited state, and polarization of the fluorescence of organic molecules in solution point to electric dipole radiation. Direct proof of this was obtained for fluorescein by Selenyi (1911, 1939) using his wide angle interference method and has been recently confirmed by Freed and Weissman (1941). If the fluorescence is excited by linearly polarized light vibrating along Oz (Fig. 4), this direction is an axis of symmetry of the system, and appli-

FLUORESCENCE POLARIZATION O F SOLUTIONS

43 1

cation of Curie’s symmetry principle (Perrin, 1929) shows that the polarization is independent of the angle $ and varies with +, becoming zero for radiation emitted along Oz, the axis of symmetry itself. This is expressed by I, = I,/ I, = I, = I,

If the exciting light is unpolarized, the direction of propagation is now an axis of symmetry, and consequently the light emitted in this direction has zero polarization. The polarization varies now with $ but not with 4. Theref ore, I , = I , = Ill I, = I , An important application of these principles can be made in the calculation of the polarization due to several species in solution, each emitting radiation of different polarization. This addition Ian. of the polarizations is (Weber. 1952a) (26)

where the minus signs correspond to excitation with polarized light vibrating normally t o the directions of propagation and observation and the signs t o excitation by natural light, the observation being as usual at right angles t o the direction of the exciting beam. fi is the fraction of the total intensity emitted by the i t h component and therefore bears a direct relation t o the proportion of the i t h component present in the solution.

+

3. Depolarization Due to Brownian Rotation. Isotropic and Nonisotropic Rotations The molecular rotations responsible for the depolarization of the fluorescence may be said to be isotropic if the average angle swept by the oscillator of emission of the excited molecules in a given time is independent of azimuth. Consider a molecule of irregular shape (Fig. 5) where Oz is the direction of the electric vector of the exciting wave and OA and OE the directions of the absorption and emission oscillators respectively. For a collection of unexcited molecules, all the positions obtained by rotation about OE are equally probable. If all such molecules were t o have equal probability of excitation, the average angle swept by OE should be independent of azimuth about the plane ZOE. This average

432

UREQORIO WEBER

angle would then bear a direct relation to the relaxation time of the rotation of the OE direction. However, the probability of excitation is proportional t o cos2w, where w is the angle between Oz and OA, so that the excited molecules are not, in general, a collection where all azimuths are equally represented. The average angle swept by OE does not bear a direct relation to the rotational relaxation time of OE in such cases. However, in certain particular instances, the probability of excitation, and therefore the angle swept by OE, becomes independent of azimuth. Such are as follows: (1) OA and OE are coincident (A = 0); (2) OA and OE are noncoincident (A # 0), but ( a ) the molecule is spherical, ( b ) the molecule is of irregular shape, but all orientations of OA and OE with respect t o a rigid coordinate system bound to the molecule are equally likely. Obviously this random orientation of the oscillators with respect to the mechanical axes of the molecule is not possible in the case 6f a small fluorescent molecule, but will very likely represent the actual case when a fluorescent unit is attached to one of many possible points of a macromolecule as in the fluorescent conjugates or adsorbates to be discussed later on. The concept of isotropic rotations is a very useful one because if the average angle of the emission oscillator with a given axis is known at time 0, the average angle at any further time may be calculated by means of Eq. (11). 2

FIG.5.

FIG.6.

4. Depolarization by Isotropic Rotutions. Perrin's Law of Depolarization Consider the polarization observed along Ox when (Fig. 6) the emitting oscillators make an angle 8 with Oz, all azimuths $ being equally probable (case of polarized excitation). We have

I, 'I

-

I , = I , = sin2 e cos2$ = = cos2 9 =1 1 1 =

sin2B

433

FLUORESCENCE POLARIZATION OF SOLUTIONS

the polarization of the light emitted along Ox may be defined by -1- - =1 - 4

3

Pa

3.5

+ L - i = Ill - 11 3

(274

3 cos2 6 - 1 ( 2

)

According to Eq. (26) the polarization due to all oscillators making variable angles 9, is

since q e ) = 1. Consider now the polarizationsat times 0 and 1 after the excitation. They are respectively,

But if the rotations are isotropic 3

et

COS~

- 1

2

eo = (3 2 )(3 COS~

1

C O S ~a ( t )

2

-1

)

where a(t) is the angle swept by OE between times 0 and t. We thus have 1 Pt

1 3

2

A similar derivation shows that in the case of excitation by natural light, 2 Pt

To calculate the polarization observed at any time after the excitation we may again use Eq. (26) obtaining,

where f(t) is the fraction of the total intensity due to molecules emitting

434

GREGORIO WEBER

t seconds after the excitation. If a constant rate of emission has been reached f(t) = exp ( - t / d / 7 0 and fc

m

t=O

For a spherical molecule cos2 a(t) =

+ + Q exp (3t/po)

where po is the relaxation time of the rotation. Introduction of this into the last equation and integration yields

The last equation was first derived by Perrin (1926, 1929) in a different way. If the probability of emission is that given by Eq. (24), the last becomes

5. Signijicance of po The preceding equations tell nothing about the value and significance of P O , except that this is the limiting polarization attained in the absence of rotations. A theory due to Jablonski (1935) shows that Po

=

3 cos2 x - 1 3 + c0s2 x ;

pn0

=

3 cos2 x - 1 7 - cos2 x

where p o and p , ~are the polarizations observed with polarized and unpolarized excitation respectively, and X is the angle between OA and OE. As 0 5 X 5 ?r/2 I Po I $; -4 I p n 0 5 ii

-+

It is experimentally observed that po is a function of the exciting wavelength. Grisebach (1936) and Pheophilov (1943) have studied the socalled polarization spectrum of dyes. This is the set of values of p , ohtained on varying continuously the wavelength of the exciting light. The data can be interpreted (Pheophilov, 1943) on the picture that there is only one emission oscillator and several absorption oscillators making variable angles with the former, all rigidly bound t o the molecule. It is found that at one or more particular wavelengths pa = 0. Equation (28)

FLUORESCENCE POLARIZATION O F SOLUTIONS

435

predicts that in such case p = 0 at all times after the excitation. The theory of the anisotropic rotations developed by Perrin (1936a) shows that in such cases a polarization may be introduced by the Brownian rotations even if po = 0. Under certain conditions this behavior may be used as an experimental test of the isotropy of the rotations. 6. Experimental Proof of Perrin's Theory of Depolarization Equation (28) can be tested for consistency by plotting l / p against

T/q. Since p is a linear function of q/T, a straight line should be obtained.

