Analytical Prediction of the Spatiotemporal Distribution of Chemoattractants around Their Source: Theory and Application to Complement-Mediated Chemotaxis

Volkmar Heinrich, Wooten D. Simpson, Emmet A. Francis

The ability of motile immune cells to detect and follow gradients of chemoattractant is critical to numerous vital functions, including their recruitment to sites of infection and-in emerging immunotherapeutic applications-to malignant tumors. Facilitated by a multitude of chemotactic receptors, the cells navigate a maze of stimuli to home in on their target. Distinct chemotactic processes direct this navigation at particular times and cell-target distances. The expedient coordination of this spatiotemporal hierarchy of chemotactic stages is the central element of a key paradigm of immunotaxis. Understanding this hierarchy is an enormous interdisciplinary challenge that requires, among others, quantitative insight into the shape, range, and dynamics of the profiles of chemoattractants around their sources. We here present a closed-form solution to a diffusion-reaction problem that describes the evolution of the concentration gradient of chemoattractant under various conditions. Our ready-to-use mathematical prescription captures many biological situations reasonably well and can be explored with standard graphing software, making it a valuable resource for every researcher studying chemotaxis. We here apply this mathematical model to characterize the chemoattractant cloud of anaphylatoxins that forms around bacterial and fungal pathogens in the presence of host serum. We analyze the spatial reach, rate of formation, and rate of dispersal of this locator cloud under realistic physiological conditions. Our analysis predicts that simply being small is an effective protective strategy of pathogens against complement-mediated discovery by host immune cells over moderate-to-large distances. Leveraging our predictions against single-cell, pure-chemotaxis experiments that use human immune cells as biosensors, we are able to explain the limited distance over which the cells recognize microbes. We conclude that complement-mediated chemotaxis is a universal, but short-range, homing mechanism by which chemotaxing immune cells can implement a last-minute course correction toward pathogenic microbes. Thus, the integration of theory and experiments provides a sound mechanistic explanation of the primary role of complement-mediated chemotaxis within the hierarchy of immunotaxis, and why other chemotactic processes are required for the successful recruitment of immune cells over large distances.