Memory in repetitive protein–protein interaction series

Over 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.¹ These assays use an ultrasensitive force transducer functionalized with specific ligands, such as the micropipette (MP)² [supplementary material Fig. 1(a)], biomembrane force probe (BFP)^3,4 [supplementary material Fig. 1(b)], and atomic force microscopy (AFM)^5,6 [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.^3,5 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,^7,8 a cell collision assay,^9,10 or a resetting assay.¹¹ 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 assay^2,12,13 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.¹⁴ 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 timescale¹⁴ 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 α_IIbβ₃ 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.

We used the adhesion frequency assay^2,12,13 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,^2,15,16 (2) a glass bead attached to the pressurized RBC, or BFP,^17,18 and (3) an AFM cantilever^5,19,20 [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.¹² 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.

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 P_a. In our experiments, the ligand site densities were adjusted to such a range that the adhesion frequency would be 15% < P_a < 85%. This condition ensures binding to be mediated by a low number of receptor–ligand bonds for the Poisson distribution of bonds to apply.² 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, m_r, and ligands, m_l, via mass action) and first-order reverse (driven by the average number of bonds, ⟨n⟩) reversible reaction, P_a can be related to experimentally controlled and measured variables by^2,12

where A_c (kept constant throughout) and t_c (kept constant for a sequence of repeated contact-retraction cycles) are the respective contact area and contact duration. K_a is the two-dimensional (2D) affinity (with 2D area units, e.g., μm², rather than a 3D volume) and k_off is the off-rate (in s⁻¹). The 2D on-rate can be calculated as k_on = K_a × k_off (in μm² s⁻¹). The term behind the minus sign inside the curly brackets on the right-hand side of Eq. (1) can be identified as the average number of bonds ⟨n⟩, i.e.,

given that P_a = p = 1 − exp(−⟨n⟩) under the current assumption of no memory.

A close inspection of many binary adhesion score sequences suggests that the i.i.d. assumption may not be always valid as these sequences sometimes exhibit non-Bernoulli behaviors. The models used to characterize these non-Bernoulli behaviors depend on the timescale involved. For example, the i.i.d. assumption would be violated if the probability p of having a positive outcome (binding) in the current contact-retraction test becomes dependent on previous test outcomes, meaning the present has memory of the past. The one-step Markov process models the simplest deviation from the Bernoulli process, where the positive outcome of each test has two probabilities, p + Δp or p, depending on whether the outcome of the immediate past test is positive or negative. Here, Δp is termed the short-term memory index and can have a value >, < or = 0, corresponding to three scenarios of adhesion in the past that (1) enhances (positive memory), (2) inhibits (negative memory), or (3) has no influence on (no memory) future adhesions. The memory effect quantified by Δp has a very short timescale because each contact-retraction cycle takes no more than a couple of seconds cycling time plus the contact duration. Another reason for the short timescale is that the one-step Markov process considers memory only of the immediate past.

We previously developed a set of models for such short memory effects.^14,21,22 The memory index Δp can be evaluated using two methods, direct calculation or fitting to adhesion cluster distribution,¹⁴ or logistic models.^21,22 The direct calculation is based on the definitions:

1. p + Δp is the conditional probability of positive outcome of the present contact-retraction test given that the outcome of the immediate past test is positive;

2. p is the conditional probability of positive outcome of the present test given that the outcome of the immediate past test is negative;

3. 1 − (p + Δp) is the conditional probability of negative outcome of the present test given that the outcome of the immediate past test is positive; and

4. 1 − p is the conditional probability of negative outcome of the present test, given that the outcome of the immediate past test is negative.

From the adhesion score sequences measured from a given biological system, we segregated the binding events into four types [cf. Fig. 2(a)] and enumerated each: (1) binding events when the immediate past test also is a binding event, n₁₁; (2) binding events when the immediate past test is a no binding event, n₀₁; (3) no binding events when the immediate past test is a binding event, n₁₀; and (4) no binding events when the immediate past test also is a no binding event, n₀₀. Their occurrence frequencies, n₁₁/(n₁₁ + n₁₀), n₀₁/(n₁₁ + n₁₀), n₁₀/(n₀₁ + n₀₀), and n₀₀/(n₀₁ + n₀₀), where n₁₁ + n₁₀ = n₀₁ + n₀₀ = n is the total test events in a particular adhesion test sequence, can be used as estimates of p + Δp, p, 1 − (p + Δp), and 1 − p.¹⁴ Therefore,

The second method to evaluate p and Δp from experiment is fitting the experimentally measured to the theoretically expected cluster size distribution:¹⁴ 

where m is the cluster size, i.e., the number of positive outcomes appeared consecutively [cf. Fig. 2(a)]. For a given adhesion test sequence of n total events, we can enumerate the frequency M of cluster size of m (m = 1, 2, …, n) and fit Eq. (3) to the data to evaluate p and Δp as fitting parameters.

Due to the presence of the memory effect, the adhesion frequency P_a is a function of p and Δp,¹⁴ 

The far-right side of Eq. (4) approximates for large n (usually ≥ 50). When Δp = 0, P_a = p. Note that the average number of bonds ⟨n⟩ relates to p instead of P_a regardless of the Δp value, i.e.,

The upper branch of Eq. (5) is identical to Eq. (1), whereas the lower branch corrects for the case when Δp ≠ 0. Note ⟨n⟩ = −ln(1 − p) is related to the effective 2D affinity (A_cK_a) and off-rate (k_off) of the receptor−ligand interaction by Eq. (1b).

Therefore, for a given set of adhesion test sequences, we need to first determine from either direct calculation [Eq. (2a)] or fitting to the adhesion cluster distribution [Eq. (3)] to obtain p as a function of the receptor density m_r, ligand density m_l, and contact duration t_c before evaluating for A_cK_a and k_off from Eq. (1b).

Let us next consider memory effects of an intermediate timescale of minutes, as exemplified by the fast dissociation of peptide from the MHC molecules [supplementary material Fig. 1(a)]. In the adhesion frequency assay, after coating and washing, the pMHC molecules coated on the RBCs were exposed to an infinitely dilute solution, enabling peptide dissociation from the pMHC complex, manifesting a declining adhesion probability over a time sequence containing many contact cycles, and giving rise to a memory effect. Three other examples of memory effects arisen from gradual gain or loss of binding function are shown in Fig. 3(c) and supplementary material Fig. 2, which are caused by different mechanisms.

