{"paper_id":"304b751b-b0c9-4df2-ab55-71b3b710841a","body_text":"1 \n \nSubstrate mediated mechanical forces enable optimal kinetic proofreading by T-1 \ncell receptors  2 \nNicholas Jeffreys 1,2,7,8*, Joshua M. Brockman 1,2,5, Tiam Heydari 7,8, Bryan A. Nerger 1,2, Wei-Hung 3 \nJung1,2, Peter W. Zandstra7,8,9, L. Mahadevan1,3,6,a), David J. Mooney1,2,a), Suraj Shankar3,4,a)*, 4 \n1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, 5 \nMassachusetts 02138, USA. 2Wyss Institute for Biologically Inspired Engineering, Boston, 6 \nMassachusetts 02215, USA. 3Department of Physics, Harvard University, Cambridge, Massachusetts 7 \n02138, USA. 4Department of Physics, University of Michigan, Ann Arbor, Michigan, 48109, USA. 8 \n5Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, Wisconsin 9 \n53706, USA. 6Department of Organismic and Evolutionary Biology, Harvard University, Cambridge 1 0 \n02138. 7School of Biomedical Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, 1 1 \nCA, 8Michael Smith Laboratories, University of British Columbia, Vancouver, BC V6T 1Z4, CA. 1 2 \n9Department of Medical Genetics, University of British Columbia, Vancouver, BC V6T 1Z3, CA. 1 3 \na)Correspondence: L. Mahadevan (lmahadev@g.harvard.edu), David J. Mooney 1 4 \n(mooneyd@seas.harvard.edu), and S. Shankar (surajsh@umich.edu)  1 5 \nKeywords: Mechanical proofreading, kinetic proofreading, catch bond, slip bond, molecular clutch, T-1 6 \ncell receptor, Lymphocyte function-associated antigen-1,  1 7 \n*These authors contributed equally to this work.  1 8 \nAbstract (202 words)  1 9 \nT-cells use molecular reactions with nonequilibrium error correction, i.e., proofreading, to 2 0 \ndiscriminate between nearly identical antigens with high specificity and sensitivity. These receptor 2 1 \nbinding events are known to be force sensitive, yet traditional schemes of proofreading focus on 2 2 \nreaction kinetics alone and do not consider the role of force dependent catch/slip bond behavior or 2 3 \ninteractions with mechanically engaged coreceptors such as adhesion molecules. To address this, we 2 4 \npropose a minimal framework for proofreading  of ligand discrimination by T-cell receptors (TCRs) 2 5 \nthat uses endogenous TCR mechanosensation and substrate-mediated mechanical interactions with 2 6 \nadhesive proteins (load sharing) to improve recognition fidelity. We leverage the catch bond behavior 2 7 \nof cognate antigens to delay decision making and amplify TCR signaling while discarding noncognate 2 8 \nslip bond ligands in the presence of a force. By integrating our model with existing structural and 2 9 \nmolecular data, we show that substrate mechanics regulates the transmission of active cytoskeletal 3 0 \nforces through a molecular clutch and controls the energization of bound TCRs needed for optimal 3 1 \nproofreading. Our work demonstrates how mechanical forces and substrate properties can augment 3 2 \nkinetic proofreading in T-cells, suggesting biomaterial design strategies for immunotherapies that tune 3 3 \nthe mechanical microenvironment of T-cells to achieve high fidelity TCR-ligand discrimination, antigen 3 4 \nrecognition, and activation.  3 5 \nMain (1965 words) 3 6 \nThe immune system recognizes and discriminates between self and foreign antigens. T-cells 3 7 \nperform this task by binding T-cell receptors (TCRs) to peptide-loaded major histocompatibility 3 8 \ncomplexes (pMHCs) decorated on antigen presenting cell (APC) surfaces. That TCRs can detect rare 3 9 \ncognate pMHCs in a vast array of noncognate pMHCs with exceptionally high specificity and 4 0 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n2 \n \nsensitivity is known to require a mechanism of nonequilibrium error correction1–4. Kinetic proofreading 4 1 \nmodels have been suggested to explain this behavior by considering the activation of a TCR signaling 4 2 \ncascade that expends energy to facilitate a sequence of kinetic delays 1-5. During these delays, the 4 3 \nprogressive phosphorylation of available immunoreceptor tyrosine-based activation motifs (ITAMs) 4 4 \nwithin the TCR/CD3-ζζ  complex kinetically competes with the dissociation of the TCR-pMHC bond 5,6. 4 5 \nConsequently, transient interactions between TCRs and noncognate pMHC (n-pMHC) are unlikely to 4 6 \ntrigger T-cell activation, whereas longer-lived interactions between TCRs and cognate pMHC (c-4 7 \npMHC) are more likely to support the formation of stable signaling complexes that enable T-cell 4 8 \nactivation (e.g., the LAT signalosome)7,8. 4 9 \nComplementing this biochemical picture, in recent years it has been suggested that physical 5 0 \nforces can also support enhanced proofreading by dissipation of mechanical rather than chemical 5 1 \nenergy9–13. In-vitro experiments show that mechanically loaded TCR-pMHC complexes display force-5 2 \ndependent kinetics that can modulate proofreading 20,21, through catch bond formation (with c-5 3 \npMHC)14,15, slip bond formation (with n-pMHC) 16, and T-cell adhesion to APCs (via LFA-1-ICAM-1 5 4 \ncatch bonds) 17,18. Molecular dynamics simulations of TCR-pMHC bond engagement and TCR 5 5 \nmechanical allostery additionally support these experimental observations 9–11,19. These studies 5 6 \nlargely focus on a fixed applied force, resulting in a constant mechanical energy budget for 5 7 \nproofreading13,15-17. But cells can adaptively regulate cytoskeletal force generation through feedback 5 8 \nto tune antigen discrimination, a feature that is often neglected; recent work in B-cells are an 5 9 \nexception20,21. Furthermore, it remains unclear how active forces are transmitted to TCRs. Direct 6 0 \nloading by motors is unlikely as TCRs are only weakly coupled to the actin cytoskeleton 22,23, lacking 6 1 \ndirect structural connections24. This suggests that indirect force transmission through the environment 6 2 \nis necessary for triggering mechanosensitive effects. While recent studies have highlighted how 6 3 \nsubstrate properties can influence TCR discrimination efficacy 25,26, an integrated framework for 6 4 \nproofreading that couples cytoskeletal force generation, molecular kinetics, and substrate mechanics 6 5 \nremains lacking.  6 6 \nWe address this challenge by developing a minimal model for mechanically regulated 6 7 \nproofreading that combines the reaction-limited kinetics of TCR-ligand discrimination with a molecular 6 8 \nclutch description of LFA-1 adhesion to an elastic substrate exposing ICAM-1 ligands, rare c-pMHCs, 6 9 \nor a large array of n-pMHCs. By incorporating experimentally known structural and molecular 7 0 \nconstraints, our framework captures key features of T-cell/APC contact mechanics during T-cell 7 1 \nantigen discrimination, and incorporates catch/slip behavior exhibited by TCRs and LFA-1 7 2 \ncoreceptors. Active forces are self-regulated by the molecular clutch and transmitted through the 7 3 \nsubstrate, enabling mechanical cooperation between TCR-ligand and LFA-1 adhesion kinetics. 