What are the structural factors affect enzyme's Km?
Computationally, using molecular dynamics (MD) simulations, it is difficult but not impossible, to quantitatively reproduce the effect of mutations on ligand-binding free energies, and activation and reaction free energies of enzymatic reactions. The most useful MD simulation methods for such a purpose are: free energy perturbation (FEP), linear interaction energy (LIE), linear response approximation (LRA), empirical valence bond EVB), and their combinations---developed by Arieh Warshel (The Nobel Prize in Chemistry 2013).

Mechanistically, mutations affect short- (van der Waals and electrostatic) and long-range (electrostatic) interactions with the surrounding environment, which comprises the rest of the protein and the solvent. Note that free energy is an attribute of an ensemble, not of a single 3D structure---which is why exploring a single structure of the mutated protein is unlikely to reveal the effect of the mutation qualitatively, not to mention quantitatively. One has to sample the conformational space of the protein---and MD simulation is the most efficient computational technique for such a sampling.

In summary, the effects are simple, but the system is extremely complex . . .

Klvana et al. (2012) Biochemistry 51: 8829-8843.

Klvana et al. (2016) J. Phys. Chem. B 120: 13017-13030.