Substrate mediated mechanical forces enable optimal kinetic proofreading by T-cell receptors

Mechanical proofreading, kinetic proofreading, catch bond, slip bond, molecular clutch, T-1 6 cell receptor, Lymphocyte function-associated antigen-1, 1 7 *These authors contributed equally to this work. 1 8

(202 words) 1 9 T-cells use molecular reactions with nonequilibrium error correction, i.e., proofreading, to 2 0 discriminate between nearly identical antigens with high specificity and sensitivity. These receptor 2 1 binding events are known to be force sensitive, yet traditional schemes of proofreading focus on 2 2 reaction kinetics alone and do not consider the role of force dependent catch/slip bond behavior or 2 3 interactions with mechanically engaged coreceptors such as adhesion molecules. To address this, we 2 4 propose a minimal framework for proofreading of ligand discrimination by T-cell receptors (TCRs) 2 5 that uses endogenous TCR mechanosensation and substrate-mediated mechanical interactions with 2 6 adhesive proteins (load sharing) to improve recognition fidelity. We leverage the catch bond behavior 2 7 of cognate antigens to delay decision making and amplify TCR signaling while discarding noncognate 2 8 slip bond ligands in the presence of a force. By integrating our model with existing structural and 2 9 molecular data, we show that substrate mechanics regulates the transmission of active cytoskeletal 3 0 forces through a molecular clutch and controls the energization of bound TCRs needed for optimal 3 1 proofreading. Our work demonstrates how mechanical forces and substrate properties can augment 3 2 kinetic proofreading in T-cells, suggesting biomaterial design strategies for immunotherapies that tune 3 3 the mechanical microenvironment of T-cells to achieve high fidelity TCR-ligand discrimination, antigen 3 4 recognition, and activation. 3 5 Main (1965 words) 3 6 The immune system recognizes and discriminates between self and foreign antigens. T-cells 3 7 perform this task by binding T-cell receptors (TCRs) to peptide-loaded major histocompatibility 3 8 complexes (pMHCs) decorated on antigen presenting cell (APC) surfaces. That TCRs can detect rare 3 9 cognate pMHCs in a vast array of noncognate pMHCs with exceptionally high specificity and 4 0 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 2 sensitivity is known to require a mechanism of nonequilibrium error correction1–4. Kinetic proofreading 4 1 models have been suggested to explain this behavior by considering the activation of a TCR signaling 4 2 cascade that expends energy to facilitate a sequence of kinetic delays 1-5. During these delays, the 4 3 progressive phosphorylation of available immunoreceptor tyrosine-based activation motifs (ITAMs) 4 4 within the TCR/CD3-ζζ complex kinetically competes with the dissociation of the TCR-pMHC bond 5,6. 4 5 Consequently, transient interactions between TCRs and noncognate pMHC (n-pMHC) are unlikely to 4 6 trigger T-cell activation, whereas longer-lived interactions between TCRs and cognate pMHC (c-4 7 pMHC) are more likely to support the formation of stable signaling complexes that enable T-cell 4 8 activation (e.g., the LAT signalosome)7,8. 4 9 Complementing this biochemical picture, in recent years it has been suggested that physical 5 0 forces can also support enhanced proofreading by dissipation of mechanical rather than chemical 5 1 energy9–13. In-vitro experiments show that mechanically loaded TCR-pMHC complexes display force-5 2 dependent kinetics that can modulate proofreading 20,21, through catch bond formation (with c-5 3 pMHC)14,15, slip bond formation (with n-pMHC) 16, and T-cell adhesion to APCs (via LFA-1-ICAM-1 5 4 catch bonds) 17,18. Molecular dynamics simulations of TCR-pMHC bond engagement and TCR 5 5 mechanical allostery additionally support these experimental observations 9–11,19. These studies 5 6 largely focus on a fixed applied force, resulting in a constant mechanical energy budget for 5 7 proofreading13,15-17. But cells can adaptively regulate cytoskeletal force generation through feedback 5 8 to tune antigen discrimination, a feature that is often neglected; recent work in B-cells are an 5 9 exception20,21. Furthermore, it remains unclear how active forces are transmitted to TCRs. Direct 6 0 loading by motors is unlikely as TCRs are only weakly coupled to the actin cytoskeleton 22,23, lacking 6 1 direct structural connections24. This suggests that indirect force transmission through the environment 6 2 is necessary for triggering mechanosensitive effects. While recent studies have highlighted how 6 3 substrate properties can influence TCR discrimination efficacy 25,26, an integrated framework for 6 4 proofreading that couples cytoskeletal force generation, molecular kinetics, and substrate mechanics 6 5 remains lacking. 6 6 We address this challenge by developing a minimal model for mechanically regulated 6 7 proofreading that combines the reaction-limited kinetics of TCR-ligand discrimination with a molecular 6 8 clutch description of LFA-1 adhesion to an elastic substrate exposing ICAM-1 ligands, rare c-pMHCs, 6 9 or a large array of n-pMHCs. By incorporating experimentally known structural and molecular 7 0 constraints, our framework captures key features of T-cell/APC contact mechanics during T-cell 7 1 antigen discrimination, and incorporates catch/slip behavior exhibited by TCRs and LFA-1 7 2 coreceptors. Active forces are self-regulated by the molecular clutch and transmitted through the 7 3 substrate, enabling mechanical cooperation between TCR-ligand and LFA-1 adhesion kinetics. 7 4 Numerical simulations of the steady-state behavior show that resistance supplied by the substrate 7 5 stiffness modulates the magnitude of piconewton (pN)-level loads generated by the LFA-1 clutch, and 7 6 supplies TCR-pMHC bonds with mechanical energy during ligand discrimination. While extremely 7 7 floppy or stiff APC surfaces abrogate TCR signal amplification by rare c-pMHCs, soft APC surfaces 7 8 with intermediate stiffness convey physiological pN-loads to TCR-pMHC bonds, allowing optimal 7 9 discrimination. Unlike conventional kinetic proofreading (where the amount of free energy that is 8 0 expended to improve precision is fixed a priori in a speed/energy dissipation tradeoff), ‘mechanical’ 8 1 proofreading depends on the mechanical properties of the T-cell microenvironment, such that energy 8 2 transport to the TCR is dictated by mechanical filtering with LFA-1-generated forces against the APC 8 3 substrate through actomyosin contractility. 