The efficient recruitment of immune cells is a vital cornerstone of our defense against infections and a key challenge of immunotherapeutic applications. It relies on the ability of chemotaxing cells to prioritize their responses to different stimuli. For example, immune cells are known to abandon gradients of host-cell-produced cytokines in favor of complement-derived anaphylatoxins, which then guide the cells toward nearby pathogen surfaces. The aptitude to triage stimuli depends on the cells' specific sensitivities to different chemoattractants. We here use human neutrophils as uniquely capable biodetectors to map out the anaphylatoxic cloud that surrounds microbes in the presence of host serum. We quantify the neutrophil sensitivity in terms of the ratio between the chemoattractant concentration c and the production rate j 0 of the chemoattractant at the source surface. An integrative experimental/theoretical approach allows us to estimate the c/j 0 -threshold at which human neutrophils first detect nearby b-glucan surfaces as c/j 0 z 0.0044 s/mm.How does an immune cell cope with situations in which it faces multiple chemotactic stimuli? How does the cell decide on a particular response? Such questions touch on the core of our mechanistic understanding of immune-cell behavior, and have inspired the paradigm that immunotaxis comprises an intricate spatiotemporal hierarchy of distinct chemotactic processes (1-6). The systematic dissection of this hierarchy is an enormous interdisciplinary challenge that requires, among others, quantitative analyses of the stimulus-specific sensitivity of the responding cells.Complement-mediated chemotaxis has emerged as a universal, short-range homing mechanism by which chemotaxing immune cells can implement a last-minute course correction toward pathogenic bacteria and fungi. Recent single-cell experiments have validated human neutrophils as uniquely capable biodetectors of minuscule amounts of complement-derived anaphylatoxins in the proximity of microbial and model pathogens (Fig. 1) (6-8). But the question just how sensitive these immune cells are was not addressed by earlier studies.We here use an integrative theoretical/experimental strategy to tackle this difficult question. A recently found closed-form solution of the appropriate reaction-diffusion problem (V.H., E.A.F., and W.D. Simpson, unpublished data) predicts the spatiotemporal distribution of anaphylatoxins as a function of the time t and the radial distance from the source, Dr ¼ r À R (Fig. 1 B; Supporting Material). In the considered scenario, the source of chemoattractant is a sphere of radius R that, at time t ¼ 0, starts releasing anaphylatoxins at a constant rate given by the boundary flux j 0 . The chemoattractant is redistributed in the surrounding infinite space by diffusion. A realistic estimate gives a diffusion coefficient of D z 130 mm 2 /s for the dominant anaphylatoxin C5a (V.H., E.A.F., and W.D. Simpson, unpublished data). We further model the deactivation of chemoattractant by carboxype...