Light Scattering from Motile Bacteria

The (( Intermediate scattering function )t I(K, t ) of light scattered by motile bacteria is shown to be I(K, t ) = rn sin KVt jo T v T Ps(V) dV, (1) where Ps(V) is the distribution of swimming speeds of the bacteria. ~cattercd spectra from motile E, Coli Klz bacteria have been investigated by laser light intensity correlation spectroscopy. [Z(K, t ) ] z is obtained from the data and its angular dependence is shown to agree with that predicted theoretically by eq. (1). In contrast, bacteria whose motility has been arrested by addition of 1 0 2 M CuC12 are found to scatter light with a spectrum characteristic of large Brownian particles. The swimming speed distribution Ps(V) may be determined by performing appropriate Fourier inversions of the data taken from the motile bacteria. The manner by which the distribution changes when environmental factors are varied is indicated. We have been using laser light intensity correlation spectroscopy to determine various quantities related to the motility of bacteria. Particular attention has been given to the longitudinal swimming speed distribution of the bacteria Ps(V), which is especially easy to obtain. In the following we first review the theoretical relationships between Ps(V) and the intermediate scattering function I(K, t ) . The latter may be obtained directly from the light scattering data, and we discuss various measurements of bacterial motion based upon these considerations. We also report upon a preliminary experiment showing the possibility of studying the chemotactic responses of the bacteria. Motile strains of E. Coli K,, bacteria [I] are of specific interest to us. When these bacteria are observed under a microscope they appear to move at constant speed in straight lines. These motions persist for times of the order of seconds before the bacteria change directions. Such times are long when compared with typical decay times of bacterial scattering spectra. Consequently, for the purpose of calculating I(K, t ) , one may assert that the velocities of the individual Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972131 C1-172 R. NOSSAL AND S. H. CHEN bacteria remain unchanged over measurement times relevant to the scattering experiments. It is then particularly easy to calculate I(K, t), since the effect of the bacteria simply is to cause a Doppler shift of the frequency of the laser beam [2], [3]. Indeed, for such a homogeneous sample of swimming bacteria, I(K, t) is given as where V is the bacterial velocity, K is the Bragg wave vector, and t is the time. If no external forces are acting upon the bacteria, the velocity distribution is isotropic, and we have < eiK. vt , 1 : [",lZeiKVtcosO sin 8[v2 P(V)I x " sin KVt [4 7cv2 P(Q] dV . (2) Upon identifying the swimming speed distribution