Photon correlation study of spermatozoa motility

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Photon correlation study of spermatozoa motility

B. Herpigny, J.-P. Boon

To cite this version:

B. Herpigny, J.-P. Boon. Photon correlation study of spermatozoa motility. Journal de Physique,

1979, 40 (11), pp.1085-1088. �10.1051/jphys:0197900400110108500�. �jpa-00209195�

Photon correlation study ^of spermatozoa motility (*)

B. Herpigny ^{and J.-P. Boon}

Faculté des Sciences, ^C.P. 231, Université Libre de Bruxelles, ¹⁰⁵⁰ Bruxelles, Belgium

(Reçu ^{le 2 mai} 1979, révisé le 25 juin ^1979, accepté ^{le 6} juillet 1979)

Résumé.

Nous avons appliqué ^la spectroscopie par corrélation de photons à l’étude de la mobilité des sper- matozoides d’échinodermes (Astérias) ^{et nous avons} développé ^{une méthode} d’analyse ^des spectres qui permet de déterminer aisément les facteurs caractéristiques ^{du mouvement.}

Abstract.

We report measurements of echinoderm (Asterias) spermatozoa motility by photon correlation spectroscopy ^{and we} present ^{a method of} spectral analysis from which the characteristic factors of the motion

are easily determined.

Classification Physics ^Abstracts 07.65 - 87.45 - 87.80

1. Introduction.

The motility ^of living ^{cells like} flagellated bacteria and spermatozoa ^{exhibits an}

important part ^of autonomous motion due to the mechanical action of the flagellum. ^The flagella ^act

as a propulsion device whose efficiency depends ^on

the physical ^and chemical conditions of the swimming

medium. In general, ^the resulting motion is the conse-

quence of a complex mechanism related in the case

of bacteria to chemotactic _processes and for _sper- matozoa to specific physiological conditions. So moti-

lity measurements and their detailed analysis prove to be important ^{in the} interpretation ^{of stimulus}

response type processes which _govem the dynamical

behaviour of microorganisms [1, 2] ^and spermatozoa [3]. The motion of motile living ^{cells can be detected}

either directly by ^{methods based on} microscope

observations [4] ^or indirectly by ^laser light scattering spectroscopy [5]. ^{These two} classes of techniques

should be considered as complementary; ^however,

one of the virtues of the light scattering ^{method is}

to offer an analytical ^{measure of the movement whose} importance is crucial in quantitative studies of the

dynamics ^of living ^cells [6]. Photon correlation _spec- troscopy (PCS) ^is particularly ^well adapted ^{to such}

studies [7].

2. Expérimental aspects.

^We have used the PCS method to study ^the motility ^of spermatozoa ^of echinoderms (Asterias). ^Two determining ^factors jus-

(*) ^Work supported ⁱⁿ part by the « Fonds National de la Recherche Scientifique » (FNRS, Belgium).

tify the choice of the biological material. Echinoderms

reproduce by extemal fecondation and the experi-

ments can therefore be performed ⁱⁿ laboratory

conditions corresponding ^{to those} encountered in the natural physical medium : the spermatozoa ^{are sus-} pended ^{in sea water at about 10 OC and at low concen-}

tration (of ^{the order of 106 cells} per cc). ^{On the other} hand, ^Asterias spermatozoa ^{have a} nearly spherical shape of about 3 _pm in diameter [8] (including ^the

middle piece ^and excluding ^the flagellum ^{which is}

about twenty times thinner and whose contribution to the scattering ^of light may therefore be ignored).

So complications ^{due to} complex structure, multiple scattering ^and screening ^effects

^{as in the} study ^of

human _sperm [9]

^are avoided in the spectral ^ana- lysis. ^In addition echinoderm _sperm generally ^{has a} high concentration of motile spermatozoa, ^{the sam-} ples ^are usually quite homogeneous, ^and the sperma- tozoa have a rather long ^{life time} (of the order of 24 hours after the sample ^{has been} taken). ^{These are}

additional factors that make Asterias spermatozoa good candidates for motility ^studies by ^laser light scattering. According ^to the above considerations we

have performed ^PCS experiments ^{on dilute} suspen- sions of Asterias spermatozoa ^{in filtered sea water}

at 10 °C . The optical and detection set up ^was standard for intensity correlation measurements : it is essen-

tially ^{the same} equipment ^{as used} for earlier studies [10]

and is described elsewhere [11]. ^{We used an} argon ion laser at À

4 880 A and a home made 124 channel real time clipped correlator [11, 12] ; ^the signal ^was

detected in the homodyne ^{mode with a 56 TVP} pho- tomultiplier ^{at various} scattering angles (500, 70°, ⁹⁰⁰ and 1100).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197900400110108500

1086

3. Spectral analysis.

^The intensity correlation function obtained by homodyne ^{detection is} given by [7, 12]

where C is an amplitude ^factor (determined by ^the experimental space and time coherence conditions)

and g(1)(t) ^is the first-order normalized correlation function of the scattered field.

