T cells exhibit unexpectedly low discriminatory power and can respond to ultra-low affinity peptide-MHC ligands

T cells use their T cell receptors (TCRs) to discriminate between peptide MHC (pMHC) ligands that bind with different affinities but precisely how different remains controversial. This is partly because the affinities of physiologically relevant interactions are often too weak to measure. Here, we introduce a surface plasmon resonance protocol to measure ultra-low TCR/pMHC affinities (KD ~ 1000 μM). Using naïve, memory, and blasted human CD8+ T cells we find that their discrimination power is unexpectedly low, in that they require a large >100-fold decrease in affinity to abolish responses. Interestingly, the discrimination power reduces further when antigen is presented in isolation on artificial surfaces but can be partially restored by adding ligands to CD2 or LFA-1. We were able to fit the kinetic proof-reading model to our data, yielding the first estimates for both the time delay (2.8 s) and number of biochemical steps (2.67). The fractional number of steps suggest that one of the proof-reading steps is not easily reversible.


Introduction
translational T cell immunology.

Measurements of ultra-low TCR/pMHC affinities at 37°C
The discrimination power of T cells is surprisingly low 88 To quantify the degree of discrimination, we introduced the 1G4 TCR into quiescent naïve or memory CD8 + T 89 cells that were then co-cultured with autologous monocyte-derived dendritic cells (moDCs) pulsed with each 90 peptide ( Figure 2A). Using surface CD69 as a marker for T cell activation, we found that lowering the affinity 91 gradually reduced the response without the sharp affinity threshold predicted by perfect discrimination, and 92 remarkably, responses could be measured to ultra-low affinity peptides, such as NYE 5F (K D ∼1309 µM; see 93 Figure 2B,C). To exclude that this may be a result of preferential loading and/or stability of ultra-low affinity 94 peptides, we pulsed the TAP-deficient T2 cell lines with all peptides and found similar HLA upregulation, 95 suggesting similar peptide presentation ( Figure S1). We quantified the functional potency as the concentration 96 of peptide required to reach 15 % activation (P 15 ), which correlated with K D (Figure 2D,E). 97 We next investigated discrimination in CD8 + T cell blasts Figure 2F, which serve as an in vitro model for effector 98 T cells and are commonly used in adoptive cell therapy. 1G4-expressing T cell blasts also exhibited a graded 99 loss of the response and, as before, activation could be observed to ultra-low affinity peptides ( Figure 2G). 100 To independently corroborate antigen discrimination with a second TCR, we repeated these experiments with Taken together, these results reveal that the discrimination power of the TCR reduces to baseline when recognising 141 antigen in isolation and that the co-signalling receptors CD2 and LFA-1 enhance not only antigen sensitivity but 142 also antigen discrimination.

143
Kinetic proofreading explains the discrimination power with a fast proofreading time delay and 144 a fractional number of steps 145 KP is an operational model proposed to explain the discrimination power of T cells (9). It relies on a sequence 146 of biochemical steps that introduce a time delay (τ KP ) between the initial binding step (step 0) and the final 147 signalling step (step N). In addition, it relies on pMHC unbinding instantly reversing all steps returning the TCR 148 to its basal state ( Figure 4A). Despite being introduced more than 20 years ago and underlying all models of T cell 149 activation (46), there are no estimates of either the number of steps or the time delay for T cells discriminating 150 antigens on APCs. These parameters not only provide molecular insights but also determine whether the KP 151 mechanism is sufficient to explain discrimination (16,19,23,26). 152 In order to estimate these parameters, we directly fitted the KP model to either all the APC data or all the plate 153 data separately. The KP model parameters included the number of steps (N ) and the rate of each step (k p ), 154 which together determine the proofreading time delay (τ KP = N /k p ), and can be visualised on the potency 155 plots ( Figure 4B). The KP model produced an excellent fit to each data set (e.g. Figure 4B, Figure S6A, B) and, 156 importantly, the fit method we implemented showed that N and k p can be uniquely determined ( Figure S6C-H).
We found that the fitted k p values were similar within the APC experiments but generally slower than the plate experiments ( Figure 4D), and because a similar number of steps were observed in both, this observation translated to the time delay which was longer on the APCs ( Figure 4E). Therefore, the higher discrimination 176 power observed on APCs compared to the plate ( Figure 3F) is a result of a longer time delay (9, 16) produced 177 not by more steps but rather a slower rate of each step. This makes conceptual sense because the number of 178 steps is constrained by the signalling architecture whereas the rate of each step can be regulated. We found that 179 all APC data produced similar KP parameters, and therefore combined these values to provide an average time 180 delay of τ KP = 2.8 s using N = 2.67 ( Figure 4F). 181 We next sought to determine whether these KP parameters, which we have shown can explain the discrimination 182 power, can also explain antigen sensitivity. To do this, we used a previously described measure of sensitivity 183 ([k p /(k p + k off )] N ) (16), which is the fraction of times that pMHC binding reaches the final signalling state. 184 Using k off = 0.33 s -1 (1G4 binding to 9V (31)) and the averaged KP parameters above, we find that 45 % of 185 pMHC binding events will reach the final productive signalling state consistent with high sensitivity.

