Rotational-translational models for interpretation of quasi-elastic light scattering spectra of motile bacteria

Intramolecular interference effects in dynamic light scattering: rigid double spirals and superhelical DNAs

A theory is developed for dynamic light scattering (DLS) from rigid double spirals by treating an invisible rigid cylinder with two helical scattering stripes on opposite sides of its cylindrical surface. The exact initial, or first cumulant, diffusion coefficient Dapp (K) is obtained in terms of the translational diffusion coefficients (D parallel and D perpendicular) parallel and perpendicular to the symmetry axis, the rotational diffusion coefficients (DR parallel and DR perpendicular) around the symmetry and transverse axes, the length (L) and radius (b) of the cylindrical surface bearing the stripes, and the pitch (p). Interference effects, namely geometrical antiresonances, between strands, produce deep minima in the static structure factor S (K) and corresponding prominent peaks in Dapp (K). These peaks in Dapp (K) depend sensitively on the rotational dynamics around the symmetry axis, and nearly vanish when DR parallel = 0. Some results for single spirals are also presented. A simpler model in which scattering points are attached at opposite ends of an otherwise invisible thin rigid rod is also treated, and shown to exhibit modest minima in S (K) and corresponding maxima in Dapp (K). Confining this rod to a plane containing K enhances the amplitudes of the oscillations in S (K) and Dapp (K), as expected. Rigid double spirals are employed as crude models for interwound supercoiled DNAs in order to assess the possible occurrence of interference effects. Although native supercoiled DNAs exhibit a cylinder diameter that is much too small to exhibit geometrical antiresonances in the presently accessible range of K2, nearly relaxed supercoiled DNAs are predicted to exhibit their first maximum in Dapp (K) just inside this range. Previously reported data for the effect of Escherichia coli single-strand binding (ssb) protein on the DLS of supercoiled pBR322 DNA cannot be mimicked by a gradual homogeneous reduction of superhelix density with increasing ssb, but instead can be mimicked by inhomogeneous all-or-none binding in which uncomplexed native DNAs and nearly relaxed saturated ssb/DNA complexes coexist in varying proportions. Experimental Dapp (K) and S (K) data for a sample of relaxed pUC8 dimers display, respectively, a broad maximum and a corresponding minimum, in qualitative agreement with rough theoretical predictions.

Rotational and translational swimming of human spermatozoa: a dynamic laser light scattering study

The rotational swimming motion of human spermatozoa is evaluated from measurements of depolarized dynamic laser light scattering at zero angle. The analysis is based on a Maxwellian angular velocity distribution and yields a rotational frequency of about 4 Hz that is ascribed to the rotation of the sperm head. From comparison with the translational swimming motion, a propelling efficiency of about 10 micron per turn is deduced. This parameter describes the linkage between the rotational and translational swimming motion and is likely to be discriminatory in the analysis of physiological and pathological sperm motions.

A low angle quasi-elastic light scattering investigation of Chlamydomonas reinhardtii

This paper outlines the results of the first homodyning low angle scattering experiment known to have been reported for motile particles. Low angle scattering QELS studies were carried out on a wild strain of Chlamydomonas reinhardtii at scattering angles of 3.3 degrees, 2.6 degrees and 1.7 degrees. The resultant experimental autocorrelation functions and scaling curves were compared with a theoretical model that had been successful previously at scattering angles greater than 15 degrees.

A quasi-elastic light scattering and cinematographical comparison of three strains of motile Chlamydomonas reinhardtii: a wild type strain, a colchicine resistant mutant and a backward swimming mutant

Quasi-elastic light scattering and cinematographical techniques were used to investigate the motility of three strains of Chlamydomonas reinhardtii: a wild cell type (WI), a colchicine resistant mutant (CO), and a backward swimming mutant (BA). Mathematical models were developed which reproduced the experimental autocorrelation functions for each of the three types of cells. These models were based on the physical characteristics of the cells' motion and the values of the parameters in the models were compared with those values that could be obtained from cinematography. Mean progressive speeds for these cells were found to be 84 microns s-1 (WI), 70 microns s-1 (CO) and 30 microns s-1 (BA).