Perrin (1926, 1929) found that fluorescein and other dyes in glycerolwater mixtures of different viscosity kept at the same temperature yielded the expected linear relation, but for viscosities smaller than about 10 centipoises the plot showed curvature convex toward the T/q axis, i.e., the polarization was smaller than expected. Similar observations have been made by other authors (Wavilov, 1936; Weber, 1947). Curvature of the same type is also observed if one solvent (glycerol) at different temperatures is used. The causes for this departure from the linear law are not clear. Two possibilities are as follows: ( a ) For small molecules in media of low viscosity the elementary displacements may be larger than predicted by Einstein's equations (Perrin, 1936). (b) If the probability of emission is given by Eq. (29), a curvature of the required shape is observed if r 1 is sufficiently large. The magnitude of the deviation from the linear law is not large in itself. For fluorescein in water at 20" the calculated polarization from the slope obtained at high viscosities is 0.023 while the observed is 0.017. This difference appears magnified when the reciprocal of these small quantities is plotted. A better idea of the discrepancy may be obtained by considering the value of cos2 a(t) corare respectively responding to both polarizations. The two values of 36.5" and 37.2" respectively. The absolute magnitudes of the calculated and observed rotations differ by less than 3%. Although the possibility first enumerated appears the more likely, the presence of a second transition (b) deserves some consideration: If Eq. (29) is used in the case of fluorescein rl/ro equals 0.02, a magnitude that does not appear unreasonable. The curvature obtained for eosin gives TI/TO = 0.02 and for riboflavin (Weber, 1947) r1/r0 = 0.01.

m

7. Determination of ro by Polarization Measurements According to the Laplace transformation indicated by Eq. (27c) and (28) the linear law follows whenever cos2a ( t ) and f ( t ) are exponential functions of the time. A direct proof of the theory of Perrin may be obtained by comparing the values of T O directly determined (e.g., Forster, 1951) by the fluorometer, and those determined by measurements of the

436

GREGORIO WEBER

polarization of the fluorescence. Perrin (1926, 1929) considered the molecules as spheres and used the molecular volumes determined by Marinesco (1927) from viscosity measurements. These values of the molecular volumes V are subject to some uncertainty, but in spite of these disadvantages the agreement between the values of r0 so obtained and the direct measurements is indeed remarkable. Table I1 summarizes the results TABLEI1 Comparison of Values for the Lifetime of the Excited State Obtained b y Direct Measurements and by Polarization Observationsa Polarization observations Substance Fluorescein Chlorophyll Quinine Anthracene

Solvent

v

Water-glycerol Cyclohexanol Water-H2SOc glycerol Ricin oil

500 2500 506

170

x

Fluorometer 109

4.3 30 40 250

Solvent Water Alcohol, acetone Water Acetone

x

109

4.8

> 5 and < 40 42

>50

n The polarization observations of Perrin (1929) and the values of Rnu (1949) obtained by the fluorometer have been used. V is the molecular volume used by Perrin. This was obtained from the measurements of Marinesco (1927).

obtained by both methods in so far as direct measurements by the fluorometer are available. The purity of some of the substances used appears doubtful (e.g., eosin, and chlorophyll which in Perrin’s experiments was probably a mixture of a and b chlorophylls). It is to be hoped that in the future such measurements will be performed with substances of chromatographic purity. The direct measurement of T O was first done by Gaviola (1927) using modulation of the exciting light by Kerr cells, a method lately improved by Szymanovski (1935). Ultrasonic modulation, using the Brillouin effect (Debye and Sears, 1932) was introduced by Maerks (1938) and has been recently used by Kirchhoff (1940), Rau (1949), and Galanin (1950). Although the polarization measurements and the direct measurements agree well for fluorescein and eosin, the recent measurements of Rau extend this agreement to quinine sulfate, and probably t o anthracene, which has a mean life longer than 5.10V sec. The value for chlorophyll quoted by Perrin (3.10+ see.) falls within the range of values observed by Rau. Two other methods are available for the determination of T ~ neither , of which is very accurate. The determination by quenching with potassium iodide (Wavilov, 1929) is approximately valid for some molecules like fluorescein and riboflavin, but quite inaccurate for the naphthalene derivatives, and indeed many other molecules. The values of T~ obtained

FLUORESCENCE POLARIZATION O F SOLUTIONS

437

by integration of the absorption band corresponding t o the first electronic transition is at best an approximation. As pointed out by Joos (in Kirchhoff, 1940) i t rests on a relation between line width and radiation damping which is valid for emission by undisturbed atoms but cannot be expected t o yield precise results in the case of polyatomic molecules.

8. Depolarization Due to Rotation of Ellipsoids of Revolution

If the rotations are isotropic the depolarization is a function of the relaxation time of the rotation of the direction containing the emission oscillator OE. This relaxation time may be expressed as a function of the principal relaxation times pa and Pb. As the rotations can be isotropic only if O E makes a random angle with the axis of revolution, it is necessary t o calculate the depolarization due to a collection of molecules in which the angle between that axis and O E assumes all values between 0 and ~ / 2 . This can be done by means of Eq. (26). The following result is thus obtained (Weber, 1952a),

, -

1 + 1 - + - - 1 -

where nl = ~ . / P Oand n2 = p b / p ~ .P O is the relaxation time of a sphere of volume V e equal to th at of the ellipsoid. On plotting l / p T $5 against ~ ~ / or p which ~ , is equivalent, against T/q, the initial slope is

+

where ph = 2 / ( l / p a l / p b ) is the mean harmonic of the principal relaxation times of the ellipsoid. A somewhat more general treatment (Weber, 1953c) takes into account differences in the average orientation of the emission oscillators. Calling p the angle that the emission oscillators makes with the axis of revolution of the ellipsoid, it is found th a t in the plot of l / p against T/q the ratio of the initial slope to the slope of the sphere of equal volume is SI

sil

- cos2 p

nl

-

1 - (3082 p rL 2

The initial slope is thus.proportiona1 to the mean harmonic of the principal relaxation times of the ellipsoid weighted according t o the mean

438

GREGORIO WEBER

cosine square of the angle determined by the emission oscillators and the axis of revolution. I n the derivation of Eq. (31a) (Weber, 1952a) it was assumed t ha t cos2 p = $5. This does not take into account the element. of volume available to each orientation, and therefore it does not correspond t o truly random conditions. In the latter case cos2 p = $5 and the equivalents of Eqs. (31a) and (31b) are, respectively:

-

If n1 2 2nz, under ordinary experimental conditions a curvature may be obtained on plotting l / p against T/q and this curvature is concave toward the latter axis. Oblate ellipsoids for which nl and n2 do not ever differ markedly should always yield a straight line but prolate ellipsoids may show curvature if sufficiently high values of the ratio ~ ~ may / be p reached. ~ If T O N lo-* sec. when water up to 50' is used as solvent we have ( ~ o / p o ) < 1.5 if V , > lo4 and ( ~ ~ / < p ~0.15 ) if V , > lo6. I n the latter case any elongation may fail t o produce curvature whereas in the former curvature could be detected if the axial ratio is superior t o 5. Figure 7 shows the plotting of ph/pO against the elongation or flatness (long axis/short axis) for prolate and oblate ellipsoids. It appears th a t p,&/p0 remains practically constant for prolate ellipsoids of axial ratio greater than 10. If by any other means (e.g., specific viscosity) the axial ratio is estimated, it would be possible t o determine unequivocally the volume of the hydrated particle and if allowance is made for hydration, the molecular weight may be estimated. On the other hand, if the molecular weight is known ph/po' gives a measure of the departure from the value corresponding to an unhydrated sphere and has a significance similar t o t ha t of f/fo in translational diffusion. Notice, however, th a t PO) is the relaxation time of the unhydrated sphere while po appearing in Eqs. (31) and (32) is the volume of the hydrated molecule. The observations on dyes show that deviations from the linear law appear only when the molecular rotations are large, and it is t o be expected that such deviations will not be observed with macromolecules. The presence of more than one relaxation time, whether belonging to the same or different molecules, results always in curvature concave toward the T/a

439

FLUORESCENCE POLARIZATION O F SOLUTIONS

axis. A curvature convex toward the latter axis can be present only if the reIaxation times themselves are not linear functions of q/T. There are in this case several possibilities: (a) a decrease in the particle size due to thermal dissociation into rigid units (translational and rotational dissociation); ( b ) change in shape toward a form having a lower value of p h / p o ; (c) The appearance of new rotational degrees of freedom that were frozen at lower temperatures. This may include the appearance of independent rotation of rigid subunits inside the molecule (rotational dissociation without translational dissociation).