187
Using a new SPR protocol, we accurately measured ultra-low TCR/pMHC affinities finding T cell responses 188 to these antigens at ultra-high concentrations. This enabled us to measure the discriminatory power of TCR 189 recognition with unprecedented accuracy. Quantifying the discrimination power produces values of 1.9-2.1 190 using APCs. In a separate analysis of the published literature, we found similar discrimination powers for other 191 human and mouse TCRs (2.0 with 95% CI of 1.5-2.4) that were significantly lower than those for the original 192 murine TCR data (∼9.0) (34). The discrimination power we report is significantly higher than the baseline 193 predicted by a receptor occupancy model (1.0) and can readily be explained by a KP mechanism.

194
The discrepancy between previous work (4-8, 19, 25, 27) and other human and mouse TCRs (34), including the 195 present work, is likely a result of inaccurate SPR affinity measurements. In addition to temperature and protein 196 aggregation (see Introduction), we have found that extrapolating the K D from non-saturating binding curves 197 reduces precision and underestimates the K D . Given that fitting programs report extrapolated K D values without 198 warnings, it is important that caution is used when interpreting these. By constraining B max using a standard 199 curve based on the W6/32 antibody binding, we avoided this, enabling us to provide accurate K D values into the 200 ultra-low 1000 µM regime. This method may be useful to measure TCR binding to low-affinity self pMHCs. 201 We have found that the KP mechanism can simultaneously explain both high sensitivity and the discrimination 202 power of T cells. This is achieved by a few fractional steps (2.67) and a short proofreading time delay (2.8 s).

203
This time delay is at the lower end of the range reported using soluble tetramers (8 s with 95 % CI: 3-19 s) 204 (48) and consistent with the 4 s time delay between pMHC binding and LAT phosphorylation (49). The small 205 number of steps is reasonable because, although the TCR undergoes a large number of biochemical modifications 206 (2, 3), only steps that must be sequential contribute. It follows that individual ITAMs acting in parallel cannot 207 extend the proofreading chain. This is consistent with the fact that the number of steps we report for the TCR 208 (10 ITAMs) is the same as the number reported for a CAR (6 ITAMs) (47). Moreover, the fact that this number 209 is fractional suggests that one (or more) step(s) is not easily reversible. This step may be ZAP70 recruitment, 210 which has a lifetime at the membrane that is longer than the TCR/pMHC lifetime (50-52) and therefore, it may 211 sustain intermediate signalling for a period of time. This ability is consistent with reports suggesting that the 212 TCR can integrate signals across multiple rebinding events (21, 25, 31, 32).

213
The KP mechanism couples discrimination and sensitivity so that increases in sensitivity lead to decreases in 214 discrimination (16). Unexpectedly, we found similar discrimination powers yet large differences in sensitivity between readouts (CD69 vs. IL-2). This suggests that the coupling between discrimination and sensitivity may 217 be lower than previously thought. Consistent with this, we found that ligation of CD2 or LFA-1 dramatically 218 increased sensitivity and increased the discrimination power. These observations can be reconciled with the 219 KP mechanism if sensitivity is not limited by the proofreading time delay but rather by downstream signalling 220 modules that set the effective threshold on the number of productive TCR signals required to activate T cells.

221
Put differently, T cells may operate in a discrimination regime that produces TCR signals even with low affinity 222 ligands but the decision to respond is made further downstream, and can be regulated both by the T cell state and 223 by engagement of co-signalling receptors.