7 4 \nNumerical simulations of the steady-state behavior show that resistance supplied by the substrate 7 5 \nstiffness modulates the magnitude of piconewton (pN)-level loads generated by the LFA-1 clutch, and 7 6 \nsupplies TCR-pMHC bonds with mechanical energy during ligand discrimination. While extremely 7 7 \nfloppy or stiff APC surfaces abrogate TCR signal amplification by rare c-pMHCs, soft APC surfaces 7 8 \nwith intermediate stiffness convey physiological pN-loads to TCR-pMHC bonds, allowing optimal 7 9 \ndiscrimination. Unlike conventional kinetic proofreading (where the amount of free energy that is 8 0 \nexpended to improve precision is fixed a priori in a speed/energy dissipation tradeoff), ‘mechanical’ 8 1 \nproofreading depends on the mechanical properties of the T-cell microenvironment, such that energy 8 2 \ntransport to the TCR is dictated by mechanical filtering with LFA-1-generated forces against the APC 8 3 \nsubstrate through actomyosin contractility.  8 4 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n3 \n \nAdditionally, in the context of mechanical proofreading, the physical basis for discriminating 8 5 \nbetween cognate and noncognate antigens hinges on the force-dependent kinetics of the TCR. 8 6 \nSpecifically, high-fidelity discrimination requires a maximal bond lifetime at a finite force that is 8 7 \ncharacteristic of the catch/slip transition. The ratio of ‘correct’ to ‘incorrect’ signaling TCR-pMHC 8 8 \nbonds (and by proxy, force-dependent bond lifetimes) yields a proofreading precision that distinctly 8 9 \npeaks at this finite transition force. A fundamental question naturally arises: what dictates the 9 0 \nmagnitude of this applied force in the immunological synapse? Our model reveals that this optimal 9 1 \nforce is governed not solely by internal actomyosin contractility, but by the interplay between the 9 2 \nsubstrate stiffness and the intrinsic rigidity of the T-cell membrane. In the extreme limits of substrate 9 3 \ncompliance—approaching either zero or infinite stiffness—the forces exerted on the TCR are 9 4 \ngenerated almost exclusively by membrane mechanics rather than actomyosin motor activity through 9 5 \nLFA-1. Consequently, a critical boundary condition for successful mechanical proofreading is that the 9 6 \nforce required to reach the catch/slip transition must be smaller than the maximal restoring force 9 7 \ncapable of being generated by the deformed membrane. Our results emphasize the potential 9 8 \nmechanical determinants of TCR signal amplification, with implications for in vitro  T-cell-material 9 9 \ninterface design and future mechanoimmunological investigation of TCR-ligand discrimination, 0 0 \nantigen recognition, and activation. 0 1 \nOur mathematical framework for mechanical proofreading  couples three basic modules:  0 2 \n 0 3 \ni) TCR-ligand discrimination of c- or n-pMHCs through ITAM phosphorylation based 0 4 \nproofreading steps. 0 5 \nii) kinetics of an LFA-1-ICAM-1 molecular clutch 12,27. 0 6 \niii) T-cell adhesion-surface mechanics 28,29. 0 7 \n 0 8 \nReaction-limited, steady-state mechanokinetics of TCR-ligand discrimination with limited signaling (i) 0 9 \n 1 0 \n We model TCR-ligand binding as a bimolecular reaction with distinct force dependent kinetic 1 1 \nrates for cognate and noncognate ligands. Consistent with experimental measurements, we 1 2 \nparametrize the TCR dissociation rate from c-pMHCs (k /g2925/g2916/g2916\n/g2913 /gm555 F /g2955 /gm557) using a two-pathway model to capture 1 3 \na transition from catch to slip behavior ( eq. 1 )30, but instead use a simple Bell model for the 1 4 \ndissociation rate from n-pMHCs (k /g2925/g2916/g2916\n/g2924\n/gm555 F /g2955 /gm557), which only display slip bonding (eq. 2)31: 1 5 \n 1 6 \n(1) 1 7 \n k /g2925/g2916/g2916\n/g2913 /g4PPPF /g2955 /g4PP7 /g3404k /g2913,/g2913\n/g2868 exp /g4P78/g3398 F /g2955\nF /g2913,/g2913\n/g2868 /g4P79/g3397k /g2929,/g2913\n/g2868\nexp /g4P78 F /g2955\nF /g2929,/g2913\n/g2868 /g4P79 \n(2) 1 8 \n k /g2925/g2916/g2916\n/g2924 /g4PPPF /g2955 /g4PP7/g3404k /g2929,/g2924\n/g2868 exp /g4P78 F /g2955\nF /g2929,/g2924\n/g2868 /g4P79 \nHere, k /g2913,/g2913\n/g2868  and k /g2929,/g2913\n/g2868\n are the catch/slip rates for TCR-c-pMHC unbinding at zero load, k /g2929,/g2924\n/g2868\n is the slip rate 1 9 \nfor TCR-n-pMHC unbinding at zero load, and F /g2913\n/g2868  F /g2929\n/g2868  are the force thresholds for the catch and slip 2 0 \nbonds, respectively. We choose exponential forms for ease though there is emerging evidence that 2 1 \nthe bond lifetime distributions may be fat-tailed 32,33. The force F /g2955  experienced by a single bound TCR 2 2 \nto either c or n-pMHC presented from the surface is modeled as a Hookean spring (eq. 3): 2 3 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n4 \n \n(3) 2 4 \nF /g2955 /g3404 κ /g2904 /g3401/g4PPP l/g2904 /g3398l /g2904\n/g2868 /g4PP7 \nin 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 \nbond, and l Τ\n/g2868  ~ 15 nm is the TCR-pMHC rest length35.  2 6 \nAssuming mass conservation for the total number of receptors and ligands, we can solve the 2 7 \nmass action kinetic equations (see Appendix for details) at steady-state to obtain the surface density 2 8 \nof TCRs bound to either c or n-pMHCs (Π /g2913  or Π /g2924 ) to be (eq. 4 and eq. 5): 2 9 \n(4) 3 0 \nΠ /g2913 /g3404 1\n2 /g4PPPp /g2913 /g3397Τ /g2868 /g3397K /g2888\n/g2913 /g4PP7 /g3398 1\n2 /g3495 /g4PPPp /g2913 /g3397Τ /g2868 /g3397K /g2888\n/g2913 /g4PP7/g2870 /g33984 p /g2913 Τ /g2868  \n(5) 3 1 \nΠ /g2924 /g3404 1\n2 /g4PPPp /g2924 /g3397Τ /g2868 /g3397K /g2888\n/g2924 /g4PP7 /g3398 1\n2 /g3495 /g4PPPp /g2924 /g3397Τ /g2868 /g3397K /g2888\n/g2924 /g4PP7/g2870 /g33984 p /g2924 Τ /g2868  \nwhere Τ /g2868  is the T-cell membrane density of available TCRs in the contact area (reacting-limiting), p /g2913  3 2 \n( p /g2924 )  are the dosed densities of c-pMHCs (n-pMHCs) presented on the surface, and 3 3 \nK /g2888\n/g2913 /g∑mΔm k /g2925/g2916/g2916\n/g2913 /gm555 F /g2955 /gm557 k /g2925/g2924\n/g2955⁄  ( K /g2888\n/g2924 /g∑mΔm k /g2925/g2916/g2916\n/g2924 /gm555 F /g2955 /gm557 k /g2925/g2924\n/g2955⁄  ) are the force-dependent dissociation constants of TCR-c-3 4 \npMHC (TCR-n-pMHC) bonds.  3 5 \n Kinetic proofreading is enabled by irreversible phosphorylation of bound TCRs. After θ  3 6 \nconsecutive proofreading steps, the steady-state solution yields the density of activated, stable TCR-3 7 \nc-pMHC signaling complexes Π /g2968\n/g2913  (eq. 6) or aberrant TCR-n-pMHC signaling complexes Π /g2968\n/g2924  (eq. 7) to 3 8 \nbe (see Appendix for details), 3 9 \n(6) 4 0 \nΠ /g2968\n/g2913 /g3404  k /g2925/g2916/g2916\n/g2913 /g4PPPF /g2955 /g4PP7\n k /g2925/g2916/g2916\n/g2913\n/g4PPPF /g2955 /g4PP7 /g3397/g1284 ·α /g2913\n/g2968 Π /g2913  \n(7) 4 1 \nΠ /g2968\n/g2924 /g3404  k /g2925/g2916/g2916\n/g2924 /g4PPPF /g2955 /g4PP7\n k /g2925/g2916/g2916\n/g2924\n/g4PPPF /g2955 /g4PP7 /g3397/g1284 ·α /g2924\n/g2968 Π /g2924  \nwhere /gµ·8m  is the limited signaling decay rate for rendering activated signaling complexes as non-4 2 \nsignaling, and the ratios, α /g2913 /g3404\n/g2921 /g3174\n/g2921 /g3174 /g2878 /g2921 /g3173/g3164/g3164\n/g3161 /g4666 /g2890 /g3203 /g4667  and α /g2924 /g3404\n/g2921 /g3174\n/g2921 /g3174 /g2878 /g2921 /g3173/g3164/g3164\n/g3172\n/g4666 /g2890 /g3203 /g4667  capture the kinetic competition 4 3 \nbetween the sequential