Summary
The T-cell receptor (TCR) must discriminate between peptides bound to major histocompatibility complex proteins and yet it can be triggered even without ligands at close contacts characterized by local depletion of the phosphatase, CD45. Here, we use a quantitative treatment of signaling that incorporates moving-boundary passage time calculations and is reliant only upon receptor dwell-time at close contacts to reconcile the contradictory properties of TCR triggering. We validate the model by showing that signaling is inversely related to close contact growth-rate and sensitive to the local balance of kinase and phosphatase activities. The model predicts that the small size of close contacts imposed by cell topography, and their short duration owing to the destabilizing effects of, for example, the glycocalyx, crucially underpins ligand discrimination by T cells without recourse to classical proofreading schemes. Based on simple physical principles, therefore, our model accounts for the main features of TCR triggering.
Introduction
Triggering of the T-cell receptor (TCR) following binding to peptide-MHC complexes (pMHC) on antigen-presenting cells (APCs) sets T cells on course to responding to pathogens and tumors (Smith-Garvin et al., 2009). Inefficient pMHC discrimination may lead to immunodeficiency or autoimmunity. TCR triggering is very sensitive, selective and fast: binding to a single pMHC is sufficient to induce TCR triggering, that is, increased tyrosine phosphorylation of signaling motifs located within the cytoplasmic domains of the CD3 subunits associated with the TCRαβ heterodimer, within seconds of pMHC binding (Huang et al., 2013; Irvine et al., 2002; Purbhoo et al., 2004). However, the mechanistic basis of TCR sensitivity and specificity is still poorly understood (for a detailed review see Chakraborty and Weiss, 2014).
The kinetic-segregation (KS) model proposes that in resting T-cells, TCR phosphorylation by kinases is kept in check by the counter-activity of large phosphatases (CD45; Davis and van der Merwe, 2006). This equilibrium is perturbed when contacts are formed between T cells and APCs that exclude the receptor-type protein tyrosine phosphatase CD45, resulting in net receptor phosphorylation. Recently, Chang et al. (2016) showed that CD45 spontaneously segregates from the TCR and Lck present in close contacts that are created when T cells interact with artificial and model cell surfaces. In agreement with predictions of the KS model, TCR triggering was observed under these conditions even when receptor ligands were absent. These findings suggested that TCR triggering is not explicitly ligand dependent, i.e. reliant on e.g. conformational changes or oligomerization, or on mechanical forces acting through the TCR. However, the work of Chang et al. introduced a new problem insofar as it was unclear what it is that allows T-cells to respond to, and to discriminate between, cognate ligands. One possibility is that interactions with ligands influence the dwell-time of the TCR in CD45-depleted close contacts, and that other factors underpin ligand discrimination.
But what could these factors be? Historically, TCR triggering was assumed to rely exclusively on pMHC binding and, in modeling the process, little consideration is usually given to the structure or dynamics of the contacts formed between T cells and APCs. Importantly, encounters between T-cells and APCs are known to be transient and several reports indicate that initial close contacts are only sub-μm in size (Sage et al., 2012; Stoll et al., 2002). In contrast, the model surfaces often used to study the early and late stages of T-cell activation, including protein-coated glass surfaces and supported lipid bilayers (SLBs), tend to favor the formation of stable and large cellular contacts (Grakoui et al., 1999; Groves and Dustin, 2003). Moreover, although it is known that heavily glycosylated proteins such as CD43 influence both T-cell contact formation and TCR signaling (Ardman et al., 1992; Manjunath et al., 1993, 1995; Mazurov et al., 2012), these proteins are not routinely incorporated into model surfaces. In addition, adhesion proteins such as CD2 that are likely to profoundly affect contact structure and to facilitate the scanning of pMHCs for cognate peptides (van der Merwe et al. 1995) are usually left out of the experiments. Finally, the actual role of integrins in mediating close contact formation is unclear given that the activities of integrins themselves are affected by receptor signaling (Dustin and Springer, 1989; Kinashi, 2005). At present, therefore, we have a very limited understanding of whether or how the structure and dynamics of contact formation influence TCR signaling per se, and especially ligand discrimination.
Here, we undertake a quantitative analysis of signaling initiated when T cells interact with surfaces lacking TCR ligands, using single-molecule imaging to characterize the behavior of CD45, Lck and the TCR, and calcium reporters to simultaneously monitor cellular responses. We develop a new theoretical treatment of T-cell signaling utilizing moving-boundary passage time calculations that is reliant only upon TCR occupancy of close contacts from which CD45 is depleted, and that we validate by showing that signaling lag-time is inversely related to close contact growth-rate. Our model allows signaling to occur ligand independently and identifies conditions that might even reinforce signaling by increasing the fraction of triggered receptors beyond those bound by ligands. Most importantly, ligand discrimination emerges as a robust consequence of topography-based dwell-time modulation at close contacts, without recourse to conventional proof-reading schemes. A theory of signaling contingent only upon receptor occupancy of phosphatase-depleted close contacts, therefore, accounts for the main features of TCR triggering.