Effect of temperature, nutrients, calcium, and cAMP on motility of human spermatozoa

The motility of human spermatozoa and its regulation were examined on cells isolated from other seminal components and purified into fractions of uniform progressive motility. The percent motile cells and estimates of their translational speed were determined by visual inspection, by stroboscopy, and by photon correlation spectroscopy; microcinematography and gradient centrifugation were occasionally used to clarify discrepancies. The motility of isolated spermatozoa could be maintained for periods up to 24 h at 4 or 37 degrees C; the presence of seminal fluid was not required and even provoked a reversible inhibition at 4 degrees C. Albumin facilitated cell movement between microscopic glass plates but had no effect on progressive motility per se, as evidenced by other techniques. During incubations of up to 2 h, progressive cell motility occurred independently of extracellular glucose and calcium but responded to variations in adenosine 3',5'-cyclic monophosphate and calcium. Dibutyryl cAMP increased forward motility, whereas ethyleneglycol-bis(beta-aminoethylether)-N,N'-tetraacetic acid reversibly immobilized the spermatozoa in a calcium-dependent manner; phosphodiesterase inhibition resulted in increased vibration of sperm heads without any effect on progressive motility. Longer incubation periods required the presence of extracellular nutrients. These experiments further demonstrate that several motility measuring techniques should be used in parallel to distinguish the various components of cell movement, to exclude aspecific effects, and to supplement the shortcomings of each individual technique. Such procedure could clarify the various discrepancies that have been reported so far and should lead to a better understanding of the regulation of human sperm motility.

Scaling properties of light scattering spectra for particles moving with helical trajectories

This investigation indicates that model quasi-elastic light scattering spectra from particles moving on a helical trajectory exhibit nonscaling behavior. At low q light scattering samples the average progressive speed of the center of mass, while at large q it is the trajectory speed which is important. The extent of this non-scaling depends critically on the pitch and radius of the helix. For spherical scatterers the largest effect is seen when the ratio of the pitch to the radius is ~0.1. Interpreting data from such a system by using a point particle approximation would lead to a sizable underestimate of the speed of the scatterer. In the high q limit the scaling level of the model correlation functions is independent of the product of the curvature of the helix and q. The results for rotating disk-shaped ellipsoidal scatterers parallel those for spheres. The critical parameter for cases where the radius of the disk is large compared with the radius of the helix is the radius of the disk itself. When the radius of the disk is larger than the wavelength of the light the scaling behavior is determined primarily by rotational motion. Deviation from this behavior due to helical motion occurs only at extremely low values of q.

Determination of motile behaviour of prokaryotic and eukaryotic cells by quasi-elastic light scattering

Information on the swimming motion of microscopic calls and the factors which affect it is important to a wide range of disciplines. The functions of the motile apparatus of simpler organisms such as bacteria or algae can provide useful clues on the operation of more complex contractile systems such as muscles. Often celluar motility is a response to conditions external to the cell (e.g. chemotaxis) and, hence, can lead to increased understanding of the cell's sensory capability. On the medical front there is a physical similarity between the flagellar beat of the motile spermatozoa and the ciliary activity of epithelial lining of respiratory and reproductive tracts. Impairment of the motile apparatus can lead to sterility and to a variety of pathological conditions. In animal husbandry, in the artificial insemination industry and in sperm banking estimates of the extent of cellular motility and the fraction of cells which are motile are key quantities which can determmine the fertilization capability of a semen sample.

Motility assay of human sperm by photon correlation spectroscopy

Microscopic methods of performing motility assays of spermatozoa are slow, subjective, and involve a small number of spermatozoa. Laser light-scattering methods can analyze the motility of many spermatozoa within minutes. The swimming speed distribution of human spermatozoa was investigated by photon correlation spectroscopy. The sperm was diluted in seminal plasma to avoid modifying the viscosity. The swimming speed distribution was reconstructed from the correlation data by Stock's method of splines. When compared with a videomicroscopic assay, the reconstructed swimming speed distribution accurately reflects translational motion between 0 and 80 micrometers per second, while for speeds greater than 80 micrometers per second the distribution is distorted by the effects of rotational motion.

Accuracy of RGD approximation for computing light scattering properties of diffusing and motile bacteria

The quasi-elastic light scattering has become an established technique for a rapid and quantitative characterization of an average motility pattern of motile bacteria in suspensions. Essentially all interpretations of the measured light scattering intensities and spectra so far are based on the Rayleigh-Gans-Debye (RGD) approximation. Since the range of sizes of bacteria of interest is generally larger than the wavelength of light used in the measurement, one is not certain of the justification for the use of the RGD approximation. In this paper we formulate a method by which both the scattering intensity and the quasi-elastic light scattering spectra can be calculated from a rigorous scattering theory. For a specific application we study the case of bacteria Escherichia coli (about 1 microm in size) by using numerical solutions of the scattering field amplitudes from a prolate spheroid, which is known to simulate optical properties of the bacteria well. We have computed (1) polarized scattered light intensity vs scattering angle for a randomly oriented bacteria population; (2) polarized scattered field correlation functions for both a freely diffusing bacterium and for a bacterium undergoing a straight line motion in random directions and with a Maxwellian speed distribution; and (3) the corresponding depolarized scattered intensity and field correlation functions. In each case sensitivity of the result to variations of the index of refraction and size of the bacterium is investigated. The conclusion is that within a reasonable range of parameters applicable to E. coli, the accuracy of the RGD is good to within 10% at all angles for the properties (1) and (2), and the depolarized contributions in (3) are generally very small.