tyrosine phosphorylation rate k /g2926 , and the pMHC unbinding rate during each 4 4 \nproofreading step. 4 5 \nPrecision in TCR signal amplification and proofreading error rate  4 6 \nTo quantify proofreading accuracy, we assume TCR signal amplification (denoted by R ) is 4 7 \nproportional to the density of activated signaling complexes, namely R /g2913  ~ Π θ\nc  and R /g2924  ~ Π θ\nn\n  (Eqs. (6)  4 8 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n5 \n \nand (7)) for cognate and non-cognate ligands, respectively . The ratio of correct versus aberrant 4 9 \nsignal amplification then provides a measure of proofreading precision λ /g2911 /g∑mΔm R /g2913 R /g2924⁄  (eq. 10): 5 0 \n(10) 5 1 \nλ /g2911 /g3404 /g343P α /g2913\nα  /g2924\n/g3440\n/g2968\n/g343P β /g2913\nβ /g2924\n/g3440 /g3401 p /g2913 /g3397Τ /g2868 /g3397K /g2888\n/g2913 /g3398 /g3493 /g4PPPp /g2913 /g3397Τ /g2868 /g3397K /g2888\n/g2913 /g4PP7/g2870 /g33984 p /g2913 Τ /g2868\np /g2924 /g3397Τ /g2868 /g3397K /g2888\n/g2924\n/g3398 /g3493 /g4PPPp /g2924 /g3397Τ /g2868 /g3397K /g2888\n/g2924\n/g4PP7/g2870 /g33984 p /g2924 Τ /g2868\n  \nwhere β c /g3404  k off\nc /g4666 F Τ /g4667\n k off\nc\n/g4666 F Τ /g4667 /g3397/g1284  and β /g2924 /g3404\n /g2921 /g3173/g3164/g3164\n/g3172 /g4666 /g2890 /g3203 /g4667\n /g2921 /g3173/g3164/g3164\n/g3172\n/g4666 /g2890 /g3203 /g4667 /g2878/g2990  capture the kinetic competition between the limited 5 2 \nsignaling decay rate /gµ·8m , and the pMHC unbinding rates. The inverse of λ /g2911  gives a  proofreading error 5 3 \nrate f /g2868 /g∑mΔm 1/λ /g2911  . 5 4 \nMolecular clutch dynamics of LFA-1-ICAM-1-mediated surface adhesion (ii) 5 5 \nDynamics of active surface adhesion is modeled as a molecular clutch, wherein the reversible 5 6 \nbinding of LFA-1 coreceptors to ICAM-1 is described using first order kinetics (eq. 14): 5 7 \n(14) 5 8 \ndi/g4PPPt/g4PP7\ndt /g3404k /g2925/g2924\n/g2919 /g3401/g4PPPi /g2868 /g3398i /g4PPP t /g4PP7 /g4PP7 /g3398k /g2925/g2916/g2916\n/g2919 /g4PPPF /g2919 /g4PP7 /g3401 i/g4PPPt/g4PP7  \nHere, 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 \ncoreceptors, k /g2925/g2924\n/g2919  is the binding rate, and k /g2925/g2916/g2916\n/g2919 /gm555F /g2919 /gm557 is the force-dependent unbinding rate. The force 6 0 \nexerted by a single bound adhesion complex is F /g2919 /g∑mΔmκ /g2919 /g∑mΔµ/gm555 l /g2919 /g∑∑98l /g2919\n/g2868 /gm557 , where  l /g2919  is the total bond length, κ /g2919  6 1 \n~ 0.2 pN/nm the  bond stiffness36, and  l /g2919\n/g2868\n ~ 40 nm the rest length35. Catch bond behavior of integrins is 6 2 \nincorporated in the unbinding rate k /g2925/g2916/g2916\n/g2919 /gm555F /g2919 /gm557 , parametrized by  a two-pathway model (eq. 15): 6 3 \n(15) 6 4 \nk /g2925/g2916/g2916\n/g2919 /g4PPPF /g2919 /g4PP7 /g3404k /g2913,/g2919\n/g2868 exp /g4P78/g3398 F /g2919\nF /g2913,/g2919\n/g2868 /g4P79/g3397k /g2929,/g2919\n/g2868\nexp /g4P78 F /g2919\nF /g2929,/g2919\n/g2868 /g4P79 \nthat transitions to slip bonding at large loads. The zero load catch and slip rates are k /g2913,/g2919\n/g2868  and k /g2929,/g2919\n/g2868\n, along 6 5 \nwith the corresponding transition forces ,  F /g2913,/g2919\n/g2868  and  F /g2929,/g2919\n/g2868  . When bound, the LFA-1-ICAM-1 adhesion complex 6 6 \nengages with the actomyosin cytoskeleton and is stretched by motor activity, but this elastic 6 7 \nextension yi is relaxed upon unbinding 37. Using a mean-field approach that averages over stochastic 6 8 \nbinding events (see Appendix for derivation), we obtain the dynamics of the average stretch /gµ7∑µy /g2919 /gµ7∑· to be  6 9 \n(eq. 16): 7 0 \n(16) 7 1 \nd /g1731y /g2919 /g1732 \ndt /g3404v /g2911 /g4PPPF /g2919 /g4PP7/g3398k /g2925/g2924\n/g2919 /g3401/g343P i /g2868\ni /g4PPPt /g4PP7 /g33981 /g3440  /g1731y /g2919 /g1732 \nwhere v /g2911 /gm555 F i /gm557 ,  the retrograde flow velocity of the actomyosin gel obeys a simple linear force-retrograde 7 2 \nflow velocity relationship (eq. 17): 7 3 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n6 \n \n(17) 7 4 \nv /g2911 /g4PPPF /g2919 /g4PP7/g3404v /g2868 ·/g4P78 1/g3398 i /g4PPPt /g4PP7 /g3401F /g2919\nσ /g2911\n/g4P79 \nwith v /g2868 ~ 60 nm/s  being the maximal (zero load) retrograde flow velocity, and σ /g2911  ~ 1 kPa being the 7 5 \ncontractile actomyosin stall stress38,39, beyond which actin flows are arrested. 7 6 \n At steady-state, the kinetics and kinematics of LFA-1-mediated adhesion can be solved to 7 7 \nobtain  (eq. 18 and eq. 19): 7 8 \n(18) 7 9 \ni/g3404 i /g2868\n1/g3397K /g2888\n/g2919  \n(19) 8 0 \n/g1731y /g2919 /g1732 /g3404 v /g2868\nk /g2925/g2924/g2919 K /g2888\n/g2919 · /g343P1/g3398 i·F /g2919\nσ /g2911\n/g3440 \nwhere K /g2888\n/g2919 /g∑mΔmk /g2925/g2916/g2916\n/g2919 /gm555 F i /gm557 /k /g2925/g2924\n/g2919  is the force dependent equilibrium dissociation constant. Eq. 19 encodes 8 1 \nmechanical feedback in active force generation and can be simply understood by noting that the 8 2 \nadhesion complex stretches at speed v /g2911  for a bond lifetime ~ 1/ k /g2925/g2916/g2916\n/g2919  , yielding an average extension 8 3 \nl /g2919 = v /g2911 /gm555 F i /gm557/k /g2925/g2916/g2916\n/g2919\n/gm555 F i /gm557 . To relate this actively generated intracellular stretch (/g1731y /g2919 /g1732) to the total length of the 8 4 \nadhesion complex (l /g2919 ), we need to specify the kinematics of the substrate, as done below. 8 5 \nT-cell adhesion-surface mechanics (iii) 8 6 \nWe complete the model by imposing force balance to mechanically couple TCR-antigen 8 7 \nkinetics (i) with the active dynamics of adhesion (ii). In the absence of direct links to the cytoskeleton, 8 8 \nbound TCRs can stretch and generate forces only when resisted by the T-cell membrane. Previous 8 9 \nmodels of synaptic patterning 23,40,41 have shown how  differential molecular size (or receptor and 9 0 \nadhesive proteins) coupled to membrane elasticity can generate spatially segregated TCR clusters. 9 1 \nHere, we neglect this spatial patterning dynamics and instead focus on an effective description that 9 2 \npresumes the existence of preformed clusters. Assuming the T-cell and opposing APC are separated 9 3 \nby an average gap height h /g2868 ~ 50-60 nm due to large glycosylated proteins (e.g., CD45 ectodomain42), 9 4 \nwe consider TCR-antigen bonds to deform the membrane locally (displacement δh ) on the scale of a 9 5 \nTCR microcluster43–45, R ~ 50 nm 46. On the other hand, elastic deformations of the APC surface (u) 9 6 \nbalance the shared load exerted by both receptor and adhesion molecules, extended across the 9 7 \ncontact area, A /g2913  ~ 3 x 10 4 nm2, of say a microvillus 47.  Altogether, force balance at the T-cell 9 8 \nmembrane and the APC surface then yields (eq. 20 and eq. 21): 9 9 \n(20) 0 0 \n 0 1 \nA /g2913 /g3401/g4PPPF /g2904 Π /g2904 /g3397F /g2919 i /g4PP7 /g3398σ /g2885/g2900/g2887 u/g34040  \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n7 \n \n(21) 0 2 \nF /g2904 Π /g2904 /g3398 γ/g3401δ h\nR /g2870 /g3404 0  \nwhere 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 \nbond lengths that enable force generation on TCR-pMHC ( l /g2904 ) and LFA-1-ICAM-1 ( l /g2919 ) complexes are 0 4 \nrelated to the displacements of the APC surface ( u/gm557 , T-cell membrane ( δh/gm557 , and the intracellular bond 0 5 \nstretch of LFA-1-ICAM-1 /gµ7∑µy i /gµ7∑· as follows:  0 6 \nl /g2919 /g3404h /g2868 /g3397 /g1731y /g2919 /g1732 /g3398u   \nl /g2904 /g3404h /g2868 /g3398 δ h/g3398u  \nThese relations encode structural and geometric constraints intrinsic to the T-cell adhesive contact 0 7 \nand complete our model formulation. 