Depolarized laser light scattered by motile spermatozoa

Volume 22, number 3

OPTICS COMMUNICATIONS

September 1977

DEPOLARIZED LASER LIGHT SCATTERED BY MOTILE SPERMATOZOA Gen MATSUMOTO, Hideaki SHIMIZU, Junichi SHIMADA and Akiyoshi WADA* Electrotechnical Laboratory, Tanashi, Tokyo, Japan Received 26 April 1977, revised manuscript received 9 June 1977 The depolarized component of laser light scattered by swimming spermatozoa was experimentally observed wit.r use of a photoelectron counting technique. The time dependence of the observed correlation function was similar to that of the polarized component, with the exception of the characteristic decay time. This characteristic decay time was found to be a measure of motility. We concluded that the origin of the depolarized light was the scattering due to the internal motion of flagella.

1. Introduction Information concerning the motility of spermatozoa swimming in semen is important to the field of artificial fertilization because the motility of spermatozoa is known to be a factor in fertility [1]. Laser light scattering spectroscopy has been well recognized to be an appropriate tool for determining the average swimming velocity and velocity distribution of motile microorganisms such as bacteria [2,3] and spermatozoa [ 4 - 6 ] . It is important, however, to study the internal motion of spermatozoa because the internal motion is responsible for the motive force necessary for the spermatozoa to swim. By observing the depolarized component of the light scattered by spermatozoa in semen, using light scattering spectroscopy, we were able to obtain information concerning the internal motion of spermatozoa. The intensity of the depolarized scattered light depends on the molecular anisotropy of the polarizability tensor of the macromolecules which scatter the laser light. Generally, it can be said that the intensity of the depolarized component of scattered light is much weaker than the polarized one, except at very low scattering angles [7]. Therefore, it is technically much more difficult to extract the depolarized component of scattered light from the strong background light of the polarized component. * Also Department of Physics, University of Tokyo, Tokyo.

Solutions of Tabacco Mosaic Virus [7] and DNA [8,9] have been extensively studied using depolarized fight scattering. Few other reports, however, have appeared in the literature in which this technique was used. These published reports did clarify the mechanism of rotational diffusion of thermally activated macromolecules. In this report, we apply for the first time, the depolarized light scattering technique to the study of motile microorganisms.

2. Experimental method and apparatus A photoelectron counting technique was used to obtain the spectrum of the depolarized component of the light scattered by a solution of spermatozoa. Fig. 1 shows a schematic diagram of the apparatus used for observing the depolarized component of the scattered light. The optical arrangement is similar to that which was previously developed by one of authors [7]. It consists of a H e - N e laser, a polarizer, a rectangular specimen cell, an analyzer whose optical axis lies perpendicular to that of the polarizer, and a photomultiplier. The scattering angle was chosen to be almost 0 ° in order to avoid the strong background light due to the incident light and the polarized component of the forward scattering light. The deviation of the angle from 0 ° was within 2 °, so that the intensity of the polarized component could be suppressed to a level 369

Volume 22, number 3

~

Polarizer Specimen Cell Analyzer Slit 1

OPTICS COMMUNICATIONS

He-Ne Laser 28row

f ~ Slit 2 "~ PM and ~ l PM Cooler ~

.4 MW

I o'sk Memory] I

[ 16KW II ]CoreMemory

September 1977

described in ref. [12] in which G(nl)(r) ~- /, where E(t) stands for the electric field of scattered light. When the fluctuation of permeability of scattering source obeys gaussian statistics and the incident laser light is irradiated in a single mode on the specimen, the following relation holds [13] ;

G(2)(7 ) - 1 = ] G(1)(r)l 2.

(1)

In this case, therefore 7(r) = IG(nl)(r)l 2.

I r--t ~ovA I ~

, I ~ I I I I 800 ~ Oiscrimieat°r ~ ' - - - 1 Pulse Amp, t-T1Mini--Comp ~

I

Pulse tnterval Digitizer & Interface

3. Specimen and experimental results Spermatozoa of sea chestnuts (Anthocidaris crassispina) were used in these experiments. The sperma-

1.0 Fig. 1. Schematic diagram for observing the depolarized light scattered by the motile spermatozoa.

A

G(n2~T)

