Proc. Natl. Acad. Sci. USA Vol. 92, pp. 11990-11992, December 1995 Immunology

The law of mass action governs antigen-stimulated cytolytic activity of CD8+ cytotoxic T lymphocytes (receptor-ligand interactions/cell-cell interactions/antigen recognition/peptide-major histocompatibility protein complexes) YURI SYKULEV, RICHARD J. COHEN, AND HERMAN N. EISEN Center for Cancer Research and Department of Biology, Massachusetts Institute of Technology, and Harvard-Massachusetts Institute of Technology Division of Health Sciences and Technology, Cambridge, MA 02139 Contributed by Herman N. Eisen, September 12, 1995

ABSTRACT An analysis of the initial antigen-recognition any effects on epitope binding attributable to the fact that step in the destruction of target cells by CD8+ cytolytic T TCRs are confined to the surface of the CTLs. [TCR] is taken lymphocytes (CTLs) shows that a relationship in the form of to be the same as the effective concentration of total TCRs the law of mass action can be used to describe interactions because ordinarily only a very small fraction of the TCR between antigen-specific receptors on T cells (TCRs) and their molecules on a T cell are engaged by pepMHC complexes in natural ligands on target cells (peptide-major histocompat- any particular T cell-target cell encounter (see below). ibility protein complexes, termed pepMHC complexes), even [TCR-pepMHC] and [pepMHC] refer respectively to the num- though these reactants are confined to their respective cell ber of pepMHC complexes per target cell that are engaged or membranes. For a designated level of lysis and receptor unengaged by TCRs. K ("TCR affinity") is the intrinsic affinities below about 5 x 106 M-1, the product of the required equilibrium association constant for the TCR-pepMHC reac- number of pepMHC complexes per target cell ("epitope tion. (The epitopes or pepMHC complexes referred to, density") and TCR affinity for pepMHC complexes is con- whether total, free, or engaged-by TCRs, are, of course, just stant; therefore, over this range TCR affinities can be pre- those that can be specifically recognized by the TCRs.) By dicted from epitope densities (or vice versa). At higher recep- designating the total epitope density as [pepMHC]o and tor affinities ("affinity ceiling") the epitope density required substituting [pepMHC]o - [TCR-pepMHC] for [pepMHC] for half-maximal lysis reaches a lower limit of less than 10 in Eq. 1, we obtain complexes per target cell. log[pepMHC]O = log[TCR.pepMHC] [2] CD8+ cytolytic T lymphocytes (CTLs) are well adapted to destroy a wide variety of virus-infected cells, tumor cells, 1 K[TCR]) transplanted normal allogenic cells, or even normal syngeneic g1 + KtTCR]- cells involved in autoimmune reactions, providing the CTL recognizes surface antigenic ligands on these target cells. Our If one assumes that [TCR-pepMHC] is fixed for a given level aim here is to outline a quantitative framework for analyzing of cytolysis and for a particular CTL-target cell system and the initial antigen-recognition step in the destruction of target assay conditions, then at a given level of cytolysis Eq. 2 specifies cells by CTLs. This step is commonly assumed to be governed the relationship between total epitope density ([pepMHC]o) by the affinity of the antigen-specific T-cell receptors (TCRs) and TCR affinity (K). for peptide-major histocompatibility protein (pepMHC) com- To test the relationship predicted by Eq. 2, we have plotted plexes, their natural ligands, as though the TCR-pepMHC in Fig. 1 the logarithm of the total epitope density at half- reaction were subject to the law of mass action.. However, this maximal lysis versus the logarithm of the TCR affinity for the law ordinarily deals with reactants that are free to diffuse in various pepMHC complexes listed in Table 1. The values in three-dimensional space, and since TCR and pepMHC are Table 1 for total epitope densities at half-maximal lysis are confined to the cell surface membrane of T cells and target based on cytolytic assays in which the 5tCr-labeled target cells cells, respectively, the question arises as to whether it is feasible (called T2-Ld and T2-Kb cells) have a defect in intracellular and useful to describe their interaction by means of the law of peptide trafficking (5); hence the surface class I MHC proteins mass action. In this paper we show that, indeed, a simple on these cells are largely devoid of peptides (5) unless loaded quantitative analysis based on a relationship in the form of this with peptides from the extracellular medium (for review, see law can successfully account for the dependence of cytolytic ref. 7). The epitope density on these cells in conventional 4-hr activity on TCR affinity for the pepMHC complexes it recog- cytolytic assays