Results
Single-molecule behavior of CD45, Lck and TCR at close contacts
The goal of this study was to understand how an intrinsically ligand-independent triggering mechanism discriminates between ligands. To this end, we developed and tested a new theoretical treatment of T-cell signaling contingent only upon TCR occupancy close contacts. To parameterize variables used in the model, we analyzed the diffusion and distribution of key signaling molecules during the earliest stages of close contact formation as T cells spread on IgG-coated glass surfaces and SLBs. We used two-color total internal reflection fluorescence (TIRF) microscopy to localize close contacts and to simultaneously track CD45, Lck and TCR at the single-molecule level. To achieve this, we used high-density labeling of CD45 to define the boundaries of the close contacts and sub-stoichiometric labeling of Lck, TCR or CD45 (Figure 1A). For T cells interacting with IgG-coated glass surfaces, 96.8±0.1% of CD45 molecules were excluded from the close contacts (Figure 1B, and Table S1). An extracellular domain (ECD)-truncated form of CD45 (HA-CD45) was less excluded (86±2%; Figure S1A and Table S1). While 6±1% of wild-type Lck was found inside the close contacts (Figure 1C and Table S1), this fraction increased to 33±3% when residues involved in Lck-CD4 pairing were mutated (mLck; Kim et al., 2003; Table S1), suggesting that the exclusion of Lck is at least partially dependent on its association with CD4. Only 5±2% of all detected TCRs were in close contacts (Figure 1D, Table S1 and Movie S1). The high levels of protein segregation observed for CD45, Lck/CD4 and the TCR suggest that the contacts formed between T cells and protein-coated glass surfaces are narrow enough to exclude large fractions of all proteins with extracellular regions >75 Å. Close contacts are dynamic structures and the initial small multifocal contacts were observed to merge into single larger contacts (Movie S2 and Figure S1B and S1C). T-cell close contact growth over time therefore results in increasingly larger CD45-depleted regions.
To create contacts with defined separation of the T cell‐ and model-surfaces like those expected to form in vivo, we used supported lipid bilayers (SLBs) wherein contact formation was initiated by rCD2-rCD48 interactions (Chang et al., 2016). Jurkat T-cells expressing signaling-deficient, CD48-T92A were allowed to settle on SLBs presenting rCD2 (CD48TM-T92A binds rCD2 with a Kd of ~11 uM, similar to the hCD58/CD2 interaction; Evans et al., 2006). In these experiments, CD45, Lck and TCR segregation from close contacts was reduced compared to that for T-cell interactions with glass surfaces (Figure 1H and Table S2). Nevertheless, CD45 still exhibited the strongest segregation: 13±3% of CD45 molecules were found inside the close contacts (Figure 1E), versus 56±7% and 40±6% of Lck and TCR proteins, respectively (Figures 1F and 1G). Despite the differences in their exclusion from contacts formed on glass or SLBs, the ratio of CD45 to Lck inside the close contacts was similar between the two model surfaces, i.e. approximately 2:1 on SLBs and 2.5:1 on IgG-coated glass. The initial CD45/Lck ratio of 5 to 1 at the unperturbed T-cell surface was thereby reduced by ~50% (Figure S2A; Chang et al., 2016).
Quantitative analysis of CD45, Lck and TCR motion for cells interacting with the SLBs revealed that TCR diffusion was ~2-fold slower compared to CD45 and Lck, and that the mean diffusion coefficients for molecules diffusing inside and outside the contacts were similar (Figure 1H and Figure S2B). Stochastic optical reconstruction microscopy (Figures 1I and S3A, S3B) revealed that CD45 exclusion is not contact-size dependent, as CD45 was excluded from all contacts including those with sizes smaller than the diffraction limit (~80 nm). Because these contacts were formed within seconds of T-cell/surface interaction, this suggests that CD45 segregation occurs simultaneously with close contact formation. CD45 segregation also occurred independently of active cell processes as Jurkat-CD48TM T-cells treated with sodium azide formed close contacts from which CD45 was excluded (Figure S3C). Furthermore, for Jurkat-CD48TM T-cells interacting with SLBs loaded with equal amounts of fluorescently-labeled CD45RABC and rCD2, CD45 was readily excluded from each contact, further confirming that CD45 segregation occurs passively (Figure S3D and Movie S3). Overall, the Lck/TCR ratio, which was ~2.7 prior to contact (based on 40,000 Lck molecules/cell), increased to 5.4 and 3.3 upon contact with the IgG-coated glass surfaces and SLBs, respectively. In contrast, the CD45/TCR ratio dropped from 13.3 prior to contact to 6.5-6.8 inside the close contacts. These effects would each be expected to favor TCR phosphorylation.
T-cell signaling dynamics following close contact formation
Having characterized the organization of close contacts, we next sought to explore the relationship between their spatiotemporal dynamics and T-cell signaling. To do so, we used interference reflection microscopy (IRM) to identify the areas of the close contact on IgG-coated surfaces, coupled with the simultaneous detection of cytoplasmic Ca2+ reporter (Fluo-4; Figure 2A and Figure S4 and Movie S4). At the time of Ca2+ release, cells formed a median total contact area of 19 μm2 (Figure 2C, upper panel). For cells interacting with SLBs, TIRF was used to simultaneously measure CD45 distribution and Fluo-4 fluorescence intensity (Figure 2B and Movies S5, S6). In this case signaling was detected as cells reached a median contact area of 6 μm2 (Figure 2C, lower panel). The median delays between initial contact and signaling for the IgG-coated glass and SLB were 121 s and 146 s, respectively (Figure 2D). Using the median area reached at the time of signaling, we estimate that ~34 TCRs on IgG coated surfaces and ~86 TCRs on the SLBs were inside each close contact at the time signaling was detected, assuming a cell diameter of 11.5 µm and 15,000 TCR/cell (Figure S5B). Ligand-induced signaling has been shown to require fewer than 10 pMHCs and less than one minute (Irvine et al., 2002; O’Donoghue et al., 2013). Receptor triggering in the absence of ligands seems to rely on more TCRs and relatively large, stable contacts but otherwise readily occurs in our experiments. This implies that ligand-independent triggering must be actively constrained in vivo.