224
The level of antigen discrimination we report in this study and in an analysis of the literature (34) can be 225 explained by the standard KP model. A number of studies, including work from our lab, have reported additional 226 mechanisms beyond the standard KP model to explain the higher level of discrimination originally reported 227 (17-32). Given that these mechanisms augment the standard proofreading model, they can all explain the lower 228 level of discrimination that we report. Future work is needed to dissect the precise contribution of each molecular 229 mechanism to the overall discrimination power of T cells.

230
The broad range of mechanisms that can produce high discrimination powers (17-32) suggests the observed 231 low discrimination power may be a feature rather than a design flaw of T cells. A possible feature is the 232 ability to perform expression-level discrimination of self pMHCs so that T cells can recognise and appropriately 233 respond to cells over-expressing self antigens. Recently, a compelling theory proposed that expression-level 234 discrimination is required to maintain homeostasis of endocrine tissues by killing hyper-secreting mutants (53).

235
The flip-side of a lower discrimination power is the critical requirement for additional regulatory mechanisms to 236 maintain tolerance, such as the established mechanisms of co-signalling receptors and T regs (54). The finding 237 that co-signalling receptors can control not only sensitivity but also discrimination, suggests new avenues to 238 optimise T cell discrimination for therapeutic purposes.

Materials and Methods
Protein production 241 Class I pMHCs were refolded as previously described (55). Human HLA-A*0201 heavy chain (UniProt residues 242 25-298) with a C-terminal AviTag/BirA recognition sequence and human beta-2 microgolublin were expressed 243 in Escherichia coli and isolated from inclusion bodies. Trimer was refolded by consecutively adding peptide, 244 β2M and heavy chain into refolding buffer and incubating for 2-3 days at 4°C. Protein was filtered, concentrated    Biolegend) was injected for 10 min. Maximal W6/32 binding was used to generate the empirical standard curve 280 and to infer the B max of TCRs from the standard curve. The empirical standard curve only contained data where 281 the ratio of the highest concentration of TCR to the fitted K D value (obtained using the standard method with B max fitted) was 2.5 or more. This threshold ensured that the binding response curves saturated so that only 283 accurate measurements of B max were included. All interactions were fit using both the fitted and constrained 284 B max method ( Figure 1E). For constrained K D s above 20 µM we reported the constrained K D , otherwise we use 285 the B max fitted K D .

286
Co-culture of naïve & memory T cells 287 The assay was performed as previously described (58). Naïve and memory T cells were isolated from anonymized    Peptides and loading 356 We used peptide ligands that were either described previously (31, 59-64) or designed by us based on the 357 published crystal structures of these TCRs in complex with MHC (1G4: PDB 2BNQ, A6: PDB 1AO7).

358
Peptides were synthesised at a purity of >95 % (Peptide Protein Research, UK). Tax WT is a 9 amino acid, class 359 I peptide derived from HTLV-1 Tax 11-19 (39, 65). NYE 9V refers to a heteroclitic (improved stability on MHC), 360 9 amino acid, class I peptide derived from the wild type NYE-ESO 157-165 9C peptide (38). See Table S1 and   361   Table S2 for a list of peptides.     Quantitative analysis of antigen discrimination was performed by first fitting dose-response data with a 4-387 parameter sigmoidal model on a linear scale in Python v3.7 and lmfit v0.9.13 using Levenberg-Marquardt: where x refers to the peptide concentration used to pulse the target cells (in µM) or the amount of pMHC used to coat the well of a plate (in ng/well). The curve produced by this fit was used to interpolate potency as the 390 concentration of antigen required to induce activation of 15 % for CD69 (P 15 ) and 10 % for IL2 (P 10 ). These 391 percentages were chosen based on noise levels and to include lower affinity antigens in the potency plots. Potency 392 values exceeding doses used for pulsing or coating were excluded from the analysis (i.e. no extrapolated data 393 was included in the analysis).

