B E Farrell | PubMed Health

PubMed1990

Quantitative relationships between single-cell and cell-population model parameters for chemosensory migration responses of alveolar macrophages to C5a.

Phenomenological parameters from a mathematical model of cell motility are used to quantitatively characterize chemosensory migration responses of rat alveolar macrophages migrating to C5a in the linear under-agarose assay, simultaneously at the levels of both single cells and cell populations. This model provides theoretical relationships between single-cell and cell-population motility parameters. Our experiments offer a critical test of these theoretical linking relationships, by comparison of results obtained at the cell population level to results obtained at the single-cell level. Random motility of a cell population is characterized by the random motility coefficient, mu (analogous to a particle diffusion coefficient), whereas single-cell random motility is described by cell speed, s, and persistence time, P (related to the period of time that a cell moves in one direction before changing direction). Population chemotaxis is quantified by the chemotactic sensitivity, chi 0, which provides a measure of the minimum attractant gradient necessary to elicit a specified chemotactic response. Single-cell chemotaxis is characterized by the chemotactic index, CI, which ranges from 0 for purely random motility to 1 for perfectly directed motility. Measurements of cell number versus migration distance were analyzed in conjunction with the phenomenological model to determine the population parameters while paths of individual cells in the same experiment were analyzed in order to determine the single-cell parameters. The parameter mu shows a biphasic dependence on C5a concentration with a maximum of 1.9 x 10(-8) cm2/sec at 10(-11) M C5a and relative minima of 0.86 x 10(-8) cm2/sec at 10(-7) M C5a and 1.1 x 10(-8) cm2/sec in the absence of Ca; s and P remain fairly constant with C5a concentration, with s ranging from 2.1 to 2.5 microns/min and P varying from 22 to 32 min. chi 0 is equal to 1.0 x 10(-6) cm/receptor for all C5a concentrations tested, corresponding to 60% correct orientation for a difference of 500 bound C5a receptors across a 20 microns cell length. The maximum CI measured was 0.2. Values for the population parameters mu and chi 0 were calculated from single-cell parameter values using the aforementioned theoretical linking relationships. The values of mu and chi 0 calculated from single-cell parameters agreed with values of mu and chi 0 determined independently from population migrations, over the full range of C5a concentrations, confirming the validity of the linking equations. Experimental confirmation of such relationships between single-cell and cell-population parameters has not previously been reported.

Animals↗

PubMed1989

The motile response of alveolar macrophages. An experimental study using single-cell and cell population approaches.

In this report, we studied the applicability of a random walk model of individual cell motility in predicting the motile behavior of alveolar macrophage populations under agarose. The migration of a population of cells in the absence of a chemotactic or chemokinetic gradient can be characterized by the random motility coefficient, mu, which is analogous to a particle diffusion coefficient. Random walk theory relates this latter coefficient to particle speed and collision time (equivalent to the time between changes in particle direction). By analogy, according to a similar random walk theory for cell migration, mu for a cell population is a function of the speed and persistence time (with direction changes governed by cell behavioral processes rather than by collisions) of individual cells. To test the model, normal guinea pig alveolar macrophages were incubated in the presence or absence of uniform concentrations of the chemotactic tripeptide formyl-norleucyl leucyl phenylalanine (FNLLP) to elicit different levels of motile activity. Mu was calculated from cell population density profiles obtained by fixing and staining cultures after 2, 3, or 4 days. In parallel experiments, individual cell speeds and persistence times were measured from 1-h, time-lapse video microscopy recordings. The value of mu calculated from single-cell measurements was in good agreement with that from population studies for stimulated random migration (at 10(-7) to 10(-11) M FNLLP), but not in the absence of stimulant. Overall, these results support the applicability of the random walk model of individual cell migration to randomly migrating alveolar macrophage populations.

Animals↗