A new theoretical treatment of TCR signaling
Its ability to be triggered ligand-independently seemed at odds with the requirement that the TCR discriminate between ligands of differing quality. We investigated the extent to which these apparently contradictory features of TCR signaling could be reconciled by a theory of signaling contingent only upon TCR occupancy of close contacts. The model incorporated the following observables and parameters: (1) changes in CD45/Lck ratio, (2) TCR density and diffusion inside regions of close contact, and (3) the size and duration of close contacts. For circular close contacts, the mean dwell-time for a freely-diffusing TCR inside the contacts(τm) is dependent on their radius r and inversely proportional to the diffusion coefficient D of the TCR (Figure 3A):
We assume that receptor triggering (CD3 ITAM phosphorylation) occurs if a single TCR remains inside the close contact for at least 2 seconds (τ=tmin=2s), based on the finding that TCR triggering occurs within two seconds of pMHC binding (Feinerman et al., 2008; Huse et al., 2007; Palmer and Naeher, 2009; Williams et al., 1999) and on our estimation of the effective Lck activity inside close contacts (close to 2.2 pTyr/s; see Hui and Vale, 2014 for the CD45/Lck ratio measured, i.e. 2 to 2.5). Since it is known that single ligands can trigger signaling in T cells (Irvine et al., 2002), and since TCRs will enter close contacts from their edges, a simple model based on mean dwell-time might not capture the actual distribution and contribution of individual receptors to signaling. We therefore developed a formal treatment of the evolution of TCR distribution and dwell-times in close contacts using partial differential equations and an equation describing TCR entrance rate (Weaver, 1983).
Using this model we calculated the dwell-times of individual TCRs and determined the probability p that any given receptor resides within a close contact for a dwell-time τ > 2s, for contacts of various radii r (assuming a radius-dependent rate of entrance of TCRs into the contacts, Movie S7; see Supplementary Information for a full mathematical description; Model 1). The model predicts that the likelihood a TCR remains for longer than 2 s inside a close contact increases sharply with close contact radius (Figure 3B; see Table S3 for all parameter values used) and that p is >0.1 for fixed-size close contacts of the size we observed at the time of signaling when T cells contact IgG-coated glass or SLBs (Figure 2). Given this probability, the overall TCR density (Figure S5B), and the level of TCR exclusion from the contacts (i.e. 60-95%, see Figure 1H), we calculated the number of triggered TCRs to be ~6 and ~16 on IgG-glass and the SLBs, respectively (Figure 3C). However, since close contacts were observed to grow in our experiments, we also calculated the triggering probability for contacts that grow to radius r by incorporating a novel moving-boundary analysis. In this case, TCR triggering probability increases sharply in the absence of ligands when close contacts reach ~0.2 µm radius, in agreement with the findings of Chang et al. (2016; Figure 3D; see Table S3 for all parameter values used). For close contacts persisting for 120 to 180 seconds, the dependence of triggering probability on contact size was very similar (Figure S5A), indicating that for the timescales during which ligand-independent signaling is observed on these surfaces (Figure 2), triggering probability is not affected by contact duration.
It is noteworthy that a simpler treatment of the problem, which assumes a random, uniform distribution of TCRs inside the close contact and uses ordinary differential equations facilitating calculations, also shows that the probability of a TCR being triggered increases with close contact area (Figure S6, see Supplementary Information for a full mathematical description of the model; Model 2). Importantly, for both models TCR dwell-time is the sole parameter underpinning signaling; the models differ only in their assumptions and in their treatment of TCR density and distribution as close contacts grow.
Validation of the model
Since the residence time of a TCR in the close contact depends on the radius of the contact, growth of close contacts on time scales similar to or faster than TCR diffusion would be expected to induce faster receptor triggering (i.e. triggering after a shorter lag; Figure 3E and Figure S5C; see Supplementary Information for further details). Similar predictions are made by Model 2 (see Figure S6C). The triggering time is also directly related to tmin, the minimum time a TCR must remain within the close contact to be phosphorylated. We assumed tmin to be 2 seconds, based on in vitro measurements of Lck kcat at a CD45/Lck ratio of ~2.3:1 (Hui and Vale, 2014), the ratio measured at close contacts. For comparison, if the kcat of Lck were 10-fold lower (e.g. due to a higher CD45/Lck ratio), tmin would increase to 20s, reducing the likelihood of signaling and shifting the curve to longer triggering times (Figure 3E; blue line). Since close contact growth-rates and triggering time are parameters that are experimentally accessible, we could use the relationship between them to test two predictions of the new model: (1) that triggering is delayed for lower levels of CD45 segregation; and (2) that close contact growth-rate and the time taken for a cell to trigger are inversely correlated.
To test the first prediction, we compared the triggering times of Jurkat T-cells and cells expressing a form of CD45 (HA-CD45) lacking its extracellular domain, which is excluded from close contacts less efficiently than wild-type CD45 (Figure S1A). Expression of HA-CD45 at 5% of the total CD45 (i.e. ~10,000 copies/cell; Figure S5E) delayed triggering by almost 20 seconds (p < 0.05, two-tailed t test; Figure 3F). To test the second prediction, we simultaneously measured close contact growth-rates and signaling times. Both for contacts formed on IgG-coated glass and rCD2-SLBs, faster triggering was observed in cells with faster close contact growth-rates in good agreement with the predicted inverse relationship between close contact growth rate and the lag time preceding signaling (Figure 3G and Figure S5D). These observations indicate (1) that TCR triggering is indeed dependent on TCR dwell-time at close contacts, and (2) that the mean residence time, corresponding to a certain close contact area (Eq. 1), must exceed a threshold for triggering to occur (Figure S5D).
