Systems model of T cell receptor proximal signaling reveals emergent ultrasensitivity

Abstract

Receptor phosphorylation is thought to be tightly regulated because phosphorylated receptors initiate signaling cascades leading to cellular activation. The T cell antigen receptor (TCR) on the surface of T cells is phosphorylated by the kinase Lck and dephosphorylated by the phosphatase CD45 on multiple immunoreceptor tyrosine-based activation motifs (ITAMs). Intriguingly, Lck sequentially phosphorylates ITAMs and ZAP-70, a cytosolic kinase, binds to phosphorylated ITAMs with differential affinities. The purpose of multiple ITAMs, their sequential phosphorylation, and the differential ZAP-70 affinities are unknown. Here, we use a systems model to show that this signaling architecture produces emergent ultrasensitivity resulting in switch-like responses at the scale of individual TCRs. Importantly, this switch-like response is an emergent property, so that removal of multiple ITAMs, sequential phosphorylation, or differential affinities abolishes the switch. We propose that highly regulated TCR phosphorylation is achieved by an emergent switch-like response and use the systems model to design novel chimeric antigen receptors for therapy.

Figure 1. Schematic of the T cell receptor proximal signaling molecules considered in the systems model.

We consider the TCR-chain containing three ITAMs, labelled as 3 (membrane-distal) to 1 (membrane-proximal). These ITAMs are sequentially phosphorylated by the tyrosine kinase Lck and dephosphorylated by the phosphatase CD45. The cytosolic kinase ZAP-70 contains tandem SH2 domains which are able to bind to doubly (fully) phosphorylated ITAMs with differential affinities, with the smallest affinity to 3 and largest affinity to 1. When bound to phosphorylated ITAMs, ZAP-70 is able to propagate signaling by phosphorylating downstream signaling molecules and adaptors.

Figure 2. Multiple -chain ITAMs not only mediate signal amplification, but also increase potency and sensitivity.

A) The concentration of ITAM-bound ZAP-70 as a function of the relative kinase (E) to phosphatase (F) concentration. As expected, when the phosphatase is in excess the -chain is dephosphorylated and ZAP-70 cannot bind whereas when the kinase is in excess the -chain is phosphorylated and ZAP-70 is fully bound. Results are shown for the wild-type -chain (123) and for -chains where the first and second ITAMs are removed, X23 and XX3, respectively. Inset shows normalized curves, highlighting differences in potency () and sensitivity (Hill number), which is a measure of the curve steepness. Each curve is fit to a Hill function to extract estimates of B) the maximum (), C) the potency (), and D) the sensitivity (Hill number). Model and parameter values can be found in Methods.

Figure 3. ZAP-70 binding to phosphorylated ITAMs enhances both ultrasensitivity and potency.

A) The concentration of total -chain phosphorylation as a function of the relative concentration of active kinase (E) to phosphatase (F). Results are shown for sequential phosphorylation (blue, green) and random phosphorylation (red, orange) in the absence (blue, red) and presence (green, orange) of ZAP-70. B) Hill numbers and C) for all four curves reveal that ZAP-70 binding dramatically increases both ultrasensitivity and potency when phosphorylation is sequential but not random.

Figure 4. The absolute ZAP-70 affinity for -chain ITAMs modulates potency.

A) The concentration of bound ZAP-70 as a function of the concentration of active kinase (E) to phosphatase (F). Results are shown for the wild-type -chain (123) and for three additional -chains that contain all high affinity ITAM 1 (111), intermediate affinity ITAM 2 (222), or low affinity ITAM 3 (333). Comparison of these -chains reveals that B) sensitivity is unchanged whilst C) potency is modulated.

Figure 5. Differential ZAP-70 affinity and sequential phosphorylation produces ultrasensitivity.

A) The concentration of bound ZAP-70 as a function of the relative concentration of active kinase (E) to phosphatase (F). Shown are the wild-type -chain (123), and additional constructs where all ITAMs are identical (222), switched (321), or where phosphorylation is no longer sequential (123 Random). The Hill numbers (inset) reveal that ultrasensitivity is decreased if ZAP-70 does not exhibit differential affinity (222), if the affinity decreases as the is sequentially phosphorylated (321), or if phosphorylation is no longer sequential. B) Heat map of Hill numbers as a function of the ZAP-70 unbinding rate for ITAM 1 (Z) and ITAM 3 (Z), where the unbinding rate for ITAM 2 is fixed at 1 s⁻¹. The calculation is performed under sequential phosphorylation. Maximum sensitivity is found in the top left of the heat map, where ZAP-70 binds with the largest affinity to ITAM 1 and with lowest affinity to ITAM 3. The heat map is repeated using an alternate measure of sensitivity in Fig. S3. Note that the heat map colour scheme in panel B is not related to the colour scheme in panel A.

Figure 6. The mathematical model predicts novel chimeric antigen receptors (CARs) design.

A) The concentration of bound ZAP-70 as a function of the relative concentration of active kinase (E) to phosphatase (F) for six cytoplasmic CAR domains. These domains include the wild-type -chain (blue), chains containing 3 copies of the low affinity ITAM from FCRI- (green) and FCRI- (red), a single high affinity -chain ITAM (orange), and chains containing a single copy of the low affinity ITAM from FCRI- (magenta) and FCRI- (grey). B-C) Illustrates the and for all CARs shown in panel A. Most CARs are developed based on the wild-type -chain but this construct, although having a large has an undesirably large potency (low ). Novel CARs containing multiple low affinity ITAMs (e.g. (FCRI-)x3, (FCRI-)x3) have the desirably low potency (large ) while maintaining the desirably large .