INTRODUCTION

Section:

ChooseTop of pageABSTRACTINTRODUCTION <<MODEL DEVELOPMENTRESULTSDISCUSSIONMETHODSSUPPLEMENTARY MATERIALOver the past three decades, several mechanical-based assays have been developed to measure the in situ reaction kinetics of receptor–ligand interactions in the absence and presence of force, respectively, on the surface of a living cell.11. B. Liu, W. Chen, and C. Zhu, “ Molecular force spectroscopy on cells,” Annu. Rev. Phys. Chem. 66, 427–451 (2014). https://doi.org/10.1146/annurev-physchem-040214-121742 These assays use an ultrasensitive force transducer functionalized with specific ligands, such as the micropipette (MP)22. S. E. Chesla, P. Selvaraj, and C. Zhu, “ Measuring two-dimensional receptor-ligand binding kinetics by micropipette,” Biophys. J 75(3), 1553–1572 (1998). https://doi.org/10.1016/S0006-3495(98)74074-3 [supplementary material Fig. 1(a)], biomembrane force probe (BFP)3,43. W. Chen, J. Lou, and C. Zhu, “ Forcing switch from short- to intermediate- and long-lived states of the alphaA domain generates LFA-1/ICAM-1 catch bonds,” J. Biol. Chem. 285(46), 35967–35978 (2010). https://doi.org/10.1074/jbc.M110.1557704. Y. Chen, B. Liu, L. Ju, J. Hong, Q. Ji, W. Chen, and C. Zhu, “ Fluorescence biomembrane force probe: Concurrent quantitation of receptor-ligand kinetics and binding-induced intracellular signaling on a single cell,” J. Vis. Exp. 285, 35967 (2015). [supplementary material Fig. 1(b)], and atomic force microscopy (AFM)5,65. B. T. Marshall, M. Long, J. W. Piper, T. Yago, R. P. McEver, and C. Zhu, “ Direct observation of catch bonds involving cell-adhesion molecules,” Nature 423(6936), 190–193 (2003). https://doi.org/10.1038/nature016056. K. K. Sarangapani, T. Yago, A. G. Klopocki, M. B. Lawrence, C. B. Fieger, S. D. Rosen, R. P. McEver, and C. Zhu, “ Low force decelerates L-selectin dissociation from P-selectin glycoprotein ligand-1 and endoglycan,” J. Biol. Chem. 279(3), 2291–2298 (2004). https://doi.org/10.1074/jbc.M310396200 [supplementary material Fig. 1(c)], to repeatedly contact a cell expressing, or a surface functionalized with, receptors of interest to enable formation of a low number of bonds for measurement. However, receptor–ligand interactions at this level are stochastic. Despite the best effort of the experimenter to ensure similarity between two contacts, the measurement outcomes are unlikely to be the same because they are random. Whether any single contact would result in binding is probabilistic, whether a binding event would survive ramping force to generate a lifetime event is probabilistic, and the level of ramp force at which a bond would rupture and the duration for which a bond would last are also randomly distributed.3,53. W. Chen, J. Lou, and C. Zhu, “ Forcing switch from short- to intermediate- and long-lived states of the alphaA domain generates LFA-1/ICAM-1 catch bonds,” J. Biol. Chem. 285(46), 35967–35978 (2010). https://doi.org/10.1074/jbc.M110.1557705. B. T. Marshall, M. Long, J. W. Piper, T. Yago, R. P. McEver, and C. Zhu, “ Direct observation of catch bonds involving cell-adhesion molecules,” Nature 423(6936), 190–193 (2003). https://doi.org/10.1038/nature01605 Therefore, many tests are required to estimate the probabilities or probability distributions of these random variables. One approach is to simultaneously measure a large number of cells in parallel, such as those done using a centrifugation assay,7,87. P. Li, P. Selvaraj, and C. Zhu, “ Analysis of competition binding between soluble and membrane-bound ligands for cell surface receptors,” Biophys. J. 77(6), 3394–3406 (1999). https://doi.org/10.1016/S0006-3495(99)77171-78. J. W. Piper, R. A. Swerlick, and C. Zhu, “ Determining force dependence of two-dimensional receptor-ligand binding affinity by centrifugation,” Biophys. J. 74(1), 492–513 (1998). https://doi.org/10.1016/S0006-3495(98)77807-5 a cell collision assay,9,109. W. Chen and C. Zhu, “ A model for single-substrate trimolecular enzymatic kinetics,” Biophys. J. 98(9), 1957–1965 (2010). https://doi.org/10.1016/j.bpj.2010.01.02010. M. Long, H. L. Goldsmith, D. F. Tees, and C. Zhu, “ Probabilistic modeling of shear-induced formation and breakage of doublets cross-linked by receptor-ligand bonds,” Biophys. J. 76(2), 1112–1128 (1999). https://doi.org/10.1016/S0006-3495(99)77276-0 or a resetting assay.1111. M. Long, J. Chen, N. Jiang, P. Selvaraj, R. P. McEver, and C. Zhu, “ Probabilistic modeling of rosette formation,” Biophys. J. 91(1), 352–363 (2006). https://doi.org/10.1529/biophysj.106.082909 A more commonly used approach tests one cell at a time but repeats the test many times in series. This is the approach