can be estimated from the concentration of nizes and the number of these complexes per target cell extracellular peptide, the number of accessible MHC binding ("epitope density"). The analysis also shows that at a given sites per cell, and the equilibrium constant for the peptide's level of cytolytic activity and over a range of TCR affinities, binding to the MHC of interest (6). Epitope density values one may predict the otherwise difficult to measure TCR determined in this way have been confirmed by direct mea- affinity from the epitope density (or vice versa). surement using an isotope-labeled peptide ofvery high specific To analyze the dependence of epitope density on TCR activity (Y.S., M. Joo, I. Y. Vturina, T. J. Tsomides, and affinity, we assume from the law of mass action that H.N.E., unpublished work). Fig. 1 shows a satisfactory fit between the relationship [TCR pepMHC]J=K[TCR][pepMHC]. [1] predicted in Eq. 2 and the experimentally determined values of the total epitope density and the TCR affinity. As predicted [TCR] represents the effective concentration of unengaged by this equation, over a wide range of affinity values (<104 TCRs, taking into account their nominal concentration and Abbreviations: CTL, cytolytic T lymphocyte; MHC, proteins encoded The publication costs of this article were defrayed in part by page charge by genes in the major histocompatibility complex; pepMHC com- payment. This article must therefore be hereby marked "advertisement" in plexes, complexes formed by peptides and MHC proteins; TCR, accordance with 18 U.S.C. §1734 solely to indicate this fact. antigen-specific T-cell receptor. 11990 Downloaded by guest on September 30, 2021 Immunology: Sykulev et al. Proc. Natl. Acad. Sci. USA 92 (1995) 11991 That the product of epitope density and affinity at a given level of cytolytic activity is constant, as expected from the law of mass action, is of special interest in light of analyses by Bell et al. (9). Studying cell-cell adhesion, they proposed that the U) unqualified use of this law to analyze interactions between cell -oQ U1) surface molecules involved in adhesion is inappropriate, be- 0 cause diffusion of the interacting molecules is limited to their 0L respective cell membranes. Since they regard interactions U) between cell surface adhesion molecules as essentially the 0 same as interactions between receptors on one cell with their 03) 0 ligands on another cell, their view suggests that the TCR- -J pepMHC reactions involved in T cell-target cell encounters are also not subject to description by this law. However, Spits et al. (10) have shown that adhesion of T cells to other cells is 1 0 initially due to antigen-nonspecific interactions, and that it is Log K only after T cell-target cell conjugates are formed that the TCR and their pepMHC ligands, brought into the same FIG. 1. Dependence of the logarithm (base ten) of total epitope reaction volume, are free to interact. These circumstances and density per target cell on the logarithm (base ten) of intrinsic affinity of TCR-pepMHC reactions. Experimentally determined values for our results indicate that despite the complexities involved in total epitope densities and TCR affinities shown in Table 1 were fitted cell-cell interactions the overall extent of ligation of a T cell's to Eq. 2 by a simplex method. The best fit, shown by the solid curve, TCRs by pepMHC complexes on target cells can be described corresponds to a TCR concentration of 10-7M and an epitope density by a relationship in the form of the law of mass action, even limit of about 10 pepMHC complexes per target cell. Curves that also though the reactants are confined to the membranes of fit the same experimental values satisfactorily, but were selected for different cells. limiting total epitope density values of 3 or 1 complex per target cell, Whatever the precise details may be, the validity of our are represented by the dashed lines. For 8 of the 10 data points (a-f, hypothesis can be tested by its predictive ability: Given a new k, and 1) the target cells were T2-Ld, the CTLs were from the 2C clone, peptide whose required epitope density for half-maximal lysis and the peptides had overlapping sequences from murine a-ketoglut- arate dehydrogenase (1). Two data points (g and h) are based on the has been determined, can the model predict the TCR affinity use of T2-Kb target cells, and one point (g) is from assays that used a for that peptide in association with the appropriate class I MHC different T-cell clone (4G3) and a peptide from ovalbumin (pOV8). protein? An opportunity to answer the question is emerging from The solid squares (k and 1) are based on unpublished results, added a study of peptides whose sequences differ by single residues after completion of