CD4 and CD8 binding to MHC molecules primarily acts to enhance Lck delivery

First, we studied whether coreceptors can stabilize TCR–pMHC interactions. For these simulations we assumed a T-cell–antigen-presenting cell (APC) interface of 1 μm²-area containing 300 T-cell receptors, 100 coreceptors, and 100 pMHC complexes (these concentrations are typical for in vitro experiments) (17). The biochemical reactions that could occur upon the appropriate proteins encountering each other were (scheme 1 in Fig. 1) TCR–pMHC binding and unbinding, coreceptor binding to MHC, and coreceptor binding to TCR via Lck (Fig. 1). TCR, coreceptors, and pMHC were allowed to diffuse on the T-cell and APC surface. To determine the apparent dissociation rate of pMHC molecules off the T-cell surface we initialized the simulation with 100 pMHC proteins bound to TCRs. We then simulated the biochemical reactions noted above, using the Stochastic Simulation Compiler (18) that allows the efficient implementation of the Gillespie algorithm (Methods and ref. 19) to study cell signaling processes, including protein motion and stochastic effects (details in SI Methods). Several replicate simulations for each scenario were carried out, and average values of the dissociation rate of pMHC proteins in the presence and absence of coreceptors were obtained.

If a pMHC molecule dissociated from the T-cell surface during the simulation, we removed it, thereby preventing rebinding. This removal mimics experiments where antibodies are used to achieve the same end. The parameters used to simulate situations with and without coreceptors were identical (Table 1), and we studied the effects of varying the dissociation rate of the coreceptor–MHC bond (k_off), keeping the on rate the same. These calculations aimed to explore whether the higher affinity of CD8 for MHC class I proteins, versus CD4-MHC class II interactions, could explain why CD8, but not CD4, is observed to stabilize TCR–pMHC interactions (9–11, 13, 14, 20).

On the basis of the arguments noted above, we expected differences in the half-life of coreceptor–MHC interactions to have a minimal effect on the dissociation rate of pMHC molecules from the T-cell surface. However, our results (Fig. 2A) indicate that this is not necessarily true. For coreceptor–MHC interactions with a k_off value on the order of 20 s⁻¹, the effective half-life of pMHC molecules bound to TCRs on the T-cell surface is enhanced by about a factor of 1.5. However, a fourfold lower coreceptor–MHC affinity (k_off ∼ 80 s⁻¹) results in an effective dissociation rate from the T-cell surface that is indistinguishable from simulation results without the coreceptor. These results recapitulate the experimental observation that CD4, which binds MHC class II proteins with a two- to fourfold lower affinity compared with CD8 binding to MHC class I (5), does not stabilize the TCR–pMHC bond, but CD8 does (9–11, 13, 14). Thus the strikingly different experimental results for CD4 and CD8 (9–11, 13, 14) can be explained on simple kinetic grounds. We also carried out simulations with values of TCR–pMHC dissociation rates that are 10 times faster than that used to obtain the results in Fig. 1 as recent experiments suggest such faster kinetics at the cell–cell interphase (9). The qualitative results are identical for this situation Fig. S1.

However, what was wrong with the argument made earlier, which suggested that the fleeting interactions between MHC proteins and CD4 or CD8 could not stabilize TCR–pMHC bonds? That argument did not account for the fact that a coreceptor-associated Lck also interacts with the TCR through its complex with the CD3 molecules. Thus, a coreceptor's interactions with a TCR–pMHC complex are functionally bivalent, with one arm binding to the MHC and the other to the TCR (cartoon on Right in Fig. 1). If the coreceptor dissociates from the MHC, it is still bound via Lck to the TCR–pMHC complex, thus allowing rapid rebinding to the MHC. A similar effect is in play if Lck dissociates from the TCR. Our results show that such cooperative interactions can cause coreceptor-mediated stabilization of the TCR–pMHC bond only if coreceptor–MHC interactions have a dissociation rate not much larger than 20 s⁻¹ Fig. S2.