5-

4-

30

m

Axial ratio

FIG.7.

Occasionally a distinction between these possibilities may be drawn from the polarization data themselves, but in general the study of sedimentation or translational diffusion will be necessary. It may be pointed out that small changes in molecular shape or volume are much more likely to be detected by a study of the rotational diffusion than by sedimentation or translational diffusion. For a globular molecule the translational diffusion constant is roughly proportional to the cube root of the volume whereas the rotational relaxation time is proportional to the volume itself. Also the ratiof/fo varies from 1 t o 1.6 when the axial ratio of the prolate ellipsoid varies from 1 to 10. Under the same circumstances Ph/po’ varies from 1 to 1.9.

440

GREGORIO WEBER

9. E$ect of Intramolecular Rotations on the Depolarixation I n what precedes, the particles have been considered as rigid units having only three degrees of rotational freedom. For proteins this hypothesis is a plausible one in view of the extensive intramolecular bonding prevalent in them, but even here two limitations have t o be considered: ( a ) The molecule may consist of two or more units each of which is kept rigid by strong intramolecular bonding although still capable of certain rotations independent of the other units; ( b ) the molecular backbone as a whole may be rigid but the side chains may have rotational freedom about various C-C bonds.

A

a

B

-a

C

FIG.8.

We need consider here only the cases where the rotational freedom itself is not a function of the temperature so that a straight line or a curve concave toward the T / q axis is obtained. It is also necessary t o limit the analysis t o those cases in which the molecular shape is not conspicuously altered by the intramolecular rotations. This is equivalent in most cases to the assumption that the independent rotations take place about one axis alone, the other two being axes of rotation of the molecule as a whole. The rotation of the internal units may be considered in relation t o the models shown in Fig. 8 where it is assumed th at the whole particle and the internal units are ellipsoids of revolution t o which Eqs. (32) may be applied as a first approximation. I n all three models a is assumed to be the axis of independent rotation, b and c axes of rotation of the particles as a whole. With these premises it is apparent that the relaxation time of the a axis is_that of the whole particle, while the relaxation time of the b or c axes is

FLUORESCENCE POLARIZATION O F SOLUTIONS

44 1

nearly that corresponding to a spherical particle of the volume of the internal unit. If the large particle is now “dissolved,” that is, if now we let the subunits acquire translational as well as rotational freedom, a difference appears between A and B on one side and C on the other. In A and B if the internal units, as well as the whole particle, have elongation greater than 10, the relaxation about a does not contribute t o the depolarization either in the original whole particle or in the dissolved subunits and the polarization is the same for both. Conversely, if independent elongated units polymerize end to end to yield a long fiber in which each unit has freedom of rotation about the fiber axis, the polarization of the fluorescence remains unchanged. In C when translational freedom of the subunits appears, the new relaxation time about a is now of the same order as that about b, and a decrease in the polarization corresponding t o a decrease in relaxation time up to twice the original may be observed. Conversely, if independent quasi spherical units polymerize linearly to yield a fiber, while preserving freedom of rotation about the fiber axis, the observed relaxation time may increase up to twice the original value. These remarks may be of importance in the interpretation of data obtained by Massey (1953b) on fumarase and Tsao (1953) on myosin and actin. The relaxation time of the rotation of a side chain p c must be negligible when compared with the relaxation time of the protein molecule as a whole, while the amplitude of the rotations is limited by the neighboring chains. If the fluorescent oscillator is attached to a side chain, as in the case of the conjugates t o be considered here, there will be two relaxation times to be considered: ph, the mean harmonic of the principal relaxation times of the particle, and pc, the relaxation time of the chain carrying the oscillator. If the range of values of T / q explored is such that 3 7 0 / p c >> 1, the linear law is still valid (Weber, 195213) but the extrapolated value of pa is lower than in the absence of the independent rotation of the side chain. It is not clear how the latter rotations are affected by an increase in the viscosity of the solvent due to addition of foreign substances, but it appears likely that they are far less affected than the rotations of the molecule as a whole. Thus the good agreement between the values of PO obtained by extrapolation and those observed in a medium of high viscosity (60% sucrose) may be explained (Weber, 1953a; Tsao, 1953). OF PROTEINS A N D PROTEIN CONJUGATES 111. FLUORESCENCE

The absorption spectra of proteins in the ultraviolet above 2500 A is due mainly to the aromatic amino acids. Quantitative measurements, recently reviewed in this series (Beaven and Holiday, 1952) show that the position and shape of the bands are very similar or identical in the free

442

OREGORIO WEBER

amino acids and in the protein. It may therefore be expected that the fluorescence of proteins will be to a large extent that of the aromatic amino acids present. 1. Visible Fluorescence of Proteins

I n order to attribute fluorescence to a definite compound it is necessary to show that the emission is a maximum when the wavelength of the exciting light is that of the absorption band of least frequency, dropping abruptly as the excitation is carried to longer wavelengths.’ Failure to apply this elementary criterion vitiates many experiments and is responsible for many strange statements in the literature, particularly as regards the fluorescence of proteins and nucleic acids and their derivatives. I n protein solutions excited by the 3660 A group of lines of the Hg arc weak visible fluorescence has been commonly observed. However, if the exciting light is the much more strongly absorbed 2537 A Hg line, the fluorescence not only does not increase, but altogether disappears. That? this visible fluorescence is due to impurities essentially non-protein in nature is also borne out by the following observations: (a) The fluorescence is invariably stronger in impure protein solutions than in solutions of proteins recrystallized several times. ( b ) It is particularly noticeable in solutions of serum albumin, a protein notorious for its binding properties. (c) It is altogether absent in tropomyosin where prolonged treatment with organic solvents (Bailey, 1948) might conceivably remove waterinsoluble fluorescent impurities. Vl6s (1946) has reported fluorescence in crystals of amino acids and in proteins both in the solid and in solution. Examination of his data show that the results obtained with amino acids must be due to impurities. Thus, in the case of tyrosine, excitation with the wavelength of nearly maximum absorption resulted in no fluorescence being emitted, while emission took place on excitation with shorter or longer wavelengths. This is exactly what one would consider necessary to show that the fluorescence was due to an impurity and not to the tyrosine itself. A similar criticism applies to Vl8s’ results with serum albumin. His conclusion thatzthe results obtained with proteins are explainable on the basis of an “antistokes” effect rests on a definition of the term which is peculiar t o this author. This experiment is easily performed by observing from above the fluorescence of a dilute solution iluminated with the required wavelength in the Beckman spectrophotometer in a darkened room. As the wavelength is changed the fluorescence passes through maxima and minima of brightness. In compounds with appreciable fluorescence the maxima and minima of absorption may be located in this way with fair accuracy.