of the adhesion frequency assay and force-clamp spectroscopic assay, which generate a random sequence of binary adhesion scores and a random series of bond lifetimes, respectively.Data from the adhesion frequency assay and force-clamp spectroscopic assay are unique in their ability to bridge knowledge about the structure and function of proteins and cells. Despite these advantages and utilities, such data remain underanalyzed and underutilized. In particular, the original analysis of the adhesion frequency assay2,12,132. S. E. Chesla, P. Selvaraj, and C. Zhu, “ Measuring two-dimensional receptor-ligand binding kinetics by micropipette,” Biophys. J 75(3), 1553–1572 (1998). https://doi.org/10.1016/S0006-3495(98)74074-312. W. Chen, V. I. Zarnitsyna, K. K. Sarangapani, J. Huang, and C. Zhu, “ Measuring receptor-ligand binding kinetics on cell surfaces: From adhesion frequency to thermal fluctuation methods,” Cell Mol. Bioeng. 1(4), 276–288 (2008). https://doi.org/10.1007/s12195-008-0024-813. V. I. Zarnitsyna and C. Zhu, “ Adhesion frequency assay for in situ kinetics analysis of cross-junctional molecular interactions at the cell-cell interface,” J. Vis. Exp. 57, e3519 (2011). https://doi.org/10.3791/3519 treats the experimentally generated binary adhesion score sequence as a Bernoulli process of an independent and identically distributed (i.i.d.) random variable neglecting any relationship between past and current interactions, i.e., assumes no memory. In many biological systems, however, prior molecular interactions can and do influence subsequent interactions, as exemplified in this work, although the underlying mechanisms vary from case to case. The relationship between prior and current interactions may reveal feedback mechanisms that could be important to many properties of the biological systems, such as sensitivity, stability, robustness, adaptiveness, resilience, etc., even at molecular and cellular levels. As an initial step toward developing methods for characterizing feedback systems, we built a model for analyzing the impact on current interaction by the outcome of the immediate past interaction, i.e., short-term memory.1414. V. I. Zarnitsyna, J. Huang, F. Zhang, Y. H. Chien, D. Leckband, and C. Zhu, “ Memory in receptor-ligand-mediated cell adhesion,” Proc. Natl. Acad. Sci. U. S. A. 104(46), 18037–18042 (2007). https://doi.org/10.1073/pnas.0704811104 Within the context of this work, we refer to phenomena that molecular and cellular systems retain information about past molecular interactions as memory. Memory can manifest as both irreversible and reversible changes that influence subsequent interactions and may reflect mechanisms that occur in different timescales ranging from seconds, minutes, to hours. At a molecular level, memory can involve interactions between proteins mediating reversible changes like phosphorylation and de-phosphorylation and irreversible changes such as proteolytic cleavage. At a cellular level, memory can be caused by changes in receptor expression through internalization, degradation, and recycling, as well as proteolytic shedding.In this work, we employ three models to capture memory effects in three different timescales, ranging from seconds, minutes, to hours. We use our previous model for memory effect in the short timescale1414. V. I. Zarnitsyna, J. Huang, F. Zhang, Y. H. Chien, D. Leckband, and C. Zhu, “ Memory in receptor-ligand-mediated cell adhesion,” Proc. Natl. Acad. Sci. U. S. A. 104(46), 18037–18042 (2007). https://doi.org/10.1073/pnas.0704811104 to analyze new cases and develop two new models for the analyses of memory effects in the intermediate and long timescales. We apply these three memory models to a wide range of data collected over decades by different students and postdoctoral scholars of the Zhu lab, focusing on interactions of T cell antigen receptors (TCR) with peptide-major histocompatibility complex (pMHC) ligands but also including those of integrin αIIbβ3 with fibronectin (FN), Fc γ receptor IIIa (FcγRIIIa) with IgG Fc and anti-FcγRIIIa, and glycoprotein Ibα (GPIbα) with von Willebrand factor (VWF). We extend the short-term memory analysis from adhesion probability to bond lifetime under a range of forces, which are, respectively, related to binding affinity and force-dependent off-rate of dissociation. Our results demonstrate the validity and utility of the models, which provide analytical tools to classify and organize data as well as extract quantitative information in the forms of three memory indices. Future studies will apply these models to more systems and relate the memory indices to biological functions and mechanisms.