8 4 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 3 Additionally, in the context of mechanical proofreading, the physical basis for discriminating 8 5 between cognate and noncognate antigens hinges on the force-dependent kinetics of the TCR. 8 6 Specifically, high-fidelity discrimination requires a maximal bond lifetime at a finite force that is 8 7 characteristic of the catch/slip transition. The ratio of ‘correct’ to ‘incorrect’ signaling TCR-pMHC 8 8 bonds (and by proxy, force-dependent bond lifetimes) yields a proofreading precision that distinctly 8 9 peaks at this finite transition force. A fundamental question naturally arises: what dictates the 9 0 magnitude of this applied force in the immunological synapse? Our model reveals that this optimal 9 1 force is governed not solely by internal actomyosin contractility, but by the interplay between the 9 2 substrate stiffness and the intrinsic rigidity of the T-cell membrane. In the extreme limits of substrate 9 3 compliance—approaching either zero or infinite stiffness—the forces exerted on the TCR are 9 4 generated almost exclusively by membrane mechanics rather than actomyosin motor activity through 9 5 LFA-1. Consequently, a critical boundary condition for successful mechanical proofreading is that the 9 6 force required to reach the catch/slip transition must be smaller than the maximal restoring force 9 7 capable of being generated by the deformed membrane. Our results emphasize the potential 9 8 mechanical determinants of TCR signal amplification, with implications for in vitro T-cell-material 9 9 interface design and future mechanoimmunological investigation of TCR-ligand discrimination, 0 0 antigen recognition, and activation. 0 1 Our mathematical framework for mechanical proofreading couples three basic modules: 0 2 0 3 i) TCR-ligand discrimination of c- or n-pMHCs through ITAM phosphorylation based 0 4 proofreading steps. 0 5 ii) kinetics of an LFA-1-ICAM-1 molecular clutch 12,27. 0 6 iii) T-cell adhesion-surface mechanics 28,29. 0 7 0 8 Reaction-limited, steady-state mechanokinetics of TCR-ligand discrimination with limited signaling (i) 0 9 1 0 We model TCR-ligand binding as a bimolecular reaction with distinct force dependent kinetic 1 1 rates for cognate and noncognate ligands. Consistent with experimental measurements, we 1 2 parametrize the TCR dissociation rate from c-pMHCs (k /g2925/g2916/g2916 /g2913 /gm555 F /g2955 /gm557) using a two-pathway model to capture 1 3 a transition from catch to slip behavior ( eq. 1 )30, but instead use a simple Bell model for the 1 4 dissociation rate from n-pMHCs (k /g2925/g2916/g2916 /g2924 /gm555 F /g2955 /gm557), which only display slip bonding (eq. 2)31: 1 5 1 6 (1) 1 7 k /g2925/g2916/g2916 /g2913 /g4PPPF /g2955 /g4PP7 /g3404k /g2913,/g2913 /g2868 exp /g4P78/g3398 F /g2955 F /g2913,/g2913 /g2868 /g4P79/g3397k /g2929,/g2913 /g2868 exp /g4P78 F /g2955 F /g2929,/g2913 /g2868 /g4P79 (2) 1 8 k /g2925/g2916/g2916 /g2924 /g4PPPF /g2955 /g4PP7/g3404k /g2929,/g2924 /g2868 exp /g4P78 F /g2955 F /g2929,/g2924 /g2868 /g4P79 Here, k /g2913,/g2913 /g2868 and k /g2929,/g2913 /g2868 are the catch/slip rates for TCR-c-pMHC unbinding at zero load, k /g2929,/g2924 /g2868 is the slip rate 1 9 for TCR-n-pMHC unbinding at zero load, and F /g2913 /g2868 F /g2929 /g2868 are the force thresholds for the catch and slip 2 0 bonds, respectively. We choose exponential forms for ease though there is emerging evidence that 2 1 the bond lifetime distributions may be fat-tailed 32,33. The force F /g2955 experienced by a single bound TCR 2 2 to either c or n-pMHC presented from the surface is modeled as a Hookean spring (eq. 3): 2 3 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 4 (3) 2 4 F /g2955 /g3404 κ /g2904 /g3401/g4PPP l/g2904 /g3398l /g2904 /g2868 /g4PP7 in which κ /g2904 ~ 0.6 pN/nm is the TCR-pMHC bond stiffness 34, l /g2904 is the total length of the TCR-pMHC 2 5 bond, and l Τ /g2868 ~ 15 nm is the TCR-pMHC rest length35. 2 6 Assuming mass conservation for the total number of receptors and ligands, we can solve the 2 7 mass action kinetic equations (see Appendix for details) at steady-state to obtain the surface density 2 8 of TCRs bound to either c or n-pMHCs (Π /g2913 or Π /g2924 ) to be (eq. 4 and eq. 5): 2 9 (4) 3 0 Π /g2913 /g3404 1 2 /g4PPPp /g2913 /g3397Τ /g2868 /g3397K /g2888 /g2913 /g4PP7 /g3398 1 2 /g3495 /g4PPPp /g2913 /g3397Τ /g2868 /g3397K /g2888 /g2913 /g4PP7/g2870 /g33984 p /g2913 Τ /g2868 (5) 3 1 Π /g2924 /g3404 1 2 /g4PPPp /g2924 /g3397Τ /g2868 /g3397K /g2888 /g2924 /g4PP7 /g3398 1 2 /g3495 /g4PPPp /g2924 /g3397Τ /g2868 /g3397K /g2888 /g2924 /g4PP7/g2870 /g33984 p /g2924 Τ /g2868 where Τ /g2868 is the T-cell membrane density of available TCRs in the contact area (reacting-limiting), p /g2913 3 2 ( p /g2924 ) are the dosed densities of c-pMHCs (n-pMHCs) presented on the surface, and 3 3 K /g2888 /g2913 /g∑mΔm k /g2925/g2916/g2916 /g2913 /gm555 F /g2955 /gm557 k /g2925/g2924 /g2955⁄ ( K /g2888 /g2924 /g∑mΔm k /g2925/g2916/g2916 /g2924 /gm555 F /g2955 /gm557 k /g2925/g2924 /g2955⁄ ) are the force-dependent dissociation constants of TCR-c-3 4 pMHC (TCR-n-pMHC) bonds. 3 5 Kinetic proofreading is enabled by irreversible phosphorylation of bound TCRs. After θ 3 6 consecutive proofreading steps, the steady-state solution yields the density of activated, stable TCR-3 7 c-pMHC signaling complexes Π /g2968 /g2913 (eq. 6) or aberrant TCR-n-pMHC signaling complexes Π /g2968 /g2924 (eq. 7) to 3 8 be (see Appendix for details), 3 9 (6) 4 0 Π /g2968 /g2913 /g3404 k /g2925/g2916/g2916 /g2913 /g4PPPF /g2955 /g4PP7 k /g2925/g2916/g2916 /g2913 /g4PPPF /g2955 /g4PP7 /g3397/g1284 ·α /g2913 /g2968 Π /g2913 (7) 4 1 Π /g2968 /g2924 /g3404 k /g2925/g2916/g2916 /g2924 /g4PPPF /g2955 /g4PP7 k /g2925/g2916/g2916 /g2924 /g4PPPF /g2955 /g4PP7 /g3397/g1284 ·α /g2924 /g2968 Π /g2924 where /gµ·8m is the limited signaling decay rate for rendering activated signaling complexes as non-4 2 signaling, and the ratios, α /g2913 /g3404 /g2921 /g3174 /g2921 /g3174 /g2878 /g2921 /g3173/g3164/g3164 /g3161 /g4666 /g2890 /g3203 /g4667 and α /g2924 /g3404 /g2921 /g3174 /g2921 /g3174 /g2878 /g2921 /g3173/g3164/g3164 /g3172 /g4666 /g2890 /g3203 /g4667 capture the kinetic competition 4 3 between the sequential tyrosine phosphorylation rate k /g2926 , and the pMHC unbinding rate during each 4 4 proofreading step. 4 5 Precision in TCR signal amplification and proofreading error rate 4 6 To quantify proofreading accuracy, we assume TCR signal amplification (denoted by R ) is 4 7 proportional to the density of activated signaling complexes, namely R /g2913 ~ Π θ c and R /g2924 ~ Π θ n (Eqs. (6) 4 8 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 5 and (7)) for cognate and non-cognate ligands, respectively . The ratio of correct versus aberrant 4 9 signal amplification then provides a measure of proofreading precision λ /g2911 /g∑mΔm R /g2913 R /g2924⁄ (eq. 10): 5 0 (10) 5 1 λ /g2911 /g3404 /g343P α /g2913 α /g2924 /g3440 /g2968 /g343P β /g2913 β /g2924 /g3440 /g3401 p /g2913 /g3397Τ /g2868 /g3397K /g2888 /g2913 /g3398 /g3493 /g4PPPp /g2913 /g3397Τ /g2868 /g3397K /g2888 /g2913 /g4PP7/g2870 /g33984 p /g2913 Τ /g2868 p /g2924 /g3397Τ /g2868 /g3397K /g2888 /g2924 /g3398 /g3493 /g4PPPp /g2924 /g3397Τ /g2868 /g3397K /g2888 /g2924 /g4PP7/g2870 /g33984 p /g2924 Τ /g2868 where β c /g3404 k off c /g4666 F Τ /g4667 k off c /g4666 F Τ /g4667 /g3397/g1284 and β /g2924 /g3404 /g2921 /g3173/g3164/g3164 /g3172 /g4666 /g2890 /g3203 /g4667 /g2921 /g3173/g3164/g3164 /g3172 /g4666 /g2890 /g3203 /g4667 /g2878/g2990 capture the kinetic competition between the limited 5 2 signaling decay rate /gµ·8m , and the pMHC unbinding rates. The inverse of λ /g2911 gives a proofreading error 5 3 rate f /g2868 /g∑mΔm 1/λ /g2911 . 