In these irreversible processes, the present test outcome would be affected not only by the outcome of the immediate past test, but all previous test sequence outcomes. Take for example the experiment that tested the proteolytic cleavage of the VWF A1A2A3 tri-domain by the enzyme A Distintegrin And Metalloproteinase with a ThromboSpondin type 1 motif, member 13 (ADAMTS13) [supplementary material Fig. 1(c)]. The tri-domain cleaved at the jth test would not be available for binding in not only the (j + 1)th test, but also any other tests after that. In other words, binding's impact is cumulative. Since a full repeated test cycle sequence usually takes several minutes to complete experimentally, such memory effect has an intermediate timescale of minutes. Here, we used a phenomenological model for this type of processes that exhibits a cumulative effect over a progressively changing running adhesion frequency,²³ 

where F_j is the random variable for the running adhesion frequency over j repetitive adhesion tests. E(F_j) and V(F_j) are the expected average and variance of F_j, respectively. I_m is an irreversibility index for measuring the intermediate timescale memory effect. In the absence of irreversibility, I_m = 0, Eqs. (6a) and (6b) reduce to

and we recover Bernoulli process properties. Thus, the non-zero I_m captures the non-Bernoulli effect. The positive and negative I_m values correspond to two scenarios: adhesions in the past progressively (1) reducing and (2) enhancing future adhesions, respectively.

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 k_p is the peptide dissociation rate constant and t_e is the elapsed time during which peptide dissociates to describe the exponential decay of the functional pMHC density from m_l0 to m_l. It follows from Eqs. (1) and (7) that

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 k_p value. In practice, the experimenter usually uses a sufficiently large t_c to simplify Eqs. (8a) and (8b) because exp(–k_offt_c) → 0 as t_c → ∞. The simplified equations are

A related parameter is the half time of peptide dissociation, t_1/2, defined as time required for dissociation of half of the original pMHC ligands, i.e., m_l(t_1/2) = 1/2 m_l0. It follows from Eq. (7) that t_1/2 = ln2/k_p.

We used the adhesion frequency assay^2,12,13 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-E^k, p:H2-D^bα3A2, p:H2-K^bα3A2, 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-D^bα3A2 [for P14 TCR, Fig. 1(a)], p:H2-K^bα3A2 [for OT1 TCR, Fig. 1(b)], p:I-E^k [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 OT1,¹⁷ 3.L2,¹⁵ P14,²⁴ and E8²⁵ 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 P_a vs contact duration t_c 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 A_cK_a and off-rate k_off for 3.L2 TCR interaction with three peptides, Hb, I72, and D73 presented by mouse pMHC class II, I-E^k [Figs. 1(f) and 1(g)].

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.¹⁴ In particular, the OT1 TCR interaction with the agonist peptide OVA presented by mouse MHC class I H2-K^bα3A2 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 F_j vs j curve or a cluster of the same binary score before changing the trend of F_j 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.¹⁴ The model fit returned the p and Δp values for the P14 TCR–gp33:H2-D^bα3A2 interaction [Fig. 2(b)]. The Δp values of the OT1 TCR interactions with OVA and R4 peptides presented by H2-K^bα3A2 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-E^k 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-D^bα3A2 interaction¹⁴ (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-E^k interactions in Fig. 2(d), we can now correct the 2D affinity values estimated using the model of no memory. From Eq. (4), P_a ≈ p/(1 − Δp). From Eq. (1b), A_cK_a = −ln[1 − p(∞)]/m_rm_l ≈ −ln[1 − (1 − Δp)P_a(∞)]/m_rm_l, 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)].

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 P_a 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-E^k [Fig. 3(a)], (2) integrin α_IIbβ₃ 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.²⁶ 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 α_IIbβ₃ 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).²⁷ For the mechanically pre-primed platelets in the presence of extracellular calcium, the repetitive formation of α_IIbβ₃–FN bonds and their forced dissociation induced mechanotransduction through α_IIbβ₃, 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 α_IIbβ₃–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 α_IIbβ₃ to be pre-primed by mechano-signaling through GPIbα–VWF-A1 engagement²⁷ [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).²⁸ 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.²⁸ 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 bond) might uproot it from the cell membrane because the GPI anchor is thought to be weaker than the antigen–antibody bond (but not the FcγR–IgG Fc bond) [supplementary material Fig. 2(a)].²³ 

In the fourth case, GP1bα on the platelet membrane binds the A1 domain of the plasma protein VWF to initiate the hemostatic and thrombotic cascade.²⁰ VWF uses the A3 domain interaction with collagen to immobilize on subendothelial surface of disrupted blood vessel wall. The adhesiveness depends on VWF multimer size, which is regulated by the plasma proteolytic enzyme ADAMTS13 that cleaves an A2 domain peptide bond. This cleavage site is cryptic because it is buried inside the folded A2 domain. Mechanical force on the VWF unfolds the A2 domain, enabling ADAMTS13 to access the exposed cryptic site for proteolytic cleavage, breaking the VWF into smaller multimers.¹⁹ We previously used the AFM [supplementary material Fig. 1(c)] to demonstrate this process of pulling-induced unfolding and resulting cleavage by ADAMTS13 of the A2 domain in vitro,¹⁹ giving rise to a progressive decline in the running adhesion frequency [supplementary material Fig. 2(b)].

While the biological mechanisms differ, a common feature of the aforementioned processes can be revealed by another non-Bernoulli behavior of the binary adhesion score sequences. This feature manifests as a gradual change in the running adhesion frequency as the number of repeated test cycles becomes larger and larger, as illustrated in Figs. 3(a) and 3(c), and supplementary material Fig. 2. Since a full sequence of test cycles usually takes several minutes to complete experimentally, the memory effect accumulation has an intermediate timescale of minutes. We have developed a phenomenological model for this type of processes that exhibits a cumulative effect over a progressive change in running adhesion frequency, capturing the memory effect by an irreversibility index I_m²³ [see Eq. (6) in model development]. Comparisons of the model prediction and experimental data are illustrated in Figs. 3(a) and 3(c) and supplementary material Fig. 2, showing that our model is indeed capable of fitting the data well in all four cases. The irreversibility indices extracted from 3.L2 TCR interacting with the Hb and IAEM peptides presented by I-E^k are shown in Fig. 3(b) and those extracted from integrin α_IIbβ₃ interacting with FN are shown in Fig. 3(d). The different I_m values in the TCR case can be explained by the long-term memory analysis because the dissociation half times for Hb and IAEM pMHCs are >100 h and <20 min, respectively (see below).

