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Cell adhesion is mediated by numerous membrane receptors. It is desirable to derive the outcome of a cell-surface encounter from the molecular properties of interacting receptors and ligands. However, conventional parameters such as affinity or kinetic constants are often insufficient to account for receptor efficiency. Avidity is a qualitative concept frequently used to describe biomolecule interactions: this includes incompletely defined properties such as the capacity to form multivalent attachments. The aim of this study is to produce a working description of monovalent attachments formed by a model system, then to measure and interpret the behavior of divalent attachments under force. We investigated attachments between antibody-coated microspheres and surfaces coated with sparse monomeric or dimeric ligands. When bonds were subjected to a pulling force, they exhibited both a force-dependent dissociation consistent with Bell's empirical formula and a force- and time-dependent strengthening well described by a single parameter. Divalent attachments were stronger and less dependent on forces than monovalent ones. The proportion of divalent attachments resisting a force of 30 piconewtons for at least 5 s was 3.7 fold higher than that of monovalent attachments. Quantitative modeling showed that this required rebinding, i.e. additional bond formation between surfaces linked by divalent receptors forming only one bond. Further, experimental data were compatible with but did not require stress sharing between bonds within divalent attachments. Thus many ligand-receptor interactions do not behave as single-step reactions in the millisecond to second timescale. Rather, they exhibit progressive stabilization. This explains the high efficiency of multimerized or clustered receptors even when bonds are only subjected to moderate forces. Our approach provides a quantitative way of relating binding avidity to measurable parameters including bond maturation, rebinding and force sharing, provided these parameters have been determined. Also, this provides a quantitative description of the phenomenon of bond strengthening. [ABSTRACT FROM AUTHOR]