From the point ^{of view of data} analysis, ^{it is most}

convenient to work with the function g(I)(t) ^{12 which}

is obtained as follows. We denote by ⁱ the correlator channel number (i

t/8 ^where 0 is the sampling time), by Ni ^{the number} of photoncounts ^{in channel i,}

and by ^B the uncorrelated background. ^Then g (2)

has the value NilB at ^{time t}

10 and N; = o /B

^{1 + C}

at the initial time t

0. It then follows from (1) ^that

at any time t

10, ) 1 g(l) 12 ^is given by

So, ^to obtain 1 g(’)(t) ^{l’ it suffices to} subtract from the measured spectrum ^the background signal ^com- puted from the last channels of the correlator [13]

and to normalize the result so obtained by dividing

it by ^the initial value Ni= 0 ^{from which the} background

was previously subtracted. For instance, ^Brownian

scatterers would then yield [14]

where D is the diffusion coefficient and k the scattering

wavenumber. The above procedure ^was indeed tested for several species ^of polystyrene spheres suspended

in ethanol and the results yielded consistent values of the spheres diameter in agreement (to ^{within 1} %)

with the values claimed by ^the supplying company.

Motile cells moving independently according ^{to trans-}

lational displacements ^{exhibit a} spectrum given by [14]

where the brackets denote an average ^over the velocity

distribution. The above expression is valid when the

wavelength ^{of the} probe ^{is short} compared ^{to the}

characteristic displacement ^{1 of the} scatterer. For the

experiments discussed here k - 105 cm-1 and 1

30 to 50 _03BCm so that kl > 1.

For isotropic ^{motions, one} finds after integration

over the angles [15]

where P(v) ^{is the} velocity distribution function. Pre- vious experiments ^and cross-checking with micro-

cinematography analysis has shown that the following expression ^describes quite ^{well the} velocity distribution of spermatozoa [8]

where _v, is the characteristic velocity ^{of the motile}

cells. Combining (5) ^with (6) yields ^{a Lorentzian} spectrum

Now in addition to autonomous displacements ^the

cells also undergo diffusion, and therefore the spectrum is given by ^the product

where Deff ^{is the} effective diffusion coefficient of the spermatozoa. ^{From our} measurements performed ^on

dead spermatozoa ^we find that Deff ^{is of the order}

of 10-9 cm’ s-’, ^whereas typically Vc 1’-1 ⁴⁰ Jlms-l,

which corresponds ^to displacements ^{about one thou-}

sand times faster than those due to Brownian motion.

Therefore the exponential ^function decays ^{much more} slowly ^{than the} Lorentzian function and to a very

good approximation eq. (7) ^can be considered as des-

cribing ^the spectrum ^{of the} light ^scattered by ^{the motile}

cells. However there is always ^a part of non-motile spermatozoa (whether ^{dead or} alive) ^that undergo simple Brownian motion. So denoting by ^a the fraction of motile cells, ^{the total} spectrum ^is given by

where the three characteristic parameters ^{to be deter-} mined are a, Vc’ and Deff’ The latter parameter ^is

straightforwardly ^obtained by experiments performed

on dead spermatozoa (measurements ^{carried out}

48 hours after samples ^were taken) ^{and a} and Vc ^are

determined by the method of integrated spectra, ^which consists in the following procedure. ^{We measure the} experimental function 1 ^g(l)(t) 12 ^as described above.

By ^time integration, ^we obtain from _eq. (8)

The first term on the r.h.s. of (9) ^is independent ^of

the wavenumber, ^{so that from two} spectra ^{taken at}

two scattering angles ^{one has}

Thus

and, ^from (9),

(11) ^and (12) ^{show how a} and Vc ^can be determined from two spectra ^{taken at two} different scattering angles ^once Deff ^is known. So in principle only ^three spectra ^are necessary ^to compute the characteristic parameters ^of spermatozoa motility. ^In practice ^it

may be desirable to use more spectra ^to improve ^the

statistical _accuracy.