As another way to evaluate PPI memory of the intermediate timescale, we compared adhesion probabilities estimated from different segments of the binary adhesion score sequence measured from the same cell over time. We ran repetitive adhesion tests using multiple cells. For each cell the data were segregated into two groups consisting of adhesion scores measured from the first and last half of the contact cycles to estimate two adhesion frequencies. For each group, the adhesion frequencies P_a at the same contact time t_c were pooled from all cells tested to generate two P_a vs t_c plots to compare with each other and with all the data without segregation. We generated such P_a vs t_c plots for adhesions mediated by interactions of E8 TCR on Jurkat cells with TPI:HLA-DR1 on BFP beads [Fig. 3(e)], and E8 TCR on BFP beads with TPI:HLA-DR1 on THP-1 cells [Fig. 3(f)]. In both cases, the effective 2D affinity A_cK_a and off-rate k_off evaluated from the three groups of data are statistically indistinguishable [Figs. 3(g) and 3(h)], indicating the lack of memory and the stability of the pMHC.

Depending on the peptide, the timescale of peptide dissociation from MHC molecules varied from minutes to over 100 h. The latter time is much longer than the time spent measuring a typical sequence of repeated adhesion tests, making it difficult to quantify the long-term memory effect using the irreversibility index I_m. To assess the loss of binding function due to slow dissociation of the peptide from the pMHC complex, we developed an adhesion frequency-based assay where the cognate peptide dissociated from the RBC-coated pMHC molecule in a solution without cognate peptide but with a high concentration of null peptide to block rebinding of the dissociated cognate peptide (see Methods). Using five pairs of T cells and RBCs, we performed five sequences of 50 repeated adhesion tests of 5-s contact duration each for each TCR–pMHC pair. Given the fast off-rates of the TCR–pMHC interactions studied here, 5-s contact duration is long enough (i.e., k_off⋅t_c ≫ 1) for the adhesion frequency P_a to reach steady-state^15,17 [see Figs. 1(e), 3(e), and 3(f)]. Although ∼30 min was required to measure five pairs of cells, we assumed that the mean ± SEM P_a values were measured at a single elapsed time point starting from the initial time (t_e = 0). We then generated two sets of steady-state P_a vs elapsed time t_e data, one for OT1 TCR and the other 3.L2 TCR, each interacting with a panel of its specific pMHC ligands [Figs. 4(a)–4(c)]. As can be seen, the P_a for different peptides displayed different rates of decay over time. The data were fitted by Eq. (8d) to evaluate the peptide dissociation rate constant, k_p, or the half time for peptide dissociation, t_1/2 = ln2/k_p. The t_1/2 values for the two TCRs interacting with their corresponding pMHCs are plotted in Figs. 4(d) and 4(e) showed wide variations depending on the peptide.

For a peptide that dissociates at a t_1/2 of several tens of minutes, the interval between two successive elapsed time points should be no longer than 10 min to obtain enough time points in a dissociation curve for fitting. As such, the ∼30 min time required to measure five sequences of 50 repeated adhesion tests each is too long to be approximated by a single time point. We therefore developed a hybrid analysis to bridge the intermediate and long timescales (see Methods). We began the experiment at t_e = 0 and performed five 50 repeated adhesion tests at 0, 10, 20, 40, and 50 min to generate five P_a values at these time points using a single pair of cells. This was repeated four times using another four pairs of cells to generate four more mean ± SEM P_a values at the midpoints of the ∼5.8 min period taken to complete each 50 consecutive tests, each right-shifted by 10 min relative to the previous point. We then fitted our P_a vs t_e data with Eq. (8d) to evaluate a long timescale memory index, k_p = 0.04 ± 0.006 s⁻¹, and the calculated half-time for peptide dissociation, t_1/2 = 17.4 ± 0.7 s [Fig. 4(f)].

Alternatively, we plotted the mean ± SEM running adhesion frequency F_j of the five 50 contact cycle sequences vs test cycle number j (second x-axis) and elapsed time (first x-axis) in the same graph [Fig. 4(g)] but the starting point of each sequence was right-shifted by 10 min. These data were fitted to Eq. (8d) to evaluate another k_p (= 0.038 ± 0.0022 s⁻¹) and t_1/2 (= 18.4 ± 0.4 s) statistically indistinguishable from the respective previous values obtained from the first approach, shown by their comparable peptide dissociation half times [Figs. 4(f) and 4(g)].

The data in Fig. 4(g) were also fitted by Eq. (6) to evaluate an I_m, the memory index of the intermediate timescale. The best-fit F_j vs j curve plotted in Fig. 4(g) was similar to the best-fit P_a vs t_e curve. The t_1/2 = 24 min evaluated from the dissociation analysis corresponds to 214 contact cycles and an I_m value of 0.011.

As mentioned earlier, the original goal of the adhesion frequency assay was to measure in situ cross-junctional receptor–ligand interaction kinetics on living cell surfaces.^2,12,13 In the no memory, short-term memory, intermediate-term memory, and long-term memory cases, the 2D kinetic parameters could be calculated from p using Eqs. (1), (5), (6), and (8), respectively. In the latter three cases, the memory effects in the short, intermediate, and long timescales were quantified by Δp, I_m, and k_p, respectively. Note that the effective 2D affinity A_cK_a estimated from adhesion frequency P_a has to be corrected in the presence of a nonzero Δp [Fig. 1(f)]. Since affinity is the ratio of on-rate over off-rate, we asked the question of whether the presence of memory effect impacts on-rate, off-rate, or both.