Close contact topography underpins signaling outcome
The foregoing analysis shows why receptor triggering is uncoupled from ligand binding if the cell forms stable and/or large enough close contacts depleted of CD45. Questions that arise are: how do T cells prevent ligand-independent TCR triggering in vivo, and what ensures the antigen specificity of responses? Our results indicate that T-cell signaling is sensitive to contact area and contact duration. Springer and co-workers measured T cell/APC contacts diameters of 0.43 ± 0.04 µm using TEM (Sage et al., 2012), and other work shows that T cell/APC contacts are brief, lasting between 1-5 minutes (Deguine et al., 2010; Ritter et al., 2015; Stoll et al., 2002). We therefore used our model to explore the extent to which signaling specificity might depend on close contact area and duration.
In the absence of ligands and for close contacts with a fixed r of 0.22 μm, the model predicted that it would take ~18 hours to achieve a 50% probability that any given TCR is triggered (Figure 4A and Supplementary Information), implying that ligand-independent triggering is highly unlikely for close contacts of the size reported by Sage et al. (2012). Strikingly, however, a 2-fold change in close contact radius yielded a ~1,000-fold increase in the probability of TCR triggering in the absence of in vivo ligands, resulting in 50% signaling likelihood being reached in just 70 s (Figure 4A). These observations suggest that close contact growth needs to be constrained in vivo to prevent unspecific T-cell activation.
To explore the extent to which ligands might further reduce the time required to reach 50% signaling probability via effects on TCR dwell-time at close contacts, we extended the model by incorporating the kon and koff (life-time, 1/ koff) of TCR/pMHC interactions (Supplementary Information). Assuming low levels of agonist pMHC (30 pMHC/μm2) and a contact radius of 0.22 μm, agonist pMHC binding (koff = 1 s; kon = 0.1 μm2s-1) drastically reduced the time taken to reach 50% likelihood of signaling ~12,000-fold, i.e. from 18 hours to 5 seconds (close to tmin; Figure 4B). For pMHC/TCR interactions with koff = 50 s-1 and for pMHC at 300 molecules/μm2, i.e. at the observed lower-affinity threshold for agonistic TCR-pMHC interactions (Huang et al., 2010; Huppa et al., 2010; Krogsgaard et al., 2005; Morris and Allen, 2012), TCR signaling required the formation of stable contacts lasting 2.5 hours (Figure 4B), which is unlikely given the short-lived nature of T-cell/APC interactions (Deguine et al., 2010; Ritter et al., 2015; Stoll et al., 2002). Moreover, as expected, changes to both kon or koff altered the triggering probability profoundly (Figure 4C). Importantly, the model discriminated between known agonists and non-agonists using reported 2D pMHC/TCR interaction kinetics (Figure 4D; Huang et al. 2011). Similar results were obtained with Model 2 (Figure S7).
A final implication of the modeling is that, whereas ligand-independent TCR signaling was markedly dependent on close contact radius, agonist signaling was less so (Figure 4E), which profoundly skews their contributions to signaling as contact size varies. For close contacts smaller than 0.25 μm radius, the model predicts that pMHC agonists are the main drivers of TCR signaling (Figure 4F, violet, orange, red and green traces) whereas, for contacts larger than 0.25 μm radius, signaling readily occurs in the absence of ligand engagement (Figure 4F, Figure S8; blue traces). Therefore, the combination of pMHC/TCR affinity and close-contact size determines the number of triggered TCRs, and the ratio that are triggered ligand-dependently and –independently (Figure 4F, insert). Using the parameters in Supplementary Table S4 and Model 2, it can be calculated that, for a contact of radius 0.8 µm, 27 TCRs sample 20 pMHCs on average, leading to 10 of the TCRs initiating signaling but only three of these being triggered ligand-dependently (Figure S8). Following an episode of specific signaling, therefore, continued growth of the contact could conceivably start to initiate significant levels of ligand-independent TCR triggering, amplifying incipient signaling.
The glycocalyx constrains close contact formation
We previously suggested that the formation of small close-contacts might help to restrict T-cell responses to cognate ligands in vivo (Chang et al., 2016), suggestions now reinforced by our modelling. But what factors might determine close contacts size? All lymphoid cells express very large amounts of highly glycosylated proteins such as CD45 and CD43, forming the glycocalyx, but these proteins are rarely if ever included in model bilayer systems and so their impact on T-cell contact formation is unclear. We studied the interaction of T cells with surfaces containing CD45 to mimic the glycocalyx and CD2 to favor adhesion. In the absence of CD45, large fractions of Jurkat T-cells contacting Ni-NTA-coated, histidine-tagged CD2-presenting glass surfaces released Ca2+ and formed frequent and stable attachments to the surface (Figure 5A). Addition of histidine-tagged CD45RABC at a CD2/CD45RABC ratio of 1:15 reduced the fractions of triggered cells more than three-fold and attached cells more than four-fold (Figure 5A and D). Similarly, incorporation of CD45RABC into SLBs co-presenting physiological levels of CD2 (200-300 molecules/μm2) reduced the numbers of contact-forming cells more than 5-fold (Figure 5B-D; Supplementary Figure 9 and Movie S8) and reduced signaling 40-fold (Figure 5B-D). On the rare occasions close contact formation was observed, the SLB-bound CD45 was excluded from the contacts and around 75% of these cells produced calcium responses (Movie S9), indicating that the presence of CD45 on model surfaces prevents TCR triggering by inhibiting close contact formation in the first place. These observations suggest that the glycocalyx likely comprises a substantial barrier to ligand-independent TCR triggering in vivo.
Discussion
Here, we sought the reasons why TCR signaling can be ligand-specific without the triggering mechanism being strictly ligand-dependent (Chang et al., 2016). We characterized the diffusion of signaling proteins at close contacts on model surfaces lacking TCR ligands, and then developed a theoretical treatment of receptor triggering that reveals how signaling is likely to be influenced by the spatiotemporal properties of contact formation.
