(A) Reaction scheme showing two linked thermodynamic cycles. (B) Equations relating thermodynamic parameters and ligand-binding kinetics for reactions in panel A. Equations S8–S10 are based on thermodynamic cycles for ligand binding and conformational change shown in panel A. (C) Population of each state in the absence of ligand and in the presence of saturating concentration of ligand for integrins α4β1 and α5β1 on the cell surface and in preparations of purified integrin fragments, based on previous measurements (Li and Springer, 2018; Li et al., 2017). The data are for integrins on cells in suspension or for purified integrin fragments binding to soluble ligands. When a fraction x of integrins is bound to ligand, the population percentages may be multiplied by x to give ligand-bound integrin populations and by (1-x) to give the unbound populations. Data on integrins on intact cells will be affected by basal binding of other cellular components including intracellular cytoskeletal adaptors. During adhesion to ligands on substrates, engagement of adaptors and the cytoskeleton, and application of tensile force to ligand-bound integrins, the populations will be shifted as described (Li and Springer, 2017) Data for intact α4β1 on cells were determined in Figure 4 and data for α4β1 unclasped ectodomains and headpiece were determined in Figure 3 in Li and Springer, 2018. Data for intact α5β1 on cells were determined in Figure 7 and data for α5β1 ectodomains and headpiece were determined in Figures 5 and 6, respectively, in Li et al., 2017. Populations of ligand-bound states were calculated from Eqs. S5–S10 shown in panel (B). In Eqs. S8–S10, the ratios are used of intrinsic affinities of the extended-open (EO) to the bent-closed (BC) and extended-closed (EC) states. For integrin α4β1, the ratios were averaged to 729 ± 211 from six α4β1 preparations shown in the table in Li and Springer, 2018; for integrin α5β1, ratios were averaged to 3106 ± 1,689 from eight soluble α5β1 preparations, including the affinities of cRGD peptide for six ectodomain preparations either clasped or unclasped and with three different N-glycosylation forms (Figure 5), the affinities of cRGD peptide for high-mannose headpiece and semi-truncated ectodomain (Figure 6C), as well as the affinity of Fn39-10 to unclasped ectodomain with high mannose N-glycans (Figure 4D) in Li et al., 2017.