To answer this question, we used the BFP force-clamp assay to measure single receptor–ligand bond lifetimes under a range of constant forces.^{15,17,18,25,29} Like the adhesion frequency assay, the force-clamp assay also generates a time series from each cell tested repeatedly. Unlike the adhesion frequency assay that generates two types of events (binding and no-binding), the time series resulted from the force-clamp assay includes three types of events: no-binding events, binding events, and lifetime events [Fig. 5(a)]. Like the adhesion frequency assay, the first two types of events can be respectively quantified by binary scores of 0's and 1's. Unlike the adhesion frequency assay, the last type of events must be quantified by a continuous positive variable of bond lifetime t_b (in s). The reciprocal average bond lifetime is equal to off-rate, i.e., ⟨t_b⟩ = 1/k_off for a first-order irreversible dissociation.⁵ A short-term memory index can be defined in a similar fashion to the definition of Δp but quantifies memory using a differential bond lifetime Δ⟨t_b⟩. This can be done by letting the average of bond lifetimes measured from lifetime events following a no-binding event be ⟨t_b⟩, the average of bond lifetimes measured from lifetime events following a binding event be ⟨t_b⟩+ Δ⟨t_b⟩₁, and the average of bond lifetimes measured from lifetime events following a lifetime event be ⟨t_b⟩+ Δ⟨t_b⟩₂ [Fig. 5(a)]. To evaluate Δ⟨t_b⟩₁ and Δ⟨t_b⟩₂ for the P14 TCR–gp33:H2-D^bα3A2 interaction, all bond lifetime measurements were segregated into three groups: (1) those measured from lifetime events following a no-binding event (group 1), a binding event (group 2), and a lifetime event (group 3). Unsegregated and segregated bond lifetime measurements were binned according to the forces under which they were measured, averaged, and plotted vs force. It is evident from Figs. 5(b) and 5(c) that the average bond lifetime vs force curves of all six cases are statistically indistinguishable, indicating the lack of short-term memory in the P14 TCR–gp33:H2-D^bα3A2 bond lifetimes. Since the adhesion frequency test sequences contain a positive Δp [Fig. 2(e)], our results suggest that short-term memory only impacts on-rate but not off-rate for P14 TCR–gp33:H2-D^bα3A2 interactions.

As a first approximation toward estimating the impact of intermediate memory on off-rate, we asked whether repeated contact cycles on the same T cell would result in changing bond lifetime over time or not. To answer this question, TCR–pMHC bond lifetimes were measured from multiple T cells each repeatedly tested 500–1000 contact cycles, resulting in hundreds of bond lifetime measurements. For each cell the data were segregated into two groups, consisting of bond lifetimes measured from the first and last half of the contact cycles. For each group the bond lifetimes were pooled from all cells tested and plotted vs force, which were compared with each other and with all the data without segregation. Two sets of experiments were performed: (1) purified E8 TCRαβ ectodomain proteins coated on BFP glass beads interacting with TPI:HLA-DR1 expressing on THP-1 cells [Fig. 5(d)], and (2) purified TPI:HLA-DR1 ectodomain proteins coated on BFP glass beads interacting with TCR expressing on Jurkat T cells [Fig. 5(e)]. In both cases, interestingly, the average bond lifetime vs force curves were statistically indistinguishable among the three groups, suggesting the lack impact of intermediate memory on off-rates and isolating the impact on on-rates.

The corresponding author joined the Bioengineering faculty of Georgia Institute of Technology led by the late Professor Robert M. Nerem in 1990 as a mathematical modeler. Under the support and mentorship of the late Professor Nerem, he developed a series of experimental capabilities in his laboratory with his students over the past three decades. In the memory of the late Professor Nerem, we summarized several observations made, ideas conceptualized, and mathematical models developed during this period for quantitatively analyzing memory effects in repetitive protein–protein interactions. Specifically, we developed, tested, and/or applied three mathematical models that describe the non-Bernoulli behaviors exhibited in random binary score sequences generated by the adhesion frequency assay^2,12,13,27 and continuous time series generated by the force-clamp spectroscopy assay.^{15,17,18,25,29} These two assays are designed to mechanically measure the in situ reaction kinetics of receptor–ligand interactions at the level of low number—as low as a single-receptor–ligand bond, which generate a random sequence of binary adhesion scores and a random series of bond lifetimes, respectively.

To extract receptor–ligand binding kinetics information from the random sequence of binary adhesion scores requires two steps: (1) estimate the probability of adhesion and (2) relate the adhesion probability to the kinetic parameters and other experimentally controlled variables. For the second step, we developed a probabilistic equivalent of the well-established deterministic reaction kinetics model by replacing the bond density with the bond probability distributions^2,12 [Eq. (1)]. For the first step, our initial publication assumed repeated contact-retraction test cycle sequences could be modeled as a Bernoulli sequence.² Bernoulli sequences assume i.i.d. and neglect influences of the past on the present, thereby neglecting memory to simplify the analysis. Nearly a decade after the first publication of the adhesion frequency assay, we reported an improved treatment of the random sequence of binary adhesion scores by modeling it as a one-step Markov process without the i.i.d. assumption.^14,21,22 By taking into consideration the influences of the past on the present, which we termed here as memory of a short timescale (seconds), we extracted additional information, the memory index Δp from the binary time sequences.

The present work first extended the application of the Markovian model to four TCRs interacting with their corresponding panels of pMHCs of class I or II, which further confirmed model validity and demonstrated that short-term memory is not an isolated phenomenon but commonly observable in TCR–pMHC interactions. Whereas many aspects of the underlying biological mechanisms for the short timescale memory remain to be elucidated, we showed that this memory requires the full-length TCR-CD3 complex to reside on the T cell, as memory vanished when soluble TCRαβ ectodomain was tested. Also, the 2D affinity estimated from the adhesion frequency assay should be modified to take into consideration the memory effect without which the A_cK_a value would be overestimated (for the case of positive Δp). Importantly, we did not observe accumulation of memory in TCR interactions with peptides stably bound to MHC, as seen to the case of memory in the intermediate timescale in which the peptide binding to MHC was unstable. This result indicates that the short timescale memory is unlikely caused by changes in TCR expression level, which is reasonable as TCR expression is not expected to change in such a short timescale.