5 4 Molecular clutch dynamics of LFA-1-ICAM-1-mediated surface adhesion (ii) 5 5 Dynamics of active surface adhesion is modeled as a molecular clutch, wherein the reversible 5 6 binding of LFA-1 coreceptors to ICAM-1 is described using first order kinetics (eq. 14): 5 7 (14) 5 8 di/g4PPPt/g4PP7 dt /g3404k /g2925/g2924 /g2919 /g3401/g4PPPi /g2868 /g3398i /g4PPP t /g4PP7 /g4PP7 /g3398k /g2925/g2916/g2916 /g2919 /g4PPPF /g2919 /g4PP7 /g3401 i/g4PPPt/g4PP7 Here, i/gm555t/gm557 is the surface density of bound LFA-1-ICAM-1 complexes, i /g2868 is the surface density of LFA-1 5 9 coreceptors, k /g2925/g2924 /g2919 is the binding rate, and k /g2925/g2916/g2916 /g2919 /gm555F /g2919 /gm557 is the force-dependent unbinding rate. The force 6 0 exerted by a single bound adhesion complex is F /g2919 /g∑mΔmκ /g2919 /g∑mΔµ/gm555 l /g2919 /g∑∑98l /g2919 /g2868 /gm557 , where l /g2919 is the total bond length, κ /g2919 6 1 ~ 0.2 pN/nm the bond stiffness36, and l /g2919 /g2868 ~ 40 nm the rest length35. Catch bond behavior of integrins is 6 2 incorporated in the unbinding rate k /g2925/g2916/g2916 /g2919 /gm555F /g2919 /gm557 , parametrized by a two-pathway model (eq. 15): 6 3 (15) 6 4 k /g2925/g2916/g2916 /g2919 /g4PPPF /g2919 /g4PP7 /g3404k /g2913,/g2919 /g2868 exp /g4P78/g3398 F /g2919 F /g2913,/g2919 /g2868 /g4P79/g3397k /g2929,/g2919 /g2868 exp /g4P78 F /g2919 F /g2929,/g2919 /g2868 /g4P79 that transitions to slip bonding at large loads. The zero load catch and slip rates are k /g2913,/g2919 /g2868 and k /g2929,/g2919 /g2868 , along 6 5 with the corresponding transition forces , F /g2913,/g2919 /g2868 and F /g2929,/g2919 /g2868 . When bound, the LFA-1-ICAM-1 adhesion complex 6 6 engages with the actomyosin cytoskeleton and is stretched by motor activity, but this elastic 6 7 extension yi is relaxed upon unbinding 37. Using a mean-field approach that averages over stochastic 6 8 binding events (see Appendix for derivation), we obtain the dynamics of the average stretch /gµ7∑µy /g2919 /gµ7∑· to be 6 9 (eq. 16): 7 0 (16) 7 1 d /g1731y /g2919 /g1732 dt /g3404v /g2911 /g4PPPF /g2919 /g4PP7/g3398k /g2925/g2924 /g2919 /g3401/g343P i /g2868 i /g4PPPt /g4PP7 /g33981 /g3440 /g1731y /g2919 /g1732 where v /g2911 /gm555 F i /gm557 , the retrograde flow velocity of the actomyosin gel obeys a simple linear force-retrograde 7 2 flow velocity relationship (eq. 17): 7 3 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 6 (17) 7 4 v /g2911 /g4PPPF /g2919 /g4PP7/g3404v /g2868 ·/g4P78 1/g3398 i /g4PPPt /g4PP7 /g3401F /g2919 σ /g2911 /g4P79 with v /g2868 ~ 60 nm/s being the maximal (zero load) retrograde flow velocity, and σ /g2911 ~ 1 kPa being the 7 5 contractile actomyosin stall stress38,39, beyond which actin flows are arrested. 7 6 At steady-state, the kinetics and kinematics of LFA-1-mediated adhesion can be solved to 7 7 obtain (eq. 18 and eq. 19): 7 8 (18) 7 9 i/g3404 i /g2868 1/g3397K /g2888 /g2919 (19) 8 0 /g1731y /g2919 /g1732 /g3404 v /g2868 k /g2925/g2924/g2919 K /g2888 /g2919 · /g343P1/g3398 i·F /g2919 σ /g2911 /g3440 where K /g2888 /g2919 /g∑mΔmk /g2925/g2916/g2916 /g2919 /gm555 F i /gm557 /k /g2925/g2924 /g2919 is the force dependent equilibrium dissociation constant. Eq. 19 encodes 8 1 mechanical feedback in active force generation and can be simply understood by noting that the 8 2 adhesion complex stretches at speed v /g2911 for a bond lifetime ~ 1/ k /g2925/g2916/g2916 /g2919 , yielding an average extension 8 3 l /g2919 = v /g2911 /gm555 F i /gm557/k /g2925/g2916/g2916 /g2919 /gm555 F i /gm557 . To relate this actively generated intracellular stretch (/g1731y /g2919 /g1732) to the total length of the 8 4 adhesion complex (l /g2919 ), we need to specify the kinematics of the substrate, as done below. 8 5 T-cell adhesion-surface mechanics (iii) 8 6 We complete the model by imposing force balance to mechanically couple TCR-antigen 8 7 kinetics (i) with the active dynamics of adhesion (ii). In the absence of direct links to the cytoskeleton, 8 8 bound TCRs can stretch and generate forces only when resisted by the T-cell membrane. Previous 8 9 models of synaptic patterning 23,40,41 have shown how differential molecular size (or receptor and 9 0 adhesive proteins) coupled to membrane elasticity can generate spatially segregated TCR clusters. 9 1 Here, we neglect this spatial patterning dynamics and instead focus on an effective description that 9 2 presumes the existence of preformed clusters. Assuming the T-cell and opposing APC are separated 9 3 by an average gap height h /g2868 ~ 50-60 nm due to large glycosylated proteins (e.g., CD45 ectodomain42), 9 4 we consider TCR-antigen bonds to deform the membrane locally (displacement δh ) on the scale of a 9 5 TCR microcluster43–45, R ~ 50 nm 46. On the other hand, elastic deformations of the APC surface (u) 9 6 balance the shared load exerted by both receptor and adhesion molecules, extended across the 9 7 contact area, A /g2913 ~ 3 x 10 4 nm2, of say a microvillus 47. Altogether, force balance at the T-cell 9 8 membrane and the APC surface then yields (eq. 20 and eq. 21): 9 9 (20) 0 0 0 1 A /g2913 /g3401/g4PPPF /g2904 Π /g2904 /g3397F /g2919 i /g4PP7 /g3398σ /g2885/g2900/g2887 u/g34040 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 7 (21) 0 2 F /g2904 Π /g2904 /g3398 γ/g3401δ h R /g2870 /g3404 0 where σ /g2885/g2900/g2887 is the APC surface stiffness and γ ~ 0.03 pN/nm is the T-cell membrane tension. The total 0 3 bond lengths that enable force generation on TCR-pMHC ( l /g2904 ) and LFA-1-ICAM-1 ( l /g2919 ) complexes are 0 4 related to the displacements of the APC surface ( u/gm557 , T-cell membrane ( δh/gm557 , and the intracellular bond 0 5 stretch of LFA-1-ICAM-1 /gµ7∑µy i /gµ7∑· as follows: 0 6 l /g2919 /g3404h /g2868 /g3397 /g1731y /g2919 /g1732 /g3398u l /g2904 /g3404h /g2868 /g3398 δ h/g3398u These relations encode structural and geometric constraints intrinsic to the T-cell adhesive contact 0 7 and complete our model formulation. 0 8