0 8 \nResults (2713 words) 0 9 \nThe magnitude of receptor-ligand force modulates reaction rates in the mechanical proofreading 1 0 \nframework 1 1 \n As a first step, we ask: how do receptor-ligand forces impact kinetic proofreading? Kinetic 1 2 \nproofreading models with limited signaling have been shown to be consistent with the majority of 1 3 \npublished experimental data1. We incorporate force dependence within this framework simply via the 1 4 \nforce-sensitive unbinding rates (eq. 1 -2, eq. 15), see Fig. 1a-1d . For simplicity, here we directly 1 5 \nspecify the force on each bond and neglect substrate mediated mechanical couplings.  In Fig. 1e, we 1 6 \nplot the force-sensitive bond lifetimes ( 1k /g2925/g2916/g2916 /gm555F/gm557⁄ ) and dissociation constants ( K /g2888 ) against 1 7 \nphysiological pN-level loads for human OT1(†) TCRs binding either c-pMHCs (OVA antigen on H2-Kb 1 8 \nMHC class I) or n-pMHCs (R4 antigen on H2-Kb MHC class I), and LFA-1 binding ICAM-1 (in the 1 9 \npresence of Ca 2+, Mg2+, and CXCL12) using parameters extracted from 2-dimensional micropipette 2 0 \naspiration experiments ( Appendix Table a1 )30,31. The maximal bond lifetimes for TCR-c-pMHC and 2 1 \nLFA-1-ICAM-1 center around 8-12pN of load, while TCR-n-pMHC exhibits an exponential decaying 2 2 \nbond lifetime under increasing load14,17. To quantify relative competition in unbinding, we examine the  2 3 \nratios of off rates as a function of a common force ( Fig. 1f). Upon increasing the load, TCR-n-pMHC 2 4 \noff rates dominate over that of TCR-c-pMHC, whereas LFA-1-ICAM-1 off rates always exceeded the 2 5 \nrates of TCR-antigen unbinding (cognate and noncognate). This is simply understood by noting that 2 6 \ncognate antigens form catch bonds with longer lifetimes at high load, in contrast to short lived slip 2 7 \nbonds formed by noncognate antigens.  2 8 \n Mechanical forces also influence the proportion of bound TCRs that survive TCR-ITAM 2 9 \nphosphorylation by tyrosine kinases (e.g., ZAP-70 48) during a proofreading step. We find that the 3 0 \nphosphorylation rate for TCR-c-pMHCs (quantified by  α /g2913 ) dominates over the off rate  around 8-3 1 \n10pN, whereas relative phosphatase activity decreases at loads greater than 15pN (Fig. 1g). In 3 2 \ncontrast, the phosphatase activity for TCR-n-pMHCs( α /g2924 ) continually decreases with respect to 3 3 \nincreasing load ( Fig. 1g ). In addition, both TCR-c-pMHCs and TCR-n-pMHCs can form stable 3 4 \nsignaling complexes post-proofreading that can be rendered non-signaling and dissociated due to a 3 5 \nsignal decay rate /gµ·8m  (Fig. 1b ). We quantify this kinetic competition using β /g2913  and β /g2924  and plot their 3 6 \ndependence on the force in Fig. 1h. For signaling TCR-c-pMHCs under 8-10pN of load, the signal 3 7 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n8 \n \ndecay rate dominates over the off rate, whereas signaling TCR-n-pMHCs have a larger unbinding 3 8 \nrate compared to signal decay. 3 9 \nThe magnitude of receptor-ligand force controls TCR-ligand proofreading precision and error 4 0 \n  To assess how proofreading is impacted by forces, we next compute the steady-state densities 4 1 \nfor the cognate and noncognate ligands. ( eq. 6-10). We choose the n-pMHC surface density ( p /g2924 = 4 2 \n2·104 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 \ndiscrimination of rare cognate antigen from noncognate antigen decorating APC surfaces ( Appendix 4 4 \nTable a1 )47. Despite this difference in density, cognate antigens form long-lived catch bonds in 4 5 \ncontrast to short-lived slip bonds formed by noncognate antigens. So we expect an applied force can 4 6 \nstill enhance TCR-ligand discrimination by minimizing the formation of erroneous TCR-n-pMHC 4 7 \nsignaling complexes, while maximizing the formation of ‘correct’ TCR-c-pMHC signaling complexes 4 8 \n(Fig. 2a ). Fig. 2b shows the impact of receptor-ligand force on the formation of signaling TCR-c-4 9 \npMHC and TCR-n-pMHC complexes ( eq. 6-7) across θ  proofreading sequences. Here, θ  is set to 10 5 0 \nas the TCR uniquely contains 10 ITAMs to transduce pMHC binding into downstream signaling 5 1 \ncascades (Appendix Table a1 )49. Corresponding to the optimal TCR-c-pMHC bond lifetime, we find 5 2 \nthat the maximal formation of stable, signaling TCR-c-pMHC complexes is centered around an 5 3 \napplied load F ~ 8-10pN ( Fig. 2b). Conversely, force application and proofreading both suppress the 5 4 \nformation of  erroneous TCR-n-pMHC signaling complexes through rapid dissociation (Fig. 2c). 5 5 \n Combining these results, we plot the precision (eq. 10) and error rate (eq. 13) of TCR signal 5 6 \namplification during proofreading as a function of the applied force (Fig. 2d-f). As expected, precision 5 7 \nis increased with each proofreading sequence with optimal performance achieved at a load F ~ 10 pN 5 8 \ncorresponding to the characteristic force scale at which cognate bonds transition from catch to slip 5 9 \nbehavior. This response is predominantly controlled by the proofreading metrics ( α /g2913  and α /g2924 , eq. 8-9) 6 0 \nthat quantify the kinetic competition between the sequential tyrosine phosphorylation rate k /g2926 , and the 6 1 \nc or n-pMHC off rate during each proofreading step, as seen in Fig. 2e. Similar trends are also 6 2 \nobserved in the accumulated precision (or error) across all proofreading steps ( Fig. 2f, 2g ), 6 3 \nconsistent with recent results13. 6 4 \nLFA-1 molecular clutch dynamics modulate the mechanics of LFA-1-ICAM-1 adhesion and TCR-6 5 \nligand bond formation 6 6 \n We now relax the assumption of a constant force and investigate how actively regulated forces 6 7 \nand substrate mediated mechanical cooperation between LFA-1 and TCR modulate their kinetics. As 6 8 \nthe TCR is not directly coupled to actomyosin, TCR force generation in the model is mediated by the 6 9 \nLFA-1 molecular clutch through deformations of the T-cell membrane and adherent APC surface ( eq. 7 0 \n20-21)9,18,50,51. TCRs binding to n-pMHC cause larger deformation and stress in the T-cell membrane, 7 1 \ncompared to c-pMHCs across varying APC surface stiffness ( Appendix Fig. 1a ), despite negligible 7 2 \ndifference in APC surface displacement between cognate and noncognate antigens ( Appendix Fig. 7 3 \n1b). This suggests that membrane flexibility primarily controls the differential forces experienced by 7 4 \nTCR-c-pMHC and TCR-n-pMHC bonds. Increasing APC stiffness > 1 pN/nm causes the actomyosin 7 5 \nretrograde flow to stall ( Appendix Fig. 2a ) as the density of LFA-1-ICAM-1 bonds saturates 7 6 \n(Appendix Fig. 2b ). Correspondingly,  the forces generated by LFA-1, TCRs engaged with c-pMHC 7 7 \nor n-pMHC, all follow a sigmoidal increase with APC stiffness, with values within their physiologically 7 8 \nmeasured ranges ( Appendix Fig. 2a)14,18. In other words, the APC surface mechanically gates the 7 9 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n9 \n \ntransmitted force, switching on the maximum load on receptor antigen bonds beyond a characteristic 8 0 \nstiffness ~ 1 pN/nm, when the motor (actomyosin flow) stalls. 