FLUORESCENCE POLARIZATION O F SOLUTIONS

443

Reeder & Nelson (1940) detected weak visible fluorescence in protein hydrolyzates, excitable only by wavelengths from 3000 to 4000 A. This was clearly due to impurities or to products formed during hydrolysis.

2. Ultraviolet Fluorescence of Proteins Ley and v. Englehardt (1910), Kowalski (1911), and Marsh (1924) have investigated the ultraviolet fluorescence of phenol and phenolic derivatives. They found broad emission bands extending from 2700 A to 4000 A with maxima usually in the region of 3000 A. Similar bands may be expected for tyrosine and phenylalanine and in the absence of internal quenching effects, also in proteins. A study of the ultraviolet fluorescence of aromatic amino acids and proteins would no doubt provide interesting details as regards the interaction of the aromatic residues in the protein molecules as well as help in the interpretation of the absorption spectra themselves.

3. Fluorescence of Natural Conjugated Proteins Conjugated proteins possessing visible fluorescence are found in the tissues of plants and animals. Diaphorase (Straub, 1938) shows fluorescence corresponding in color and intensity to that of its prosthetic group, flavin adenine dinucleotide. Dilute solutions of diaphorase show strongly polarized fluorescence ( p 0.38 at room temperature) while solutions of its prosthetic group give off practically unpolarized radiation (Weber, 1947). Most of the flavoproteins which have been described show no detectable fluorescence, for instance xanthine oxidase (Morell, 1952) and notatin (Keilin and Hartree, 1946). Polarization observations (Morell, 1952) show that the fluorescence of preparations of xanthine oxidase is due to a trace of prosthetic group in solution and not to the conjugated protein. Phycoerythrin, a photosynthesizing pigment from red algae (Blinks, 1949) and the chlorophyll-protein complexes described by Takashima (1952) show visible fluorescence. Neither heme itself nor the heme proteins show detectable fluorescence.

-

4. Artijicial Fluorescent Conjugates Fluorescent carbamido conjugates of several proteins have been prepared by Creech and co-workers by reaction with polycyclic aromatic isocyanates. 1 : 2 Benzanthryl isocyanate was used by Creech and Jones (1940, 1941), and the same authors coupled several other isocyanates, using the protein conjugates for immunological studies (Creech, Oginsky, and Cheever, 1947). They determined the prosthetic group content of the conjugates by spectrophotometric observations. More recently Creech and Peck (1952) have described conjugates of serum albumin with 4 di-

444

GREGORIO WEBER

methylaminostilbene and 2 amino fluorene isocyanates. No quantitative observations on the yield and on the polarization of the fluorescence of these conjugates has so far been reported. They should prove suitable for the study of the rotational relaxation times of proteins of high molecular weight since anthracene (Perrin, 1929; Rau, 1950) has a mean life of the order of sec., and similar values may very likely be found for other polycyclic aromatic hydrocarbons (Chakravarty and Ganguly, 1947). Coons, Creech, Jones, and Berliner (1942) have also prepared conjugates from serum proteins and a fluorescent isocyanate. The latter was obtained by nitration of fluorescein, catalytic reduction t o the amine and subsequent conversion to the isocyanate by phosgene. The isocyanate, presumably a mixture of isomers, was not isolated. More recently Coons and Kaplan (1950) have separated (though not characterized) the two nitrofluoresceins obtained by condensation of 4-nitrophthalic acid with resorcinol. They converted the isomer amines t o the isocyanates and used the protein conjugates (antibodies) to trace antigens in the tissues by means of fluorescence microscopy. As the natural lifetime of the xanthydrols is about 6.10+ sec. (Perrin, 1926), it appears that these conjugates may be useful for the study of the relaxation times of small molecular weight proteins. Weber (1952, 1953) has obtained sulfonamido protein conjugates by reaction of several proteins with 1 dimethylaminonaphthalene 5 sulfonyl chloride. The preparation of some simple sulfonamido derivatives has shown that as in the conjugates of Creech et al. the spectrophotometric method could be used to determine the amount coupled with the protein. The existence of unspecific adsorption, side by side with chemical combination, is one of importance. Creech el al. (1941), who purified their conjugates by acetone precipitation, observed that a constJant ratio of hydrocarbon to protein was reached after several precipitations. Paper chromatography in a medium where the conjugate is insoluble while the adsorbed molecules have some solubility has been used by Weber (1953a) to show the absence of adsorbed material and more recently the same author has used paper electrophoresis for the same purpose (Weber, 1953b). The purification of the conjugates has been achieved by fractionation with organic solvents (Creech, 1941) or by the use of ion exchange resins (Weber, 1953a). There are few reports about the modifications of the protein induced by the coupling. Sulfonamido conjugates of ovalbumin (Weber, 195213) have a solubility at the isoelectric point similar t o t h a t of the native protein and become insoluble after denaturation by heat, urea, acid, or alkali. Fumarase conjugates of the same type (Massey, 195313) have 80% of the original catalytic activity after introduction of 5 groups/mole, and

FLUORESCENCE POLARIZATION O F SOLUTIONS

445

some activity remains even after introduction of 30 groups/mole. Creech and Peck (1952) state th at serum albumin conjugates with stilbene isocyanates are more easily denatured by acetone than other conjugates, although it is not clear whether the difference was due to the much larger number of stilbene groups which were introduced (up t o 60 groups/mole). 5. Absorption and Fluorescence Spectra of the Conjugates The absorption spectra of the carbamido conjugates of Creech and Jones (1941) were largely those of the prosthetic group in the region where the protein absorption is negligible. The bands in the shorter ultraviolet were more seriously affected by the coupling. I n their study of stilbene carbamido conjugates Creech and Peck (1952) have shown that, in contrast t o the free prosthetic substance, the spectra do not change on illumination. The sulfonamido conjugates of Weber (1952b) showed a broad band which in serum albumin conjugates had a maximum a t distinctly shorter wavelengths (- 332 mp) than in egg albumin or insulin conjugates (- 343 mp) . The corresponding fluorescent spectra were also displaced toward the longer wavelengths in the latter conjugates t o judge by the color of the fluorescence. An increase in the 0-0’ frequency difference may also be expected (Samburski and Wolfsohn, 1941), and it would be natural to attribute these differences to the more or less polar character of the protein environment, as has been done by Laurence (1952). Quantitative studies of the fluorescent spectra of the conjugates have not yet been carried out, but many data of interest may be expected from them. The conjugates of aromatic polycyclic hydrocarbons seem particularly interesting in this respect, because both the parent compound and the conjugates exhibit vibrational fine structure.