Although CD4 does not stabilize TCR–pMHC interactions (9, 13, 14), like CD8, it does enhance T-cell responses (1, 9). This result raises the question of whether CD4 can enhance Lck recruitment to the TCR complex and, more generally, whether CD4 and CD8 enhance T-cell sensitivity to antigen in different ways.

To examine these issues, we carried out computer simulations of the type used to obtain the results in Fig. 2A except that the set of possible biochemical reactions was augmented to include one of the earliest events in TCR signaling, phosphorylation of the TCR immunoreceptor tyrosine-based phosphorylation motifs (ITAMs) by Lck (scheme 2 in figure 1 of ref. 35). Multiple phosphorylation states of the ITAMs on ζ-chains of the TCR were represented by two phosphorylation states—partially and fully phosphorylated TCRs (see, for example, ref. 21). To assess the role of the coreceptor in TCR triggering, we studied two situations: (i) Lck is present as a free membrane-associated molecule and there are no coreceptors, and (ii) Lck is associated with the coreceptor. We carried out computer simulations for these two situations, with all parameters being identical (Table 1), and compared the levels of TCR phosphorylation (readout of signal strength). Varying the off rate of coreceptor–MHC interactions did not affect the qualitative results of these simulations (Fig. S7).

Fig. 2B shows simulation results of signal strength as a function of the off rate characterizing TCR–pMHC interactions. The simulations correctly recapitulate experimental observations in that TCR phosphorylation discriminates between stimulatory and nonstimulatory ligands. The border between stimulating and nonstimulating peptides (∼0.1–1 s⁻¹ in the simulations carried out with coreceptors present, black line in Fig. 2B) is dependent on the on rate of the TCR–pMHC interaction. The simulations correspond to this rate being 10⁴ M⁻¹·s⁻¹, as is experimentally measured for typically good agonists. But for higher values of the on rate, pMHC ligands that bind TCR with off rates >1 s⁻¹ are stimulatory.

Importantly, coreceptors clearly enhance TCR phosphorylation. As shown in Fig. 2B, if a threshold amount of TCR phosphorylation is required for downstream digital signaling modules (22–24) to be activated (resulting in T-cell responses), peptides that bind to TCR with off rates in the range of 0.04–0.2 s⁻¹ are stimulatory only when the coreceptor is present, but barely stimulate TCR phosphorylation without the coreceptor. pMHC ligands that bind TCR with longer half-lives are stimulatory even without the coreceptor. This result is consistent with reports of coreceptor-dependent and independent ligands in both CD4 and CD8 systems (2, 12, 25). Dose–response curves obtained from the simulations further support this point (Fig. S8).

We used the computational models to parse the relative contributions of TCR–pMHC stabilization and Lck recruitment to coreceptor-mediated signal enhancement in a way that is difficult to accomplish experimentally. We carried out computer simulations where the only effect of coreceptors was to enhance Lck recruitment. This procedure was achieved by simulating systems where ITAM phosphorylation was allowed only if TCR and pMHC were directly bonded and not if they were a part of the TCR–pMHC–coreceptor complex. These simulations showed results (Fig. 2C) similar to those in Fig. 2B. We also carried out computer simulations where the only effect of the coreceptor was to enhance the stability of the TCR–pMHC bond by a factor of 1.5 (per results in Fig. 2A for k_off = 20 s⁻¹, corresponding to CD8–MHC interactions). This effect was realized by simulating situations without the coreceptor (no enhancement of Lck recruitment), but with TCR–pMHC half-lives enhanced to mimic coreceptor-mediated stabilization. The results (blue line, Fig. 2C) show that stabilizing the TCR–pMHC bond makes only a minor contribution to coreceptor-mediated enhancement of TCR signaling. Thus, even for CD8, the main effect of the coreceptor is to enhance Lck recruitment to the TCR complex, and for CD4 it is the only effect. The importance of CD8-mediated Lck recruitment for T-cell activation is also indicated by data showing that CD8⁻ and CD8⁺ T cells are indistinguishable for T-cell activation by allogeneic MHC alleles (20).

