The present work analyzes binary random sequences measured by the micropipette adhesion frequency assay (4) presented in the introduction. The experiments, performed to address questions other than adhesion memory issues, are described in refs. 10 and 21 and in Y.-H.C., N. Jiang, F.Z., C.Z., and D.L., unpublished data. Only brief descriptions are given below.
K562 cells expressing LFA-1 were a gift from T. A. Springer (Harvard Medical School, Boston, MA). Purified mouse glycosyl phosphatidylinositol (GPI)-anchored ICAM-1 was a gift from P. Selvaraj (Emory University School of Medicine, Atlanta, GA). T cells from OTI transgenic mice expressing H-2Kb MHC-restricted OTI TCR specific for an OVA peptide were a gift from B. D. Evavold (Emory University School of Medicine). Mouse H-2Kb MHC bound with an ovalbumin-derived peptide OVA (SIINFEKL, amino acids 257–264) was produced by the National Institutes of Health Tetramer Facility at Emory University. To isolate TCR binding, a chimeric MHC molecule that replaced the mouse H-2Kb3 domain with the human HLA-A2 3 domain was used to eliminate CD8 binding and was a gift from J. Altman (Emory University School of Medicine). CHO cells expressing full-length C-cadherin were generated with a plasmid provided by B. Gumbiner (University of Virginia School of Medicine, Charlottesville, VA), who also provided stably transfected CHO cells that secreted Fc-tagged C-cadherin, which was purified as described previously (22).
Human RBCs were isolated from whole peripheral blood of healthy donors, in accordance with a protocol approved by the Institutional Review Board of the Georgia Institute of Technology. GPI-ICAM-1 was reconstituted in RBC membrane by a 2.5-hr incubation. Biotin–streptavidin coupling was used to coat biotinylated pMHC monomers onto the RBC surface. Chromium chloride coupling was used to coat an anti-human IgG Fc antibody (Sigma–Aldrich, St. Louis, MO) on the RBC surface, with subsequent incubation of the RBCs with Fc-tagged C-cadherin.
Site densities of the receptors and ligands on cell membranes were measured by flow cytometry. The specificity of measured adhesion was confirmed by using blocking monoclonal antibodies directed against the receptors and/or ligands involved, by not coating the ligands on the RBCs, and by using EDTA to chelate the divalent cations required for LFA-I/CAM-1 binding and for C-cadherin binding. All treatments substantially reduced average adhesion frequencies.
Three methods were used to evaluate the memory index. Direct calculation uses the transition probabilities defined by Eq. 1 to express p:
The theoretical prediction MM(m, n, p, p) from Eq. 4 was fit either to the experimental distribution of adhesion clusters, Mexp(m), shown in Fig. 3, or to the measured number of clusters of size 1, Mexp (1), shown in Fig. 4B by the least squares method. p in Eq. 4 as a function of Pa, p, and n is solved from Eq. 5 as follows:
The same fitting was applied to cluster size distributions obtained from computer-simulated Bernoulli sequences to generate 2,000 random samples of p. Histogram analysis showed that p obeyed a normal distribution with zero mean and a standard deviation, (= 0.156 ± 0.005), that depended on n (= 50) but was insensitive to p in the range of the experiment (0.1–0.75, cf. Fig. 5). This allowed us to use the one-sample z test to assess the statistical significance for nonzero p (8).