Is TCR/pMHC Affinity a Good Estimate of the T-cell Response? An Answer Based on Predictions From 12 Phenotypic Models

Abstract

On the T-cell surface the TCR is the only molecule that senses antigen, and the engagement of TCR with its specific antigenic peptide (agonist)/MHC complex (pMHC) is determined by the biochemical parameters of the TCR-pMHC interaction. This interaction is the keystone of the adaptive immune response by triggering intracellular signaling pathways that induce the expression of genes required for T cell-mediated effector functions, such as T cell proliferation, cytokine secretion and cytotoxicity. To study the TCR-pMHC interaction one of its properties most extensively analyzed has been TCR-pMHC affinity. However, and despite of intensive experimental research, the results obtained are far from conclusive. Here, to determine if TCR-pMHC affinity is a reliable parameter to characterize T-cell responses, a systematic study has been performed based on the predictions of 12 phenotypic models. This approach has the advantage that allow us to study the response of a given system as a function of only those parameters in which we are interested while other system parameters remain constant. A little surprising, only the simple occupancy model predicts a direct relationship between affinity and response so that an increase in affinity always leads to larger responses. Conversely, in the others more elaborate models this clear situation does not occur, i.e., that a general positive correlation between affinity and immune response does not exist. This is mainly because affinity values are given by the quotient k_on/k_off where k_on and k_off are the rate constants of the binding process (i.e., affinity is in fact the quotient of two parameters), so that different sets of these rate constants can give the same value of affinity. However, except in the occupancy model, the predicted T-cell responses depend on the individual values of k_on and k_off rather than on their quotient k_on/k_off. This allows: a) that systems with the same affinity can show quite different responses; and b) that systems with low affinity may exhibit larger responses than systems with higher affinities. This would make affinity a poor estimate of T-cell responses and, as a result, data correlations between affinity and immune response should be interpreted and used with caution.

Keywords: T-cell activation; TCR-pMHC interaction; affinity; correlation between affinity immune response; phenotypic models.

Figure 1A

Schemes of the phenotypic models. Panel models: (a) occupancy; (b) basic kpr; (c) kpr with limited signaling; (d) kpr with sustained signaling; (e) kpr with negative feedback; (f) kpr with induced rebinding. A full description of these models are found in the references given in main text.

Figure 1B

Schemes of the phenotypic models. Panel models: (g) kpr with stabilizing activation chain; (h) kpr with limited and sustained signaling; (i) kpr with negative feedback and limited signaling; (j) kpr with stabilizing activation chain and limited signaling; (k) kpr with stabilizing activation chain and sustained signaling; (l) kpr with limited signaling coupled to an incoherent feed-forward loop (kpl-iff). A full description of these models are found in the references given in main text.

Figure 2A

Dependence of the values of R on time for three systems with equal affinity (A) but different values of $k_{\text{on}}(s^{-1})$ and $k_{\text{off}}(s^{-1})$ given always in the form (k_on,k_off): system 1: (k_on, 0.01), τ = 100s, A = 100k_on (blue); system 2: (5k_on, 0.05), τ = 20s, A = 100k_on (red); system 3: (10k_on, 0.10), τ = 10s, A = 100k_on (black). Panel models: (a) occupancy model; (b) basic kpr; (c) kpr with limited signaling; (d) kpr with sustained signaling; (e) kpr with negative feedback; (f) kpr with induced rebinding. Plots were obtained as described in main text and in Appendix. Number of pMHCs, P_T = 100. The values of the remaining parameters needed for computation in the different models are given in subsection 2.2.

Figure 2B

Dependence of the values of R on time for three systems with equal affinity (A) but different values of $k_{\text{on}}(s^{-1})$ and $k_{\text{off}}(s^{-1})$. Panel models: (g) kpr with stabilizing activation chain; (h) kpr with limited and sustained signaling; (i) kpr with negative feedback and limited signaling; (j) kpr with stabilizing activation chain and limited signaling; (k) kpr with stabilizing activation chain and sustained signaling; (l) kpr with limited signaling coupled to an incoherent feed-forward loop. Other conditions as in Figure 2A.

Figure 3A

Dependence of the values of R on time for three systems with different affinities (A) and different values of $k_{\text{on}}(s^{-1})$ and $k_{\text{off}}(s^{-1})$ given in the form (k_on,k_off): system 1: (1000k_on, 1), τ = 1s, A = 1000k_on (blue); system 2: (10k_on, 0.10), τ = 10s, A = 100k_on (red); system 3: (0.1k_on, 0.01), τ = 100s, A = 10k_on (black). Panel models: (a) occupancy model; (b) basic kpr; (c) kpr with limited signaling; (d) kpr with sustained signaling; (e) kpr with negative feedback; (f) kpr with induced rebinding. In some cases (v.g. b, blue curve), R-values are so small that their plots are almost coincident with the x-axis. Other conditions as in Figure 2A.

Figure 3B

Dependence of the values of R on time for three systems with different affinities (A) and different values of $k_{\text{on}}(s^{-1})$ and $k_{\text{off}}(s^{-1})$. Panel models: (g) kpr with stabilizing activation chain; (h) kpr with limited and sustained signaling; (i) kpr with negative feedback and limited signaling; (j) kpr with stabilizing activation chain and limited signaling; (k) kpr with stabilizing activation chain and sustained signaling; (l) kpr with limited signaling coupled to an incoherent feed-forward loop. Other conditions as in Figures 2A, 3A.

