Structure-based elastic network models (ENMs) have been remarkably successful in describing conformational transitions in a variety of biological systems. Low-frequency normal modes are usually calculated from the ENM that characterizes elastic interactions between residues in contact in a given protein structure with a uniform force constant. To explore the dynamical effects of nonuniform elastic interactions, we calculate the robustness and coupling of the low-frequency modes in the presence of nonuniform variations in the ENM force constant. The variations in the elastic interactions, approximated here by Gaussian noise, approximately account for perturbation effects of heterogeneous residue-residue interactions or evolutionary sequence changes within a protein family. First-order perturbation theory provides an efficient and qualitatively correct estimate of the mode robustness and mode coupling for finite perturbations to the ENM force constant. The mode coupling analysis and the mode robustness analysis identify groups of strongly coupled modes that encode for protein functional motions. We illustrate the new concepts using myosin II motor protein as an example. The biological implications of mode coupling in tuning the allosteric couplings among the actin-binding site, the nucleotide-binding site, and the force-generating converter and lever arm in myosin isoforms are discussed. We evaluate the robustness of the correlation functions that quantify the allosteric couplings among these three key structural motifs.