8 1 \nThe bond lifetimes and dissociation constants for TCR-c-pMHCs, TCR-n-pMHCs, and LFA-1-8 2 \nICAM-1 complexes vary with respect to the APC stiffness through the force they respectively 8 3 \nexperience (Appendix Fig. 2c). LFA-1-ICAM-1 bond lifetimes increases with APC surface stiffness, 8 4 \nplateauing at ~1.5 seconds, consistent with the stalling of actomyosin observed and the formation of 8 5 \nLFA-1-ICAM-1 adhesion complexes (Appendix Fig. 2a, 2b). TCR-c-pMHC bond lifetime instead has 8 6 \na biphasic dependency on APC surface stiffness, reflecting the transition from catch to slip behavior, 8 7 \nwith the maximal lifetime achieved for a stiffness ~ 1 pN/nm. Conversely, TCR-n-pMHC bond lifetimes 8 8 \ndecay as surface stiffness is increased. As a result, the formation of TCR-c-pMHC bonds is increased 8 9 \naround an APC surface stiffness of 1 pN/nm, but TCR-n-pMHC slip bonds simply dissociate as APC 9 0 \nsurface stiffness approaches supraphysiological membrane rigidities (e.g., 1000 pN/nm) ( Appendix 9 1 \nFig. 2d).  9 2 \nHow does this response depend on the extent of catch or slip bonding behavior? As an 9 3 \nexample, we consider human OT1(†) TCRs binding c-pMHCs of varying catch bond amplitude (OVA, 9 4 \nA2, G4, or E1 loaded on H2-Kb MHC class I, Appendix Table a2 ) and compare them against the 9 5 \nTCR-n-pMHC (OT1(†) TCR binding R4 antigen loaded on H2-Kb MHC class I) slip bond as a function 9 6 \nof receptor-ligand force and APC surface stiffness 14,52. We compute the change in the Gibbs free 9 7 \nenergy of binding ( ∆G ° , Appendix eq. a19 ) to quantify the thermodynamics of TCR engagement. 9 8 \nConsistent with our previous analysis of the TCR-pMHC dissociation constant ( K /g2888 , Fig. 1e  and 9 9 \nAppendix Fig. 2c), we find that the largest decrease in free energy (in units of k /g2886 T ) is achieved for 0 0 \nOT1(†) TCR-OVA-MHC-I catch bonds at intermediate loads (force ~ 8-12 pN, or APC stiffness ~ 1 0 1 \npN/nm; see Fig. 3a-d). In contrast, cognate antigens forming weaker catch bonds (e.g., E1, G4) 0 2 \nminimize their change in Gibbs free in energy at zero load or low APC stiffness ( Fig. 3a, 3c ) and do 0 3 \nnot benefit from mechanical forces in improving TCR engagement. This implies that the 0 4 \namplitude/magnitude of the TCR-ligand catch bond, not just its presence, crucially matters in 0 5 \ndetermining whether mechanical forces can induce a spontaneous thermodynamic process53 allowing 0 6 \nTCR signal amplification against a slip-bonding n-pMHC. 0 7 \nSoft APC surfaces maximize TCR-ligand proofreading precision 0 8 \n We combine the above results to evaluate the impact of surface mechanics on TCR-ligand 0 9 \nproofreading precision (Fig. 4a). Figs. 4b, 4c show the density of signaling TCR-c-pMHC and TCR-n-1 0 \npMHC complexes across θ  = 10 proofreading sequences as a function of APC surface stiffness. We 1 1 \nfind that soft APC surfaces with intermediate stiffness ~ 1 pN/nm allow for the optimal TCR-c-pMHC 1 2 \nbond lifetime accompanied by the maximal formation of stable, signaling TCR-c-pMHC complexes, 1 3 \nwhereas stiffnesses approaching 0 pN/nm or 1000 pN/nm leads to suboptimal signaling (Fig. 4b ). 1 4 \nThis is additionally reflected in the suppressed formation of erroneous TCR-n-pMHC signaling 1 5 \ncomplexes for stiff substrates ( σ /g2885/g2900/g2887  ≥  1 pN/nm), see Fig. 4c . As a result, we find that TCR 1 6 \nproofreading precision is optimal for soft APC surfaces across all θ  proofreading step (Fig. 4d-e), with 1 7 \na concomitant enhancement of the accumulated precision as well ( Fig. 4e ). Very low or high APC 1 8 \nstiffness (> 1 pN/nm) leads to lower proofreading precision (and thus greater error), suggesting that 1 9 \nthe substrate serves as a mechanical filter that enables optimal performance when force generation 2 0 \nby the molecular clutch is matched with force transmission through the environment. Finally, to test 2 1 \nthe dosage dependence of our results, we increase the c-pMHC dose to supraphysiological values 2 2 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n10 \n \nand find the receptor-ligand force is diminished (due to load sharing), causing the optimal stiffness to 2 3 \nshift to higher values ( Appendix Fig. 3a, 3b) , consistent with experimental observations 9,54. 2 4 \nEventually, for very high c-pMHC doses, the biphasic dependence of precision on stiffness is 2 5 \naltogether abolished ( Appendix Fig. 3a, 3b).  Similarly, decreasing n-pMHC dose enhances 2 6 \nproofreading precision, transitioning from a monotonic to a biphasic response as well (Appendix Fig. 2 7 \n3c, 3d).  2 8 \nTCR signal amplification is modulated by energy transport from the active power generated by LFA-1-2 9 \nICAM-1 adhesions 3 0 \n What are the energetic costs of this mechanism of proofreading? Conventional kinetic 3 1 \nproofreading biases reactions to amplify discrimination accuracy by dissipating a fixed budget of 3 2 \nchemical free energy55–57, as captured by the irreversible ITAM phosphorylation steps in our model. 3 3 \nBut here, reactions can also be biased by forces that are actively generated and regulated, leading to 3 4 \nmechanical energy costs that we focus on. To assess how  mechanical energy is partitioned during 3 5 \nantigen discrimination, we separately evaluate the elastic energy stored in the APC surface ( /g1847/g3002/g3017/g3004 /g34043 6 \n/g2869\n/g2870 /g202P/g3002/g3017/g3004 /g3401/g1873/g2870 ), LFA-1-ICAM-1 adhesions /g1847 /g3036 /g3404\n/g2869\n/g2870\n/g2018/g3036 /g3401/g3435/g18P4/g3036 /g3398/g18P4 /g3036\n/g2868 /g3439\n/g2870\n, and TCR-pMHC bonds ( /g1847 /g3021 /g3404\n/g2869\n/g2870\n/g2018/g3021 /g34013 7 \n/g4PPP/g18P4/g3021 /g3398/g18P4 /g3021\n/g2868 /g4PP7/g2870 ). The nonequilibrium power (P) generated by the actomyosin cortex and dissipated 3 8 \nthrough the adhesive dynamics of the molecular clutch is given by: 3 9 \n(25) 4 0 \nP/g3404v /g2911 F /g2919 /g3401 1\n1/g3397K /g2888\n/g2919  \n 4 1 \n We first examine the elastic potential energy stored in human OT1(†)  TCRs binding c-pMHCs 4 2 \nof varying catch bond amplitude (OVA, A2, G4, or E1 loaded on H2-Kb MHC class I) and compare 4 3 \nthem against the TCR-n-pMHC (OT1(†)  TCR binding R4 antigen loaded on H2-Kb MHC class I) slip 4 4 \nbond as a function APC surface stiffness (in units of k /g2886 T , Fig. 5a, eq. 22-24). In all cases, we observe 4 5 \nthat increasing APC surface stiffness allows a larger amount of elastic energy to be stored in bound 4 6 \nTCRs, with the relatively weak catch bonds, OT1(†) TCR-E1-MHC-I and OT1(†) TCR-G4-MHC-I, 4 7 \nstoring the most elastic energy. The active power dissipated by LFA-1 also increases with APC 4 8 \nstiffness, and saturates beyond σ /g2885/g2900/g2887  ≥  1 pN/nm, for the different TCRs considered. But in contrast to 4 9 \na traditional kinetic proofreading mechanism, we obs erve that greater nonequilibrium dissipation and 5 0 \nenergization of bonds  actually leads to lower proofreading precision ( Fig. 5b, 5c, eq. 25 ). Strikingly, 5 1 \nOT1(†) TCRs binding the strong catch bond forming antigen OVA-MHC-I display enhanced 5 2 \nproofreading precision with a comparable power expenditure for the cognate and non-cognate 5 3 \nantigen (relative power = P c/Pn ~ 1, Fig. 5c ). In contrast, TCRs engaging with weak catch bond 5 4 \nforming antigens (A2, G4, or E1) expend more than 3-fold the nonequilibrium power dissipated in the 5 5 \nnon-cognate case (OT1(†) TCRs binding R4 loaded MHC-I), only to have poorer discrimination 5 6 \n(precision λ /g2911  < 1 ), realizing a mechanical variant of an “anti-proofreading’’ regime58. 