MODEL DEVELOPMENT

Section:

ChooseTop of pageABSTRACTINTRODUCTIONMODEL DEVELOPMENT <<RESULTSDISCUSSIONMETHODSSUPPLEMENTARY MATERIALWe used the adhesion frequency assay2,12,132. S. E. Chesla, P. Selvaraj, and C. Zhu, “ Measuring two-dimensional receptor-ligand binding kinetics by micropipette,” Biophys. J 75(3), 1553–1572 (1998). https://doi.org/10.1016/S0006-3495(98)74074-312. W. Chen, V. I. Zarnitsyna, K. K. Sarangapani, J. Huang, and C. Zhu, “ Measuring receptor-ligand binding kinetics on cell surfaces: From adhesion frequency to thermal fluctuation methods,” Cell Mol. Bioeng. 1(4), 276–288 (2008). https://doi.org/10.1007/s12195-008-0024-813. V. I. Zarnitsyna and C. Zhu, “ Adhesion frequency assay for in situ kinetics analysis of cross-junctional molecular interactions at the cell-cell interface,” J. Vis. Exp. 57, e3519 (2011). https://doi.org/10.3791/3519 to measure in situ kinetics of cross-junctional interactions between two surfaces, respectively, expressing receptors and ligands. One surface is part of a force transducer that enables detection of tensile forces between the two surfaces as a mechanical method to detect adhesion. Three types of force transducers employed in this study include: (1) a human red blood cell (RBC) pressurized by MP aspiration,2,15,162. S. E. Chesla, P. Selvaraj, and C. Zhu, “ Measuring two-dimensional receptor-ligand binding kinetics by micropipette,” Biophys. J 75(3), 1553–1572 (1998). https://doi.org/10.1016/S0006-3495(98)74074-315. J. Hong, S. P. Persaud, S. Horvath, P. M. Allen, B. D. Evavold, and C. Zhu, “ Force-regulated in situ TCR-peptide-bound MHC class II kinetics determine functions of CD4+ T cells,” J. Immunol. 195(8), 3557–3564 (2015). https://doi.org/10.4049/jimmunol.150140716. S. Pryshchep, V. I. Zarnitsyna, J. Hong, B. D. Evavold, and C. Zhu, “ Accumulation of serial forces on TCR and CD8 frequently applied by agonist antigenic peptides embedded in MHC molecules triggers calcium in T cells,” J. Immunol. 193(1), 68–76 (2014). https://doi.org/10.4049/jimmunol.1303436 (2) a glass bead attached to the pressurized RBC, or BFP,17,1817. J. Huang, V. I. Zarnitsyna, B. Liu, L. J. Edwards, N. Jiang, B. D. Evavold, and C. Zhu, “ The kinetics of two-dimensional TCR and pMHC interactions determine T-cell responsiveness,” Nature 464(7290), 932–936 (2010). https://doi.org/10.1038/nature0894418. B. Liu, W. Chen, B. D. Evavold, and C. Zhu, “ Accumulation of dynamic catch bonds between TCR and agonist peptide-MHC triggers T cell signaling,” Cell 157(2), 357–368 (2014). https://doi.org/10.1016/j.cell.2014.02.053 and (3) an AFM cantilever5,19,205. B. T. Marshall, M. Long, J. W. Piper, T. Yago, R. P. McEver, and C. Zhu, “ Direct observation of catch bonds involving cell-adhesion molecules,” Nature 423(6936), 190–193 (2003). https://doi.org/10.1038/nature0160519. T. Wu, J. Lin, M. A. Cruz, J. F. Dong, and C. Zhu, “ Force-induced cleavage of single VWFA1A2A3 tridomains by ADAMTS-13,” Blood 115(2), 370–378 (2010). https://doi.org/10.1182/blood-2009-03-21036920. T. Yago, J. Lou, T. Wu, J. Yang, J. J. Miner, L. Coburn, J. A. Lopez, M. A. Cruz, J. F. Dong, L. V. McIntire, R. P. McEver, and C. Zhu, “ Platelet glycoprotein Ibalpha forms catch bonds with human WT vWF but not with type 2B von Willebrand disease vWF,” J. Clin. Invest. 118(9), 3195–3207 (2008). https://doi.org/10.1172/JCI35754 [supplementary material Figs. 1(a)–1(c), see Methods]. These ultrasensitive transducers have a single piconewton (pN) force sensitivity, which detect adhesion mediated by as low as a single receptor–ligand bond.1212. W. Chen, V. I. Zarnitsyna, K. K. Sarangapani, J. Huang, and C. Zhu, “ Measuring receptor-ligand binding kinetics on cell surfaces: From adhesion frequency to thermal fluctuation methods,” Cell Mol. Bioeng. 1(4), 276–288 (2008). https://doi.org/10.1007/s12195-008-0024-8 The adhesion frequency assay used a series of repeated contact-retraction cycles between a single-paired receptor-bearing cell surface and ligand-coated force transducer to generate a binary sequence of positive or negative outcomes (1 for adhesion and 0 for no adhesion), which contain memory information in both short and intermediate timescales.

