The directed movement of human polymorphonuclear leukocytes (PMN) in a plane (Zigmond chamber assay) is described by a statistical model. We demonstrate that (a) the movement of a single cell is a superposition of a directed and a random movement, and (b) the degree of orientation, P1, of moving cells in a chemotactic gradient can be determined either by the time average of a single cell or by the average of movement of multiple cells at a fixed time (Ergoden hypothesis). However, an homogeneous cell population is a necessary condition. P1, which is identical with the McCutcheon index, is derived from the measured angular distribution function of moving cells. The statistical model allows one to distinguish between chemotaxis and chemokinesis. Applying this model to the temperature-dependent changes of cell movement, we found that P1 = 0.82 (37 degrees C) decreased to P1 = 0.4 (22 degrees C). The average speed of moving cells exhibits a very strong temperature-dependent variation from 30 microns/min (37 degrees C) to 5 microns/min (22 degrees C), indicating a different temperature dependence of chemotaxis and chemokinesis. At a fixed temperature (37 degrees C) the stability of the chemotactic gradient can also be checked by the angular distribution function. In addition, this model was applied to investigate the enteric cytopathogenic human orphan, strain 9 (ECHO 9) virus-induced disturbances of cell movement. We found: (a) The average speed of cell movement is not affected by the virus. (b) The degree of orientation is not affected for virus doses below a critical virus dose, ao (virus/PMN = 0.8:1). (c) The degree of orientation above this critical value exhibits a time- and virus-dose-dependence. (d) At a fixed viral dose, the time-dependent decrease of P1 is described by an exponential law (virus/PMN = 5:1, the characteristic time is 110 min). (e) This characteristic time investigated as a function of viral dose results in a logarithmic law analogous with the Weber-Fechner law. These findings indicate that only chemotactic and not chemokinetic response is disturbed by ECHO 9 virus.
Analysis of the directed and nondirected movement of human granulocytes: influence of temperature and ECHO 9 virus on N-formylmethionylleucylphenylalanine-induced chemokinesis and chemotaxis.
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B D Bültmann, H Gruler; Analysis of the directed and nondirected movement of human granulocytes: influence of temperature and ECHO 9 virus on N-formylmethionylleucylphenylalanine-induced chemokinesis and chemotaxis.. J Cell Biol 1 June 1983; 96 (6): 1708–1716. doi: https://doi.org/10.1083/jcb.96.6.1708
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