In the filter assay, DFRO decays slowly (Fig. to a random-motility control. Results show, for example, that in the filter assay, 2C4 times Isosorbide dinitrate as many neutrophils pass through the filter when exposed to a gradient as when the gradient is absent. However, in the other combinations of cells and assays we considered, only 10C20% more cells are counted as having migrated in a directed, rather than random, motility condition. We also discuss the design of appropriate controls for these assays, which is difficult for the under-agarose and agarose spot assays. Moreover, although straightforward to perform with the filter assay, reliable controls are often not done. Consequently, we infer that chemotaxis is frequently over-reported, especially for cells like MDA-MB-231 cells, which Isosorbide dinitrate move slowly and are relatively insensitive to gradients. Such results provide insights into the use of chemotaxis assays, particularly if one wants to acquire and analyze quantitative data. is the chemoattractant concentration on the surface and is the dissociation coefficient for the chemoattractant-receptor interaction, that is, is the concentration at which half of the receptors would be bound. The difference in fractional receptor occupancy, DFRO, across the length of the cell, is obtained by taking the derivative of FRO with respect to (the direction in which concentration varies), and scaling by the length, is the angle of the cell with respect to the chemoattractant gradient, such that = 0 if the cell is Isosorbide dinitrate oriented up the gradient and = if the cell is oriented down the gradient. The function represents the bias in the cell orientation distribution. A more biased distribution has a greater number of cells oriented close to the direction of the gradient. Figure 4 shows angle distributions for different levels of bias. We use (cells (Fisher et al., 1989) and to model pseudopod extension (van Haastert, 2010a,b). Neutrophil orientations also appear to fall on bell curves (Zigmond, 1977). Open in a separate window Figure 4 Bias in cell angle distributions is characterized by = 0 (a), = 0.1 (b), = 0.3 (c), and = 0.5 (d). Experimental data on orientations or trajectories of directed cell motion is sometimes presented in this form. Random orientation corresponds to = 0. Neutrophils are more sensitive to gradients than MDA-MB-231 cells: = 0.1 is typical for MDA-MB-231 cells in a 4% gradient, but = 0.5 is possible for neutrophils in a much shallower 0.6% gradient. In the analysis here, the effect of chemotactic gradient sensing is modeled as a bias in the orientation distribution of motile cells. We shall assume that bias is proportional to the difference in fractional receptor occupancy, that is, =?is the sensitivity. This parameter depends on the cell type and identity of the chemoattractant. 2.4. Cell orientation distributions describe cell behavior In this subsection, we develop functions that Isosorbide dinitrate relate the bias in cell orientations, = 0), and can increase by a factor of as increases. The percent of cells that are oriented up the gradient (Eq. 10) is 50% for randomly-oriented cells. The chemotactic index (Eq. 11), the ratio of distance traveled up the gradient to total path length, varies from 0 to 100%. A major readout for the filter, under-agarose, and agarose spot assays is the number of cells that cross a boundary, crawling Isosorbide dinitrate into or through the filter, or under the gel in the under-agarose and agarose spot assays. The flux of cells, i.e., the number of cells that cross the boundary per unit time, depends on the angle distribution: with a greater fraction of cells oriented up the gradient, more cells would cross the boundary in a given interval of time. Moreover, cells are more likely to cross the boundary if they are pointed directly perpendicular to the boundary rather than at some angle. With cell orientations on an angular distribution, ((follow from Eqs. Cd163 5 and 6. Cells in the filter assay are essentially undergoing 3D migration, with an extra degree of freedom for the cell orientation. As this extra degree of freedom only affects motion.