Figure 4A

Dependence of the values of R on time for three systems with different affinities (A), different values of $k_{\text{on}}(s^{-1})$ and equal values of $k_{\text{off}}(s^{-1})$ given in the form (k_on,k_off): system 1: (0.01k_on, 0.1), τ = 10s, A = 0.1k_on (blue); system 2: (k_on, 0.1), τ = 10s, A = 10k_on (red); system 3: (100k_on, 0.1), τ = 10s, A = 1000k_on (black). Panel models: (a) occupancy model; (b) basic kpr; (c) kpr with limited signaling; (d) kpr with sustained signaling; (e) kpr with negative feedback; (f) kpr with induced rebinding. Other conditions as in Figure 2A.

Figure 4B

Dependence of the values of R on time for three systems with different affinities (A), different values of $k_{\text{on}}(s^{-1})$ and equal values of $k_{\text{off}}(s^{-1})$. Panel models: (g) kpr with stabilizing activation chain; (h) kpr with limited and sustained signaling; (i) kpr with negative feedback and limited signaling; (j) kpr with stabilizing activation chain and limited signaling; (k) kpr with stabilizing activation chain and sustained signaling; (l) kpr with limited signaling coupled to an incoherent feed-forward loop. Other conditions as in Figures 2A, 4A.

Figure 5A

Dependence of the values of R on time for five systems with different affinities (A), different values of $k_{\text{off}}(s^{-1})$ and equal values of $k_{\text{on}}(s^{-1})$ given in the form (k_on,k_off): system 1: (k_on, 10), τ = 0.1s, A = 0.1k_on (blue); system 2: (k_on, 1), τ = 1s, A = k_on (red); system 3: (k_on, 0.5), τ = 2s, A = 2k_on (green); system 4: (k_on, 0.2), τ = 5s, A = 5k_on (magenta); system 5: (k_on, 0.05), τ = 20s, A = 20k_on (black). Panel models: (a) occupancy model; (b) basic kpr; (c) kpr with limited signaling; (d) kpr with sustained signaling; (e) kpr with negative feedback; (f) kpr with induced rebinding. Other conditions as in Figure 2A.

Figure 5B

Dependence of the values of R on time for five systems with different affinities (A), different values of $k_{\text{off}}(s^{-1})$ and equal values of $k_{\text{on}}(s^{-1})$. Panel models: (g) kpr with stabilizing activation chain; (h) kpr with limited and sustained signaling; (i) kpr with negative feedback and limited signaling; (j) kpr with stabilizing activation chain and limited signaling; (k) kpr with stabilizing activation chain and sustained signaling; (l) kpr with limited signaling coupled to an incoherent feed-forward loop. Other conditions as in Figures 2A, 5A.

Figure 6A

Dependence of the values of R on time for five systems with different affinities (A), different values of $k_{\text{off}}(s^{-1})$ and equal values of $k_{\text{on}}(s^{-1})$ given in the form (k_on,k_off): system 6: (k_on, 0.02), τ = 50s, A = 50k_on (blue); system 7: (k_on, 0.01), τ = 100s, A = 100k_on (red); system 8: (k_on, 0.002), τ = 500s, A = 500k_on (green); system 9: (k_on, 0.001), τ = 1000s, A = 1000k_on (magenta); system 10: (k_on, 0.0001), τ = 10000s, A = 10000k_on (black). Panel models: (a) occupancy model; (b) basic kpr; (c) kpr with limited signaling; (d) kpr with sustained signaling; (e) kpr with negative feedback; (f) kpr with induced rebinding. Other conditions as in Figure 2A.

Figure 6B

Dependence of the values of R on time for five systems with different affinities (A), different values of $k_{\text{off}}(s^{-1})$ and equal values of $k_{\text{on}}(s^{-1})$. Panel models: (g) kpr with stabilizing activation chain; (h) kpr with limited and sustained signaling; (i) kpr with negative feedback and limited signaling; (j) kpr with stabilizing activation chain and limited signaling; (k) kpr with stabilizing activation chain and sustained signaling; (l) kpr with limited signaling coupled to an incoherent feed-forward loop. Other conditions as in Figures 2A, 6A.

Figure 7A

Dependence of the values of R on time for three systems with equal affinity (A = 10k_on, $k_{\text{off}}=0.1s^{-1}$), but different values of $k_p(s^{-1})$: system 1: k_p = 1 (blue); system 2: k_p = 0.5 (red); system 3: k_p = 0.1 (black). Panel models: (a) occupancy model; (b) basic kpr; (c) kpr with limited signaling; (d) kpr with sustained signaling; (e) kpr with negative feedback; (f) kpr with induced rebinding. In some cases, R-values are so small that their plots are almost coincident with the x-axis. Other conditions as in Figure 2A.

Figure 7B

As in Figure 7A, but panel models are now: (g) kpr with stabilizing activation chain; (h) kpr with limited and sustained signaling; (i) kpr with negative feedback and limited signaling; (j) kpr with stabilizing activation chain and limited signaling; (k) kpr with stabilizing activation chain and sustained signaling; (l) kpr with limited signaling coupled to an incoherent feed-forward loop.