A theoretical model for estimating the margination constant of leukocytes

Abstract Background Blood leukocytes constitute two interchangeable sub-populations, the marginated and circulating pools. These two sub-compartments are found in normal conditions and are potentially affected by non-normal situations, either pathological or physiological. The dynamics between the compartments is governed by rate constants of margination (M) and return to circulation (R). Therefore, estimates of M and R may prove of great importance to a deeper understanding of many conditions. However, there has been a lack of formalism in order to approach such estimates. The few attempts to furnish an estimation of M and R neither rely on clearly stated models that precisely say which rate constant is under estimation nor recognize which factors may influence the estimation. Results The returning of the blood pools to a steady-state value after a perturbation (e.g., epinephrine injection) was modeled by a second-order differential equation. This equation has two eigenvalues, related to a fast- and to a slow-component of the dynamics. The model makes it possible to identify that these components are partitioned into three constants: R, M and SB; where SB is a time-invariant exit to tissues rate constant. Three examples of the computations are worked and a tentative estimation of R for mouse monocytes is presented. Conclusions This study establishes a firm theoretical basis for the estimation of the rate constants of the dynamics between the blood sub-compartments of white cells. It shows, for the first time, that the estimation must also take into account the exit to tissues rate constant, SB.

This study was supported by a FAPESP (State of São Paulo Science Foundation) undergraduate fellowship to K.I. (process number 00/01112-7) and by a FAPESP research grant to J.G.C.B. (process number 00/02287-5).

This study was supported by a FAPESP (State of São Paulo Science Foundation) undergraduate fellowship to K.I. (process number 00/011127) and by a FAPESP research grant to J.G.C.B. (process number 00/022875).

This manuscript was significantly improved by the comments of two anonymous referees.

This manuscript was significantly improved by the comments of two anonymous referees.