this study, with two other peptides, T2-Ld target from peptides p2Ca (LSPFPFDL) and QL9 (QLSPFPFDL). cells, and 2C CTLs. Preliminary results show that such predictions are possible; e.g., for one variant the epitope density required for half- M-1 to - 5 x 106 M-1) the logarithm of total epitope density maximal lysis by 2C CTLs was 50-100 times higher then for the is a linear function of the logarithm of TCR affinity with a QL9-Ld complex on the same target cell (see Table 1), and the slope of -1. At high levels of TCR affinity Eq. 2 predicts that 2C TCR affinity for this peptide in association with Ld appears the total epitope density will plateau at a minimum value which to be 50-100 times lower than for QL9-Ld (unpublished data). corresponds to the minimum number of ligated pepMHC Inspection of Fig. 1 shows that the model's ability to predict complexes per target cell required to achieve the designated TCR affinity is limited to a range of affinity values below about level of lysis. The data do not permit us to assign a unique value 106 M-1; at higher values, epitope density is insensitive to to this minimum by fitting Eq. 2. However, visual inspection of variations in TCR affinity. These limitations aside, the general Fig. 1 shows that the minimum cannot exceed 10 complexes per usefulness of the present model for predicting TCR affinities target cell, and since a plateau level of < 1 is probably or epitope densities or the outcome of T cell-target cell unreasonable, we conclude that the minimum density required encounters should become clear when it is tested with diverse for half-maximal lysis is between 1 and 10 pepMHC complexes T-cell clones and a wide variety of pepMHC ligands. per target cell. Using different approaches, Brower et al. (8) Although the present analysis considers TCR affinity to be and Kageyama et al. (6) have suggested values in this range. the critical determinant of CTL responses, it is possible that Whatever the precise lower limit for the total epitope under some circumstances off-rates for TCR-pepMHC bonds density may be, it is important to note that it is approached as might determine whether or not a response can occur if, say, the TCR affinity approaches an upper limit (the "affinity the lifetimes of these bonds were less than or equal to the ceiling"). According to the model (Eq. 2), this limit is equal to residence time required to trigger that response. A correlation the reciprocal of the effective TCR concentration. In the between dissociation rates and T-cell responsiveness was re- Davis and colleagues based on their finding that absence of data at sufficiently high affinities we cannot deter- ported by (11) mine the value for this effective which is the TCR of a CD4+ T-cell hybridoma had approximately the concentration, same low affinity (_104 M-1) for three closely related peptides probably determined by a multiplicity of factors including the in association with a class II MHC protein (I-Ek), but markedly number of TCR molecules per T cell and details of T cell- different concentrations of the peptides had to be added to target cell adhesion. However, the fit of Eq. 2 to the data I-Ek+ presenting cells to elicit equivalent responses (measured indicates that in the assay system represented in Table 1 this as interleukin 2 production). Based on the assumption that concentration is 10 M; it is interesting that the concen- I-Ek had approximately equal affinities for these peptides, they tration of TCR molecules in the "cellular phase" occupied by concluded that the different peptide concentrations required T cells and target cells in the assay microculture is also about may have resulted from the differing rates of TCR dissociation 10-7 M (if we assume a 3:1 ratio of CTLs to target cells, cell from the respective pepMHC complexes (t,12 = 2-12 sec). Even diameters of 10 ,um, and 105 TCRs per CTL; refs. 3 and 4). though the evidence cited (12) does not support this assump- With TCR affinities above the reciprocal of the effective TCR tion (it demonstrates only that affinities of the peptides for I-Ek concentration most of the accessible cognate pepMHC com- all exceed the affinity of a reference peptide), the idea is of plexes on the target cell would be engaged at equilibrium by the interest. It may well be that it is not only the number of T cell's TCRs; affinities above this limit would result in no TCR-pepMHC bonds, as emphasized in our model, but, under significant increase in the number of ligated TCRs. some circumstances, also bond lifetimes that determine T-cell Downloaded by guest on September 30, 2021 11992 Immunology: Sykulev et al. Proc. Natl. Acad. Sci. USA 92 (1995) Table 1. TCR affinities and epitope densities required for half-maximal T-cell cytolytic responses Peptide