To carry out their functions in cells, proteins are required to fold into well-defined three-dimensional conformations. The stability of the folded state dictates several aspects of protein life, such as their evolution, interactions, and selection of structures that are ultimately linked to activity. Sequence mutations may change the stability profile and consequently impact structure and function. Here, we use a simple, molecular dynamics-based energy decomposition approach to map the response to mutations of each amino acid in the sequences of a set of five test proteins with different lengths, folds, and topologies. To this end, we make use of the decomposition of the residue-pair nonbonded energy matrix. We show that parameters obtained from this analysis, namely the main eigenvalue reporting on the most stabilizing energy contributions and the spectral gap of the matrix (ENergy Gap), reproduce experimentally determined stability trends. At the same time, our approach identifies the residue-pair couplings that play key roles in defining the 3D properties of a certain fold. We discuss the relevance of these results for the design of protein mutants for experimental applications and the possibility for our energy decomposition approach to complement other computational and experimental analyses of conformational stability.