Mathematical Modeling Reveals Kinetics of Lymphocyte Recirculation in the Whole Organism
Figure 6
The mathematical model accurately describes the kinetics of lymphocyte migration via major lymphoid organs (panel A) and kinetics of labeled lymphocytes exit during the thoracic duct cannulation (panel B).
We fit the basic mathematical model (eqn. (1) – (6)) simultaneously to the data on lymphocyte migration (Figure 3) and lymphocyte output via the thoracic duct (Figure 4) using generalized likelihood method assuming subcompartments in LNs and PPs (see Materials and Methods). In panel A, symbol and line labeling is similar to that of Figure 3. The model predicts that the
of lymphocytes exiting SCLNs migrate to the blood via the right lymphatic duct and thus are not sampled during the thoracic duct cannulation. Numbers in parentheses in panel B indicate the percent of cells exiting into blood from different LNs in 45 hours as predicted by the model (lines) or as observed in the data (dots). In the data, 55% of transferred TDLs were collected during 45 hours of the thoracic duct cannulation. The model also predicts the contribution of lymphocytes exiting SCLNs (short dashed line in panel B) and MLNs (long dashed line in panel B) via the thoracic duct. To explain the data, the rate of egress of lymphocytes from LNs and PPs declines exponentially with time during cannulation at an estimated rate
min
. Other parameters for the migration kinetics of TDLs are nearly identical to those given in Table 1. We fixed
in fits of these data. Estimated standard errors are
and
(see eqn. (8)).