Figure 1.
Representative diagram of intermediate affinity IL-15 receptor binding, trafficking and synthesis interactions.
Quiescent NK cells constitutively express the β and γ subunits of IL-15R. A. Binding: IL-15 binds to receptors on the cell surface with rate kf and dissociate from IL-15R with rate kr. Inside the endosome, the on and off rates kfe and kre reflect modified binding affinity at lower pH. B. Trafficking: Free IL-15 receptors are constitutively internalized with rate kendo, and the ligand bound receptor complexes are internalized with rate kint. The IL-15 ligand recycles from the endosome back to the surface with rate krec, and the receptors and complexes are sorted for degradation with rate kdeg. C. Synthesis: The IL-15R synthesis is constitutive with rate Vs and can be induced (ksyn) by signaling initiated by the surface complexes.
Figure 2.
IL-15 concentration quantitatively influences the receptors, complexes and ligands on the surface and in endosomes of quiescent NK cells.
Simulations of intermediate affinity receptor binding on NK cells were performed using estimates of kinetic parameters derived from published studies. Solutions of differential equations were depicted in two columns, showing receptor, IL-15/IL-15R complex numbers, and ligand concentration at the cell surface (A, C, E), and in endosomes (B, D, F). The model solutions were obtained from simulations where IL-15 concentration serially doubled from 3.9 ng/ml to 2000 ng/ml, depicted by different lines. The arrow represents increasing IL-15 concentrations.
Table 1.
Differential equation variables and initial values.
Table 2.
Parameters for intermediate and high affinity binding models.
Figure 3.
Steady state cell surface complexes determine NK cell recruitment to the cell cycle.
A. Surface IL-15/IL-15R complex numbers were calculated from model simulations for IL-15 concentrations of 9, 25, 50, and 75 ng/ml and were plotted for t hours. The arrow represents increasing IL-15 concentration. B–E. The cell cycle threshold (generated Cs from the immediate affinity model) is used to predict the fraction of NK cells recruited to divide at various times. The model predictions (solid lines) are compared with results generated from independent experiments (filled circles) where IL-15 concentrations were 9 ng/ml (B, n = 3), 25 ng/ml (C, n = 4), 50 ng/ml (D, n = 2), and 75 ng/ml (E, n = 3). The quality of prediction is represented by the normalized root mean squared deviation (NRMSD). The NRMSD of model prediction vs. experimental data are shown as percentages in the upper left of each graph. For reference, linear regression was performed for all four sets of experimental data, and the NRMSD values of the linear regressions were 12% (9 ng/ml), 5% (25 ng/ml), 19% (50 ng/ml), and 9% (75 ng/ml).
Figure 4.
The quantitative influence of intermediate affinity binding model parameters on the steady state cell surface receptor and complex numbers.
Model simulations were performed with the value of the parameter of interest varied by a factor of ,
,
,
,
,
, 10, 33, and 100, while the values of all other parameters were held constant. Changes in cell surface receptor and complex numbers as a result of variations in parameter values are shown. Receptor and complex numbers corresponding to different values of the parameter of interest are shown by the dashed curves (with the arrow representing increasing values of the parameter being varied) while the solid curves represent the parameters at their original values. Simulations were performed for model parameters kf (A), kr (B), kf and kr (C), kendo (D), kint (E), ks (F), and ksyn (G) at an IL-15 concentration of 25 ng/ml. Large increases (>10-fold) in ksyn resulted in large perturbations in receptor and complexes numbers (data not shown).
Figure 5.
Representative diagram of intermediate and high affinity IL-15 receptor binding, trafficking and synthesis interactions.
Activated NK cells upregulate the expression of the high affinity α subunit of IL-15R. A. Binding: IL-15Rβγ associates with IL-15 with on and off rates kf and kr at the cell surface and kfe and kre in endosomes. All IL-15Rα are assumed to rapidly bind IL-15, forming the high affinity ligand for IL-15Rβγ. IL-15/IL-15Rα binds IL-15Rβγ with on and off rates kf′ and kr′ at the cell surface and kfe′ and kre′ in endosomes. B. Trafficking: Unbound IL-15Rs are constitutively internalized with rate kendo. IL-15/IL-15Rβγ and IL-15/IL-15Rαβγ complexes are internalized with rate kint. Soluble IL-15 and the high affinity ligand (IL-15/IL-15Rα) in the endosome recycle to the surface with rate krec. Intermediate and high affinity complexes are sorted for degradation with rate kdeg. C. Synthesis: The constitutive synthesis of IL-15Rβγ is represented by Vs. Cs and Cs′ induce the synthesis of IL-15Rβγ with rate ksyn and the synthesis of IL-15Rα with rate ksyn′.
Figure 6.
The upregulation of IL-15Rα amplifies IL-15R signaling and modulates the steady state numbers of receptors, complexes, and ligands on the cell surface and in endosomes of dividing NK cells.
Numerical solutions of the computational model are depicted in two columns, showing receptor, intermediate affinity complex, and high affinity complex at the cell surface (A, C, E) and in endosomes (B, D, F). Model solutions were obtained from simulations where IL-15 concentration serially doubled from 3.9 ng/ml to 2000 ng/ml, represented by different lines with the arrow denoting increasing IL-15 concentration. G. The total number of signaling complexes at the cell surface is shown as the sum of intermediate and high affinity complexes. H. Fold change in total steady state cell surface IL-15/IL-15R complex numbers on dividing cells (with upregulation IL-15Rα) compared with quiescent NK cells (which express no appreciable IL-15Rα). The fold changes in this ratio at different IL-15 concentrations (serially doubled from 3.9 to 2000 ng/ml) are depicted by solid bars.
Figure 7.
Formation of high affinity receptor-ligand complexes facilitates exponential expansion of dividing NK cells.
A. The total steady state cell surface IL-15/IL-15R complex numbers in the high affinity binding model stimulate an exponential proliferative response, illustrated by plotting the fraction of maximal response vs. total Cs at the corresponding IL-15 concentrations. B. The maximum number of divisions calculated from the time elapsed since recruitment to cell division by the interdivision time for four different IL-15 concentrations. Solid lines represent model predictions, and filled circles represent the maximum detectable number of NK cell divisions obtained from independent experiments (9 ng/ml n = 3, 25 ng/ml n = 4, 50 ng/ml n = 2, and 75 ng/ml n = 3). The quality of prediction is represented by the normalized root mean squared deviation (NRMSD). The NRMSD of model prediction vs. experimental data are shown as percentages in the upper left of each graph. For reference, linear regression was performed for all four sets of experimental data, and the NRMSD values of the linear regressions were 9% (9 ng/ml), 10% (25 ng/ml), 14% (50 ng/ml), and 12% (75 ng/ml). C. Population mean division rate is estimated from the interdivision time for four IL-15 concentrations. White bars represent model predictions while black bars represent experimental data from the analysis of NK cell populations in 2–4 independent experiments.
Table 3.
Estimates of NK cell interdivision times and division rates.