Measurement of the chemotaxis coefficient for human neutrophils in the under‐agarose migration assay
Authors: Tranquillo R. T. , Zigmond S. H. , Lauffenburger D. A. 
Published: February 2005

Clinical and scientific investigations of leukocyte chemotaxis will be greatly aided by an ability to measure quantitative parameters characterizing the intrinsic random motility, chemokinetic, and chemotactic properties of cell populations responding to a given attractant. Quantities typically used at present, such as leading front distances, migrating cell numbers, etc., are unsatisfactory in this regard because their values are affected by many aspects of the assay system unrelated to cell behavioral properties.

In this paper we demonstrate the measurement of cell migration parameters that do, in fact, characterize the intrinsic cell chemosensory movement responses using cell density profiles obtained in the linear under‐agarose assay. These parameters are the random motility coefficient, μ, and the chemotaxis coefficient, χ, which appear in a theoretical expression for cell population migration. We propose a priori the dependence of χ on attractant concentration, based on an independent experimental correlation of individual cell orientation bias in an attractant gradient with a spatial difference in receptor occupancy. Our under‐agarose population migration results are consistent with this proposition, allowing chemotaxis to be reliably characterized by a chemotactic sensitivity constant, χ, to which χ is directly proportional. Further, χo has fundamental significance; it represents the reciprocal of the difference in number of bound receptors across cell dimensions required for directional orientation bias.

In particular, for the system of human peripheral blood polymorphonuclear neutrophil leukocytes responding to FNLLP, we find that the chemotaxis coefficient is a function of attractant concentration, a, following the expression:
χ=χoNTO f(a) S(a) Kd/(Kd + a)2

Where Kd is the FNLLP‐receptor equilibrium dissociation constant and NTO is the total number of cell surface receptors for FNLLP. f(a) is the fraction of surface receptors remaining after down‐regulation, and S(a) is the cell movement speed, both known functions of FNLLP concentration. We find that χ0NTO = 0.2 cm; according to a theoretical argument outlined in the Appendix this means that these cells exhibit 75% orientation toward higher attractant concentration when the absolute spatial difference in bound receptors is 0.0025NTO over 10 μm. (For example, if NTO = 50,000 this would correspond to a spatial difference of 125 bound receptors over 10 μm.) This result can be compared with estimates obtained from visual studies of individual neutrophils.

This work thus represents the first satisfactory quantitative measurement of intrinsic chemokinesis and chemotaxis properties using a population migration assay. Of great significance is that our theoretical model permits population migration behavior to be compared to observations of individual cell movement properties. Further, these parameter values can be used to quantitatively elucidate the relative contributions of chemokinesis and chemotaxis in this commonly used assay.