A cantilever device based on competitive binding of an immobilized receptor to immobilized and soluble ligand and capable of measuring solution-phase thermodynamic quantities is described. Through multiple binary queries, the device stochastically measures the probability of the formation of a bound complex between immobilized protein and immobilized ligand as a function of soluble ligand concentration. The resulting binding isotherm is described by a binding polynomial consisting of the activities of soluble and immobilized ligand and binding constants for the association of immobilized protein with free and immobilized ligand. Evaluation of the polynomial reveals an association constant for the formation of a complex between immobilized ligand and immobilized protein close to that for the formation of complex between soluble protein and soluble ligand. The methodology lays the foundation for construction of practical portable sensing devices.force spectroscopy ͉ ligand binding ͉ sensors ͉ competitive binding T echnologies that permit the rapid quantitative determination of analytes have myriad applications in point-of-care diagnostics and environmental and food safety monitoring. Most rely on the formation of specific complexes between an analyte and a receptor and require an experimentally observable measure of binding. By far, the most commonly used signal is a change in optical properties, either absorptive or emissive. However, many systems of interest lack useable optical properties, either because of the inherent optical properties of the analytes themselves or because of the characteristics of the sample milieu, and in recent years a number of general approaches have emerged for the measurement of intermolecular binding. During the past several years, titration microcalorimeters have become commercially available (1, 2). These instruments measure the heat evolved during ligand binding as a function of ligand concentration; this information can be fit to a simple binding isotherm to reveal binding free energies and enthalpies. Another group of techniques, typified by surface plasmon resonance and quartz crystal microbalance, use changes in the electro-optical properties of a surface as a small-or macromolecular species is deposited (3-5). This signal is used to determine kinetic values for binding and unbinding, and the ratio of these parameters furnishes a binding constant. Although broadly applicable, both techniques require long sampling times (hours) and have material and operational characteristics that preclude their utility in field applications.Dynamic force spectroscopy, typified by the atomic force microscope (AFM) and the optical trap, measures the force required to unbind individual molecular complexes (6-20). Unbinding forces are not simply related to free energies or to association rates, because the application of force necessarily removes the bound complex from an equilibrium condition (21). The study of unbinding kinetics by dynamic force spectroscopy is further complicated by the applic...