TIRF imaging showed that close contacts are dynamic structures with small, multifocal, initially-formed contacts merging into single, larger ones over time. Super-resolution imaging implied that close contacts form spontaneously and passively since CD45 was excluded from contacts as small as ~80 nm. Tracking the TCR, CD45 and Lck revealed that IgG-coated glass surfaces induce the exclusion (>80%) of all proteins with extracellular domains. Intriguingly, two-thirds of Lck molecules were also excluded from close contacts, implying that the “barrier” extends across the cell membrane. Possible explanations for this are that crowding effects operate at the contact boundary, or that a diffusional barrier is created by interactions between CD45 and the cytoskeleton following receptor signaling (Freeman et al., 2016). On SLBs, which more closely mimic the close contacts expected to form in vivo, the overall extent of CD45, Lck and TCR segregation was lower, with CD45 being most affected (also >80% excluded). However, the Lck/CD45 ratio increased only ~2-fold inside the contacts formed on both model surfaces, and for SLBs there were similar small increases in Lck/TCR (3 fold) and TCR/CD45 (6 fold) ratio. Overall, relatively modest changes in TCR/Lck/CD45 equilibrium seem therefore to be capable of initiating signaling in T cells, explaining the dramatic effects of e.g. pharmacological interventions (O’Shea et al., 1992). TCR diffusion was ~2-fold slower compared to CD45 and Lck, but unchanged in close contacts formed on SLBs, indicating that close contact formation will only ever enhance TCR scanning of APCs for antigen. Larger median areas of contact were required for signaling to be initiated on IgG-coated glass than on SLBs (19 μm2 versus 6 μm2), likely reflecting differences in TCR densities (and thus numbers present) in the close contacts (~34 and 86 TCRs, respectively).
Our new theoretical treatment of signaling, which depends only on TCR dwell-time at close contacts, accounts for both ligand discrimination and sensitivity. The model used measurements of (1) changes in CD45/Lck ratio at close contacts; (2) TCR density and diffusion; (3) the size and duration of close contacts; and (4) estimates of Lck activity expected at the CD45 and Lck segregation levels observed (Hui and Vale, 2014). Based on these parameters, we modeled the evolution of TCR density (and therefore dwell-time) in close contacts, using either moving-boundary passage time calculations accounting for the effect of contact growth and initial TCR position on the probability of TCR escape from the close contact, or a second approach that simply assumes an even distribution of TCRs across the contact and thus greatly facilitates calculations. Both approaches gave similar results, suggesting that the predictions of the model are robust with respect to the exact treatment of TCR distribution and flux. We validated the model by showing that in the absence of TCR ligands signaling was delayed when there was less CD45 segregation and that the rate of close contact growth and triggering time were inversely correlated. The model suggested that the probability of ligand-independent TCR triggering increases sharply for close contacts of radius ~0.2 µm. For close contacts formed on IgG-coated glass and SLBs in our experiments, we estimated that ~30-80 TCRs would be present at the time of signaling and that ~20% of these would be triggered (i.e. spend >2 s in close contacts), despite the absence of ligands. A similar number of TCRs have to be engaged by conventional ligands in order to observe T-cell signaling when CD4+ T-cells interact with APCs in the absence of co-receptor engagement (~30 TCRs; Irvine et al., 2002). Overall, our observations suggest that TCR triggering could be so simple as to depend only on receptor occupancy of close contacts, with mean residence time having only to exceed a threshold for triggering to occur. Based on this, we propose that pMHC specific responses are governed by the thermodynamics of TCR/pMHC interactions (Boniface et al., 1999; Willcox et al., 1999; Wu et al., 2002) along with TCR diffusion rate, CD45 exclusion efficiency and T-cell topography, as all of these components influence mean residence time.
We used the model to ask how T cells avoid ligand-independent TCR triggering in vivo, and how the TCR discriminates between different-quality ligands. In the absence of ligands and for close contacts of the size observed in vivo, i.e. r=0.22 μm, our model suggests that it would take several days to trigger just one TCR, implying that ligand-independent triggering, although readily observable in vitro, is unlikely to generate unwanted signaling in vivo. A very surprising outcome was the remarkable sensitivity of ligand-independent signaling to close contact area, however: an increase in contact radius of only 2-fold produced a three orders-of-magnitude increase in the probability of signaling, making it likely to occur within 70s. The size of close contacts observed in vivo therefore seems to be close to the threshold needed for ligand-independent TCR signaling. The dependence of triggering probability on the radius is sigmoidal, suggesting that signaling could be subject to switch-like behavior. These findings have several interesting implications. First, the size of close contacts committing T-cells to synapse formation might be tightly controlled so that non-specific activation is avoided. Second, for close contacts increasing beyond the threshold favoring ligand-specific responses and following, perhaps, an initial round of receptor triggering, ligand-independent triggering could act to reinforce or amplify signaling by increasing the number of triggered receptors beyond those engaged by ligands. Third, defects in cellular processes constraining close contacts size could predispose to autoimmunity by increasing non-specific (ligand-independent) receptor triggering.