(2713 words) 0 9 The magnitude of receptor-ligand force modulates reaction rates in the mechanical proofreading 1 0 framework 1 1 As a first step, we ask: how do receptor-ligand forces impact kinetic proofreading? Kinetic 1 2 proofreading models with limited signaling have been shown to be consistent with the majority of 1 3 published experimental data1. We incorporate force dependence within this framework simply via the 1 4 force-sensitive unbinding rates (eq. 1 -2, eq. 15), see Fig. 1a-1d . For simplicity, here we directly 1 5 specify the force on each bond and neglect substrate mediated mechanical couplings. In Fig. 1e, we 1 6 plot the force-sensitive bond lifetimes ( 1k /g2925/g2916/g2916 /gm555F/gm557⁄ ) and dissociation constants ( K /g2888 ) against 1 7 physiological pN-level loads for human OT1(†) TCRs binding either c-pMHCs (OVA antigen on H2-Kb 1 8 MHC class I) or n-pMHCs (R4 antigen on H2-Kb MHC class I), and LFA-1 binding ICAM-1 (in the 1 9 presence of Ca 2+, Mg2+, and CXCL12) using parameters extracted from 2-dimensional micropipette 2 0 aspiration experiments ( Appendix Table a1 )30,31. The maximal bond lifetimes for TCR-c-pMHC and 2 1 LFA-1-ICAM-1 center around 8-12pN of load, while TCR-n-pMHC exhibits an exponential decaying 2 2 bond lifetime under increasing load14,17. To quantify relative competition in unbinding, we examine the 2 3 ratios of off rates as a function of a common force ( Fig. 1f). Upon increasing the load, TCR-n-pMHC 2 4 off rates dominate over that of TCR-c-pMHC, whereas LFA-1-ICAM-1 off rates always exceeded the 2 5 rates of TCR-antigen unbinding (cognate and noncognate). This is simply understood by noting that 2 6 cognate antigens form catch bonds with longer lifetimes at high load, in contrast to short lived slip 2 7 bonds formed by noncognate antigens. 2 8 Mechanical forces also influence the proportion of bound TCRs that survive TCR-ITAM 2 9 phosphorylation by tyrosine kinases (e.g., ZAP-70 48) during a proofreading step. We find that the 3 0 phosphorylation rate for TCR-c-pMHCs (quantified by α /g2913 ) dominates over the off rate around 8-3 1 10pN, whereas relative phosphatase activity decreases at loads greater than 15pN (Fig. 1g). In 3 2 contrast, the phosphatase activity for TCR-n-pMHCs( α /g2924 ) continually decreases with respect to 3 3 increasing load ( Fig. 1g ). In addition, both TCR-c-pMHCs and TCR-n-pMHCs can form stable 3 4 signaling complexes post-proofreading that can be rendered non-signaling and dissociated due to a 3 5 signal decay rate /gµ·8m (Fig. 1b ). We quantify this kinetic competition using β /g2913 and β /g2924 and plot their 3 6 dependence on the force in Fig. 1h. For signaling TCR-c-pMHCs under 8-10pN of load, the signal 3 7 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 8 decay rate dominates over the off rate, whereas signaling TCR-n-pMHCs have a larger unbinding 3 8 rate compared to signal decay. 3 9 The magnitude of receptor-ligand force controls TCR-ligand proofreading precision and error 4 0 To assess how proofreading is impacted by forces, we next compute the steady-state densities 4 1 for the cognate and noncognate ligands. ( eq. 6-10). We choose the n-pMHC surface density ( p /g2924 = 4 2 2·104 μ m-2) to be 10-fold higher than the c-pMHC and TCR densities ( p /g2913 , Τ /g2868 = 2·103 μ m-2) to mimic 4 3 discrimination of rare cognate antigen from noncognate antigen decorating APC surfaces ( Appendix 4 4 Table a1 )47. Despite this difference in density, cognate antigens form long-lived catch bonds in 4 5 contrast to short-lived slip bonds formed by noncognate antigens. So we expect an applied force can 4 6 still enhance TCR-ligand discrimination by minimizing the formation of erroneous TCR-n-pMHC 4 7 signaling complexes, while maximizing the formation of ‘correct’ TCR-c-pMHC signaling complexes 4 8 (Fig. 2a ). Fig. 2b shows the impact of receptor-ligand force on the formation of signaling TCR-c-4 9 pMHC and TCR-n-pMHC complexes ( eq. 6-7) across θ proofreading sequences. Here, θ is set to 10 5 0 as the TCR uniquely contains 10 ITAMs to transduce pMHC binding into downstream signaling 5 1 cascades (Appendix Table a1 )49. Corresponding to the optimal TCR-c-pMHC bond lifetime, we find 5 2 that the maximal formation of stable, signaling TCR-c-pMHC complexes is centered around an 5 3 applied load F ~ 8-10pN ( Fig. 2b). Conversely, force application and proofreading both suppress the 5 4 formation of erroneous TCR-n-pMHC signaling complexes through rapid dissociation (Fig. 2c). 5 5 Combining these results, we plot the precision (eq. 10) and error rate (eq. 13) of TCR signal 5 6 amplification during proofreading as a function of the applied force (Fig. 2d-f). As expected, precision 5 7 is increased with each proofreading sequence with optimal performance achieved at a load F ~ 10 pN 5 8 corresponding to the characteristic force scale at which cognate bonds transition from catch to slip 5 9 behavior. This response is predominantly controlled by the proofreading metrics ( α /g2913 and α /g2924 , eq. 8-9) 6 0 that quantify the kinetic competition between the sequential tyrosine phosphorylation rate k /g2926 , and the 6 1 c or n-pMHC off rate during each proofreading step, as seen in Fig. 2e. Similar trends are also 6 2 observed in the accumulated precision (or error) across all proofreading steps ( Fig. 2f, 2g ), 6 3 consistent with recent results13. 6 4 LFA-1 molecular clutch dynamics modulate the mechanics of LFA-1-ICAM-1 adhesion and TCR-6 5 ligand bond formation 6 6 We now relax the assumption of a constant force and investigate how actively regulated forces 6 7 and substrate mediated mechanical cooperation between LFA-1 and TCR modulate their kinetics. As 6 8 the TCR is not directly coupled to actomyosin, TCR force generation in the model is mediated by the 6 9 LFA-1 molecular clutch through deformations of the T-cell membrane and adherent APC surface ( eq. 7 0 20-21)9,18,50,51. TCRs binding to n-pMHC cause larger deformation and stress in the T-cell membrane, 7 1 compared to c-pMHCs across varying APC surface stiffness ( Appendix Fig. 1a ), despite negligible 7 2 difference in APC surface displacement between cognate and noncognate antigens ( Appendix Fig. 7 3 1b). This suggests that membrane flexibility primarily controls the differential forces experienced by 7 4 TCR-c-pMHC and TCR-n-pMHC bonds. Increasing APC stiffness > 1 pN/nm causes the actomyosin 7 5 retrograde flow to stall ( Appendix Fig. 2a ) as the density of LFA-1-ICAM-1 bonds saturates 7 6 (Appendix Fig. 2b ). Correspondingly, the forces generated by LFA-1, TCRs engaged with c-pMHC 7 7 or n-pMHC, all follow a sigmoidal increase with APC stiffness, with values within their physiologically 7 8 measured ranges ( Appendix Fig. 2a)14,18. In other words, the APC surface mechanically gates the 7 9 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 9 transmitted force, switching on the maximum load on receptor antigen bonds beyond a characteristic 8 0 stiffness ~ 1 pN/nm, when the motor (actomyosin flow) stalls. 