The main part of this paper was the development, validation, and application of two new models for analysis of the random sequences of binary adhesion scores to capture non-Bernoulli behaviors in intermediate (minutes) and long (hours) timescales. The model of intermediate timescale considers the cumulative memory effect of the entire past event sequence, not just the immediate past of the current event as in the case of the one-step Markovian model for the short timescale memory. Several mechanisms have been suggested to give rise to memory effects in the intermediate and/or long timescales. These include receptor up- or down-regulation due to cell activation, inhibition, or trafficking, receptor extraction from the cell membrane by mechanical force, ligand instability due to peptide dissociation, ligand fragmentation by proteolytic cleavage, etc. By extending the original adhesion frequency assay, we presented examples of some of these cases to demonstrate the universal applicability of our models. Not only do our models help organize the data and provide more accurate results, but they also extract new information that otherwise was unobtainable, including the irreversibility index I_m and the peptide dissociation rate constant k_p or the half time for peptide dissociation t_1/2.

We generalized the short-term memory metric from Δp measured by the adhesion frequency assay to Δ⟨n⟩₁ and Δ⟨n⟩₂ measured by force-clamp assay. Regardless of the metrices and how they are quantified, the concept is the same, i.e., whether and how a past interaction influences the present interaction. The generalization lies in the parameter used to characterize interaction. It is necessary because we model receptor–ligand interaction by reaction kinetics, which requires at least two parameters for its characterization; therefore, two types of memory metrices are required to determine which kinetic parameter, or both, exhibit memory effects. Our data suggest that for TCR–pMHC interactions, only the on-rate, but not the off-rate, exhibits short-term memory. This finding, together with the finding that only cell surface TCR, but not soluble TCR, exhibits short-term memory, indicate that Δp is underlain by interaction of the TCR with cellular molecules rather than the properties of the TCRαβ ectodomain.

An interesting question is whether the Δp is carried via the organization/reorganization of membrane composition/compartmentalization or via the physical coupling of membrane receptors/proteins with underlying cytoskeleton. We previously showed that 2D on-rate, but not force-dependent 2D off-rate, of TCR–pMHC interactions is impacted by pharmacological perturbations of the cell membrane composition/compartmentalization and the cytoskeleton.³⁰ We hypothesize that the memory effect of the short timescale may stem from transition among different TCR states,^31,32 which should be tested in future studies.

By using ultrasensitive force techniques to measure receptor–ligand interaction at the level of a low number of bonds, we avoid perturbing the cell under investigation as much as possible. Still, one might ask whether minute stimulations from serial and intermittent engagements and force applications on individual receptors over time would alter the measurements. After all, we have observed that such repeated binding cycles resulted in intracellular calcium signaling.^16,18,33 To address this question, we segregated the time series of random outcomes generated by testing a single cell in a large number of repeated test cycles into subgroups depending on when they were measured in the time series (e.g., the first half vs the last half) and comparing the adhesion frequencies and bond lifetimes measured from the different subgroups, which could be thought of as quantifying intermediate memory in a model-independent way. Applying this analysis to the TCR–pMHC interactions, we tested whether the kinetic parameters measured by the adhesion frequency and force-clamp assays were convoluted by cellular changes induced by repeated cycles of serially engaging and exerting force on TCRs on the same cell over time. Our data indicate that there are no detectable changes in the force-dependent TCR–pMHC kinetic parameters within the intermediate timescale during which we tested a single cell, despite that T cells are known to be triggered to signal by such repeated test cycles.^16,18 Future studies will extend these models and methods to new applications for different biological systems, relate the memory effects to the biological functions of specific cells and specific receptors, and elucidate different biological mechanisms that can give rise to memory effects.

Transgenic P14 TCR, OT1, and 3.L2 TCR mice were housed at the Emory University Department of Animal Resources facility and experiments followed guidelines of the National Institutes of Health and protocols approved by the Institutional Animal Care and Use Committee of Emory University (IACUC Protocol No. 201700372). Naive T cells were purified via magnetic negative selection from spleens of six- to eight-week old mice using either CD4⁺ (for 3.L2) or CD8⁺ (for P14 and OT1) T-cell isolation kit (Miltenyi Biotec) according to the manufacturer's instructions. Cells were washed and stored at 4 °C for up to 24 h in R10 media, which consists of RPMI 1640 (Cellgro) supplemented with 10% fetal bovine serum (FBS, Cellgro), 2 mM L-glutamine (Cellgro), 0.01M HEPES buffer (Cellgro), 100 μg/ml gentamicin (Cellgro), and 20 μM 2-β-mercaptoethanol (2-BM) (Sigma-Aldrich).

Human platelets and red blood cells (RBCs) were isolated from the whole blood of healthy volunteers according to a protocol approved by the Institutional Review Board of the Georgia Institute of Technology (IRB Protocol No. H18296). For platelet isolation, blood was drawn to fill in a 3 ml syringe preloaded with 0.43 ml ACD buffer (85 mM sodium citrate, 72.9 mM citric acid anhydrous, 110 mM D-glucose, and 70 mM Theophylline, pH 4.6). Whole blood was transferred into a 15 ml tube pre-loaded with apyrase (0.005 U ml⁻¹) and Clexane (20 U ml⁻¹). After resting for 15 min at 37 °C, whole blood was centrifuged at 200 g for 10 min without brake. Platelet-rich plasma was extracted, allowed to rest for 10 min at 37 °C and centrifuged at 1700 g for another 5 min. The platelet pellet was resuspended into platelet washing buffer (4.3 mM K₂HPO₄, 4.3 mM Na₂HPO₄, 24.3 mM NaH₂PO₄, 113 mM NaCl, 5.5 mM D-glucose, 10 mM theophylline, and 1% BSA, pH 6.5) pre-added with Clexane (20 U ml⁻¹) and apyrase (0.01 U ml⁻¹), rested for 10 min and centrifuged again at 1500 g for 5 min. The platelet pellet was resuspended into HEPES-Tyrode buffer (134 mM NaCl, 12 mM NaHCO₃, 2.9 mM KCl, 0.34 mM sodium phosphate monobasic, 5 mM HEPES, and 5 mM glucose, 1% BSA, pH 7.4) pre-added with apyrase (0.02 U ml⁻¹) with a platelet count at 3 × 10⁸ ml⁻¹, read from a Sysmex KX-21N hematology analyzer (Kobe, Japan), and placed in a 37 °C water bath for 30 min before use. RBCs were purified by Histopaque-1077, washed with ice cold PBS, and resuspended in EAS-45 buffer (2 mM Adenine, 110 mM D-glucose, 55 mM D-Mannitol, 50 mM sodium chloride, 20 mM sodium phosphate, and 10 mM L-glutamine). Equal aliquots of RBCs were then mixed with various concentrations of EZ-Link Sulfo-NHS-LC-Biotin (Thermo Scientific) at a pH of 7.2 for 30 min at room temperature, yielding different densities of biotin sites on RBC surfaces. Biotinylated RBCs were washed with EAS-45 buffer and stored at 4 °C. For BFP experiments, freshly isolated human RBCs were biotinylated with biotin-PEG3500-NHS (Jenkem Technology) and then incubated with nystatin in N2 buffer (265.2 mM KCl, 38.8 mM NaCl, 0.94 mM KH2PO4, 4.74 mM Na₂HPO₄, and 27 mM sucrose; pH 7.2 at 588 mOsm) for 30 min on ice. Nystatin-treated biotinylated RBCs were washed twice with N₂ buffer and stored at 4 °C for BFP experiments.