5 7 \nMechanical filtering with LFA-1-ICAM-1 adhesions determines TCR signal amplification 5 8 \n How can we understand these results? Unlike conventional proofreading where energy is 5 9 \ndirectly provided to the discriminating reaction, here, TCRs can harness nonequilibrium mechanical 6 0 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n11 \n \nenergy only indirectly, by transmission through substrate adhesion. This suggests the force 6 1 \ngenerating motor (actomyosin and LFA-1-ICAM-1), the transmitter (substrate), and force receiver 6 2 \n(TCR-antigen bond) must all be ‘impedance matched’, to use an electrical analogy, for optimal 6 3 \ntransfer of usable power for signal amplification. Without the optimal coupling, the nonequilibrium 6 4 \ndissipation is futile and unavailable to aid proofreading. To quantify such impedance matching, we  6 5 \ndirectly compare the stored elastic energy in the APC surface, along with the OT1(†) TCR-OVA-MHC-6 6 \nI (cognate), OT1(†) TCR-R4-MHC-I (noncognate) and LFA-1-ICAM-1 receptor-ligand bonds (Fig. 6a).  6 7 \nConsistent with the results in Fig. 5, as APC surface stiffness is increased, more elastic energy (in 6 8 \nunits of kBT) is stored in the TCR-ligand and adhesion bonds, with the greatest amount stored in LFA-6 9 \n1-ICAM-1 complexes, followed by OT1(†)  TCR-OVA-MHC-I and OT1(†) TCR-R4-MHC-I complexes. 7 0 \nBut the elastic energy stored in the APC surface varies non-monotonically, reaching a peak near the 7 1 \noptimal surface stiffness (~1 pN/nm) followed by a rapid decrease at large stiffness values ( > 100 7 2 \npN/nm). This is consistent with the view of impedance matching; wherein soft APCs optimally transmit 7 3 \nthe deformation and force needed to improve TCR signal amplification. 7 4 \n In Fig. 6b, we also plot the active power dissipated by the collection of formed LFA-1-ICAM-1 7 5 \ncomplexes (, eq. 25) as a function of APC surface stiffness. We do not observe any significant 7 6 \ndifferences in the active power dissipated by bound LFA-1-ICAM complexes when either OT1(†)  7 7 \nTCR-OVA-MHC-I or OT1(†)  TCR-R4-MHC-I bonds are engaged. Illustrating the proofreading 7 8 \nprecision per proofreading sequence as a function of the relative active power (TCR-c-pMHC:TCR-n-7 9 \npMHC, Fig. 6b inset ) further supports this, as the maximal precision is achieved around a relative 8 0 \npower of unity (P c/Pn ~ 1). Altogether, these results suggest that unlike conventional kinetic 8 1 \nproofreading  where a fixed amount of chemical energy is spent to increase precision and speed 8 2 \n(involving a tradeoff with greater energy dissipation, Fig. 6c ), our mechanokinetic framework 8 3 \ndecouples nonequilibrium dissipation from proofreading precision by employing a soft environment as 8 4 \na mechanical bottleneck that regulates the energization of discriminating reactions (Fig. 6d).  8 5 \nTo further elucidate this, we devise a dimensionless scaling parameter Γ ~  P χ/g∑mµ2  to compare the 8 6 \nenergy cost for nonequilibrium power generated by the actomyosin cortex and dissipated through the 8 7 \nadhesive dynamics of the molecular clutch to the nonequilibrium chemical power dissipation dictated 8 8 \nby the phosphorylation kinetics of the TCR. Here , the nonequilibrium chemical power dissipation is 8 9 \nχ/g∑mΔm Δ µ /g2885/g2904/g2900 ·k /g2926 ·/gm555 Π /g2904\nT /g2868\n/g∑mµ2/gm557 ∑ α /g2968 /gm555 1/g∑∑98α /gm557·m/g2968\n/g2923/g2880/g2869 , in which Δµ /g2885/g2904/g2900  ~ 25k /g2886 T  is the chemical potential 9 0 \nassociated with ATP hydrolysis and k /g2926 ·/gm555 Π /g2904\nT /g2868\n/g∑mµ2/gm557 ∑ α /g2968 /gm5551 /g∑∑98 α/gm557 · m/g2968\n/g2923/g2880/g2869\n is the TCR phosphorylation flux. 9 1 \nIn Appendix Fig. 4a, we plot the average chemical energy necessary for TCR phosphorylation 9 2 \n( Δµ /g2885/g2904/g2900 · ∑ α /g2968 /gm5551 /g∑∑98 α/gm557 · m/g2968\n/g2923/g2880/g2869\n) as a function of APC surface stiffness. Soft APC surfaces with 9 3 \nintermediate stiffness ~ 1 pN/nm allow for optimal TCR-c-pMHC phosphorylation whereas stiffnesses 9 4 \napproaching 0 pN/nm or 1000 pN/nm leads to suboptimal chemical energy expenditures. This is 9 5 \nadditionally reflected in suppressed erroneous TCR-n-pMHC chemical energy expenditure for stiff 9 6 \nsubstrates (σ /g2885/g2900/g2887  ≥  1 pN/nm).  9 7 \nTo evaluate the overall energetic efficiency of mechanical proofreading and impedance 9 8 \nmatching, we plot the dimensionless scaling parameter Γ  as a function of normalized APC surface 9 9 \nstiffness for OT1(†) TCR-OVA-MHC-I or OT1(†) TCR-R4-MHC-I (Appendix Fig. 4b). For noncognate 0 0 \nOT1(†) TCR-R4-MHC-I slip bonds, the rapid collapse of χ  in the denominator causes Γ  to 0 1 \nmonotonically diverge as nonequilibrium power P  increases with increasing APC surface stiffness. In 0 2 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n12 \n \nthis state, LFA-1-ICAM-1 catch bonds expend mechanical work but generates little TCR signaling 0 3 \noutput. Strikingly, for cognate OT1(†)  TCR-OVA-MHC-I catch bonds, Γ  exhibits a wave-like trajectory 0 4 \nthat maps the biophysical lifecycle of TCR-c-pMHC bonds under mechanical load. At low mechanical 0 5 \npower P  (norm. APC surface stiffness ≤  1), mechanical work done by LFA-1 outpaces TCR signaling 0 6 \noutput, driving a local maximum in Γ . However, as mechanical power reaches the critical TCR-c-0 7 \npMHC catch-bond threshold (norm. APC surface stiffness ~ 1; 8-10 pN of applied force), a surge in 0 8 \nchemical dissipation χ  outpaces  P , driving a local minimum in Γ , and thus realizing a ‘optimal’ 0 9 \nmechanical proofreading regime in which the TCR extracts the maximal chemical signaling payout 1 0 \nper unit of mechanical work invested by LFA-1 (e.g., ‘mechanical’ impedance matching). When 1 1 \nmechanical power exceeds this optimum (norm. APC surface stiffness ≥  1), the TCR-c-pMHC catch 1 2 \nbond ruptures (entering the slip regime), χ  minimizes, and Γ  diverges upwards. 