The new model also explains why pMHC ligands so profoundly alter the likelihood of signaling and accounts for ligand discrimination. For TCRs interacting with typical ligands in a 0.22 μm radius close contact, agonist-dependent versus ‐idependent signaling is favored as much as 12,000-fold. On the other hand, ligands modelled at 300 molecules/μm2 and with koff 50 s-1, i.e. weak agonists or potent “self” ligands, take minutes rather than seconds to initiate signaling, allowing robust discrimination. Accordingly, we could distinguish between authentic agonists and non-agonists with known 2D pMHC/TCR interaction kinetics (Huang et al. 2011) using the new model. Previously, kinetic proofreading (KP) schemes have been used to explain ligand discrimination, with koff determining the extent of downstream processing of signaling complexes needed to distinguish between ligands (McKeithan, 1995; Burroughs et al., 2006). Ligand discrimination was proposed to require multiple, reversible intermediate steps, in contrast to “conventional” receptors such as GPCRs triggered in a binary fashion (McKeithan, 1995). The 2 s triggering threshold assumed in our model reflects the rate at which Lck phosphorylates the TCR (Hui and Vale, 2014). Our model therefore suggests that TCR phosphorylation alone allows robust discrimination between ligands. Previously, in stochastic simulations of the KS model, multiple proofreading steps and longer delays were required because kinase activity was assumed to be increased 200-fold inside versus outside close contacts (Burroughs et al. 2006). Our data indicate that relatively modest increases in net kinase activity accompany close contact formation, reducing the likelihood that weakly bound receptors are phosphorylated. If, as our data suggest, triggering depends on TCR dwell time at CD45-depleted close-contacts, discrimination will rely not only on koff but also on kon and ligand concentration. This may explain previous reports that both kon and koff can critically influence signaling outcome (Aleksic et al. 2010; Huang et al. 2010; Huppa et al. 2010). Given the importance of the size of the initial close contact formed, the size and the topography of the structures T-cells could use to probe target cells, i.e. microvilli (Jung et al. 2016) may have had some role in the evolution of a ligand discriminating mechanism.
Finally, our results indicate that any general property of the lymphocyte cell surface that impacts on the formation of close contacts will likely have a large bearing on T-cell responsiveness. A particularly noteworthy example is CD45 itself, which when placed on our model surfaces to mimic the glycocalyx present on professional APCs, profoundly blocked close contact formation and T-cell signaling in the absence of antigen but in the presence of small adhesion molecules. In this way CD45 might act as a major barrier to non-specific activation during T-cell priming in vivo. The challenge now is to understand whether T cells form close contacts while forming authentic cell-cell conjugates, and if so, how barriers to their formation such as the glycocalyx are overcome. In conclusion, our work offers new insights into the molecular basis of the initiation of T-cell responses and provides a new quantitative framework for making predictions that can be tested in future studies of TCR triggering.
Author contributions
R.A.F. and K.A.G. designed and performed experiments, analyzed data and R.A.F, K.A.G, S.J.D and D.K. wrote the manuscript with input from all authors. J.T., A.E.L, O.D. and A.T., designed all mathematical modelling. P.J., S.F.L. and M.P performed TIRF experiments and super-resolution microscopy. V.T.C expressed and purified soluble CD45. A.M.S. performed calcium experiments and IRM. B.C.M designed the IRM setup. C.M. performed single molecule tracking experiments under supervision of K.A.G. S.J.D. and D.K.conceived and supervised the project.
Quantitative modeling of TCR triggering
Both Model 1 and Model 2 seek to mathematically describe TCR behavior in close contact zones (CCZs); corresponding to close contacts described in Chang et al. and this study). Our experiments find that these contacts are initially small and grow over time (see also Figure S1 and Movie S2). Cell-cell contacts are known to be very transient in the absence of signaling. Since we are interested in signal initiation, we assume that CCZs form for finite periods (referred to as the contact duration).
In contrast to other models, the kinetic segregation (KS) model proposes that receptor triggering requires only that the TCR stays accessible to kinases within CCZs, protected from phosphatases that would otherwise terminate signaling, and for TCR phosphorylation to be sufficiently long-lived for downstream effects to be initiated. pMHC ligands, via trapping effects, serve only to increase the residence time of the TCR inside the CCZ (Davis and van der Merwe, 1998; Davis et al. 2006). We therefore assume for our modeling (1) that when a CCZ is formed, TCRs can diffuse in and out of the contact, and (2) that if the TCR binds to ligand within the CCZ, it continues to diffuse within the CCZ but is unable to leave. Any TCR that remains in the CCZ for longer than 2 seconds, irrespective of its binding status, is assumed to be triggered (see also discussion in the results section). The models can be used to calculate how TCR triggering probability is affected by CCZ size, growth and duration, and by ligands presented at different densities and affinities.
Model 1 calculates TCR density across the CCZ based on the rate of TCR entry into the CCZ (for a given CCZ radius, initial TCR density and TCR diffusion coefficient). Therefore, it can also accounts for changes in TCR entrance rate and in the dwell-time of TCRs already present inside the CCZ as the CCZ grows. This approach potentially yields more accurate calculations, but requires moving-boundary coupled partial differential equations that are computationally expensive.
Model 2 assumes a uniform distribution of TCRs inside the close contact at all times and, as the contact grows the numbers of TCRs inside the contacts is updated using the initial, assumed TCR density in the CCZ. This approach is more intuitive and simplifies the calculations since they only require the use of ordinary differential equations. For small contacts, and in the case of slow CCZ growth rates compared to TCR diffusion, as observed experimentally, the assumptions are applicable.