8 1 The bond lifetimes and dissociation constants for TCR-c-pMHCs, TCR-n-pMHCs, and LFA-1-8 2 ICAM-1 complexes vary with respect to the APC stiffness through the force they respectively 8 3 experience (Appendix Fig. 2c). LFA-1-ICAM-1 bond lifetimes increases with APC surface stiffness, 8 4 plateauing at ~1.5 seconds, consistent with the stalling of actomyosin observed and the formation of 8 5 LFA-1-ICAM-1 adhesion complexes (Appendix Fig. 2a, 2b). TCR-c-pMHC bond lifetime instead has 8 6 a biphasic dependency on APC surface stiffness, reflecting the transition from catch to slip behavior, 8 7 with the maximal lifetime achieved for a stiffness ~ 1 pN/nm. Conversely, TCR-n-pMHC bond lifetimes 8 8 decay as surface stiffness is increased. As a result, the formation of TCR-c-pMHC bonds is increased 8 9 around an APC surface stiffness of 1 pN/nm, but TCR-n-pMHC slip bonds simply dissociate as APC 9 0 surface stiffness approaches supraphysiological membrane rigidities (e.g., 1000 pN/nm) ( Appendix 9 1 Fig. 2d). 9 2 How does this response depend on the extent of catch or slip bonding behavior? As an 9 3 example, we consider human OT1(†) TCRs binding c-pMHCs of varying catch bond amplitude (OVA, 9 4 A2, G4, or E1 loaded on H2-Kb MHC class I, Appendix Table a2 ) and compare them against the 9 5 TCR-n-pMHC (OT1(†) TCR binding R4 antigen loaded on H2-Kb MHC class I) slip bond as a function 9 6 of receptor-ligand force and APC surface stiffness 14,52. We compute the change in the Gibbs free 9 7 energy of binding ( ∆G ° , Appendix eq. a19 ) to quantify the thermodynamics of TCR engagement. 9 8 Consistent with our previous analysis of the TCR-pMHC dissociation constant ( K /g2888 , Fig. 1e and 9 9 Appendix Fig. 2c), we find that the largest decrease in free energy (in units of k /g2886 T ) is achieved for 0 0 OT1(†) TCR-OVA-MHC-I catch bonds at intermediate loads (force ~ 8-12 pN, or APC stiffness ~ 1 0 1 pN/nm; see Fig. 3a-d). In contrast, cognate antigens forming weaker catch bonds (e.g., E1, G4) 0 2 minimize their change in Gibbs free in energy at zero load or low APC stiffness ( Fig. 3a, 3c ) and do 0 3 not benefit from mechanical forces in improving TCR engagement. This implies that the 0 4 amplitude/magnitude of the TCR-ligand catch bond, not just its presence, crucially matters in 0 5 determining whether mechanical forces can induce a spontaneous thermodynamic process53 allowing 0 6 TCR signal amplification against a slip-bonding n-pMHC. 0 7 Soft APC surfaces maximize TCR-ligand proofreading precision 0 8 We combine the above results to evaluate the impact of surface mechanics on TCR-ligand 0 9 proofreading precision (Fig. 4a). Figs. 4b, 4c show the density of signaling TCR-c-pMHC and TCR-n-1 0 pMHC complexes across θ = 10 proofreading sequences as a function of APC surface stiffness. We 1 1 find that soft APC surfaces with intermediate stiffness ~ 1 pN/nm allow for the optimal TCR-c-pMHC 1 2 bond lifetime accompanied by the maximal formation of stable, signaling TCR-c-pMHC complexes, 1 3 whereas stiffnesses approaching 0 pN/nm or 1000 pN/nm leads to suboptimal signaling (Fig. 4b ). 1 4 This is additionally reflected in the suppressed formation of erroneous TCR-n-pMHC signaling 1 5 complexes for stiff substrates ( σ /g2885/g2900/g2887 ≥ 1 pN/nm), see Fig. 4c . As a result, we find that TCR 1 6 proofreading precision is optimal for soft APC surfaces across all θ proofreading step (Fig. 4d-e), with 1 7 a concomitant enhancement of the accumulated precision as well ( Fig. 4e ). Very low or high APC 1 8 stiffness (> 1 pN/nm) leads to lower proofreading precision (and thus greater error), suggesting that 1 9 the substrate serves as a mechanical filter that enables optimal performance when force generation 2 0 by the molecular clutch is matched with force transmission through the environment. Finally, to test 2 1 the dosage dependence of our results, we increase the c-pMHC dose to supraphysiological values 2 2 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 10 and find the receptor-ligand force is diminished (due to load sharing), causing the optimal stiffness to 2 3 shift to higher values ( Appendix Fig. 3a, 3b) , consistent with experimental observations 9,54. 2 4 Eventually, for very high c-pMHC doses, the biphasic dependence of precision on stiffness is 2 5 altogether abolished ( Appendix Fig. 3a, 3b). Similarly, decreasing n-pMHC dose enhances 2 6 proofreading precision, transitioning from a monotonic to a biphasic response as well (Appendix Fig. 2 7 3c, 3d). 2 8 TCR signal amplification is modulated by energy transport from the active power generated by LFA-1-2 9 ICAM-1 adhesions 3 0 What are the energetic costs of this mechanism of proofreading? Conventional kinetic 3 1 proofreading biases reactions to amplify discrimination accuracy by dissipating a fixed budget of 3 2 chemical free energy55–57, as captured by the irreversible ITAM phosphorylation steps in our model. 3 3 But here, reactions can also be biased by forces that are actively generated and regulated, leading to 3 4 mechanical energy costs that we focus on. To assess how mechanical energy is partitioned during 3 5 antigen discrimination, we separately evaluate the elastic energy stored in the APC surface ( /g1847/g3002/g3017/g3004 /g34043 6 /g2869 /g2870 /g202P/g3002/g3017/g3004 /g3401/g1873/g2870 ), LFA-1-ICAM-1 adhesions /g1847 /g3036 /g3404 /g2869 /g2870 /g2018/g3036 /g3401/g3435/g18P4/g3036 /g3398/g18P4 /g3036 /g2868 /g3439 /g2870 , and TCR-pMHC bonds ( /g1847 /g3021 /g3404 /g2869 /g2870 /g2018/g3021 /g34013 7 /g4PPP/g18P4/g3021 /g3398/g18P4 /g3021 /g2868 /g4PP7/g2870 ). The nonequilibrium power (P) generated by the actomyosin cortex and dissipated 3 8 through the adhesive dynamics of the molecular clutch is given by: 3 9 (25) 4 0 P/g3404v /g2911 F /g2919 /g3401 1 1/g3397K /g2888 /g2919 4 1 We first examine the elastic potential energy stored in human OT1(†) TCRs binding c-pMHCs 4 2 of varying catch bond amplitude (OVA, A2, G4, or E1 loaded on H2-Kb MHC class I) and compare 4 3 them against the TCR-n-pMHC (OT1(†) TCR binding R4 antigen loaded on H2-Kb MHC class I) slip 4 4 bond as a function APC surface stiffness (in units of k /g2886 T , Fig. 5a, eq. 22-24). In all cases, we observe 4 5 that increasing APC surface stiffness allows a larger amount of elastic energy to be stored in bound 4 6 TCRs, with the relatively weak catch bonds, OT1(†) TCR-E1-MHC-I and OT1(†) TCR-G4-MHC-I, 4 7 storing the most elastic energy. The active power dissipated by LFA-1 also increases with APC 4 8 stiffness, and saturates beyond σ /g2885/g2900/g2887 ≥ 1 pN/nm, for the different TCRs considered. But in contrast to 4 9 a traditional kinetic proofreading mechanism, we obs erve that greater nonequilibrium dissipation and 5 0 energization of bonds actually leads to lower proofreading precision ( Fig. 5b, 5c, eq. 25 ). Strikingly, 5 1 OT1(†) TCRs binding the strong catch bond forming antigen OVA-MHC-I display enhanced 5 2 proofreading precision with a comparable power expenditure for the cognate and non-cognate 5 3 antigen (relative power = P c/Pn ~ 1, Fig. 5c ). In contrast, TCRs engaging with weak catch bond 5 4 forming antigens (A2, G4, or E1) expend more than 3-fold the nonequilibrium power dissipated in the 5 5 non-cognate case (OT1(†) TCRs binding R4 loaded MHC-I), only to have poorer discrimination 5 6 (precision λ /g2911 < 1 ), realizing a mechanical variant of an “anti-proofreading’’ regime58. 