Model for no memory

The simplest binary adhesion score sequence analysis models repeated contact-retraction cycles as a Bernoulli process satisfying the i.i.d. assumption that implies no memory. Let the probability of having the positive outcome (binding, score = 1) be p (0 ⩽ p ⩽ 1) so the probability of having the negative outcome (no binding, score = 0) be 1 − p. p can be estimated from the average of all adhesion scores in the sequence, which is the adhesion frequency Pa. In our experiments, the ligand site densities were adjusted to such a range that the adhesion frequency would be 15% Pa22. S. E. Chesla, P. Selvaraj, and C. Zhu, “ Measuring two-dimensional receptor-ligand binding kinetics by micropipette,” Biophys. J 75(3), 1553–1572 (1998). https://doi.org/10.1016/S0006-3495(98)74074-3 The Poisson distribution depends on only one parameter, ⟨n⟩, the average number of bonds per contact that relates to the probability of having no bond by 1 − p = exp(−⟨n⟩). By modeling the receptor–ligand interaction as a second-order forward (driven by the densities of receptors, mr, and ligands, ml, via mass action) and first-order reverse (driven by the average number of bonds, ⟨n⟩) reversible reaction, Pa can be related to experimentally controlled and measured variables by2,122. S. E. Chesla, P. Selvaraj, and C. Zhu, “ Measuring two-dimensional receptor-ligand binding kinetics by micropipette,” Biophys. J 75(3), 1553–1572 (1998). https://doi.org/10.1016/S0006-3495(98)74074-312. W. Chen, V. I. Zarnitsyna, K. K. Sarangapani, J. Huang, and C. Zhu, “ Measuring receptor-ligand binding kinetics on cell surfaces: From adhesion frequency to thermal fluctuation methods,” Cell Mol. Bioeng. 1(4), 276–288 (2008). https://doi.org/10.1007/s12195-008-0024-8 Patc=1−exp−n1−nImi−1,(6b)where Fj is the random variable for the running adhesion frequency over j repetitive adhesion tests. E(Fj) and V(Fj) are the expected average and variance of Fj, respectively. Im is an irreversibility index for measuring the intermediate timescale memory effect. In the absence of irreversibility, Im = 0, Eqs. (6a) and (6b) reduce to EFj=1−exp−n=p,(6a′) VFj=1jexp−n1−exp−n=1jp1−p,(6b′)and we recover Bernoulli process properties. Thus, the non-zero Im captures the non-Bernoulli effect. The positive and negative Im values correspond to two scenarios: adhesions in the past progressively (1) reducing and (2) enhancing future adhesions, respectively.

