Using methods from computational statistical mechanics, this thesis aims to elucidate the free energy landscape for protein mediated curvature induction in cell membranes. In particular, a mesoscale model of the cell membrane is utilized in this thesis to probe the thermodynamics of several membrane morphological dependent phenomena including membrane tubulation, the formation of endocytic buds, and protein recruitment on cell protrusions. This model allows for the quantification of membrane proteins curvature sensing behavior due to thermal fluctuations, and is able to predict morphologies which form due to membrane proteins cooperative effects. Analysis of the free energy landscape for generation of tubular membrane structures finds correspondence with the thermodynamics of micelle formation in amphiphilic systems. Furthermore, this research is able to quantify differential protein recruitment on protrusive membrane morphologies and inform cell network models of the interplay between membrane tension and curvature inducing protein signaling.