5 7 Mechanical filtering with LFA-1-ICAM-1 adhesions determines TCR signal amplification 5 8 How can we understand these results? Unlike conventional proofreading where energy is 5 9 directly provided to the discriminating reaction, here, TCRs can harness nonequilibrium mechanical 6 0 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 11 energy only indirectly, by transmission through substrate adhesion. This suggests the force 6 1 generating motor (actomyosin and LFA-1-ICAM-1), the transmitter (substrate), and force receiver 6 2 (TCR-antigen bond) must all be ‘impedance matched’, to use an electrical analogy, for optimal 6 3 transfer of usable power for signal amplification. Without the optimal coupling, the nonequilibrium 6 4 dissipation is futile and unavailable to aid proofreading. To quantify such impedance matching, we 6 5 directly compare the stored elastic energy in the APC surface, along with the OT1(†) TCR-OVA-MHC-6 6 I (cognate), OT1(†) TCR-R4-MHC-I (noncognate) and LFA-1-ICAM-1 receptor-ligand bonds (Fig. 6a). 6 7 Consistent with the results in Fig. 5, as APC surface stiffness is increased, more elastic energy (in 6 8 units of kBT) is stored in the TCR-ligand and adhesion bonds, with the greatest amount stored in LFA-6 9 1-ICAM-1 complexes, followed by OT1(†) TCR-OVA-MHC-I and OT1(†) TCR-R4-MHC-I complexes. 7 0 But the elastic energy stored in the APC surface varies non-monotonically, reaching a peak near the 7 1 optimal surface stiffness (~1 pN/nm) followed by a rapid decrease at large stiffness values ( > 100 7 2 pN/nm). This is consistent with the view of impedance matching; wherein soft APCs optimally transmit 7 3 the deformation and force needed to improve TCR signal amplification. 7 4 In Fig. 6b, we also plot the active power dissipated by the collection of formed LFA-1-ICAM-1 7 5 complexes (, eq. 25) as a function of APC surface stiffness. We do not observe any significant 7 6 differences in the active power dissipated by bound LFA-1-ICAM complexes when either OT1(†) 7 7 TCR-OVA-MHC-I or OT1(†) TCR-R4-MHC-I bonds are engaged. Illustrating the proofreading 7 8 precision per proofreading sequence as a function of the relative active power (TCR-c-pMHC:TCR-n-7 9 pMHC, Fig. 6b inset ) further supports this, as the maximal precision is achieved around a relative 8 0 power of unity (P c/Pn ~ 1). Altogether, these results suggest that unlike conventional kinetic 8 1 proofreading where a fixed amount of chemical energy is spent to increase precision and speed 8 2 (involving a tradeoff with greater energy dissipation, Fig. 6c ), our mechanokinetic framework 8 3 decouples nonequilibrium dissipation from proofreading precision by employing a soft environment as 8 4 a mechanical bottleneck that regulates the energization of discriminating reactions (Fig. 6d). 8 5 To further elucidate this, we devise a dimensionless scaling parameter Γ ~ P χ/g∑mµ2 to compare the 8 6 energy cost for nonequilibrium power generated by the actomyosin cortex and dissipated through the 8 7 adhesive dynamics of the molecular clutch to the nonequilibrium chemical power dissipation dictated 8 8 by the phosphorylation kinetics of the TCR. Here , the nonequilibrium chemical power dissipation is 8 9 χ/g∑mΔm Δ µ /g2885/g2904/g2900 ·k /g2926 ·/gm555 Π /g2904 T /g2868 /g∑mµ2/gm557 ∑ α /g2968 /gm555 1/g∑∑98α /gm557·m/g2968 /g2923/g2880/g2869 , in which Δµ /g2885/g2904/g2900 ~ 25k /g2886 T is the chemical potential 9 0 associated with ATP hydrolysis and k /g2926 ·/gm555 Π /g2904 T /g2868 /g∑mµ2/gm557 ∑ α /g2968 /gm5551 /g∑∑98 α/gm557 · m/g2968 /g2923/g2880/g2869 is the TCR phosphorylation flux. 9 1 In Appendix Fig. 4a, we plot the average chemical energy necessary for TCR phosphorylation 9 2 ( Δµ /g2885/g2904/g2900 · ∑ α /g2968 /gm5551 /g∑∑98 α/gm557 · m/g2968 /g2923/g2880/g2869 ) as a function of APC surface stiffness. Soft APC surfaces with 9 3 intermediate stiffness ~ 1 pN/nm allow for optimal TCR-c-pMHC phosphorylation whereas stiffnesses 9 4 approaching 0 pN/nm or 1000 pN/nm leads to suboptimal chemical energy expenditures. This is 9 5 additionally reflected in suppressed erroneous TCR-n-pMHC chemical energy expenditure for stiff 9 6 substrates (σ /g2885/g2900/g2887 ≥ 1 pN/nm). 9 7 To evaluate the overall energetic efficiency of mechanical proofreading and impedance 9 8 matching, we plot the dimensionless scaling parameter Γ as a function of normalized APC surface 9 9 stiffness for OT1(†) TCR-OVA-MHC-I or OT1(†) TCR-R4-MHC-I (Appendix Fig. 4b). For noncognate 0 0 OT1(†) TCR-R4-MHC-I slip bonds, the rapid collapse of χ in the denominator causes Γ to 0 1 monotonically diverge as nonequilibrium power P increases with increasing APC surface stiffness. In 0 2 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 12 this state, LFA-1-ICAM-1 catch bonds expend mechanical work but generates little TCR signaling 0 3 output. Strikingly, for cognate OT1(†) TCR-OVA-MHC-I catch bonds, Γ exhibits a wave-like trajectory 0 4 that maps the biophysical lifecycle of TCR-c-pMHC bonds under mechanical load. At low mechanical 0 5 power P (norm. APC surface stiffness ≤ 1), mechanical work done by LFA-1 outpaces TCR signaling 0 6 output, driving a local maximum in Γ . However, as mechanical power reaches the critical TCR-c-0 7 pMHC catch-bond threshold (norm. APC surface stiffness ~ 1; 8-10 pN of applied force), a surge in 0 8 chemical dissipation χ outpaces P , driving a local minimum in Γ , and thus realizing a ‘optimal’ 0 9 mechanical proofreading regime in which the TCR extracts the maximal chemical signaling payout 1 0 per unit of mechanical work invested by LFA-1 (e.g., ‘mechanical’ impedance matching). When 1 1 mechanical power exceeds this optimum (norm. APC surface stiffness ≥ 1), the TCR-c-pMHC catch 1 2 bond ruptures (entering the slip regime), χ minimizes, and Γ diverges upwards. 1 3