394
To determine the discrimination power α, we fitted the power law in log-space to our data: where P 15 = log 10 (P 15 ) and K D = log 10 (K D ). All data analysis was performed using GraphPad Prism 8 For KP model fitting, we derived the following equation to relate potency to the model parameters: This fitting procedure required an estimate of k off for each peptide ligand but the fast kinetics of ultra-low affinity 401 ligands meant that we were unable to resolve these using SPR. Instead, we noted that previous work has shown 402 that on-rates exhibit small variations between pMHCs that differ by few amino acids (31, 59). We therefore 403 estimated off-rates for each peptide ligand using the same on-rate (i.e. k off =k on K D ) determined previously for 404 1G4 pMHCs ( Figure S5).       Comparison of the fitted discrimination power (α) and fitted sensitivity (C). Shown is the mean with SEM with each dot representing an individual experiment (n=3-6). In (K), conditions were compared with a 1-way ANOVA and each condition was compared to α=1 (baseline discrimination provided by an occupancy model) with an independent 1-sample Student's t test. In (L), the 1G4 data was compared with a ordinary 1-way ANOVA and all data was compared using a second ordinary 1-way ANOVA with Sidak's multiple comparison for a pairwise test. 10 -4 10 -3 10 -2 10 -  Figure 2K. Plate data was compared using repeated-measure 1-way ANOVA (Geisser-Greenhouse corrected) with Sidak's comparison for indicated pairwise comparisons. CD58 and ICAM1 were compared to U87 coculture data using ordinary 1-way ANOVA. U87 and pMHC alone were compared using a Student's t-test. Each condition was compared to the discrimination power of an occupancy model (α=1) using each an independent 1-sample Student's   Peptide (μM) Normalised gMFI (%)

Supplementary Text
Deriving the expression for potency: the kinetic proofreading model The standard kinetic proofreading model (KP) for T cell receptor activation is as follows. A pMHC ligand L can bind with a T cell receptor R to create a complex C 0 at a rate k on . In order for this complex to initiate an active T cell response it must undergo a series of biochemical modifications. These modifications are modelled by kinetic proofreading steps of which there are a total of N . We denote by C i a complex which is in the i-th KP step. A complex C i becomes a complex C i+1 with a progression rate k p , for 0 ≤ i ≤ N − 1. At any KP step the pMHC ligand can detach from the complex at rate k off . Let L(t), R(t), and C i (t) be the concentration of ligand, receptor and complex in the i-th KP step at time t, respectively. The system of ordinary differential equations that govern the temporal evolution of the concentrations is given by Let the initial number of pMHC ligands and T cell receptors be L 0 and R 0 , respectively. We then define the total number of complexes at time t as C tot (t) = N i=0 C i (t), and note that we have two conservation equations, L 0 = L(t) + C tot (t) and R 0 = R(t) + C tot (t). Solving the steady state equations arising from setting the time derivatives in Eq. (1) to zero, and substituting in the conservation equations we find that where The expression in Eq.
(2) determines the concentration of complex C N , which represents the strength of the activation signal, for a given number of ligands L 0 . To fit this model to the potency data seen in the main text we are interested in calculating the concentration of pMHC ligand required to initiate a T cell response given its binding properties. We first introduce a few convenient rescalings and redefinitions. We define x = L 0 /R 0 to be the potency of ligand concentration relative to the total number of receptors and let λ = C N /R 0 be a threshold parameter that dictates how much C N complex is needed to activate a T cell response relative to the total number of receptors. Thus Eq.
(2) can be rewritten as The experimental measurements of potency do not directly correspond to the potency x in our model as the exact number of ligand and receptor is unknown. Therefore we introduce a constant of proportionality γ into our model, such that x → γx. Similarly, the ratio k off /k on is a measure of ligand affinity and is directly proportional to the experimental K D values, thus we introduce a second constant of proportionality δ such that k off /(R 0 k on ) → δK D , where we absorb the constant R 0 into the new parameter. With these adjustments Equation (4) becomes Upon rearranging Eq. (5) we find that we then square 1 both sides of Eq. (6) and find the following expression for the potency

ABC-SMC parameter estimation
Here we detail the Approximate Bayesian Computation-Sequential Monte Carlos algorithm used to determine the distribution of KP model parameters that fit the experimental data. Our KP model has five parameters, N , k p , λ, γ and δ. We fit the model parameters to the plate and the cell data separately. For both the plate and the cell data we fit N , γ and δ as a global parameter shared amongst all experimental runs. The parameters k p and λ are fitted locally for each run. We fit the potency equation to the experimental data in log space as such the log expression for potency, ρ N, k p ,λ, γ,δ , ρ N, k p ,λ, γ,δ; K D = log 10 λ + N log 10 1 + whereλ = λ/γ andδ = δ/γ. These rescalings ensure that the parameters are orthogonal and thus parameter space can be searched efficiently.
To perform ABC-SMC we first need to choose a prior distribution to initially sample the parameters. We chose uniform distributions that assume no prior knowledge about the system. However other than the parameter N , 1 Squaring both sides will not introduce a false solution so long as λ 1 + k off kp N < 1.