IV. POLARIZATION STUDIES OF CONJUGATES I n a fluorescent protein conjugate that behaves in solution a s a rigid rotator Eq. (32) shows that two of the parameters that determine the observed polarization, namely 70 and pol depend on the attached molecule; while p , the relaxation time of the rotation, depends mainly on the macromolecule. It is well to inquire what changes in these quantities are introduced by the conjugation. 1. Variations in Lifetime of the Excited State

If there are no competitive processes that diminish the yield of the fluorescence by radiationless transitions T O has its maximum value rn, which is called the naturaI mean life of the excited state. Perrin (1929) has stated “ t ha t all causes of kinetic deactivation reduce in equal pro-

446

CREGORIO WEBER

portion the yield and lifetime of the fluorescence.” Thus

where rn and r n are respectively natural lifetime and yield, and r and r the corresponding observed quantities in the presence of kinetic deactivation. Kinetic causes are all those that are not time dependent i.e., those in which there is an equal probability of the molecule undergoing the deactivating process at all times after the excitation. Collisional quenching (Wavilov, 1929) falls in this category. The fluorescent yield may be reduced in certain cases without appreciable change in the lifetime of the fluorescence if the probability of deactivation is much larger immediately after the excitation than at any other time. I n theory, for a two-step process as described by Eq. (24), if the deactivating causes can compete with the first transition but not with the second, it follows that

+

The observed mean life will be 7 0 71, and the yield may be reduced to any extent without the lifetime ever becoming shorter than 7 0 . Another case to which Eq. (33) does not apply is that of equilibrium between a fluorescent and a nonfluorescent form (tautomer or complex with a quencher molecule). In those cases, the more general equation (Weber, 1948; Forster, 1951)

applies. In this Z is the mean life of the nonfluorescent form. Thus if > 1 0 2 ~ , ( Z> 10-6 see. approximately), the change in lifetime observable on decrease of yield is negligible. Tautomeric modifications which on account of their mean life are nonseparable may thus be detected by differences in their ability to fluoresce. It has too often been assumed in the past that yield and lifetime are associated always in the manner described by Eq. (33). It is now certain that large departures from this rule may occur and that it should not be introduced unless there is some evidence as t o the time-independent nature of the quenching. If the formation of a conjugate takes place between a small molecule and a protein by means of only one type of linkage, different protein conjugates may differ only in the lifetime of the excited state by virtue of differences in the surroundings of the coupled molecule. A knowledge of the variations of r in molecules by changes of solvent and by adsorption should help to

FLUORESCENCE POLARIZATION O F SOLUTIONS

447

clear this point, but only a few data are at present available. These show that the lifetime may be the same in different solvents as is the case with fluorescein in water, ethanol, glycerol, and isobutanol, reported by Szimanovsky (1935); or it may change considerably, as with eosin in m t e r and ethanol or rhodamin B in glycerol and water (Gaviola, 1927). The effect of adsorption varies also in different cases. Thus an adsorbate of fluorescein (Rau, 1949) had a mean life of 3.7 X sec., 25% shorter than the lifetime in water. Several anthraquinone derivatives studied by Karyakin and Galanin (1949) had the same lifetime in the gas phase (measured by 0 2 quenching) and in the adsorbed state (measured by the fluorometer) . Changes of r with pH may be expected when the nonfluorescent form (Eq. 35) is short-lived. I n a purely collisional quenching (Wavilov, 1929) the quencher concentration must be of a fluorescence with 7 N 10-2-10-3 M . Obviously in cases where the fluorescence disappears at pH 4 or higher the quenching cannot be collisional, and the lifetime of the excit,ed state should not change appreciably. Such is the case for 1-dimethylaminonaphthalene-5 sulfonate and several of its derivatives (Weber, 1952b). In protein conjugates at pH below 2.5 or above 11, where the charges of the carboxyl or of the lysine amino groups respectively are abolished, the attached molecule finds itself in the field of the strongly charged protein particle. I n water solution most of the field passes through the highly polar medium and one may not expect any appreciable change in T from this cause alone. In such cases, however, an important difference between a conjugated and a nonconjugated small fluorescent molecule will be present. Ions having the same charge as the protein will find difficulty in approaching the prosthetic molecule, and conversely ions of opposite charge will be found more often in its neighborhood. If these foreign ions are quenchers or activators of the fluorescence, such effects may be studied quantitatively. Weber (195213) has reported that sulfonamido conjugates of egg albumin and serum albumin are fluorescent at pH 1.5-2 with a yield of nearly 60% of the neutral conjugate, whereas the nonconjugated sulfonamides lose their fluorescence at pH 4-5. Addition of neutral salts to the conjugates at pH 2 results in a decrease in the yield. Quantitative observations of these effects may help in studying the accessibility of groups a t the protein surface, a problem of some importance in enzymology. 2. Variations in Limiting Polarization

The limiting polarization is in general a function of the exciting wavelength so that simple changes in the absorption spectrum on coupling may be expected to give rise to changes in the limiting polarization. Such

448

QREOORIO WEBER

changes might well be called apparent and must be distinguished from real changes due to other causes. It is found in general that Po varies little in a family of substances (e.g., the xanthydrols) while the yield and lifetime vary considerably. Adsorption of simple molecules on to proteins does not seem to change substantially the limiting polarization. Thus Laurence (1952) found for eosin adsorbed by serum albumin, and Burch (1952) for rhodamin B adsorbed by liver esterase, limiting polarizations that were indistinguishable from those observed in glycerol solutions of these dyes at low temperature (0-3" C.). Laurence found that 1-dimethylaminonaphthalene-5 sulfonate adsorbed by serum albumin gave the same value of Po as the sulfonamido conjugates of these substances. The conjugates studied by Weber (1952b, 1953b), Massey (1953), and Tsao (1953) exhibited considerable differences in PO. The results of Massey (1952) with fumarase show that changes in the ionic composition and ionic strength of the solvent may result in conspicuous variations of the limiting polarization. Weber (195210) has attributed the observed changes in P O to the variable degree of rotational freedom of the prosthetic molecule about its conjugating bond. According to this view it should be possible to correlate the binding properties of the native protein with the values of Po and such data as are available support this inference. 3. Rotational Relaxation Times of Protein Conjugates The studies of Weber (1952b, 1953a,b), Tsao (1953), Smith (1953), and Massey (1953) on proteins conjugated with 1-dimethylaminonaphthalene-5-sulfonyl chloride show that the linear relation between 1/ p and T/q is followed by numerous proteins. When this linear law is followed the conjugates may be characterized by the quantity

p

=

SlOpe/(l/Po &

44) = 3qTo/phT

If the lifetime of the excited state of the conjugates is the same the quantity P is proportional to the mean rotational relaxation time. The 13 values obtained with human and bovine albumin, ovalbumin, fumarase, lysozyme, insulin, G actin, and growth hormone protein are in agreement with the accepted estimates of size derived by sedimentation and diffusion and by other methods. In most cases the observations were carried out in water solutions at temperatures from 4" to 50" and the values of PO obtained by extrapolation agreed very well with those directly observed in a solution of the conjugate in 60% sucrose at 2". The latter fact allows the conclusion that any other existent relaxation