MHC on Intrinsic affinity target SD50,t Epitope of TCR for Name Sequence cell* nM densityt pepMHC,§ M-1 p2Ca LSPFPFDL Ld 1 25 2 x 106 QL9 QLSPFPFDL 0.005 30 2 x 107 SL9 SPFPFDLLL 25 30,000 1 x 104 p2Ca-A3 LSAFPFDL 10 17,000 2 x 104 p2Ca-A5 LSPFAFDL 200 30,000 2 x 104 p2Ca-A8 LSPFPFDA 250 100 2 x 106 pOV8 SIINFEKL Kb 0.005 20 1 X 106 p2Ca LSPFPFDL 3000 4300 3 x 103 CTL clone 4G3 (2) was used in assays involving the pOV8 peptide; for the other assays the CTL clone was 2C. Assays were carried out for 4 hr at CTL/target cell ratios of 3:1 or 5:1 as described (e.g., see refs. 3 and 4). *T2 cells transfected with murine a-chain genes for Ld and Kb, termed T2-Ld and T2-Kb, were generous gifts from P. Cresswell (5). tExtracellular peptide concentration required for half-maximal lysis of target cells by respective CTLs. The values shown are averages of two or more independent titrations; they vary within a factor of 2-3. tEstimated no. of pepMHC complexes per target cell, calculated from equilibrium constant (Kp) for peptide-MHC reactions (3, 4, 6), total number of peptide binding sites (n) on target cells, and values of SD5o: i.e., Kp [SD5o]n/(1 + Kp[SD50]). Epitope densities were determined after 3-hr incubation of the peptides with the target cells; accuracy is indicated by the error bars in Fig. 1. §The equilibrium constants for TCR-pepMHC reactions were reported previously (3, 4); they were determined at 25°C and in two cases also at 37°C. The effect of temperature was small; hence we assume that in the other cases the binding constants measured at 25°C are similar to those at 37-C. activation. Just how short the bond lifetimes would have to be 1. Udaka, K., Tsomides, T. J., Walden, P., Fukusen, N. & Eisen, to become independent limiting factors in diverse T-cell H. N. (1993) Proc. Natl. Acad. Sci. USA 90, 11272-11276. responses, including cytolytic responses, remains to be seen. 2. Walden, P. R. & Eisen, H. N. (1990) Proc. Natl. Acad. Sci. USA Valitutti et al. (13) recently demonstrated that a 87, 9015-9019. pepMHC 3. Sykulev, Y., Brunmark, A., Jackson, M., Cohen, R. J., Peterson, complex,can serially engage many TCR molecules, estimating P. & Eisen, H. N. (1994) Immunity 1, 15-22. the number engaged by their disappearance from the T-cell 4. Sykulev, Y., Brunmark, A., Tsomides, T. J., Kageyama, S., Jack- surface, and suggested that the T-cell response is determined son, M., Peterson, P. A. & Eisen, H. N. (1994) Proc. Natl. Acad. by this number. Accordingly, they predicted that high TCR- Sci. USA 91, 14487-14491. pepMHC dissociation rates, which are usually found in low- 5. Alexander, J., Payne, J. A., Murrey, J. A., Frelinger, J. A. & affinity reactions, would promote T-cell responses. In contrast, Cresswell, P. (1989) Immunogenetics 29, 380-388. we find that cytolytic activity is enhanced by TCR-pepMHC 6. Kageyama, S., Tsomides, T. J., Sykulev, Y. & Eisen, H. N. (1995) J. Immunol. 154, 567-576. reactions having high affinities, which are generally associated 7. Heemels, M. T. & Ploegh, H. (1995) Annu. Rev. Biochem. 64, with low dissociation rates (for review, see ref. 14). Affinity 463-491. determines the average number of TCR-pepMHC bonds 8. Brower, R. C., England, R., Takeshita, T., Kozlowski, S., Mar- present at any given time under steady-state conditions gulies, D. H., Berzofsky, J. A. & DeLisi, C. (1994) Mol. Immunol. whether the bonds involved represent the repetitive binding of 31, 1285-1293. a limited number of TCR molecules or the serial engagement 9. Bell, G. I., Dembo, M. & Bongrad, P. (1984) Biophys. J. 45, of a larger number. Further investigation is required to deter- 1051-1064. mine whether the levels ofT-cell responses correlate more 10. Spits, H., van Schooten, W., Keizer, H., van Seventer, G., van de closely Rijn, M., Terhorst, C. & de Vries, J.-E. (1986) Science 232, with the number of different TCRs engaged over a period of time 403-405. or the average number of bonds present during that period. 11. Matsui, K., Boniface, J. J., Steffner, P., Reay, P. & Davis, M. M. (1994) Proc. Natl. Acad. Sci. USA 91, 12862-12866. We are grateful to Drs. George Benedek, Lisa Steiner, and Howard 12. Reay, P. A., Kantor, R. M. & Davis, M. M. (1994) J. Immunol. Grey for critical reviews of this paper and useful suggestions. This work 152, 3946-3957. was supported by research grants (CA60686 and A134247), a training 13. Valitutti, S., Muller, S., Cella, M., Padovan, E. & Lanzavecchia, grant (R35-CA42504), and a Cancer Center Core grant (CA14051) A. (1995) Nature (London) 375, 148-151. from the National Institutes of Health and by a National Aeronautics 14. Eisen, H. N., Sykulev, Y. K. & Tsomides, T. J. (1996) Adv. Prot. and Space Administration grant (NAGW-3927). Chem., in press. Downloaded by guest on September 30, 2021