1 3 \nDiscussion (670 words) 1 4 \nBy integrating LFA-1 molecular clutch dynamics with a previously reported kinetic proofreading 1 5 \nmodel with limited signaling, we developed a ‘mechanical’ proofreading framework of TCR-ligand 1 6 \ndiscrimination, incorporating key features of endogenous TCR mechanosensation and its mechanical 1 7 \ncooperativity with LFA-1 coreceptors. This minimal framework provides mechanistic support for how 1 8 \nTCR/LFA-1 mechanical cooperation may directly energize the TCR-pMHC bond and enable force-1 9 \nsensitive ligand discrimination 10,16,18. The integration of TCR-c-pMHC catch bonds or TCR-n-pMHC 2 0 \nslip bonds into previously reported kinetic proofreading frameworks confirms that force may enhance 2 1 \nproofreading precision by maximizing bond lifetime with c-pMHCs such that the probability of ‘correct’ 2 2 \nTCR phosphorylation by relevant adaptor molecules and subsequent activation of signaling cascades 2 3 \ndownstream of the TCR occurs (Fig. 1a-1e, Fig. 2b-2f)1. Transient TCR-n-pMHC slip bonds are more 2 4 \nlikely to exit the phosphorylation pathway with respect to greater force application, thus minimizing 2 5 \nproofreading error and erroneous activation.  2 6 \nThese mechanical ‘checkpoints’ may explain how developing thymocytes are selected within 2 7 \nthe thymus through load-sensing through the Pre-TCR and TCR 59–61, and how mature T-cells are 2 8 \nable to be activated by as rare as a single c-pMHC molecule decorating an APC surface 62. It is 2 9 \nimportant to appreciate that though this may hold true for the αβ TCR9,63, emerging evidence suggests 3 0 \nthat the γδ TCR is force-agnostic64,65.  3 1 \nEnergization of the TCR by actomyosin contractility through LFA-1-ICAM-1 adhesions is 3 2 \nspeculated to enhance TCR-ligand discrimination precision and stabilize the TCR-c-pMHC catch 3 3 \nbond18,66,67. Our framework additionally supports this hypothesis through the prediction of 3 4 \nphysiological pN-level loading regimes on the TCR and LFA-1 in response to the mechanical 3 5 \nproperties of a model APC surface ( Appendix Fig. 2b, Fig. 4b-4e )68–70. However, the role of 3 6 \nactomyosin-rich T-cell microvilli protrusions 71,72, the molecular crosstalk between TCR microcluster 3 7 \nnucleation and LFA-1-ICAM-1 adhesions 44,45, the complementary role of other co-effector molecules 3 8 \n(e.g., CD4/CD8 and CD28)73–80, and the impact of extracellular matrix (ECM) mechanics81–85 on TCR-3 9 \nligand discrimination remain significant points for further theoretical and experimental investigation. 4 0 \nSurprisingly, the mechanical cooperativity of LFA-1 coreceptors and the TCR in this framework 4 1 \ndoes not follow a conventional kinetic proofreading mechanism that involves a 4 2 \nprecision/speed/energy dissipation tradeoff (Fig. 6b, 6c )18,55–57. Rather, Mechanical filtering between 4 3 \nLFA-1 and the TCR mediated by the mechanical microenvironment determines the energy budget 4 4 \nand how that energy is expended by the TCR to improve its performance in ligand discrimination (Fig. 4 5 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n13 \n \n6d-f)63,86. Thus, if the energy budget is indeed set by the microenvironment, it is likely that other 4 6 \ntopographical87 and physicochemical aspects of the mechanical microenvironment beyond T-cell-4 7 \nAPC contact mechanics (e.g., the ECM 88,89, lymphoid tissue microenvironment in both disease and 4 8 \nhomeostasis90–92, tumor microenvironments9,93–96, etc.) are important as well97.  4 9 \nThe complex dynamics of TCR mechanical proofreading can be distilled into a simpler 5 0 \nparametric framework governed by active power and mechanical coupling. In the asymptotic limits of 5 1 \nsubstrate stiffness (approaching 0 pN/nm and 1000 pN/nm), the substrate effectively decouples the 5 2 \nTCR and LFA-1 coreceptors. In these regimes, active energy transport is minimized, and the physical 5 3 \nconstraints on the TCR are dictated entirely by the passive properties of the membrane. However, at 5 4 \nintermediate substrate stiffnesses, the substrate acts as a mechanical conduit. This allows the 5 5 \nactomyosin-driven molecular clutch of LFA-1 to ‘talk’ to the TCR, actively tuning the force landscape 5 6 \nto hit the catch/slip transition and maximize proofreading precision. To rigorously test and potentially 5 7 \nfalsify this model, future experimental strategies can actively decouple these parameters. For 5 8 \nexample, perturbing the intrinsic membrane stiffness via cholesterol doping 98, or utilizing pMHC 5 9 \nligands with artificially high catch/slip transition forces14,15,99,100, should theoretically shift or abolish the 6 0 \nproofreading optimum. By assessing TCR discriminatory precision against these modified parameters 6 1 \nacross both zero-stiffness and finite-stiffness substrates, experimentalists could directly validate the 6 2 \nnecessity of this mechanical circuit in active antigen discrimination. 6 3 \nOur findings emphasize the potential mechanical determinants of TCR signal amplification, 6 4 \nand may have utility for exploring in vitro  T-cell-material interface variable spaces and additional 6 5 \nmechanoimmunological investigation of TCR-ligand discrimination, antigen recognition, and activation. 6 6 \nThe reported mathematical framework may additionally be used to dramatically constrain and 6 7 \nformulate future mechanochemical feedback models of TCR signal transduction and T-cell activation. 6 8 \nMethods (36 words) 6 9 \nNumerical methods 7 0 \nNonlinear least-squares regression methods and simulations were implemented in MATLAB R2024a 7 1 \nto solve constitutive equations or extract parameters from the literature ( Appendix Table a1. ). Data 7 2 \nwas visualized in either MATLAB R2024a or Prism v10.4.1. 7 3 \nAcknowledgements (138 words) 7 4 \nWe thank Dr. Sungmin Nam (Harvard University), Dr. Yuesong Hu (Wyss Institute), Rohan 7 5 \nThakur (Massachusetts Institute of Technology), Dr. Kwasi Adu-Berchie (Wyss Institute), Dr. Andrew 7 6 \nKhalil (Whitehead Institute and Wyss Institute), Dr. Vinny Chandran Suja (Harvard University), Dr. 7 7 \nDebraj Ghose (Wyss Institute), Aditya Patil (Harvard University), Dr. Ross Jones (University of British 7 8 \nColumbia), Dr. Ajinkya Ghagre (University of British Columbia), and Dr. Khalid Salaita (Emory 7 9 \nUniversity) for valuable scientific discussions and/or suggestions during the preparation of this 8 0 \nmanuscript. We thank Dr. Ze Gong (University of Science and Technology of China) for valuable 8 1 \nscientific discussions on the initial theoretical concept and for providing example MATLAB 8 2 \nimplementations. We thank Dr. Melissa Lever (Marks and Clerk) for providing example MATLAB 8 3 \nimplementations. We acknowledge funding from the NIH NCI (Wyss Institute i3 center, F99/K00), 8 4 \nWellcome Leap Foundation (HOPE), and NSF (Harvard MRSEC). 8 5 \nAppendix (33 words) 8 6 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n14 \n \nKey model derivations, model parameters, parameter calculations and additional equations, and 8 7 \nadditional analytical data are provided in the appendix. MATLAB script of the model implementation 8 8 \nencompassing all master equations are uploaded on GitHub. 8 9 \nAuthor contributions (23 words) 9 0 \nN.J. and S.S. 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M echanical In ter actions Imp act th e Functi ons of Immune C ells an d7 2 \nApplicatio n in Immunoengin eering . Adv. Ther.  8 , e00067 ( 2025) . 7 3 \n98. Surls, J. et al. Incre ased Memb rane C hol e sterol in Lymphocytes D iv erts T-C ells toward an Inflammat ory 7 4 \nResponse . PLOS ONE  7 , e38733 ( 2012 ) . 