An important question emerging from our results is: How can fleeting CD4-MHC interactions, which do not stabilize the TCR–pMHC bond, enhance Lck recruitment? To answer this question, we analyzed the simulation results using the following simple arguments and calculations.

When two membrane proteins that are capable of binding approach within the range of a productive interaction, there are two possible outcomes: The proteins associate and form a complex, or they diffuse away from each other and likely never interact. These outcomes are the consequences of two competing driving forces, attractive interactions pulling them together and random diffusive forces pushing proteins apart from each other. As both processes are stochastic, each possible outcome has a certain probability of occurrence. We calculated the probability for Lck association with the TCR complex for the case when Lck is coreceptor associated and when it is not. Differences in these probabilities and their mechanistic origins shed light on how coreceptors enhance Lck recruitment.

When Lck is not coreceptor associated, nearby TCR and Lck molecules can either bind or diffuse away. The on rate of Lck–TCR association can be estimated in the following way. It has to be large enough for the time required for TCR-Lck association to be shorter than the lifetime of strong agonist pMHC-TCR complexes; otherwise these ligands would not trigger TCR in a coreceptor-independent way (Fig. 2 and refs. 2 and 12). Also, the time required for TCR-Lck association must be longer than the lifetime of endogenous pMHC-TCR bonds to prevent frequent spurious triggering of TCRs bound to endogenous ligands. These considerations imply that . As Lck association to the TCR is a surface reaction and can occur only if Lck and TCR are close to each other (i.e., within the range of interactions), the units of k_on,Lck are the same as that for a first-order reaction rate constant (see detailed description of unit conversion in SI Methods). Measured TCR–pMHC off rates thus suggest . Effects of variations in k_on,Lck are detailed in SI Methods (Fig. S3). The diffusion constant of membrane-associated proteins is typically 0.01 μm²/s (26). Assuming the range of interactions to be of the order 100 Å (0.01 μm) (27), we can compute the rate with which membrane proteins will leave the range of interactions due to diffusion to be . To find the probability of escape versus binding, we compare the rates of motion and binding to obtain

These estimates indicate that the likelihood that free Lck will form a bond with the TCR/CD3 is small and, as shown below, is much smaller than the corresponding likelihood for Lck that is associated with the coreceptor.

Now consider the situation when Lck is associated with the coreceptor. Once the coreceptor is in the vicinity of a TCR–pMHC complex, it can either diffuse away or bind to the MHC. Experimental measurements (5) estimate the on rate for coreceptor–MHC interactions to be very large: k_{on,MHC-CD4(8)} > 10⁵ M⁻¹·s⁻¹. This result leads to the following estimate for the two-dimensional value of this rate parameter (SI Methods): k_{on,MHC-CD4(8)}(2D) = 1,670[(area of interaction)/(molec × s)]. Note that this value is 16 times larger than the rate parameter corresponding to diffusive motion of proteins away from each other (k_motion ∼ 100 s⁻¹). This result suggests that the large on rate for coreceptor–MHC interactions will combat diffusive forces effectively, enabling coreceptor binding to the MHC with a high probability. Also, once this bond between two proteins anchored to apposed membranes is established, diffusion of the coreceptor and the MHC will be severely slowed down compared with a protein on a single membrane. These effects allow the coreceptor to effectively localize Lck to the TCR–pMHC complex and promote its binding.

To estimate the likelihood of successful Lck–TCR association given that the TCR-MHC–coreceptor complex has been formed, we must consider the following possible events: breaking the TCR-MHC bond (k_off ∼ 1 s⁻¹), breaking MHC–coreceptor bond (k_off ∼ 20 s⁻¹), and forming the TCR-Lck bond (k_on ∼ 1 s⁻¹). Following the argument made earlier to compute the probability of binding versus diffusion for free Lck, the probability of Lck binding to the TCR complex is found to be

Eqs. 2 and 3 show that Lck recruitment to the TCR/CD3 complex is 10 times more likely if it is associated with the coreceptor compared with when it is present as free Lck.