Influence of external concentration fluctuations on leukocyte chemotactic orientation

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Abstract
The quantitative dependence of leukocyte chemotactic orientation on imprecision in the measurement of chemoattractant concentrations from thermal fluctuations is analyzed. First, a mathematical model relating orientation to differences in receptor occupancy across cell dimensions is developed. This is then coupled with an extension of Berg and Purcell's analysis (1) of the precision of attractant concentration measurements by means of receptor occupancy. Our results show that thermal fluctuations in external concentrations can limit the accuracy of orientation, unless the measurement noise is reduced by averaging the measurements over a period of time. Comparison of our model predictions to experimental orientation data suggests that leukocytes do overcome this limitation, and allows estimation of the time-averaging period necessary to do so. For the orientation observed in a visual bridge assay by Zigmond (2) using the attractant peptide FNLLP, we estimate that receptor occupancy measurements for spatial comparison across cell dimensions must be averaged for a few minutes. Otherwise, the fluctuations in the attractant concentration near the cell will be too great to allow the observed degree of orientation. Our analysis also suggests that the ratio of signal-to-signal noise does not adequately characterize orientation accuracy. Accurate orientation can, in some situations, occur when this ratio is substantially less than unity; in other situations, a ratio much greater than unity is required for accurate orientation.