7 5 \n99. C hen, X. et al.  Ov ercoming T cell tole ranc e to tumo r self-antigens t hrough catch-b ond enginee ring. Scien7 6 \neadx3162 ( 2026) . 7 7 \n100. Mallis, R. J . et al. Biophysical and S truc tu ral Fea tures of αβT-C ell Recep tor M echa nosensing: A P aradigm a7 8 \nin Underst anding T-C ell Activ ation . Immunol. Rev.  329 , e13432 ( 2025) . 7 9 \n 8 0 \n8 1 \nFig. 1. The magnitude of receptor-ligand force dictates reaction rate competition in the mechanical proof8 2 \nframework. a) Schematic of mechanical proofreading model recapitulating key features of a T- cell adhering to an8 3 \nsurface decorated with c-pMHC, n-pMHC, and ICAM-1. b) Mechanical proofreading framework that incorporates8 4 \nsignaling and catch/slip bond behavior exhibited by TCR-ligand binding. c) Kinetics and kinematics of LFA-1-ICAM8 5 \nformation in a molecular clutch framework. Force generation in response to resistance supplied by the elastic8 6 \nfacilitates LFA-1-mediated adhesion, and passively energizes TCR- ligand binding through the injection of me8 7 \nenergy by force balance. d) TCR-c-pMHC and LFA-1-ICAM-1 bonds exhibit catch bond behavior, whereas TCR -8 8 \nbonds exhibit slip bond behavior. e) Bond lifetimes and dissociation constants of TCR-c-pMHC, TCR-n-pMHC, and8 9 \nICAM-1 binding kinetics as a function of force. f) Off rate competition between TCR catch/slip and LFA- 1 catch b9 0 \n19 \nt echnol. \nd  Their \nce 391 , \na tic Shift \n \nofreading \n an elastic \ntes limited \nM-1 bond \ntic surface \nechanical \n-n-pMHC \nnd LFA-1-\nh bond off \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n20 \n \nrates. g) ITAM phosphorylation rate competition with TCR-c-pMHC catch bonds and TCR-n-pMHC slip bonds. h) Limited 9 1 \nsignaling complex decay rate competition with TCR-c-pMHC catch bonds and TCR-n-pMHC slip bonds. 9 2 \n 9 3 \nFig. 2. The magnitude of receptor-ligand force controls TCR-ligand proofreading precision and error. a) Schematic 9 4 \nof mechanokinetic TCR-ligand discrimination with catch/slip off rates and TCR-ligand bond interfacial surface density as a 9 5 \nfunction of force. b) Signaling competent TCR-c-pMHC bond interfacial surface density as a function of force from 9 6 \n1 /g3409  /g2016 /g3409 10  proofreading sequences. c) Aberrant signaling competent TCR-n-pMHC bond interfacial surface density as a 9 7 \nfunction of force from from 1 /g3409  /g2016 /g3409 10  proofreading sequences. d) TCR signal amplification precision and error as a 9 8 \nfunction of force from 1 /g3409  /g2016 /g3409 10  proofreading sequences. e) Kinetic competition of c-pMHC and erroneous n-pMHC-9 9 \nmediated TCR phosphorylation as a function of mechanical force from 1 /g3409  /g2016 /g3409 10  proofreading sequences. f) 0 0 \naccumulate precision and error of TCR signal amplification as a function of mechanical force. g) accumulated error and 0 1 \nprecision are calculated by taking the total product of precision and error across 1 /g3409  /g2016 /g3409 10  proofreading sequences. 0 2 \nTCR force is normalized to /g2018 /g3021/g1864 /g3021\n/g2868 ~ 9 pN. 0 3 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n21 \n \n 0 4 \nFig. 3. TCR-pMHC catch/slip bond amplitude and Gibbs free energy minimization are controlled by receptor-0 5 \nligand force magnitude and APC surface stiffness. a) Standard state change in Gibbs free energy of OT1(†) TCRs 0 6 \nengaging various c-pMHCs or R4 n-pMHC as a function of force. b) Catch/slip bond behavior exhibited by OT1(†) TCR-0 7 \nligand binding as a function of force. c) Standard state change in Gibbs free energy of OT1(†) TCRs engaging various c-0 8 \npMHCs or R4 n-pMHC as a function of APC surface stiffness. d) Catch/slip bond behavior exhibited by OT1(†) TCR-0 9 \nligand binding as a function of APC surface stiffness. 1 0 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n \n1 1 \nFig. 4. LFA-1 molecular clutch dynamics at steady-state modulates TCR- ligand proofreading precision an1 2 \nin response to APC surface stiffness. a) Schematic of mechanokinetic TCR- ligand discrimination with catch1 3 \nrates in concert with LFA-1 molecular clutch dynamics. b) Signaling competent TCR-c- pMHC bond interfacial 1 4 \ndensity as a function of APC surface stiffness from  proofreading sequences. c) Aberrant signaling co1 5 \nTCR-n-pMHC bond interfacial surface density as a function of APC surface stiffness from from  proo1 6 \nsequences. d) TCR signal amplification precision and error as a function of APC surface stiffness from 1 7 \nproofreading sequences. e) accumulate precision and error of TCR signal amplification as a fu nction of APC 1 8 \nstiffness. APC surface stiffness is normalized to 1 pN/nm. 1 9 \n22 \n \n and error \ntch/slip off \nial surface \ncompetent \noofreading \n \nC surface \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n23 \n \n 2 0 \nFig. 5. Active power generated by LFA-1-ICAM-1 bonds and TCR catch/slip bond amplitude enables TCR signal 2 1 \namplification through elastic energy storage in TCR-pMHC bonds . a) Elastic energy storage (in units of kBT) in TCR-2 2 \npMHC bonds with different antigen types as a function of APC surface stiffness. b) Active power (energy transport) in total 2 3 \nbound LFA-1-ICAM-1 complexes as a function of APC surface stiffness for OT1(†) TCRs engaging varying c-pMHC or n-2 4 \npMHC. c) TCR signal amplification precision as a function of the relative ratio of active power in LFA-1-ICAM-1 complexes 2 5 \nwhen OT1(†) TCRs engage different c-pMHC relative to R4-loaded n-pMHC. 2 6 \n 2 7 \n 2 8 \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint \n\n \n2 9 \nFig. 6. Mechanical filtering with LFA-1 determines TCR signal amplification in the mechanical proof3 0 \nframework. a) Elastic energy storage (in units of k BT) in TCR-pMHC bonds, LFA-1-ICAM-1 bonds, and the APC3 1 \nas a function of APC surface stiffness. b) Active power (energy transport) in total bound LFA-1-ICAM- 1 complex3 2 \nfunction of APC surface stiffness and TCR signal amplification precision as a function of the relative ratio of activ3 3 \nin LFA-1-ICAM-1 complexes when TCRs engage c-pMHC versus n-pMHC. c) Schematic of conventional3 4 \nproofreading mechanism in TCR-ligand discrimination, where the amount of free energy that is expended to impro3 5 \nsignaling precision is fixed a priori intracellularly in a speed/energy dissipation tradeoff. d) Schematic of me3 6 \nproofreading mechanism in TCR-ligand discrimination involving cooperativity with LFA- 1 coreceptors. In me3 7 \nproofreading, Mechanical filtering between LFA-1-ICAM- 1 bonds and the TCR determines mechanical energy t3 8 \nfrom engaged contractile actomyosin filaments to the TCR to facilitate ligand proofreading precision.  3 9 \n 4 0 \n  4 1 \n 4 2 \n24 \n \nofreading \nC surface \nlexes as a \ntive power \nnal kinetic \nrove TCR \nechanical \nechanical \ny transport \n.CC-BY 4.0 International licenseavailable under a \n(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 \nThe copyright holder for this preprintthis version posted May 14, 2026. ; https://doi.org/10.64898/2026.05.12.724610doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}