Model 1: Modelling of receptor triggering using moving-boundary coupled partial differential equations to account for close contact growth
See Figures 3 and 4 and Figure S5
a. Model formulation
Since CCZs grow on time-scales similar to the diffusion of the TCR, changes in TCR density in CCZs need to be described by a coupled system of moving-boundary partial differential equations (PDEs),
where, T(r,t;tentry) and C(r,t;tentry) represent free and ligand-complexed TCRs diffusing with DT coefficient and DC, respectively, and with the receptors undergoing reversible binding with first-order rates . Note that where kon is the bimolecular on-rate (in units of μm2/s) and is the ligand concentration (in units of μm-2). The boundary conditions for the disc domain of radius R are adsorbing for T and no flux for, C,
Importantly, the domain area grows linearly in time and therefore,
where g is the growth rate (in units of μm2/s) and t is time. The initial conditions at t=tentry are as follows,
where The additional term R′(t)C, which reflects the rate of growth in the region, is a necessary addition to the usual Neumann condition in order to prevent mass of C leaving the domain. To see this, consider the change in total mass ,
The flux of T-cell receptors in complex (C) through the boundary should be zero which gives rise to the boundary condition. In the case of modeling CCZs of fixed size (Fig. 3B–E), g=0 in equation 1.3.
b. Model output
The output of the model is the probability (Ps) that a single receptor has remained within the CCZ for more than 2 seconds, for contact duration (tf),
The time-dependent rate of TCR entry into the domain (kt(t)) is expected to be proportional to the size of the domain, which increases over time. Using previously derived results (see Equations 11 in Weaver, 1983), we find,
where A=415 μm2 is the cell surface area, Tm=100μm-2 (varied over the simulations; see also Table S3) is the TCR density far away from the CCZ, and DT=0.05μm2/s (varied over the simulations, see also Table S3) is the TCR diffusion coefficient. With these numbers, we find that the rate of TCR entry into the domain (kt) increases from ≈4 s-1 to, ≈18s-1 as the domain radius increases from 0.01 µm to 2 µm.
Given that multiple receptors can enter the CCZ during the contact duration(tf), we need to calculate the probability that at least one TCR has remained within the domain for more than 2 s (Pm, referred to as “triggering probability”). The number of TCRs that have entered the domain in time interval, [titi+Δt]can be estimated as kt(tt)Δt so that Pm is estimated as follows,
In the case where Ps and kt are constants:
For the calculation of the number of TCRs expected to stay for >2 s within the CCZ in the absence of growth (g = 0, Figure 3C), a term is included in the expectation representing the initial number of TCRs in the CCZ at t = 0,
Model 2: Modelling of receptor triggering assuming a uniform distribution of TCRs inside close contacts, using ordinary differential equations
See Figures S6 and S7
This model does not incorporate the effect of CCZ growth on the TCR entrance rate (Kt(t)) into the CCZ, and assumes that the TCR is randomly and uniformly distributed with density Tm across the entire contact. The mean time an unbound TCR resides in the CCZ is given by r2/(8D), where r is the radius of the CCZ and D is the diffusion coefficient (Wofsy et al. 2001). The mean time taken for a TCR to find a pMHC is: 1/(konM) where kon is the 2D on-rate and M is the density of pMHCs (Jansson 2010). Dividing r2/(8D) with 1/konM gives the number of TCR/pMHC engagements before the TCR diffuses out of the CCZ. Multiplying the number of engagements with the lifetime of the TCR-pMHC complex (1/koff) allows calculation of the mean residence time of TCRs in the CCZ
where k is the association constant (kon/koff) for pMHC. Assuming a uniform distribution of TCRs across the contact, for a freely-diffusing TCR the residence time in the CCZ of unbound TCRs assumes an exponential distribution and the probability that an unbound TCR (k=0 in equation 2.1) stays within the CCZ for longer than tmin seconds is
where A is the area of a circular CCZ (A=πr2).
Equation 2.2 predicts the probability that a TCR stays longer than tmin seconds for a CCZ of fixed size. To account for increases in size with time, the area (A) can be substituted by the product of growth rate (g) and time (A=g.t; assuming a uniform distribution of the TCR):
To derive the relationship between time to triggering (ttrigg) and growth rate (g), equation 2.3 can be reformulated as:
While the probability (Ps) that a single unbound TCR stays longer than 2 seconds (tmin) in the CCZ can be calculated using equation 2.2, the probability that a given number k of unbound TCRs are triggered (i.e. stay longer than 2 seconds in the CCZ) can be calculated from the binomial distribution:
where k is number of successes (i.e. triggered TCRs), n is the number of TCRs that have entered within the CCZ and PS is the probability of a success (given by equation 2.2). Therefore, the probability that at least one TCR (k = 1 or greater) stays longer than 2 seconds in the CCZ (i.e. the "Triggering probability", see also Model 1) is
where k is 0 (the number of TCRs that are not triggered), n is the number of TCRs present in the close contact and ps is the probability that any given TCR remains in the CCZ for tmin 2 s. For example, using the predicted physiological size of the CCZ of r =0.22 μ m (Sage et al., 2012), Tm>=100,μm2, D=0.05μm2/s and tf=180s, the triggering probability is just 2*10−4, which suggests that ligand-independent triggering is unlikely in this case.
Equations 2.1–2.6 can be used to predict the residence time and probability that unbound TCRs stay longer than tmin seconds inside the CCZ, giving single-exponential distributions of the residence time in the CCZ. However, allowing TCRs to bind pMHC (k > 0 in eq. 2.1) in the CCZ gives biphasic distributions since two populations exist: (1) a population of unbound TCRs that are freely-diffusing and (2) a population of pMHC-bound TCRs (that cannot diffuse outside the CCZ). We model the time-dependent evolution of these populations using two simple differential equations:
where U and B are the densities of unbound and bound TCRs, respectively. Unbound TCRs can either bind pMHC (MpMHC) at rate kon, or diffuse out of the CCZ at rate 1/τ, where is τ the mean residence time. Bound TCRs dissociate at rate koff. The equations were solved with the initial TCR density of 100 molecules/µm2 (U(0) = 100) and no bound TCRs (B(0) = 0), using MATLAB R2014b with the ode15s solver (MathWorks, Inc.). The probability that a TCR remains longer than tmin seconds inside the CCZ was calculated as the fraction of the area under the curve, for U after all TCRs have diffused out of the CCZ, covering the “right-hand side” of tmin.
