Deep mutational scanning enables examination of the effects of many mutations at each amino acid position in a query protein, readily disclosing positions that are particularly sensitive. Mutations in these positions alter protein function the most. Here, on the premise that dynamics underlie function, we explore to what extent the measured sensitivity to mutations could be linked to - perhaps be explained by - the structural dynamics of the protein. We employ a minimalist perturbation-response approach based on the Gaussian Network Model (GNM) on a data set of seven proteins with deep mutational scanning data. The analysis shows that the mutation-sensitive positions are often of capacity to modulate the global dynamics and to intermediate allosteric interactions in the structure. With that, upon strain perturbation, these positions decrease residue fluctuations the most, affecting function via entropy changes. This is particularly relevant for positions that are distant from binding sites or other functional regions of the protein and are sensitive to mutations, nevertheless. Our results indicate that mutations in these positions allosterically manipulate protein function.