Variations in the composition of cell membranes can strongly influence the function of proteins embedded therein. However, in most cases it is not known whether lipids and other membrane components act by binding directly to proteins or indirectly through changes in a structural or thermodynamic property of the fluid bilayer. In the present work, we develop a simple thermodynamic analysis based on the hypothesis that variations in membrane composition induce changes in the transverse pressure profile in lipid bilayers. If protein function involves a conformational transition accompanied by a depth-dependent change in its cross-sectional area, we predict that small changes in the lateral pressure can induce a large shift in the conformational distribution. The sensitivity of the conformational equilibrium to the lateral pressure profile arises in part from the localization of the large interfacial free energy within a domain of molecular thickness and also from the difference between the logarithmic dependence of the chemical potential of a protein conformational state on its own concentration and its linear dependence on small changes in the pressure profile.