The function of many intrinsic membrane proteins requires a conformational transition that is often strongly influenced by the molecular composition of the bilayer in which the protein is embedded. Recently, a mechanism for this shift in conformational equilibrium was suggested, in which it is argued that a shift in distribution of lateral pressures of the bilayer resulting from a change in lipid composition alters the amount of mechanical work of the protein conformational transition, if the change in the cross-sectional area profile of the protein varies with depth within the bilayer. As there is little information on the change in shape of the transmembrane region of any protein, various simple geometric models are considered. For both a generic model, and more specific models that approximate likely cooperative rearrangements of alpha-helices in bundles, it is found that the conformational equilibrium depends on the first and second integral moments of the lateral pressure distribution. In addition to revealing the possible physical underpinnings of the well-known correlation between protein activity and the 'nonlamellar' tendency of bilayer lipids, this dependence on moments of the pressure profile allows for prediction of the relative effects of different lipid compositional changes even in the absence of information on specific protein shape changes. Effects of variation in acyl chain length, degree and position of cis-unsaturation, and addition of cholesterol and small interfacially-active solutes (n-alkanols) are compared.