TCR β-chain deficient Jurkat J.RT3 cells were purchased from ATCC (Manassas, VA) and cultured in RPMI 1640 supplemented with 10% FBS, 100 U/ml penicillin, 100 μg/ml streptomycin, 2 mM L-glutamine, and 20 mM HEPES. J.RT3 were transduced by lentivirus to express the E8 TCR. Briefly, E8 TCR α and β chains joined by a P2A element were subcloned into pLenti6.3 vector with a T2A-rat CD2 reporter. Lentivirus encoding E8 TCR were produced by co-transfection of HEK 293T cells with E8TCR-pLenti6.3, pMD2.G (Addgene #12259), and psPAX2 (Addgene #12260) using lipofectamine 3000 (ThermoFisher Scientific). J.RT3 cells were transduced by incubating overnight with supernatant containing lentivirus and FACS sorted using Aria cell sorter (BD Biosciences) based on the surface expression of E8 TCR.

THP-1 cells from ATCC were cultured in RPMI 1640 supplemented with 10% FBS, 100 U/ml penicillin, 100 μg/ml streptomycin, 2 mM L-glutamine, and 20 mM HEPES. One day prior to experiment, the cells were treated with 20–100 U/ml IFN-γ (R&D Systems) and 1 μM TPI peptide (Genscript) for surface expression of TPI:HLA-DR1 ligand for the E8 TCR.²⁵ 

Biotinylated FN was a generous gift from Andres Garcia (Georgia Tech, Atlanta, GA).²⁷ Biotinylated E8 TCRαβ were prepared as previously described.³⁴ Briefly, a 17-amino acid tag (TPI, GGGLNDIFEAQKIEWHE) was added to the C-terminus of the E8 TCRα ectodomain. E8 TCRαβ ectodomain protein was produced by in vitro folding from inclusion bodies expressed in E. coli.¹⁹ The purified proteins were biotinylated using biotin protein ligase (Avidity); excess biotin and ligase were removed with a Superdex 200 column (GE Healthcare).

The following recombinant pMHC class I and II monomers were from the National Institutes of Health Tetramer Core Facility at Emory University. For P14 TCR, the ligand was the LCMV Armstrong peptide gp_33–41 (KAVYNFATM) presented by H2-D^b (mouse MHC-I) with a C-terminal biotin tag.³⁵ For the OT1 TCR, the ligands consisted of the wild-type (WT) peptide OVA_323–339 (SIINFEKL) or an altered peptide R4 (SIIRFEKL) or V-OVA (RGYNYEKY), or a control peptide VSV (RGYVYQGL) presented by H2-K^b (mouse MHC-I) with a C-terminal biotin tag.¹⁷ Both mouse MHCs were mutated (MT) by replacing their α3 domain by that of the human HLA-A2 to prevent CD8 binding (H2-D^bα3A2 and H2-K^bα3A2). For the E8 TCR, the ligand was the melanoma antigenic peptide TPI derived from the glycolytic enzyme triosephosphate isomerase (GELIGTLNAAKVPAD) presented by HLA-DR1 (human MHC-II) with a C-terminal biotin tag.²⁵ 

For the 3.L2 TCR, I-E^k (mouse MHC-II), a generous gift from Peter Jensen (Emory University), was initially bound by a CLIP peptide but replaced prior to experiment by either the WT peptide murine hemoglobulin epitope Hb_64–76 (GKKVITAFNEGLK), or an altered peptide I72 (GKKVITAFIEGLK) or D73 (GKKVITAFNDGLK), or IAEM (GKKVITAAIEGLM) or MFEM (GKKVMTAFNEGLM), or a control peptide MCC from the moth cytochrome c (ANERADLIAYLKQATK).²⁶ The latter two peptides were produced by replacing two or three MHC anchor residues 68I, 71F, 73E and 78K of the Hb sequence at positions 1, 4, 6, and 9 by M, A, P, or M.²⁶ The null peptide MAEM (GKKVMTAANEGLM) was used as negative control.²⁶ 

The extracellular fragment of GPIbα (glycocalicin)³⁶ was purified from platelets as described.³⁷ Recombinant A1A2A3 with a 6-histidine tag at the C-terminus³⁸ and ADAMTS-13³⁹ were generous gifts of Miguel Cruz and Jinf-fei Dong, respectively (Baylor College of Medicine) and produced as previously described. Anti-His mAb was from Sigma (St. Louis, MO). Anti-A1 mAb CR1 was a generous gift from Michael Berndt (University College Cork, Cork, Ireland).