Model for long memory

The stability of a pMHC molecule varies depending on a few contact residues that anchor the peptide to the MHC, resulting in highly variable timescales for peptide dissociation. To analyze slow peptide dissociation in a long timescale of hours, we use a first-order irreversible dissociation kinetics model, where kp is the peptide dissociation rate constant and te is the elapsed time during which peptide dissociates to describe the exponential decay of the functional pMHC density from ml0 to ml. It follows from Eqs. (1) and (7) that ntc,te=mrml0AcKa1−exp−kofftc exp−kpte=n0tcexp−kpte,(8a) Patc,te=1−exp−n0tcexp−kpte.(8b)Equations (8) describe an exponential decrease bond formation ability due to functional ligand loss over time. Similar scenarios include receptor down-regulation over time, or even upregulation over time due to activation associated with a negative kp value. In practice, the experimenter usually uses a sufficiently large tc to simplify Eqs. (8a) and (8b) because exp(–kofftc) → 0 as tc → ∞. The simplified equations are n∞,te=mrml0AcKaexp−kpte,(8c) Pa∞,te=1−exp−mrml0AcKaexp−kpte.(8d)A related parameter is the half time of peptide dissociation, t1/2, defined as time required for dissociation of half of the original pMHC ligands, i.e., ml(t1/2) = 1/2 ml0. It follows from Eq. (7) that t1/2 = ln2/kp.

RESULTS

Section:

ChooseTop of pageABSTRACTINTRODUCTIONMODEL DEVELOPMENTRESULTS <<DISCUSSIONMETHODSSUPPLEMENTARY MATERIAL

Analysis of in situ kinetics assuming no memory

We used the adhesion frequency assay2,12,132. S. E. Chesla, P. Selvaraj, and C. Zhu, “ Measuring two-dimensional receptor-ligand binding kinetics by micropipette,” Biophys. J 75(3), 1553–1572 (1998). https://doi.org/10.1016/S0006-3495(98)74074-312. W. Chen, V. I. Zarnitsyna, K. K. Sarangapani, J. Huang, and C. Zhu, “ Measuring receptor-ligand binding kinetics on cell surfaces: From adhesion frequency to thermal fluctuation methods,” Cell Mol. Bioeng. 1(4), 276–288 (2008). https://doi.org/10.1007/s12195-008-0024-813. V. I. Zarnitsyna and C. Zhu, “ Adhesion frequency assay for in situ kinetics analysis of cross-junctional molecular interactions at the cell-cell interface,” J. Vis. Exp. 57, e3519 (2011). https://doi.org/10.3791/3519 to measure in situ kinetics of cross-junctional interactions between TCR on T cell surfaces and pMHC-functionalized surrogate antigen presenting cells (APCs). Our experiments employed both CD4+ and CD8+ T cells from 3.L2, P14, or OT1 TCR transgenic mice, and human E8 TCR expressed on a Jurkat cell line. The surrogate APCs were RBCs for MP experiments (used to test OT1 and 3.L2 T cells) and glass beads for BFP experiments (used to test P14 and E8 T cells) coated with corresponding TCR ligands: p:I-Ek, p:H2-Dbα3A2, p:H2-Kbα3A2, or p:HLA-DR1. We first performed control experiments to test whether measured adhesions were mediated by specific TCR–pMHC interactions. The specificities of the adhesion frequencies to the p:H2-Dbα3A2 [for P14 TCR, Fig. 1(a)], p:H2-Kbα3A2 [for OT1 TCR, Fig. 1(b)], p:I-Ek [for 3L.2 TCR, Fig. 1(c)], and p:HLA-DR1 [for E8 TCR, Fig. 1(d)] were confirmed as they were abolished when the TCR or pMHC were either not coated on the BFP probe [streptavdin (SA) for P14 and E8] or replaced by the same MHC but presenting null peptides [Vesicular Stomatitis Virus (VSV) peptide for OT1 or Moth Cytochrome C (MCC) peptide for 3.L2]. We previously reported the 2D kinetic parameters of the OT1,1717. J. Huang, V. I. Zarnitsyna, B. Liu, L. J. Edwards, N. Jiang, B. D. Evavold, and C. Zhu, “ The kinetics of two-dimensional TCR and pMHC interactions determine T-cell responsiveness,” Nature 464(7290), 932–936 (2010). https://doi.org/10.1038/nature08944 3.L2,1515. J. Hong, S. P. Persaud, S. Horvath, P. M. Allen, B. D. Evavold, and C. Zhu, “ Force-regulated in situ TCR-peptide-bound MHC class II kinetics determine functions of CD4+ T cells,” J. Immunol. 195(8), 3557–3564 (2015). https://doi.org/10.4049/jimmunol.1501407 P14,2424. Y. J. Seo, P. Jothikumar, M. S. Suthar, C. Zhu, and A. Grakoui, “ Local cellular and cytokine cues in the spleen regulate in situ T cell receptor affinity, function, and fate of CD8+ T cells,” Immunity 45(5), 988–998 (2016). https://doi.org/10.1016/j.immuni.2016.10.024 and E82525. M. N. Rushdi, V. Pan, K. Li, S. Travaglino, H.-K. Choi, J. Hong, F. Griffitts, P. Agnihotri, R. A. Mariuzza, Y. Ke, and C. Zhu, “ Cooperative binding of T cell receptor and CD4 to peptide-MHC enhances antigen sensitivity,” Nat. Commun. 13, 7055 (2022). https://doi.org/10.1038/s41467-022-34587-w TCRs interacting with their corresponding ligands. Here we analyzed the interactions of 3.L2 TCR with ligands coated on RBCs by the CrCl method different from the biotin-streptavidin method used in previous studies (see Methods). Using a no memory assumption, we plotted the adhesion frequency Pa vs contact duration tc data and fitted the measured binding curves with Eq. (1a) [Figs. 1(e), 3(e), and 3(f)]. Evidently, the model fits all data very well. Using receptor and ligand densities measured from independent flow cytometry experiment (see Methods) we found the best-fit parameters the effective 2D affinity AcKa and off-rate koff for 3.L2 TCR interaction with three peptides, Hb, I72, and D73 presented by mouse pMHC class II, I-Ek [Figs. 1(f) and 1(g)].

