The ability of biological membranes to bend is critical to understanding the interaction between proteins and the lipid bilayer. Experimental and computational studies have shown that the membrane can bend to expose charged and polar residues to the lipid headgroups and water, greatly reducing the cost of protein insertion. However, current computational approaches are poorly equipped to accurately model such deformation; atomistic simulations often do not reach the time-scale necessary to observe large-scale rearrangement, and continuum approaches assume a flat, rigid bilayer. In this thesis we present an efficient computational model of a deformable membrane for probing these interactions with elasticity theory and continuum electrostatics. To validate the model, we first investigate the insertion of three membrane proteins and three aqueous proteins. The model finds the membrane proteins and aqueous proteins stable and unstable in the membrane, respectively. We also investigate the sensitivity of these predictions to changes in several key parameters. The model is then applied to interactions between the membrane and the voltage sensor segments of voltage-gated potassium channels. Despite their high numbers of basic residues, experiments have shown that voltage sensors can be stably accommodated in the membrane. For simple continuum electrostatics approaches that assume a flat membrane, the penalty of inserting these charged residues would seem to prohibit voltage sensor insertion. However, in our method the membrane deforms to enable interaction between solvent and the charged residues. Our calculations predict that the highly charged S4 helices of several potassium channels are in fact stable in the membrane, in accord with experimental observations. Experimental and computational evidence has shown that the cost for inserting multiple charged amino acids into the membrane is not additive; it is not as costly to insert a second charge once a first has already been inserted. Our model reflects this phenomenon and provides a simple mechanical explanation linked to membrane deformation. We additionally consider the energetics of passive ion penetration into the membrane from bulk solvent. We use coarse-grained molecular dynamics to guide our input parameters and show that ion permeation energy profiles agree with atomistic simulations when membrane bending is included.