Two methods were used to coat pMHC on RBCs for the micropipette experiment—biotin–streptavidin (SA) coupling (for p:H2-K^b) and chromium chloride (CrCl₃) coupling (for p:I-E^k) the detailed procedures of both of which have been described previously.^2,17 Briefly, RBCs were biotinylated, conjugated with streptavidin, and incubated with C-terminally biotinylated p:H2-K^b.¹⁷ Alternatively, RBC's in 4% hematocrit were suspended in a 0.001% solution of CrCl₃ in 0.02M acetate buffer, pH 5.5. When 10 μg/ml p:I-E^k in phosphate free media was added, spontaneous coupling occurred. After 5 min the reaction was quenched with PBS, 5 mM EDTA with 1% BSA. RBC's were used immediately after protein coating.

To coat TCR or pMHC on glass beads for BFP experiments, silanized beads were covalently linked to SA-maleimide (Sigma-Aldrich) then conjugated with subsaturating C-terminally biotinylated TCR or p:MHC.^15,29,40

To functionalize the AFM system, cantilever tips were incubated with 10 μl per tip of GPIbα (10 μg/ml), CR1 (15 μg/ml), or BSA (1%) at 4 °C overnight, rinsed, and soaked in PBS containing 1% BSA to block nonspecific binding. Polystyrene dishes were thoroughly cleaned with absolute ethanol and dried with argon gas before protein adsorption. Surfaces were incubated with 10 μl per spot of A1A2A3 or anti-His mAb (15 μg/ml) at 4 °C overnight and washed two times with PBS. The anti-His mAb coated surfaces were further incubated with 10 μl per spot of A1A2A3 (5 μg/ml) at room temperature for 1 h. Dishes were then filled with PBS containing 1% BSA in the absence or presence of ADAMTS-13 (1.25–10 μg/ml) without or with 5 mM EDTA.

Site densities of TCRs, pMHCs, α_IIbβ₃, and FN were measured by flow cytometry^2,15,17,27 using fluorescent antibodies. Antibodies were used at 10 μg/ml concentration in 100 μl of FACS buffer (PBS without calcium and magnesium, 5 mM EDTA, 1% BSA, 25 mM HEPES, 0.02% sodium azide) at 4 °C for 30 min; fluorescent intensities were measured by the BD LSR II flow cytometer (BD Biosciences); and site densities were calculated by compared to the BD QuantiBRITE PE standard beads (BD Biosciences).

The detailed procedures of this assay using MP have been described previously^2,12,13,27 and it was used to test adhesions mediated by OT1 TCR–p:H2-K^b and 3.L2 TCR–p:I-E^k interactions. Briefly, two micropipettes holding a T-cell on one side and a pMHC-coated RBC on the other [supplementary material Fig. 1(a)] were controlled to make repeated contacts with a constant area (A_c). From the presence or absence of RBC shape elongation upon retraction after a contact time (t_c), the adhesion scores (1 for adhesion and 0 for no adhesion) in no less than 50 repeated contact-retraction cycles were enumerated to generate a binary sequence.

The adhesion frequency assay was also performed using BFP or AFM. The only difference was that the RBC was replaced by a ligand-coated force probe bead (in the case of BFP) or a microcantilever (in the case of AFM). Instead of observing the RBC shape elongation microscopically, the displacement of the bead or the deflection of the cantilever gave rise to a tensile force signal that signified adhesion.

Our BFP system [supplementary material Fig. 1(b)] has been described^{15,17,18,25,29} and it was used to test adhesions mediated by P14 TCR–p:H2-D^b interaction and integrin α_IIbβ₃–FN interactions.

The AFM [supplementary material Fig. 1(c)] was built in our laboratory as previously described.^5,19 It was functionalized in two ways: (1) A1A2A3 was adsorbed on a polystyrene surface and tested by an AFM tip coated with glycocalicin and (2) A1A2A3 was captured by an anti-His mAb preadsorbed on a polystyrene dish and tested by an AFM tip coated with the monoclonal antibody (mAb) CR1. To assess the memory effect in the intermediate timescale due to proteolytic cleavage, the experiments were performed with or without ADAMTS13 in the media.

To assess the memory effect of the long timescale due to ligand instability resulted from peptide dissociation from the pMHC, we first incubated the CLIP pMHC-coated RBCs in 100 μM of the peptide to be tested for a prolonged period of time to allow CLIP peptide on all pMHC molecules coated on the RBCs to be replaced by the peptide of interest. At time zero, the RBCs were spun down and the pellet was resuspended in an infinitely dilute solution to allow the peptide to dissociate from pMHC. A high concentration (100 μM) of null peptide (VSV or MCC for the RBCs bearing p:H2-K^b or p:I-E^k, respectively) was added to the solution to further block rebinding of the dissociated peptide. The clock for elapsed time was then turned from this point on. At each elapsed time point, an aliquot of RBC solution was added to a new cell chamber on top of the microscope stage and the micropipette adhesion frequency assay was performed to measure five sequences of 50 adhesion scores each using five T cell–RBC pairs to generate sufficient data for mean ± SEM. For a contact of 5-s duration, it took ∼5.8 min to perform 50 repeated contact-retraction tests using a single cell pair and ∼30 min to complete the assay with five pairs of cells. The 5-s contact time was chosen because it is long enough for the adhesion frequency P_a and adhesion probability p to reach steady-state [cf. Fig. 1(e)], which simplifies our analysis because we could take t_c as infinity in Eq. (8), making it dependent on t_e only.

For slow dissociating peptides that give rise to memory indices of long timescales (many hours), it seems reasonable to approximate a 30-min period by a single elapsed time point. The experiment was repeated in different elapsed time points to generate a P_a(∞, t_e) vs t_e curve for evaluation of k_p by fitting Eq. (8d) to the data. However, for memory effects of timescale of tens of minutes, which lies in between the intermediate and long timescales by our definitions, a 30 min period seemed too long to be considered as a single elapsed time point. To bridge the two timescales characterized by I_m and k_p, we designed the following experiment.

Instead of generating five sequences of 50 adhesion scores each using five T cell–RBC pairs upon adding to the cell chamber RBCs that had been in infinitely diluted media for peptide dissociation for a given elapsed time, we used a single RBC to test a single T cell for five sequences of 50 consecutive contact-retraction cycles upon adding to the cell chamber RBCs newly resuspended in infinitely diluted media from the cell pellet, i.e., RBCs at elapsed time zero. The experimenter started the first, second, third, fourth, and fifth 50 consecutive cycles at t_e = 0, 10, 20, 30, and 40 min. This experiment was repeated five times using five pairs of cells. These data were then analyzed in two ways.