Analysis of memory effect of a short timescale

We previously demonstrated that binary adhesion score sequences might not obey the i.i.d. assumption, manifesting as both positive (activating) or negative (inhibiting) memory effects depending on the underlying molecular interaction.1414. V. I. Zarnitsyna, J. Huang, F. Zhang, Y. H. Chien, D. Leckband, and C. Zhu, “ Memory in receptor-ligand-mediated cell adhesion,” Proc. Natl. Acad. Sci. U. S. A. 104(46), 18037–18042 (2007). https://doi.org/10.1073/pnas.0704811104 In particular, the OT1 TCR interaction with the agonist peptide OVA presented by mouse MHC class I H2-Kbα3A2 exhibited positive memory, quantified by a positive increase (Δp) in the positive outcome probability within the present adhesion test given a positive outcome of the immediate past adhesion test. Thus, the adhesion probability at the current contact-retraction test cycle is p + Δp or p depending on whether the immediate past test cycle resulted in adhesion or no adhesion.A signature of the positive memory effect is the consecutive presence of the same adhesion score (either 1 or 0) resulting in continuous increase or decrease in the running adhesion frequency Fj vs j curve or a cluster of the same binary score before changing the trend of Fj or the adhesion score value, as illustrated in Fig. 2(a). The measured P14 system cluster size distribution is illustrated in Fig. 2(b) together with the fit by our previously published model.1414. V. I. Zarnitsyna, J. Huang, F. Zhang, Y. H. Chien, D. Leckband, and C. Zhu, “ Memory in receptor-ligand-mediated cell adhesion,” Proc. Natl. Acad. Sci. U. S. A. 104(46), 18037–18042 (2007). https://doi.org/10.1073/pnas.0704811104 The model fit returned the p and Δp values for the P14 TCR–gp33:H2-Dbα3A2 interaction [Fig. 2(b)]. The Δp values of the OT1 TCR interactions with OVA and R4 peptides presented by H2-Kbα3A2 evaluated by the same fitting method are shown in Fig. 2(c). The positive Δp for OVA is consistent with our previous result, which we now extend to R4 [Fig. 2(c)]. In addition to these mouse TCRs on CD8+ T cells interacting with class I pMHCs, the interactions between the mouse 3.L2 and human E8 TCRs on CD4+ T cells with corresponding peptides presented by I-Ek and HLA-DR1, respectively, which are respective mouse and human class II MHCs, also show significant positive Δp values [Figs. 2(d) and 2(e)]. Interestingly, the memory index vanished when we used an inverted configuration to test the E8 TCR–pMHC interaction. In the normal configuration, the E8 TCR was expressed on the Jurkat T cell line and tested by soluble p:HLA-DR1 coated on the BFP glass bead surface. In the inverted configuration, the p:HLA-DR1 was expressed on THP-1 cells and tested by soluble E8 TCR ectodomain coated on the BFP glass beads. This finding suggests that the short-term memory in TCR–pMHC interactions requires the TCR to be expressed on cells.In addition to fitting the model to the data, we also used the one-step transition probability definitions to calculate directly from data [see Fig. 2(a)] the short-term memory index Δp for the P14 TCR–gp33:H2-Dbα3A2 interaction1414. V. I. Zarnitsyna, J. Huang, F. Zhang, Y. H. Chien, D. Leckband, and C. Zhu, “ Memory in receptor-ligand-mediated cell adhesion,” Proc. Natl. Acad. Sci. U. S. A. 104(46), 18037–18042 (2007). https://doi.org/10.1073/pnas.0704811104 (see Methods). Importantly, the Δp (and p) evaluated by the fitting method and the direct calculation agree well in general, as shown in the scattered plots of the values obtained by model fitting vs the values obtained by direct calculation, which line up fairly well along the 45° diagonal line for both Δp [Fig. 2(f)] and p [Fig. 2(g)], attesting to our methods' reliability.Using the non-zero Δp values for the 3.L2 TCR–p:I-Ek interactions in Fig. 2(d), we can now correct the 2D affinity values estimated using the model of no memory. From Eq. (4), Pa ≈ p/(1 − Δp). From Eq. (1b), AcKa = −ln[1 − p(∞)]/mrml ≈ −ln[1 − (1 − Δp)Pa(∞)]/mrml, indicating that the no memory assumption overestimates the effective 2D affinity. The corrected effective 2D affinity values are plotted along-side with the uncorrected values for comparison [Fig. 1(f)].