0,5 ¸

almost thirty times weaker than the depolarized one at the surface of the photocathode of the photomultiplier. The time correlation of the light intensity of the depolarized component was thus measured in a homodyne mode [10]. The photoelectron counting system used in these experiments consisted in a photomultiplier (EMI 9558 QB) whose photocathode was cooled to about 200 K, a discriminator, a pulse-interval digitizer, a data channel interface and a minicomputer system. The pulse interval digitizer digitized the time intervals between neighbouring pulses in a photoelectron pulse train. The data channel interface transferred the data from the digitizer directly to the magnetic core memory of the computer system. The computer system was used to process the stored data of pulse intervals into the auto-correlation function of time. The details of this photoelectron counting system have been previously described [ 11 ]. By using this system, the light intensity correlation function a(n2)(r) - 2 was obtained, where I(t) stands for the instantaneous light intensity at the photocathode at time t and the bracket refers to a time-averaged operation with respect to t. From the experimentally obtained quantity G(n2)(r), the time-independent part can be eliminated to yield 7(r). 7(f) is normalized, so that 7(r) is equal to 1. G(n2)(r) is related to the normalized field correlation function 370

1.0 r(r)

0.5

In(T)

0

-1

-2 0

2

4 msec

Fig. 2. Representative set of the correlation data of (a) Gtn~l(~'); (b) -).(r); and (c) log 7(r), where G(n2)(r)stands for the light intensity correlation function and 7(r) is normalized time-dependent part of G(n2)(r). The data were obtained 5 rain after the spermatozoa were ejected into the sea water, when they were moving actively. The measurement was done at room temperature with a scattering angle of 2° .

Volume 22, number 3

OPTICS COMMUNICATIONS

tozoa were obtained by injecting a 500 mM KC1 solution into the mature sea chestnut. The spermatozoa obtained in this way were at rest, but when diluted with sea water they began to swim. The spermatozoa were used right after being diluted into sea water to a final concentration o f 107 sperm/ml. All of the measurements were carried out within a few minutes of obtaining the spermatozoa. Fig. 2 shows a set of experimentally obtained correlation functions G(n2)(r), T(r) and logT(r) o f the depolarized light scattered from the specimen prepared as described above in natural sea water. In this experiment, the measurement was performed 5 min after the spermatozoa were ejected into sea water. As seen in fig. 2, the overall decay characteristic of G(2)0- ) or 7(r) resembles the one for the polarized light scattered from the specimen of motile organisms [2,3]. We obtained 552 ps as the characteristic decay time "rue defined by ")'(rl/e)/~f(O) = 1/e. The characteristic decay times T1/e changed with time, as shown in fig. 3 : 1 5 0 min after the spermatozoa were ejected, rl/e was found to be 1.4 ms and remained constant. At the same time, the decay characteristic o f the light intensity correlation function G(n2)(T) changed as the time between the spermatozoa ejection and the measurement increased, and approached a single exponential type, as shown in fig. 4. The exponential decay was expected for the light intensity correlation function of the depolarized component of the light scattered from the thermally fluctuated

September 1977

1.0

A

Gg2~r) 0.5

r('¢)

1.0

0.5

In/~('t ) 0

C

-1

-2 I,,,,

I

0

2

,

I

'Z"

4 msec

Fig. 4. Representative set of the correlation data, when the spermatozoa are almost dead, of: (a) G~)(r); (b) 3,(r); and (c) log q,(r). The data are obtained at 325 min after a chestnut ejects the spermatozoa.

msec o

solution of anisotropic macromolecules [ 14]. The characteristic decay time at the time immediately after the ejection of spermatozoa was expected to be 400/Js, a value obtained by extrapolating the experimental data from fig. 3.

15

1.0

0.5

4. Discussion 0 0

i 100

i 200

i 300

time i

400

min

Fig. 3. Observation time dependence of the characteristic decay time rl/e. rl/e is defined to satisfy the relation ~,(rl/e)/ T(0) = 1/e. Observation time is the time duration from the onset of the ejection of spermatozoa through the time when the measurement is done.

The following two pieces o f experimental evidence suggests that the function G(n2)(r) or 7(r) is due to the depolarized component o f the scattered light. First, the intensity of the depolarized component was found to be 30 times stronger than the intensity of the polarized light at the surface of the photocathode; and 371

Volume 22, number 3

OPTICS COMMUNICATIONS

second, the characteristic decay time of 400/~s was far shorter than expected for the polarized component of light scattered from a similar specimen. We found the rl/e to be 426 ps for the polarized component at the scattering angle 0 = 43 ° [15], suggesting that 7-1/e for the polarized component at the scattering angle 2 ° should be 9 ms since the angular dependence of 71/e for the polarized component is known to be inversely proportional to sin (0/2) [2,3,6]. These two experimental findings suggest that the light measured in these experiments was the depolarized component of the light scattered by spermatozoa. The depolarized component of the light scattered by the spermatozoa is composed of two elements; one from the light scattered by the heads of the spermatozoa and the other scattered by the flagella. Since the heads of the spermatozoa occupy a larger volume than the tails, we can expect the heads to scatter more light than the tails. However, the shape of the heads is almost spherical, not anisotropic, so that they do not contribute much to the depolarized component of the scattered light. If the head is taken to be an ellipsoid of revolution with long and short axes of 1 pm and 0 . 5 / a m [1,16] respectively, then the calculated value rue at thermal equilibirum, 1.25 s [16], is not in agreement with the observed value of 1.4 ms. We, therefore, concluded that the depolarized component of the scattered light must be due to the light scattered mainly by the flagella. A more detailed analysis of this data is forthcoming. After a tedious but straightforward calculation of G(nl)(T) on the basis of a fundamental scattering theory [17], we have found the expression for the depolarized component of light scattered b~/motile microorganisms, as follows [ 18 ] ;

