A window of opportunity for cooperativity in the T Cell Receptor

The T-cell antigen receptor (TCR) is pre-organised in oligomers, known as nanoclusters. Nanoclusters could provide a framework for inter-TCR cooperativity upon peptide antigen-major histocompatibility complex (pMHC) binding. Here we have used soluble pMHC oligomers in search for cooperativity effects along the plasma membrane plane. We find that initial binding events favour subsequent pMHC binding to additional TCRs, during a narrow temporal window. This behaviour can be explained by a 3-state model of TCR transition from Resting to Active, to a final Inhibited state. By disrupting nanoclusters and hampering the Active conformation, we show that TCR cooperativity is consistent with TCR nanoclusters adopting the Active state in a coordinated manner. Preferential binding of pMHC to the Active TCR at the immunological synapse suggests that there is a transient time frame for signal amplification in the TCR, allowing the T cells to keep track of antigen quantity and binding time.

magnitude and the results (for the low values of concentrations used) do not change significantly. This is probably due to the fact that cross-linking is not the main limiting time scale in the problem. Mathematically, this means that . The same argument holds for the off rates. Other approximations deserve more detailed descriptions, so we discuss them in the subsequent subsections.

Summary of parameters
In Supplementary Table 3 we summarize the parameters of the model and the references from which they have been obtained (when derived from the Literature).
where [R] R,A,I are, respectively, the number of receptors in each state. We can estimate those rates from the initial free energy landscape in Supplementary Fig. 2a.
Following the works in receptor allostery in Ref. 6 , a plausible landscape can provide free energy differences among states on the order of 2 kcal/mol. So, let F R , F A and F I the free energies of the resting, active and inhibited states, we assume F A -F R = 2 kcal/mol and F R -F I = δx2 kcal/mol, where we allow to increase δ≥1. In the Supplementary Figure 2b (right panel) we show that the location of the maximum of the active state (corresponding to the experimental maximum of APA 1/1) is robust (meaning, it falls within the observed 5-10 minute range) for δ≥2. Taking into account that the Inactive state is an ensemble of states with more degrees of freedom than the other two, this larger well depth is reasonable.
Going back to Eq.
(2), we can then assume that the initial equilibrium state ratios (prior to the addition of ligand) are given by: Where k B T = 0.543 kcal/mol at T= 0°C . Assuming that the clone with the C80G mutation has almost 0 active states, and using the slopes in Fig. 5b (right panel) up to concentrations of OVAp=200 nM, we can conclude that,

Estimation of the inter-state rates
Following the same estimations for the landscape as in Sec. 1.4, we can reduce the number of free parameters. Thus, the rates q on and q off depend on the relative free energies between the well free energies (F R and F A ) and the free energy peak, F AR between them. Thus, assuming a local equilibrium hypothesis (S.R. De Groot and P. Mazur Non-equilibrium thermodynamics. Courier Corporation, 2013), we have the following relationships: where we have used the same estimations as in Eq. (3). Likewise, This leaves us with only two free parameters, for instance, q on and q off . In order to reproduce the characteristic time of the APA 1/1 maximum we set them to Finally, as we discussed in the main text, we assume that the landscape changes induced by the conformational change that follows cross-linking. In our experiments, these changes seem to be almost independent of temperature and type of ligand,. To quantify this change, we introduce a scaling factor (n) that is, consequently, assumed to be independent of temperature. Mathematically,