(670 words) 1 4 By integrating LFA-1 molecular clutch dynamics with a previously reported kinetic proofreading 1 5 model with limited signaling, we developed a ‘mechanical’ proofreading framework of TCR-ligand 1 6 discrimination, incorporating key features of endogenous TCR mechanosensation and its mechanical 1 7 cooperativity with LFA-1 coreceptors. This minimal framework provides mechanistic support for how 1 8 TCR/LFA-1 mechanical cooperation may directly energize the TCR-pMHC bond and enable force-1 9 sensitive ligand discrimination 10,16,18. The integration of TCR-c-pMHC catch bonds or TCR-n-pMHC 2 0 slip bonds into previously reported kinetic proofreading frameworks confirms that force may enhance 2 1 proofreading precision by maximizing bond lifetime with c-pMHCs such that the probability of ‘correct’ 2 2 TCR phosphorylation by relevant adaptor molecules and subsequent activation of signaling cascades 2 3 downstream of the TCR occurs (Fig. 1a-1e, Fig. 2b-2f)1. Transient TCR-n-pMHC slip bonds are more 2 4 likely to exit the phosphorylation pathway with respect to greater force application, thus minimizing 2 5 proofreading error and erroneous activation. 2 6 These mechanical ‘checkpoints’ may explain how developing thymocytes are selected within 2 7 the thymus through load-sensing through the Pre-TCR and TCR 59–61, and how mature T-cells are 2 8 able to be activated by as rare as a single c-pMHC molecule decorating an APC surface 62. It is 2 9 important to appreciate that though this may hold true for the αβ TCR9,63, emerging evidence suggests 3 0 that the γδ TCR is force-agnostic64,65. 3 1 Energization of the TCR by actomyosin contractility through LFA-1-ICAM-1 adhesions is 3 2 speculated to enhance TCR-ligand discrimination precision and stabilize the TCR-c-pMHC catch 3 3 bond18,66,67. Our framework additionally supports this hypothesis through the prediction of 3 4 physiological pN-level loading regimes on the TCR and LFA-1 in response to the mechanical 3 5 properties of a model APC surface ( Appendix Fig. 2b, Fig. 4b-4e )68–70. However, the role of 3 6 actomyosin-rich T-cell microvilli protrusions 71,72, the molecular crosstalk between TCR microcluster 3 7 nucleation and LFA-1-ICAM-1 adhesions 44,45, the complementary role of other co-effector molecules 3 8 (e.g., CD4/CD8 and CD28)73–80, and the impact of extracellular matrix (ECM) mechanics81–85 on TCR-3 9 ligand discrimination remain significant points for further theoretical and experimental investigation. 4 0 Surprisingly, the mechanical cooperativity of LFA-1 coreceptors and the TCR in this framework 4 1 does not follow a conventional kinetic proofreading mechanism that involves a 4 2 precision/speed/energy dissipation tradeoff (Fig. 6b, 6c )18,55–57. Rather, Mechanical filtering between 4 3 LFA-1 and the TCR mediated by the mechanical microenvironment determines the energy budget 4 4 and how that energy is expended by the TCR to improve its performance in ligand discrimination (Fig. 4 5 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 13 6d-f)63,86. Thus, if the energy budget is indeed set by the microenvironment, it is likely that other 4 6 topographical87 and physicochemical aspects of the mechanical microenvironment beyond T-cell-4 7 APC contact mechanics (e.g., the ECM 88,89, lymphoid tissue microenvironment in both disease and 4 8 homeostasis90–92, tumor microenvironments9,93–96, etc.) are important as well97. 4 9 The complex dynamics of TCR mechanical proofreading can be distilled into a simpler 5 0 parametric framework governed by active power and mechanical coupling. In the asymptotic limits of 5 1 substrate stiffness (approaching 0 pN/nm and 1000 pN/nm), the substrate effectively decouples the 5 2 TCR and LFA-1 coreceptors. In these regimes, active energy transport is minimized, and the physical 5 3 constraints on the TCR are dictated entirely by the passive properties of the membrane. However, at 5 4 intermediate substrate stiffnesses, the substrate acts as a mechanical conduit. This allows the 5 5 actomyosin-driven molecular clutch of LFA-1 to ‘talk’ to the TCR, actively tuning the force landscape 5 6 to hit the catch/slip transition and maximize proofreading precision. To rigorously test and potentially 5 7 falsify this model, future experimental strategies can actively decouple these parameters. For 5 8 example, perturbing the intrinsic membrane stiffness via cholesterol doping 98, or utilizing pMHC 5 9 ligands with artificially high catch/slip transition forces14,15,99,100, should theoretically shift or abolish the 6 0 proofreading optimum. By assessing TCR discriminatory precision against these modified parameters 6 1 across both zero-stiffness and finite-stiffness substrates, experimentalists could directly validate the 6 2 necessity of this mechanical circuit in active antigen discrimination. 6 3 Our findings emphasize the potential mechanical determinants of TCR signal amplification, 6 4 and may have utility for exploring in vitro T-cell-material interface variable spaces and additional 6 5 mechanoimmunological investigation of TCR-ligand discrimination, antigen recognition, and activation. 6 6 The reported mathematical framework may additionally be used to dramatically constrain and 6 7 formulate future mechanochemical feedback models of TCR signal transduction and T-cell activation. 6 8

(36 words) 6 9 Numerical methods 7 0 Nonlinear least-squares regression methods and simulations were implemented in MATLAB R2024a 7 1 to solve constitutive equations or extract parameters from the literature ( Appendix Table a1. ). Data 7 2 was visualized in either MATLAB R2024a or Prism v10.4.1. 7 3

(138 words) 7 4 We thank Dr. Sungmin Nam (Harvard University), Dr. Yuesong Hu (Wyss Institute), Rohan 7 5 Thakur (Massachusetts Institute of Technology), Dr. Kwasi Adu-Berchie (Wyss Institute), Dr. Andrew 7 6 Khalil (Whitehead Institute and Wyss Institute), Dr. Vinny Chandran Suja (Harvard University), Dr. 7 7 Debraj Ghose (Wyss Institute), Aditya Patil (Harvard University), Dr. Ross Jones (University of British 7 8 Columbia), Dr. Ajinkya Ghagre (University of British Columbia), and Dr. Khalid Salaita (Emory 7 9 University) for valuable scientific discussions and/or suggestions during the preparation of this 8 0 manuscript. We thank Dr. Ze Gong (University of Science and Technology of China) for valuable 8 1 scientific discussions on the initial theoretical concept and for providing example MATLAB 8 2 implementations. We thank Dr. Melissa Lever (Marks and Clerk) for providing example MATLAB 8 3 implementations. We acknowledge funding from the NIH NCI (Wyss Institute i3 center, F99/K00), 8 4 Wellcome Leap Foundation (HOPE), and NSF (Harvard MRSEC). 8 5 Appendix (33 words) 8 6 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 14 Key model derivations, model parameters, parameter calculations and additional equations, and 8 7 additional analytical data are provided in the appendix. MATLAB script of the model implementation 8 8 encompassing all master equations are uploaded on GitHub. 8 9 Author contributions (23 words) 9 0 N.J. and S.S. (concept, theory, implementation, data visualization, analysis, writing). J.M.B and T.H. 9 1 (concept, theory, implementation). B.A.N. and W.H.J. (implementation). P.W.Z. (writing). L.M. and 9 2 D.J.M. (concept, theory, writing). 9 3