First, each sequence was broken down in to five subsequences of 50 binary scores each for calculation of an adhesion frequency P_a for that subsequence. The P_a values of the first subsequences of the five cell pairs were used to calculate the mean ± SEM P_a for the first elapsed time point approximated by the midpoint of the 5.8 min duration taken to complete 50 repeated tests (2.9 min). The mean ± SEM P_a values of the second, third, fourth, and fifth subsequences of the five cell pairs were also generated the same way for the second (12.9 min), third (22.9 min), fourth (32.9 min), and fifth (42.9 min) elapsed time points. These P_a vs t_e data were then fitted by Eq. (8d) to evaluate a k_p, the memory index of the long timescale [Fig. 4(f)].

Second, the mean ± SEM running adhesion frequency data of the five 50 adhesion score sequences were plotted vs the elapsed time (first x-axis) and the contact cycle number (second x-axis). The contact cycle number is related to the elapsed time by a conversion factor of 1 cycle = 7 s. Since 50 contact cycles took only ∼5.8 min, the starting time for next sequence has to be right-shifted by ∼4.2 min [Fig. 4(g)]. These data were fitted to Eq. (8d) to evaluate another k_p to compare with the previous value evaluated form the first approach. The data in Fig. 4(g) were also fitted to Eq. (6) to evaluate an I_m, the memory index of the intermediate timescale.

We first calculated the adhesion frequency P_a (= average adhesion scores) from the measured binary adhesion score sequences. We also calculated the probability of adhesion p and the short timescale memory index Δp using both the direct method [Eq. (2)] and fitting to the adhesion cluster size distribution [Eq. (3)]. Fitting Eq. (1a) to the P_a vs t_c data allowed us to evaluate the effective 2D affinity A_cK_a and off-rate k_off. Using Eq. (4) to account for the difference between P_a and p allowed us to correct the A_cK_a value in the presence of Δp [cf. Fig. 1(f)]. Fitting Eq. (6) to the running adhesion frequency data returned I_m, the memory index for intermediate timescale. Finally, fitting Eq. (8) to adhesion frequency measured at different elapsed time points returned k_p, the memory index for long timescale.

This assay has been described previously,^{15,17,18,25,29} and it was used to measure force-dependent lifetimes of P14 TCR–p:H2-D^b and E8 TCR–TPI:HLA-DR1 bonds. During the experiment, a protein-coated bead (tracking bead) was attached to the apex of a micropipette-aspirated RBC that serves as a spring with pre-adjusted spring constant of 0.1–0.3 pN/nm. For force-clamp assay, the tracking bead was repeatedly contacted by a piezo-driven target bead coated with (or target cell expressing) the corresponding binding partner(s). The displacement of tracking bead was monitored with a high-speed camera at >1000 fps and was translated into force by applying the pre-defined spring constant. During separation, bond formation between tracking bead and target bead/cell pulled the tracking bead away from its baseline, manifesting positive force loading on the molecular bond. Bond lifetime was defined as the duration from the start of clamp at the preset force level to bond rupture. Several hundred bond lifetime events were collected and pooled for various clamp force bins using multiple bead-bead or bead-cell pairs.

Model fitting primarily used GraphPad Prism version 9.4.1 compiled for Windows 10 for least squares regression except for Δp, p, and I_m which utilized Python 3.9 with the common analysis packages NumPy and SciPy for Limited-memory Broyden–Fletcher–Goldfarb–Shanno bound (L-BFGS-B) fitting with the appropriate fitting constraints.

The supplementary material includes two supplementary figures. Supplementary material Fig. 1 provides illustrations of the experimental systems used in producing the data featured within the paper. Supplementary material Fig. 2 exemplifies memory on an intermediate timescale using two experimental systems, showing the intermediate timescale model's utility in characterizing changes in receptor surface density and enzymatic cleavage.

We thank the late Professor Robert M. Nerem for his inspiration and teaching over the years. We also thank Jenny Ning Jiang, Kaitao Li, Larissa Doudy, and Laurel Ann Lawrence for technical assistance, Peter Jensen for providing purified p:I-E^k proteins, Andres Garcia for providing FN, and Roy Mariuzza for providing the E8 TCR and TPI:HLA-DR1 proteins. We acknowledge Scott E. Chesla, Tao Wu, and Jiangguo Lin for providing their published data in Refs. 19 and 28 for reanalysis and model fitting. We also acknowledge the National Institutes of Health Tetramer Core Facility at Emory University for providing the pMHC molecules. This work was supported by grants from the National Institutes of Health (Nos. T32GM008169 and U01CA214354-S1 to A.M.R., U01CA250040 to C.Z., R01AI124680 to A.G. and C.Z.) and the National Science Foundation (No. DMS-1660504 to C.Z.) and by a Postdoctoral Fellowship from the National Research Foundation of South Korea (No. 2021R1A6A3A03038382 to H.-K.C.).

The authors have no conflicts to disclose.

Ethics approval for experiments reported in the submitted manuscript on animal or human subjects was granted. As stated in “Methods” section, all mice were housed at the Emory University Department of Animal Resources facility and experiments followed guidelines of the National Institutes of Health and protocols approved by the Institutional Animal Care and Use Committee of Emory University (IACUC Protocol No. 201700372). Additionally, human RBCs and platelets were isolated by protocols approved by the Georgia Institute for Technology's Institutional Review Board (IRB Protocol No. H18296).

Aaron M. Rosado and Yan Zhang contributed equally to this work.

Aaron M. Rosado: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (lead); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Yan Zhang: Data curation (equal); Investigation (equal); Methodology (equal). Hyun-Kyu Choi: Data curation (equal); Investigation (supporting); Methodology (supporting). Yunfeng Chen: Investigation (supporting). Samuel M. Ehrlich: Formal analysis (supporting); Visualization (supporting). Fengzhi Jin: Investigation (supporting). Arash Grakoui: Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal). Brian D. Evavold: Funding acquisition (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal). Cheng Zhu: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (supporting); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.