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**Fig. 1.** Micropipette adhesion frequency assay. (A and B) (Left) A T cell held by a micropipette was driven by a piezoelectric translator through a computer program to make a controlled contact with a RBC coated with pMHC, held stationary by another micropipette (Right). Aspiration with the micropipettes precluded cell rotation, allowing the same membranes to make repeated contact. At the end of the contact phase, the translator retracted the left pipette to the starting position. (C) If adhesion resulted, the RBC apex would be stretched (see also *SI Movie 1**). (D) If adhesion did not occur at the end of the contact, the RBC would restore its shape without extension. Images in C and D were chosen to depict the same instant after cell contact. The force exerted on the adhesive bond(s) can be calculated from the RBC deformation. The bond lifetime can be measured from the video timer (hour:minute:second:fraction of a second) shown at the lower right corner of each panel. *

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**Fig. 2.** Running adhesion frequencies and scaled adhesion score sequences. The running adhesion frequency (A–C) and the scaled nonzero adhesion score (D–F) are plotted vs. the test cycle index, i. The measured adhesions were mediated by specific LFA-1/ICAM-1 (A and D), TCR/pMHC (B and E), or C-cadherin (C and F) interactions. Matched symbols (diamond, open square, open triangle) are used to show test sequences in A–C corresponding with those in D–F. Each sequence represents n (= 50) repeated tests using a single pair of cells, performed under identical experimental conditions. The average of the three averaged adhesion frequencies is shown as a solid line on D–F.

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**Fig. 3.** Cluster size distribution. The number of clusters of various sizes enumerated from Fig. 2 (bars) for LFA-1/ICAM-1 (A), TCR/pMHC (B), or C-cadherin (C) interaction were fitted by Eq. **4** (curves). Both the data and the best-fit parameters are presented as mean ± SEM.

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**Fig. 4.** Number of clusters in a repeated test sequence. (A) Expected numbers of clusters of sizes 1–4 in a Bernoulli sequence of 50 tests, M_{B}, are plotted vs. adhesion probability, P_{a} (= p), as calculated from Eq. **2** (curves). The number of clusters of size m = 1 calculated from computer simulations for 3 (open triangles) or 50 (filled triangles) Bernoulli sequences for the same range of P_{a} are shown as mean ± SEM. (B) The number of clusters of size 1 (mean ± SEM from 3–5 pairs of cells) enumerated from experimental adhesion score sequences of 50 tests each are plotted vs. averaged adhesion probability for LFA-1/ICAM-1 (open circles), TCR/pMHC (filled diamonds), or C-cadherin (filled triangles) interactions. Light gray curves show the expected number of clusters of size 1 (Eq. **4**, where p is given by Eq. **7**, n = 50), plotted vs. averaged adhesion probability, P_{a}, for p from –0.3 to 0.5 in increments of 0.1 to allow estimation of p for each experimental data point. Solid curve, p = 0; dotted curves, p > 0; dashed curves, p

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**Fig. 5.** Memory in adhesion mediated by three interactions. The memory index p is determined by fitting the measured number of clusters with Eq. **4** (solid bars) or by direct calculation using Eq. **6** (open bars) for a range of averaged adhesion probabilities (indicated) for adhesion mediated by LFA-1/ICAM-1 (A), TCR/pMHC (B), or C-cadherin (C) interactions. Data are shown as mean ± SEM. Statistically significant (P value 0.05) differences of p values from zero are marked with asterisks.

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