FLUORESCENCE POLARIZATION O F SOLUTIONS

449

time must be of a smaller order of magnitude than the one calculated from the slope, and cannot therefore be a relaxation time of the particle as a whole. Absolute values of P h require the determination of 7 0 by the fluorometer. Weber (1952b) assumed for the lifetime of the excited state of his conjugates of ovalbumin and serum albumin the value of 1.4 X sec. (1.18 X sec. if Eq. (32b) is used) because the calculated harmonic means of the rotational relaxation times of these two proteins agree very well with the results of Oncley (1941) by the dielectric method. Whenever changes in 70 may be excluded, or evaluated, changes in the polarization of the radiation can be attributed to changes in P h . The effect of temperature must be studied in all cases to determine po as well as to check the linear dependence of l/p on T/q. Changes in lifetime of the excited state or the limiting polarization with temperature need not be considered, The attribution of changes in Ph to changes in size or shape, or both, may be more difficult. Some of the possibilities have already been discussed. Weber has attributed to dissociation into subunits the changes in Ph observed in acid and alkaline solutions of bovine serum albumin. This interpretation has, however, been contested (Pedersen, 1953). Smith (1953) has observed similar changes in growth hormone protein conjugates. Increases in rotational relaxation time distinctly attributable to aggregation have been observed in ovalbumin (Weber, 1952), bovine serum albumin (Weber, 1953b) and fumarase (Massey, 1953). Tsao (1953) has studied conjugates of actin and the changes in p h brought about under the influence of substances such as adenosine-triphosphate, metals, chelating agents, and myosin itself. Two particularly interesting observations have been made by Tsao using labeled actin. The G form of actin appears to exist in two states with relaxation times in the ratio 2: 1 which apparently correspond t o dimer and monomer forms. The Iatter, which from specific viscosity increment is assigned an axial ratio of 12, has a volume corresponding to a particle weight of about 70,000.1The dimer form of actin passes on addition of salt to F-actin-a state characterized by its extreme thixotropy, flow birefringence and spontaneous birefringence. The relaxation time of F-actin in no way differs from that of the relatively nonviscous dimer, and on addition of myosin there occurs an immediate decrease in P h although the viscosity of the whole system shows a marked increase. Tsao’s molecular volume was calculated using T O = 1.4 X 10-8 sec. and p h / p 0 =0.41. If T O = 1.18 X lo-* and p h / p o = 0.52 (Eq. 32b) are introduced instead, the calculated volume is only 6 % higher. For lower values of axial ratio the difference between calculated values of molecular volume would be even smaller.

450

QREGORIO WEBER

The lack of change in p h on going from the G to the F form may be interpreted as follows. For particles of elongation greater than 10 most of the depolarization of the radiation is due t o rotation about the long axis, i.e., to the relaxation of a direction normal to it, and independent of the rotations about the short axis. Consider now the systems a, b, and c (Fig. 9) ;a representing a random arrangement of molecules, b the formation of fibrils, and c the orientation of particles by long-range forces. I n both b and c the particles have lost all or most of their translational freedom. However if the forces that produce this loss of translational freedom have cylindrical symmetry about the long axis, rotation about this can take place just as in the free particle. For particles of low asymmetry the restriction of the rotations about the short axis will produce a higher polarization in b and c than in a. For conFIG. 9. siderably elongated particles ( a / b > lo), however, there will be no observable change in going from a to b or c. Nevertheless

L

1

2

3

yqx w - 4

A

4

FIG. 10. Fluorescence polarization of labeled F-actin and of the actomyosin complex formed from it with unlabeled myosin. Solvent, 0.5 M KCl 0.006 M phosphate, pH 7 (F-actin in presence of 10-4 M ATP).

+

0 actin:myosin = 1:2 (weight ratio) 0 actin: myosin = 1:4 (weight ratio)

Effect of ATP shown for 26' (see also Fig. 11) and 22' C. (From Tsao, 1953.)

measurements of the flow viscosity or the translational diffusion of the system will reveal large differences between a on the one hand and b or c

451

FLUORESCENCE POLARIZATION O F SOLUTIONS

on the other. Whatever interpretation is placed upon the viscosity data the lack of change in P h in the G 3 F transformation restricts the choice to those models where the particles have rotational freedom about the long axis. These considerations are an example of a more general problem which to the author seems t o have considerable importance in regard to the maintenance and function of biological structures built of macromolecules. A general rule may be stated as follows. Free rotation about one of the three axes of a rigid particle may coexist with absence of translational freedom if the constraints which produce the latter have cylindrical symmetry about the axis of free rotation. This possibility may be allowed for when considering particle dissociation. One can visualize a case in which a rotational dissociation will be observed but not a translational one. This may prove to be the case for serum albumin a t low and high pH, although the hypothesis of the dissociation into completely independent subunits seems at the moment muoh the more likely. Tsao's second observation, namely that actin shows a decrease in Ph on addition of myosin, seems t o exclude a combination of actin and myosin, at least in the current meaning of this concept. Whatever the nature of the interaction it does not lead to the formation of a kinetic rotational unit.

10

20

Time ( m m )

x)

I

40

FIG. 11. Effect of ATP on the fluorescene polarization of F-actomyosin in 0.006 M phosphate, pH 7.0, 26.0" C . (From Tsao, 1953.)

0.5 M KCl

+

Polarization measurements as a function of T / q are shown for fluorescent derivatives of F-actin and actomyosin in Fig. 10. The effect of ATP on actomyosin, indicated briefly in this figure, is shown in more detail in Fig. 11. It is seen that the value of p rises abruptly, that is, l/p falls abruptly, when ATP is added. Over a period of the order of 10 min., p slowly decreases to or near its previous value. On fresh addi-

452

GREGORIO WEBER

tions of ATP the cycle can be repeated several times, as shown in the figure. Massey (1953b) has made a detailed study of ph of fumarase conjugates and has correlated certain changes in this quantity with changes in catalytic behavior. Confirmation of some of the findings was obtained

.

I

I

/

/

/ r) x10-2

1

FIG.12. Polarization of the fluorescence and sedimentation of fumarase solutions in 0.05 M phosphate buffer p H 7.4 in the presence of 0.1 M NH,SCN. The broken line in the polarization diagram is the slope before addition of thiocyanate. The numbers attached to the curves denote values of ph.

by sedimentation and diffusion. Massey’s results may be summarized as follows. a . Effect of neutral salts. The enzyme activity in the presence of neutral salts runs parallel to reversible changes in ph the minimum value of which (-J 2 X lo-’ sec.) coincides with maximum activity. b. Thiocyanate and transaconitate (both inhibitors) reduce Ph to about half the value for the most active form (-J 0.8 X 10-7 sec.). Sedimentation and diffusion studies showed that thiocyanate has the effect of splitting the enzyme into smaller units while after addition of transaconitate the molecular weight is unchanged. It appears that in the

FLUORESCENCE POLARIZATION O F SOLUTIONS

453

first case there is both rotational and translational dissociation, while in the second there is rotational but not translational dissociation. It is worthy of note that the inhibition by transaconitate is reversible while that produced by SCN is irreversible.

