Using endocytosis to switch between chemoattraction and chemorepulsion

White blood cells can be guided to targets by chemoattractant signals, but this response is complicated, including guidance toward and away from inflammation sites. We model how cells can switch between being attracted and repelled by a chemical signal. We study experiments on malignant B cell lines, which find that depending on their environment, B cells can either be attracted or repelled by signals like CCL19. The presence of chemorepulsion is also dependent on whether the receptors for CCL19 can be internalized via endocytosis. We develop a stochastic model of receptor-ligand binding and internalization where bound receptors drive a nonlinear feed-forward loop of intracellular signaling molecules, which determine the cell's direction. We recapitulate key experimental results: changing CCL19 concentration or inhibiting receptor internalization can switch the cell's direction. Our model implies that cells can navigate toward a target concentration of a signal, regulating that target by receptor internalization. We propose experiments to test this idea.