=

1 *

f P2(cos

)rco)

(2)

0 where P2(x) stands for the second order Legendre's polynomial for a variable x, w the angular frequency around the principal axis of rotation, rico) the distribution function of co, and G (1) (T) the normalized field correlation function corresponding to the rotational brownian motion. It is noted that G(nl)(r) is expressed as a product of two contributions; one from the rotational brownian motion and the other from the internal motion of motile microorganisms. On the introduction of eq. (2), we assumed that the shape 372

Frequency

September 1977 Distribution Unfts)

f (6o)

0.5

W0

200

400 Angular

6O0 Frequency ~

8OO fradian/sec)

Fig. 5. Calculated angular frequency f(co). The calculation was done through eq. (3) for the data of figs. 2 and 4. of the flagella could be approximated as a rotational ellipsoid, and also that the angular frequency be considered to be unchanged for the characteristic decay time 7"1/e. 1" (r) can be easily determined Experimentally G (_.~) through eq. (1) fromGtnZ)(7) of the result for the depolarized light scattering on the solution of almost dead spermatozoa in fig. 4. Therefore, we can get the distribution function f(co) for the swinging flagella by transforming eq. (2) inversely; 16 ~ ](co) = ~_~/ (G n(1) (r)/G n(1)*( r ) - 1/4) cos (2cor) dr. 0 (3) The result is shown in fig. 5 for the specimen of spermatozoa corresponding to the field correlation function G(1)(~-) in fig. 2. The average angular frequency c~ is obtained to be 230 radian/s from this figure. This value of ~ should be compared with the beat number of flagella 2 0 - 3 0 beats/s observed for the spermatozoa of chestnut under an optical microscope [1 ]. There is not any consistency between them. A more detailed description of the analysis is forthcoming [ 18].

Acknowledgement

The authors would like to express their sincere thanks to Dr. K. Sakurai in Electrotechnical Laboratory for his encouragements throughout this work, to Dr. S. Amemiya, of the Biological Marine Laboratory associated with the University of Tokyo at Aburatsubo, for his kind service in providing the sea chestnuts, and to Dr. Jesse Baumgotd, of the National In-

Volume 22, number 3

OPICS COMMUNICATIONS

stitute o f Mental Health, for his kindness in brushing up English.

References [1] D.W. Bishop, Physiol. Rev. 42 (1962) 1. [2] R. Nossal, S.H. Chen and C.C. Lai, Opt. Commun. 4 (1971) 35. [3] R. Nossal and S.H. Chen, J. Physique 33 (1972) C-171. [4] M. Adam, A. Hamelin, P. Berge and M. Goffaux, Ann. Biol. anita. Gioch. Biophys. 9 (1969) 651. [5] R. Combescot, J. Physique 31 (1970) 767. [6] H. Shimizu and G. Matsurnoto, IEEE Trans. B.M.E. (1977, March). [7] A. Wada, N. Suda, T. Tsuda and K. Soda, J. Chem. Phys. 50 (1969) 31.

September 1977

[8] K.S. Schmitz and J.M. Schurr, Biopolymers 12 (1973) 1021. [9] K.S. Schmitz and J.M. Schurr, Biopolymers 12 (1973) 1543. [10] A. Wada, T. Tsuda and N. Suda, Japanese J. Appl. Phys. 11 (1972) 266. [11] G. Matsumoto, H. Shimizu and J. Shimada, Rev. Sci. Instrum. 47 (1976) 861. [12] H.Z. Cummins and H.L. Swinney, Progress in Optics, Vol. VIII, Ed. E. Wolf (North-Holland, Amsterdam, 1970). [13] L. Mandel, Proc. Phys. Soc. (London) 74 (1959) 233. [14] C. Caroli and O. Parodi, J. Phys. B2 (1969) 1229. [15] H. Shimizu and G. Matsumoto, Opt. Commun. 16 (1976) 197. [16] F. Perrin, J. Phys. Radiu. 5 (1934) 497. [17] B. Chu, Laser light scattering (Academic Press, New York, 1974) p. 202. [18] H. Shimizu and G. Matsumoto, in preperation.

373