A simple, generalized transport equation for the migration of chemotactic cell populations is derived from a probabilistic model in one spatial dimension. This general equation is then made specific for the cases of flagellar bacteria and polymorphonuclear leukocytes, based on quantitative information concerning chemosensory movement behavior of individual cells of these types. The resulting specialized equations allow a priori estimation of the polulation transport coefficients (μ, the random motility coefficient, and x, the chemotaxis coefficient) in terms of individual cell movement properties (such as speed, directional persistence time, and directional orientation bias). Thus, our model permits cell population migration to be related quantitatively to individual cell behavior. Examples of application of our models to experimental data are provided. Despite the simplifying approximations involved in our derivations, especially in the extrapolation to higher spatial dimensions, the models demonstrate a satisfactory and very useful ability to quantitatively interpret population assays for bacterial and leukocyte chemotactic migration.
Bibliographical noteFunding Information:
Grant ECE 86-12987 and NIH Grants DE-00143 and AI-21538 to DAL. An extremely helpful experimental collaboration with Dr Sally Zigmond is also gratefully acknowledged. The final version of this manuscript benefited significantly from helpful comments by the referees, which are also greatly appreciated.
Acknowledgements-This work has been supported by NSF