FIG.13. Sedimentation of fumarase in the presence of thiocyanate. Sedimenta’ solution of fumarase in the presence of 0.05 M phosphate tion diagrams of a 0.45% pH 7.4 and 0.1 M NH&NS. (From studies of V. Massey and P. Johnson.) SZOof main component 8.65

8.40 8.61 5.77 6.20 5.76

Temperature Room temp. (17-20” C.)

,, ,, 11

,I

4” c.

Time after addition of thiocyanate 2 hours 7 25 49 73 96

” ” ” ” ”

The independence of the translational and rotational freedom of the subunits of fumarase has been confirmed by a study of the time course of the action of thiocyanate. On addition of 0.1 M N H 8 C N at neutral pH t o a solution of fumarase the average rotational relaxation time is markedly reduced, reaching in about an hour a steady value (1.25 X lo-’ sec. at 20”) which is maintained indefinitely (Fig. 12). There is a small,

454

GREGORIO WEBER

abrupt, and reversible change in Ph as the temperature is raised above 13", but the value found in the presence of thiocyanate is in any case only about half of that for the original enzyme which has never been exposed to thiocyanate. A sedimentation picture obtained 2 hr after the addition of the electrolyte shows no obvious changes (see Fig. 13), but soon afterwards a slow-moving peak appears and increases progressively with time so that after three days all the protein in the solution is found t o sediment with the slower speed. In contrast, no further change in P h

FIG.14. Polarization of the fluorescence of labeled fumarase. The sharp break in the curve occurs a t 18" C. Solvent, 0.06 M phosphate buffer at pH 6.35.

has occurred after the first hour. It is necessary to conclude that the slowly progressing translational dissociation, shown by the decrease of the s20 values in Fig. 13, does not appreciably increase the rotational freedom of the subunits. Whether this fact is due to the shape of the subunits or to the nature of the forces holding the subunits together is not yet known. The sedimentation pattern of fumarase in the presence of transaconitate is practically independent of time and is the same as that of the untreated protein. c. Massey (1953a) has observed changes in the heat of dissociation of the enzyme-substrate and enzyme-inhibitor complexes which take place over a narrow temperature range amounting to a critical temperature. The plot of l / p against T / q for the fumarase conjugates in the presence of the corresponding substrates or inhibitor shows similar sharp changes

FLUORESCENCE POLARIZATION O F SOLUTIONS

455

in slope taking place over a range of 3" to 4" and often less. The critical temperatures observed by both methods agree very well and lead to the hypothesis that the abrupt changes in the heat of combination are related to changes in shape or volume of the rotating unit, or perhaps to both factors simultaneously. Some of these phenomena are illustrated in Figs. 14 and 15. d. At temperatures below the critical, Ph changes with pH, and again maximum activity corresponds to minimal P h . This is observed at pH 7.4.

FIG.15. Activity of fumarase. Energy of activation of the catalyzed reaction. The solvent is t h e same as in Fig. 14, and the break in the curve in this ease also occurs at 18" C.

At present it is not yet clear which properties of protein molecules are best revealed by a study of the depolarization of the fluorescence of conjugates. The relaxation times of the rotation observed by this method appear t o give a reliable estimate of the molecular size when the shape of the molecule is taken into consideration. Several advantages of this method are: (1) It may be applied to very dilute solutions. The author has studied 0.02 % serum albumin solutions, and even smaller concentrations could be used with little improvement of the experimental tech-

456

GREGORIO WEBER

nique. (2) It is largely independent of protein and salt concentration. The latter is a decided advantage over existing methods as the study of actin shows. (3) A large temperature interval (0' t o 60' or 70') may be explored. (4) Observations can be made at pH 2 to 14. From the data so far obtained it appears that no additional corrections for pH are necessary. (5) A labeled protein molecule may be studied in a solution of arbitrary protein composition, provided the conjugate is the only fluorescent species in the solution. On account of this the method offers great promise in the study of protein interactions. (6) The observations are easily carried out experimentally; the equipment is simple and inexpensive; the causes of error (Weber, 1952a) are few and easily controlled. 4. Reversible Combination of Fluorescent Molecules with Proteins The fluorescence polarization technique may be applied successfully t o these cases as shown by the recent work of Laurence (1952) on the adsorption of dyes on serum albumin. Weber and Laurence (1953) have described a series of substances that although completely nonfluorescent in water solution become strongly fluorescent on adsorption by native serum albumin, denatured ovalbumin, filter paper, or alumina. They are also spontaneously fluorescent in certain solvents. These substances are derivatives of 3-chloro-6-methoxy-9-aminoacridine or of one of several aminonaphthalene sulfonic acids, in which one of the amino hydrogens has been substituted by a benzene ring derivative. The explanation of the behavior on adsorption lies apparently in that the radiative transition is forbidden for the nonplanar molecule but is allowed when the molecule lies on a plane as it presumably does on adsorption. This is extensively discussed by Forster (1951). Although the causes of the phenomenon are interesting in themselves, its practical applications may be of importance. Laurence and Rees (1953) have developed a method for the rapid and accurate determination of albumin in blood serum by fluorimetry using 1 N phenylaminonaphthalene-5 sulfonic acid. The detection of ovalbumin denaturation by this method also deserves consideration. The appearance of fluorescence on adsorption of auramin 0 by nucleic acids has been described by Oster (1951). The combination of an enzyme with a fluorescent inhibitor has been demonstrated by polarization measurements by Burch (1952). Rhodamin B, a competitive inhibitor of liver esterase, showed strongly polarized fluorescence when mixed with a purified solution of the enzyme. On addition of substrate (ethyl acetate) the polarization decreased markedly. Qualitatively these results indicate the formation of a complex

FLUORESCENCE POLARIZATION OF SOLUTIONS

457

lasting at least a few times the lifetime of the excited state of rhodamin B (2 x 10-9 sec.) and its dissociation on addition of substrate. Quantitatively it was not feasible in this case to correlate the inhibitor constant ( K J determined by observations on the rate of reaction with the value obtained from polarization observations, because the enzyme was not obtained in pure condition. The method offers promise of a direct determination of the relevant constant of combination and therefore of the validity of the theory of Michaelis in selected cases. The determination of hapten antibody combination by this method has not been reported but it would appear worthy of consideration.

5. Determinatiori of Microscopic Viscosities As indicated by Eq. (28), it is possible to form an idea of the microscopic viscosity of a given solvent by studying the depolarization of the fluorescence emitted by molecules of known size and lifetime of the excited state. Weber (1947) and Buchader and Lebesgue (1946) have followed the changes in viscosity during gelation by this method. Weber studied agar, gelatin, silicic acid, and dibenzoylcystine gels, using fluorescein as an indicator molecule. He found that no conspicuous change in polarization took place during gelation in agar, silicic acid, or gelatin, and concluded that the viscosity of the dispersion medium does not increase in gelation by more than 1 centipoise. In dibenzoylcystine an increase in polarization took place ( p increased from 0.02 to 0.06) which was ascribed to adsorption on the gel fibrils as they formed. This was inferred because if the gel, which is thixotropic, is liquefied by shaking, no further change in polarization takes place during either the liquefaction or the second gelation. Buchader and Lebesgue studied the changes in polarization of rhodamine S added t o silicic acid in the process of setting. The observed increase in polarization was attributed by them to restricted rotation, although it is not clear whether they consider this to be due to adsorption on the growing fibrillar matrix or to a real increase in viscosity of the dispersion medium. The former appears by far the most probable in view of the experiments with fluorescein just discussed. The adsorption of the rhodamin S through the basic --N(CH3)2 groups on to the negatively charged silicic acid appears likely. Thus the author found that rhodamin B was adsorbed so strongly by gelatin and by silicic acid gels as to be of little use in this type of experiment. REFERENCES Bailey, K. (1948). Biochem. J. 43, 271. Benoit, H. (1950). Th&se.Universite de Strasbourg, Masson et Cie, Paris. Beaven, G. H., and Holiday, E. R. (1952). Advances in Protein Chem. 7 , 319. Blinks, L. R. (1949). Private communication.