Analysis of memory effect of an intermediate timescale

In addition to short-term memory effect, which gives rise to adhesion event clusters but does not change the running adhesion frequency at the end, we sometimes observe adhesion frequency sequences in which the Pa calculated using the average of adhesion scores severely under- or overestimates the adhesion probability p, as exemplified by (1) 3.L2 TCR interacting with IAEM presented by I-Ek [Fig. 3(a)], (2) integrin αIIbβ3 interacting with FN in the presence of Ca2+/Mg2+ or Mg2+/EGTA with prior mechano-signaling via GPIbα [Fig. 3(c)], (3) FcγRIIIa interacting with anti-FcγRIIIa antibody [supplementary material Fig. 2(a)], and (4) GP1bα interacting with VWF A1A2A3 tri-domain in the presence of ADAMTS-13 in solution [supplementary material Fig. 2(b)].In the first case, the IAEM peptide is a mutant form of the WT peptide Hb for the 3.L2 TCR with residue substitutions greatly reducing peptide interaction with the MHC-II molecule.2626. K. R. Ryan, L. K. McNeil, C. Dao, P. E. Jensen, and B. D. Evavold, “ Modification of peptide interaction with MHC creates TCR partial agonists,” Cell Immunol. 227(1), 70–78 (2004). https://doi.org/10.1016/j.cellimm.2004.01.003 The weakened anchor might cause the IAEM peptide to dissociate and be replaced by the null peptide MCC (see Methods) causing the ligand to lose function, which did not occur for the WT peptide Hb as it was stably bound to MHC [Fig. 3(a)].In the second case, integrin αIIbβ3 on human platelets either at resting state or pre-primed mechanically by exerting force on their surface GPIbα via engaged VWF A1 domain were tested by BFP beads coated with FN in the presence of 1 mM of calcium and magnesium each (Ca2+/Mg2+) or 1 mM of magnesium and EGTA each (Mg2+/EGTA).2727. Y. Chen, L. A. Ju, F. Zhou, J. Liao, L. Xue, Q. P. Su, D. Jin, Y. Yuan, H. Lu, S. P. Jackson, and C. Zhu, “ An integrin alphaIIbbeta3 intermediate affinity state mediates biomechanical platelet aggregation,” Nat. Mater. 18(7), 760–769 (2019). https://doi.org/10.1038/s41563-019-0323-6 For the mechanically pre-primed platelets in the presence of extracellular calcium, the repetitive formation of αIIbβ3–FN bonds and their forced dissociation induced mechanotransduction through αIIbβ3, resulting in integrin outside-in signaling and transition from the intermediate affinity state to the high affinity state [Fig. 3(c)]. The up-regulation of integrin took place gradually in the intermediate timescale because the outside-in signaling effects are accumulated over the repeated formation and forced dissociation of individual αIIbβ3–FN bonds. When calcium was chelated by EGTA, such mechano-signaling process was inhibited because extracellular calcium is required for it to occur. As a result, the integrins gradually returned from the intermediate state to the resting state [Fig. 3(c)]. For resting platelets, this mechanotransduction of integrin did not occur because it also requires αIIbβ3 to be pre-primed by mechano-signaling through GPIbα–VWF-A1 engagement2727. Y. Chen, L. A. Ju, F. Zhou, J. Liao, L. Xue, Q. P. Su, D. Jin, Y. Yuan, H. Lu, S. P. Jackson, and C. Zhu, “ An integrin alphaIIbbeta3 intermediate affinity state mediates biomechanical platelet aggregation,” Nat. Mater. 18(7), 760–769 (2019). https://doi.org/10.1038/s41563-019-0323-6 [Fig. 3(c)].In the third case, CHO cells expressing FcγRIIIa-GPI were tested by RBCs coated with human IgG or an anti-FcγRIIIa mAb (Leu-11).2828. S. E. Chesla, P. Li, S. Nagarajan, P. Selvaraj, and C. Zhu, “ The membrane anchor influences ligand binding two-dimensional kinetic rates and three-dimensional affinity of FcgammaRIII (CD16),” J. Biol. Chem. 275(14), 10235–10246 (2000). https://doi.org/10.1074/jbc.275.14.10235 The GPI membrane isoform is a fusion protein where the transmembrane and cytoplasmic segments of the WT FcγRIIIa have been replaced by a glycosylphosphatidylinositol (GPI) C-terminus for outer leaflet plasma membrane molecule mounting.2828. S. E. Chesla, P. Li, S. Nagarajan, P. Selvaraj, and C. Zhu, “ The membrane anchor influences ligand binding two-dimensional kinetic rates and three-dimensional affinity of FcgammaRIII (CD16),” J. Biol. Chem. 275(14), 10235–10246 (2000). https://doi.org/10.1074/jbc.275.14.10235 During the retraction phase of the contact-retraction cycles, pulling the FcγRIIIa-GPI molecule via an antigen–antibody bond (but not a FcγR–IgG Fc