The coupling between the mechanical properties of enzymes and their biological activity is a well-established feature that has been the object of numerous experimental and theoretical works. In particular, recent experiments show that enzymatic function can be modulated anisotropically by mechanical stress. We study such phenomena using a method for investigating local flexibility on the residue scale that combines a reduced protein representation with Brownian dynamics simulations. We performed calculations on the enzyme guanylate kinase to study its mechanical response when submitted to anisotropic deformations. The resulting modifications of the protein's rigidity profile can be related to the changes in substrate binding affinity observed experimentally. Further analysis of the principal components of motion of the trajectories shows how the application of a mechanical constraint on the protein can disrupt its dynamics, thus leading to a decrease of the enzyme's catalytic rate. Eventually, a systematic probe of the protein surface led to the prediction of potential hotspots where the application of an external constraint would produce a large functional response both from the mechanical and dynamical points of view. Such enzyme-engineering approaches open the possibility to tune catalytic function by varying selected external forces.