Figure 4. Cell orientation in competing ligand gradients at the steady state.

(A) In competing gradients of L₁ and L₂, cells expressing normal desensitizable receptors for both ligands orient toward the distant ligand gradient. i.e., cells that are close to L₁ orient toward L₂ and cells that are close to L₂ orient toward L₁. (B) Cells expressing nondesensitizable receptors for both ligands orient toward the local ligand gradient. i.e., cells that are close to L₁ orient toward L₁ and cells that are close to L₂ orient to L₂. (C) Cells expressing nondesensitizable receptor for L₁ but desensitizable receptor for L₂ orient toward the nondesensitizing ligand gradient L₁. This effect is clear in the region where the two ligand gradients are significantly overlapped. The ligand gradients are represented by contour circles with the highest ligand concentration (17.6 nM) at the center of the contours for each gradient. The ligand concentration at the outmost contour circle is 0.1 nM, and the concentration difference between adjacent circles is 1.0 nM. Because of the magnitude difference between the orientation vector of cells expressing desensitizable and nondesensitizable receptors, the length of the arrow is adjusted, i.e., the scaling factor is set at 0.8 for Figure 4A, and 0.07 for Figure 4B and 4C. (D–E) The dependence of cell orientation (ΔLR^*) on k_des1 and k_des2 for L₁ receptor and L₂ receptor respectively that vary at the same time (D), or on k_des1 for L₁ receptor (E), for cells locates at different positions in the overlapping area of L₁ and L₂. Positive ΔLR^* indicates cell orientation toward L₁ and negative ΔLR^* indicates cell orientation toward L₂.