Quantification and Statistical analysis
Data were analysed by Graphpad Prism and Origin Lab built-in T-test (unpaired, two tailed), and results were considered significant when p < 0.05. Other statistical parameters including the number of replicates, fold-changes, percentages, SEM, SD, number of cells, number of tracks and statistical significance are reported in the figures, figures legends, supplemental table and supplemental data.
Supplementary Movies (descriptions)
Movie S1
Single-molecule tracking data (CD45, TCR; IgG-coated glass). Representative movies (raw data) showing single-molecule tracking of key signaling molecules (CD45, left, TCR, right; red) at close-contacts visualized by high-density labeling of CD45 (green). Movies are part of the data presented in Figure 1. The movie shows an overlay of the raw data for the CD45 channel (i.e. CD45 labeled with Alexa Fluor 488-tagged Gap 8.3 Fab (green), averaged over 200 frames) with the single-molecule channel (i.e. CD45/TCR labeled with Alexa Fluor 568-tagged Gap 8.3 Fab/HaloTag® TMR, red, raw data). The movie is played back in 0.5 x real-time (14 frames per second); scale bar and time are displayed in the movie.
Movie S2
Close contact growth Representative movie (raw data, 20°C) showing the merging of several individual close contacts (visible from ~1’) into one (from ~2’) over time. The movie is played back 8x faster than real-time; scale bar and time are displayed in the movie.
Movie S3
Single-molecule tracking data (CD45; rCD2-SLB). Representative movie (raw data) showing single-molecule tracking of key signalling molecules (CD45, red) at close contacts visualized by high-density labeling of CD45 (green). Movies are part of the data presented in Figure 1. The movie shows an overlay of the raw data for the CD45 channel (i.e. CD45 labeled with Alexa Fluor 488-tagged Gap 8.3 Fab, green, averaged over 200 frames) with the single-molecule channel (i.e. CD45 labeled with Alexa Fluor 568-tagged Gap 8.3 fab, red). The movie is played back in real-time (29 frames per second, indicated in top left corner); scale bar and time are displayed in the movie.
Movie S4
Ca2+ release as measured by change in Fluo-4 fluorescence in Jurkat T-cells forming contacts depleted of CD45 with glass (close-contacts visualized by interference reflection microscopy, IRM). Representative movie (raw data) showing the formation of close-contacts by a Jurkat T-cell landing on IgG coated glass using IRM (left) and fluorescence microcospy data for the simultaneous measurement Ca2+ release (Fluo-4, 488, right). The movie is played back 2-fold faster than real-time (13 frames per second). Scale bar, 5 μm.
Movie S5
Ca2+ release as measured by change in Fluo-4 fluorescence in Jurkat T-cells forming contacts depleted of CD45 (labeled) with CD2-containing SLBs. Movie collage analogous to Movie S4 for a CD48+ Jurkat T-cell; the movie combines raw data for the CD45 channel (i.e. CD45 labeled with Alexa Fluor 568-tagged Gap 8.3 Fab (red, left) with a movie of the Fluo-4 channel (green, right). The movie is played back 10-fold faster than real-time (5 frames per second). Scale bar, 5 μm.
Movie S6
Ca2+ release as measured by change in Fluo-4 fluorescence in J.RT3-T3.5 T-cells forming contacts depleted of CD45 (labeled) with CD2-containing SLBs. Movie collage analogous to Movie S5 for a J.RT3-T3.5 T-cell). The movie is played back 10-fold faster than real-time (5 frames per second). Scale bar, 5 μm.
Movie S7
Animation of the changes in the TCR probability density across a growing close contact over time corresponding to the modelling shown in Figure 3E with g = 0.1 µm2/s. Probability of occupation is plotted on the z-axis, the ‘time’ given in the title is the time post initial contact and the ‘remaining mass’ refers to the probability that the TCR is still found within the close contact.
Movie S8
CD45-RABC largely prevents formation of CD2-mediated close-contacts by Jurkat T-cells (CD48+) with CD2‐ and CD45RABC-containing SLBs. Representative movie showing that few CD48+ Jurkat T-cells form stable cell-bilayer contacts (marked by rCD2 accumulation) with rCD2- and CD45RABC-Halo containing SLB (rCD2:CD45RABC-Halo 1:2). The movie shows an xy-scan across an SLB whereby raw data for the CD2 channel (i.e. SLB contains Alexa Fluor 647-tagged CD2, read-out for CCZ formation) are interleaved with bright field images of the same sample showing the location of the T cells. Scale bar, 5 μm.
Movie S9
CD45-RABC spontaneously segregates from CD2-mediated close-contacts formed by Jurkat T-cells (CD48+) with CD2‐ and CD45RABC-containing SLBs. Representative movie showing simultaneous rCD2 accumulation and segregation of CD45RABC-Halo from stable cell-bilayer contacts of CD48+ Jurkat T-cells interacting with a rCD2- and CD45RABC-Halo containing SLB (rCD2:CD45RABC-Halo 4:1). The movie combines raw data for the CD2 channel (i.e. SLB contains Alexa Fluor 488-tagged CD2 (green, left) with a simultaneously-acquired movie of the CD45RABC-Halo channel (TMR, red, right). The movie is played back 10-fold faster than real-time (5 frames per second). Scale bar, 5 μm.
Acknowledgements
This work was funded by The Wellcome Trust, the UK Medical Research Council, the UK Biotechnology and Biological Sciences Research Council and Cancer Research UK. We thank the Wolfson Imaging Centre, University of Oxford, for access to the microscope facility. We would like to thank the Wellcome Trust for the Sir Henry Dale Fellowship of RAF (WT101609MA). We would like to thank the Royal Society for the University Research Fellowship of SFL (UF120277) and acknowledge a GSK Professorship (DK).