Note that the method is not restricted to the type of velocity distribution given by eq. (6). ^{For instance}

it is easily verified that the same results hold for a

b-function distribution, ^which corresponds ^{to the case}

where the motile cells swim with a uniform mean

translational velocity. ^In general ^{the method of inte-} grated spectra ^is applicable ^{whenever the} velocity ^dis-

tribution satisfies the following condition : for small values of v, P(v) ^{oc v03BC} where J1 ^{must be} positive ⁱⁿ

order to ensure the convergence of the integral ^on

the I.h.s. of (9). ^In practice all the functions known to give ^a satisfactory representation ^{of the} velocity

distribution of motile cells obey ^{this condition.}

4. Results and discussion.

We first tested the method described in the previous ^section by running

a program with numerical functions. We found that for a fixed value of Deff the values of the parameters ^a and _Vc were obtained with a relative _accuracy of the order of 90 to 95 % ^{of the} original values. An error

of the order of ± 5 to 10 % ^is quite acceptable ^since

we cannot expect ^{a better} accuracy from the experi-

mental data themselves when performing ^measure-

ments on biological material like _sperm. Typical

spectra ^as obtained from experiments performed ^on

Asterias spermatozoa ^{are shown in} figure ^1.

The effective diffusion coefficient Deff ^{was deter-}

mined from series of experiments performed ^{at four}

different scattering angles (50°, 70°, 90°, 1100) ^on

dead spermatozoa suspended ^{in filtered sea water} (11

^{9 x 10-3} poise). From eq. (3), least-squares ^fit

calculations yielded Deff = (1.52 ± 0.16). ^{10-9 cm’ s-’}

[16] ^{from which we obtained the} following ^{mean value}

for the spermatozoon’s head diameter : (2.88 ±0.30) pm in good agreement ^{with the value} given in the litera- ture [8].

We then applied the method of integrated spectra described in section 3 to determine the values of a

and Vc ^{from the} experiments performed ^{on motile}

spermatozoa. Using eqs. (11) ^and (12) ^{we find a=97} % and v,,,

⁴⁵ pm s - 1, ^{with a relative error} of ± ¹⁰ %.

The values of a, Vc’ and Deff ^{are then inserted} in eq. (8)

Fig. ^1.

Normalized experimental spectra ^for scattering ^from

Asterias spermatozoa. Living ^{cells :} scattering angles

^90° (black dots) ^{and 50°} (circles) ; the full lines correspond ^to eq. (8) ^where

a and _Vc have been determined by the method of integrated spectra, eqs. (11) ^and (12). Dead cells : scattering angle

^90° (crosses);

Deff ^was determined from the slope ^{of the} straight line obtained from _eq. (3) by ^a least-squares fit calculation to the experimental points. The upper and bottom time scales refer ^to the spectra ^of dead cells and living ^cells respectively. ^The corresponding sampling

times were : 0

400 _ps (crosses) ^{and 60} 03BC,s (dots ^and circles).

to compute ^the theoretical spectra ^for comparison

with the experimental ^data. Typical ^{results are shown}

in figure ^1. Taking ^{into account that} biological ^mate-

rials are always ^affected by ^a non-negligible ^amount

of natural dispersion ^and inhomogeneity, ^{one can}

consider that the agreement ^{between the calculated} and experimental spectra ^is quite good ^and argues in favor of the validity ^{of the} method of integrated spectra. Experiments ^are presently ^{in progress where}

the method is applied ^to study ^more complex ^and biologically ^more interesting situations were the effect

of egg ^{extracts on} spermatozoa motility ^is investigated

as a function of concentration, distance and tempe-

rature.

Acknowledgments.

^We thank Pierre Bergé, Monique Dubois, ^Boris Volochine, ^{and the members} of the Laboratoire d’HistologiesEmbryologie, ^C.H.U.

Bicêtre, Université Paris-Sud for stimulating ^discus-

sions. We acknowledge the collaboration of Paolo Minissi during part of this work and the assistance of Michel Jangoux ^who provided ^the biological samples.

One of us (B. H.) ^{has benefited from a} grant pro- vided by ^the I.R.S.I.A. (Institut pour l’encouragement

à la recherche scientifique dans l’industrie et l’agri-

culture, Belgique).

1088

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[13] ^{Great care was} taken in the evaluation of the background.

The sampling ^{time 03B8 was} always chosen such that the

time-dependent part of the correlation function had

effectively decayed ^{to zero over the} last fifth of the total number of channels of the autocorrelator. In practice

the measured spectrum ^{remained constant over the last} 20 channels and this value was taken as the uncorrelated

background. ^{The error} in the evaluation of B is then of the order of 1 % which is smaller than the statistical

dispersion of the data points.

[14] BERNE, ^{B. J. and} PECORA, R., Dynamic Light Scattering (John Wiley ^Publ. Co, New York), 1976, Chapter ^5.

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[16] ^{Note that we} obtain consistent values of the reciprocal ^corre-

lation time as a function of the scattering angle.