Ralph Nossal’s research while affiliated with National Institutes of Health and other places

Various aspects of random walks undertaken by motile bacteria and migrating leukocytes are discussed, including the motions of these cells when responding to gradients of chemoattractants. Brief reference also is made to studies of particle movements within the cytoplasm of eucaryotic cells.

The attraction of microorganisms by external stimuli has fascinated biologists and other natural scientists for many years. Classical papers on the behavior of plant sperm and bacteria moving in response to chemical gradients appeared almost 100 years ago (Pfeffer, 1884; Engelmann, 1881). Other stimuli which are known to affect locomotory behavior of unicellular organisms are light, heat, gravity, mechanical perturbation, and magnetic fields. However, in recent years movement of cells in chemical fields has been the most thoroughly studied. Coincidentally, most mathematical modelling of cell migration phenomena has concerned response to chemical signals.

We analyze a scheme, originally suggested by Smoluchowski, by which a diffusion coefficientD can be estimated by measuring the number of particles occupying a fixed region of a surface at various times. An expression is derived relating the variance of the estimated valueD to several experimental parameters. This expression is evaluated numerically to determine how statistical uncertainty depends on adjustable variables. Particular attention is given to experiments involving locomotion of migrating leukocytes.

A simple model is used to investigate parametric dependences of in vitro leukocyte assays for cellular immune sensitivity. The model is first tested by computing areas of cell migration occurring when migration inhibition factors (MIF) are absent from the culture medium. The theory subsequently is modified to include MIF production, and analytic expressions for the migration inhibition index are derived. These then are evaluated in order to study consequences of varying such factors as the ratios of constituent leukocytes or kinetic parameters pertaining to the ability of the culture medium to sustain migration.

A model for cell locomotion is analyzed in which directed movement results from turning-angle and turn-frequency (run-length) distributions which both are functionals of the orientation of a cell in an external field. Turning-angle probability distributions are considered to be of the form p(θ + ⨍ (φ)), where θ is the angle through which the cell turns and φ is the orientation of the cell's path prior to the turn. The run-length distribution may be any functional of φ, except that successive path segments need to be uncorrelated. Analytic expressions are derived for the directed velocity vd in terms of parameters related to these distributions.

Trajectories of polymorphonuclear leukocytes which are responding to a chemical gradient are analyzed in order to deduce probability distributions of the angles between successive path segments. The turn angle probability distributions thus obtained are seen to be strongly dependent on the direction of locomotion prior to a turn, in that cells usually turn to maintain alignment along an axis directed towards the chemoattractant source. A mathematical model based on these observations is developed in order to understand the relationship between net chemotactic response and parameters characterizing stochastic movements of individual cells. In particular, the manner in which the chemotropism index depends on details of the turn-angle distributions is examined. When bias in the direction of turn is induced by a chemotactic field, transition from random motion to directed response occurs most abruptly if the turn-angle distribution is narrow. "Accommodation," viz., a dependence of the mean angle of turn upon prior orientation, is found to have relatively little effect on the magnitude of the response.

Simple models are used to calculate the inelastic light scattering spectrum of motile bacteria when wiggling motions are included in addition to translational displacement. Computations of spectra lead to the conclusion that nontranslational motions can be neglected when swimming speeds are deduced from light-scattering data for normal vigorously motile strains. On the other hand, for slowly translating bacteria, or for strains exhibiting noticeable wiggling motion when viewed in a microscope, additional spectral components may be significant. Such components are best distinguished when measurements are made at small and intermediate scattering angles; at large angles the spectra have approximately the same scaling properties (functionals of Qt, Q being the Bragg wave vector) as those associated with simple translational motility.

Autocorrelation functions are computed for nonspherical particles whose dimensions are comparable to or greater than the wavelength of scattered light. Particular attention is given to models of motile microorganisms. Results for Gaussian ellipsoids, finite thin rods, ellipsoids with internal structures, and dumbbell-shaped scatterers are derived and compared.