S9
the parameters are uniform in log space. This allows for efficient search through parameter space over many orders of magnitude. The priors for the plate data are as follows log 10 λ ∼ Unif (−4, 1) , (9c) where the priors for the cell data are the same other than forλ where log 10 λ ∼ Unif (−6, −3).
Recall that we fit the parameters N , γ, andδ globally andλ and k p are fitted locally. For the plate data this results in 27 parameters to fit whilst for the cell data there are 37 parameters. Let Θ = N, γ,δ, k p , λ be the vector of parameters to fit such that the i-th entry of the vectors k p and λ correspond to the local parameters for the i-th experiment. Then let K D i be the vector of experimentally measured K D values, and P i be the vector of potency measurements for the i-th experiment. These vectors differ in length and so we denote by d i the number of data points in the i-th experiment. We measure the similarity between the KP model and the experimental results via the following distance function where I denotes the total number of experiments, I = 12 and I = 17 for the plate and cell data, respectively.
To perform a randomised search through the parameter space we employed the following Metropolis-Hastings algorithm. We sample an initial parameter set Θ 0 from the prior distributions detailed above. Let Θ curr denote the current set of parameters which initially is Θ 0 . A candidate set of parameters, Θ cand is found by adding a random perturbation to Θ curr . The perturbation is achieved by adding a uniform random shift to each parameter in Θ curr independently.The range of the uniform random shift is [−0.005, 0.005] multiplied by the width of the prior. For example we perturb the N parameter by adding a random uniform shift in the interval [−0.02, 0.02]. If the parameter falls outside the bounds in the prior distribution it is reflected symmetrically back within the bounds. We then have to decide whether to accept or reject the candidate set of parameters. If D (Θ cand ) < D (Θ curr ) then we accept the parameters as they share a greater similarity with the experimental data and set Θ curr = Θ cand . Otherwise we only accept the candidate parameters with probability exp (− (D (Θ cand ) − D (Θ curr )) /ξ), where ξ is a parameter that controls how likely accepting a set of parameters with a higher distance function is. The value of ξ is reduced as the algorithm gets closer to a set of parameters that minimises the distance function. Initially ξ = 10 but is subsequently reduced to {1, 0.1, 0.01, 0.005, 0.001} when the distance function of the candidate set of parameters first reaches {50, 30, 20, 18, 17.5} for the plate data and {100, 75, 50, 40, 35} for the cell data. The algorithm continues until it reaches a final set of parameters that has a distance less than 11.08 or 39.2 for the plate and cell data, respectively. For both the plate and cell data we performed this algorithm 1000 times to capture the distribution of parameter values that fit the experimental data.

Kinetic proofreading with sustained signalling
The sustained signaling kinetic proofreading model (SSKP) is a generalization of the standard kinetic proofreading model (KP), where one of the proofreading steps is difficult to revert and upon ligand dissociation there is a temporary window where a ligand can rebind to a sustained receptor and bypass some of the initial KP steps. To be precise, let there be N KP steps where the K-th step out of N is sustained. As before C i denotes a complex in the i-th KP step, and L(t) and R(t) denote the concentration of pMHC ligand and TCR, respectively at time t.
In addition, we introduce R * (t) as the concentration of unbound receptor that sustains the K-th modification. A ligand can bind with this receptor at rate k on to form complex C K , rather than C 0 . The system of ordinary differential equations that governs the temporal evolution of the concentrations is given by The initial number of pMHC ligands and TCRs is given by L 0 and R 0 , respectively. As before C tot (t) = N i=0 C i (t) denotes the total concentration of complexes. By setting the time derivatives to zero in the above system of ODEs we calculate the equilibrium concentration of C N to be where β = k off /k p and Firstly, we note that when φ → ∞ Equation (19) becomes (1 + β) −N C tot which is the standard KP model result, as to be expected. If we set φ = 0 we get C N = (1 + β) −(N −K) C tot , this is the result for standard KP with N − K steps. Thus, for φ nonzero and non-infinite we expect to see an effective number of KP steps in-between N and N − K.
Unlike the standard KP model there is no explicit formula for extracting a potency plot, the required ligand for activation as a function of the dissociation rate. Instead, the potency plot in Figure S7B was created by solving C N = λ from Equation (19) numerically to extract L 0 the minimum ligand concentration that guarantees the signaling complex C N reaches a threshold λ.