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Buchader, G., and Lebesgue, M. (1946). Compt. rend. 223, 324. Burch, J. (1952). Thesis, University of Cambridge. Cerf, R., and Scheraga, H. A. (1952). Chem. Revs. 61, 185. Chakravarty, D. C., and Ganguly, S. C. (1941). Trans. Faraday Soc. 37, 562. Chandrasekhar, S. (1943). Revs. Mod. Phys. 16, 1. Coons, A. H., Creech, H. J., Jones, R. N., and Berliner, E. (1942). J. Zmmunol. 46, 159. Coons, A. H., and Kaplan, M. H. (1950). J . Ezptl. Med. 91, 1. Creech, H. J., and Jones, R. N. (1940). J. Am. Chem. SOC.62, 1970. Creech, H. J., and Jones, R. N. (1941). J. Am. Chem. SOC.63, 1661, 1670. Creech, H. J., Oginsky, E. L., and Cheever, F. S. (1947). J. Cancer Research 7, 290. Creech, H. J., and Peck, R. M. (1952). J. Am. Chem. Sac. 74, 463, 468. Debye, P. (1929). Polar Molecules, Chemical Catalog Co., New York. Debye, P., and Sears, F. W. (1932). Proc. Natl. Acad. Sci. U. S. 18, 409. Edwardes, D. (1893). Quart. J . Pure Appl. Math. 26, 70. Einstein, A. (1906). Ann. Physik. 19, 371. Forster, T. (1951). Fluoreszenz Organischer Verbindungen. Vandenboeck u. Ruprecht, Gottingen. Franck, J., and Livingston, R. (1941). J. Chem. Phys. 9, 184. Freed, S., and Weissman, S. I. (1941). Phys. Rev. 60, 440. Frenkel, J. (1946). Kinetic Theory of Liquids, Chapter V. Oxford University Press, New York. Galanin, M. D. (1950). Compt. rend. mad. sci. U.S.S.R. 70, 989. Gans, R. (1928). Ann. Physik 86, 628. GavioIa, E. (1927). 2.Physik 42, 853, 862. Grisebach, L. (1936). 2. Physik 101, 13. Herzberg, G. (1944). Atomic Spectra and Atomic Structure. Dover Publications, New York. Jablonski, A. (1935). 2.Physik 96, 236. Karyakin, A. V., and Galanin, M. D. (1949). Compt. rend. acad. sci. U.S.S.R. 66, 37. Karyakin, A. V., and Terenin, A. (1949). Zzvest. Akad. Nauk. S.S.S.R. Ser. Fiz. 13, 9. Kasha, M. (1947). Chem. Revs. 41, 401. Keilin, D., and Hartree, E. (1946). Nature 167, 801. Kirchhoff, W. (1940). 2.Physik 116, 115. v. Kowalski, I. (1911). Physik. 2. 12, 956. Laurence, D. J. R. (1952). Biochem. J . 61, 168. Laurence, D. J. R., and Rees, D. (In press.) Ley, H., and v. Englehardt, K. (1910). 2.physik. Chem. 74, 1. Maerks, 0. (1938). 2.Physik 109, 598, 685. Marinesco, N. (1927). J . chim. phys. 24, 593. Marsh, J. K. (1924). J . Chem. SOC.126, 418. Massey, V. (1953a). Biochem. J . 63, 67, 72. Massey, V. (195313). Biochem. J. (In press.) McClure, D. S. (1949). J . Chem. Phys. 17, 905. Morell, D. B. (1952). Biochem. J . 61, 657. Oncley, J. L. (1940). J. Phys. Chem. 44, 1103. Oncley, J. L. (1942). Chem. Revs. SO, 433. Oncley, J. L. (1943). In Proteins, Amino Acids and Peptides Chapter 22, E. J. Cohn and J. T. Edsall (eds.), Reinhold Publishing Corp., New York. Oster, G. (1951). Compt. rend. 232, 1708.

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Pedersen, K. 0. (1953). Discussions Faraday SOC.,after Weber (1953a). Perrin, F. (1928). Ann. &ole Norm. Sup. 46, 1. Perrin, F. (1926). J . phys. 7, 390. Perrin, F. (1929). Ann. phys. X, 12, 169. Perrin, F. (1934). J . phys. VII, 6, 497. Perrin, F. (1936a). J . phys. VII, 7, 1. Perrin, F. (193613). Acta Phys. Polon. 6, 335. Perrin, J. (1909). Compt. rend. 149, 549. Pheofilov, P. P. (1943). J. Phys. U.S.S.R. 7, 68. Przibram, K. (1912). Sitzber. kgl. preuss. Akad. Wiss. 121, 2347. Przibram, X. (1913). Sitzber. kgl. preuss. Akad. Wiss. 122, 1895. Rau, K. L. (1949). Optik 6,277. Reeder, W., and Nelson, V. E. (1940). Proc. SOC.Exptl. Biol. Med. 46, 792. Samburski, S., and Wolfsohn, G. (1942). Phys. Rev. 62, 357. Selenyi, P. (1911). Ann. Physik 36, 444. Selenyi, P. (1939). Phys. Rev. 66, 477. Smith, R. H. (1953). To be published. Soleillet, P. (1929) Ann. phys. X, 12, 23. Straub, B. F. (1939). Biochem. J . 33, 787. and Ericksson-Quensel, I. B. (1936). Nature 137, 400. Svedberg, T., Szymanowski, W. (1935). 2.Physik 96, 440, 450, 460, 466. Takashima, S. (1952). Nature 169, 182. (According to private communication of Prof, H. Tamiya.) Tsao, T.-C. (1953). Biochim. et Biophys. Acta 11, 227, 236. VIBs, F. (1946). Arch. phys. biol. 16, 137. Wavilov, S. I. (1929). 2.Physik 63, 663. Wavilov, S. I. (1936). Acta Phys. Polon. 6, 417. Weber, G. (1947). Thesis, Cambridge University, England. Weber, G. (1948). Trans. Faraday SOC.44, 185. Weber, G. (1950). Biochem. J. 47, 114. Weber, G. (1952a). Biochem. J. 61, 145. Weber, G. (195213). Biocheiiz. J. 61, 155. Weber, G. (1953a). Discussions Faraday SOC.13, 33. Weber, G. (195313). To be published. Weber, G. (1953~).Biochem. J . (In press.) Weber, G., and Laurence, D. J. L. (1953). To be published.