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The magnitude of receptor-ligand force dictates reaction rate competition in the mechanical proof8 2 framework. a) Schematic of mechanical proofreading model recapitulating key features of a T- cell adhering to an8 3 surface decorated with c-pMHC, n-pMHC, and ICAM-1. b) Mechanical proofreading framework that incorporates8 4 signaling and catch/slip bond behavior exhibited by TCR-ligand binding. c) Kinetics and kinematics of LFA-1-ICAM8 5 formation in a molecular clutch framework. Force generation in response to resistance supplied by the elastic8 6 facilitates LFA-1-mediated adhesion, and passively energizes TCR- ligand binding through the injection of me8 7 energy by force balance. d) TCR-c-pMHC and LFA-1-ICAM-1 bonds exhibit catch bond behavior, whereas TCR -8 8 bonds exhibit slip bond behavior. e) Bond lifetimes and dissociation constants of TCR-c-pMHC, TCR-n-pMHC, and8 9 ICAM-1 binding kinetics as a function of force. f) Off rate competition between TCR catch/slip and LFA- 1 catch b9 0 19 t echnol. d Their ce 391 , a tic Shift ofreading an elastic tes limited M-1 bond tic surface echanical -n-pMHC nd LFA-1- h bond off .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 20 rates. g) ITAM phosphorylation rate competition with TCR-c-pMHC catch bonds and TCR-n-pMHC slip bonds. h) Limited 9 1 signaling complex decay rate competition with TCR-c-pMHC catch bonds and TCR-n-pMHC slip bonds. 9 2 9 3 Fig. 2. The magnitude of receptor-ligand force controls TCR-ligand proofreading precision and error. a) Schematic 9 4 of mechanokinetic TCR-ligand discrimination with catch/slip off rates and TCR-ligand bond interfacial surface density as a 9 5 function of force. b) Signaling competent TCR-c-pMHC bond interfacial surface density as a function of force from 9 6 1 /g3409 /g2016 /g3409 10 proofreading sequences. c) Aberrant signaling competent TCR-n-pMHC bond interfacial surface density as a 9 7 function of force from from 1 /g3409 /g2016 /g3409 10 proofreading sequences. d) TCR signal amplification precision and error as a 9 8 function of force from 1 /g3409 /g2016 /g3409 10 proofreading sequences. e) Kinetic competition of c-pMHC and erroneous n-pMHC-9 9 mediated TCR phosphorylation as a function of mechanical force from 1 /g3409 /g2016 /g3409 10 proofreading sequences. f) 0 0 accumulate precision and error of TCR signal amplification as a function of mechanical force. g) accumulated error and 0 1 precision are calculated by taking the total product of precision and error across 1 /g3409 /g2016 /g3409 10 proofreading sequences. 0 2 TCR force is normalized to /g2018 /g3021/g1864 /g3021 /g2868 ~ 9 pN. 0 3 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 21 0 4 Fig. 3. TCR-pMHC catch/slip bond amplitude and Gibbs free energy minimization are controlled by receptor-0 5 ligand force magnitude and APC surface stiffness. a) Standard state change in Gibbs free energy of OT1(†) TCRs 0 6 engaging various c-pMHCs or R4 n-pMHC as a function of force. b) Catch/slip bond behavior exhibited by OT1(†) TCR-0 7 ligand binding as a function of force. c) Standard state change in Gibbs free energy of OT1(†) TCRs engaging various c-0 8 pMHCs or R4 n-pMHC as a function of APC surface stiffness. d) Catch/slip bond behavior exhibited by OT1(†) TCR-0 9 ligand binding as a function of APC surface stiffness. 1 0 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 1 1 Fig. 4. LFA-1 molecular clutch dynamics at steady-state modulates TCR- ligand proofreading precision an1 2 in response to APC surface stiffness. a) Schematic of mechanokinetic TCR- ligand discrimination with catch1 3 rates in concert with LFA-1 molecular clutch dynamics. b) Signaling competent TCR-c- pMHC bond interfacial 1 4 density as a function of APC surface stiffness from proofreading sequences. c) Aberrant signaling co1 5 TCR-n-pMHC bond interfacial surface density as a function of APC surface stiffness from from proo1 6 sequences. d) TCR signal amplification precision and error as a function of APC surface stiffness from 1 7 proofreading sequences. e) accumulate precision and error of TCR signal amplification as a fu nction of APC 1 8 stiffness. APC surface stiffness is normalized to 1 pN/nm. 1 9 22 and error tch/slip off ial surface competent oofreading C surface .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 23 2 0 Fig. 5. Active power generated by LFA-1-ICAM-1 bonds and TCR catch/slip bond amplitude enables TCR signal 2 1 amplification through elastic energy storage in TCR-pMHC bonds . a) Elastic energy storage (in units of kBT) in TCR-2 2 pMHC bonds with different antigen types as a function of APC surface stiffness. b) Active power (energy transport) in total 2 3 bound LFA-1-ICAM-1 complexes as a function of APC surface stiffness for OT1(†) TCRs engaging varying c-pMHC or n-2 4 pMHC. c) TCR signal amplification precision as a function of the relative ratio of active power in LFA-1-ICAM-1 complexes 2 5 when OT1(†) TCRs engage different c-pMHC relative to R4-loaded n-pMHC. 2 6 2 7 2 8 .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint 2 9 Fig. 6. Mechanical filtering with LFA-1 determines TCR signal amplification in the mechanical proof3 0 framework. a) Elastic energy storage (in units of k BT) in TCR-pMHC bonds, LFA-1-ICAM-1 bonds, and the APC3 1 as a function of APC surface stiffness. b) Active power (energy transport) in total bound LFA-1-ICAM- 1 complex3 2 function of APC surface stiffness and TCR signal amplification precision as a function of the relative ratio of activ3 3 in LFA-1-ICAM-1 complexes when TCRs engage c-pMHC versus n-pMHC. c) Schematic of conventional3 4 proofreading mechanism in TCR-ligand discrimination, where the amount of free energy that is expended to impro3 5 signaling precision is fixed a priori intracellularly in a speed/energy dissipation tradeoff. d) Schematic of me3 6 proofreading mechanism in TCR-ligand discrimination involving cooperativity with LFA- 1 coreceptors. In me3 7 proofreading, Mechanical filtering between LFA-1-ICAM- 1 bonds and the TCR determines mechanical energy t3 8 from engaged contractile actomyosin filaments to the TCR to facilitate ligand proofreading precision. 3 9 4 0 4 1 4 2 24 ofreading C surface lexes as a tive power nal kinetic rove TCR echanical echanical y transport .CC-BY 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint