Ligand migration and binding are central to the biological functions of many proteins such as myoglobin (Mb) and it is widely thought that protein breathing motions open up ligand channels dynamically. However, how a protein exerts its control over the opening and closing of these channels through its intrinsic dynamics is not fully understood. Specifically, a quantitative delineation of the breathing motions that are needed to open ligand channels is lacking. In this work, we present and apply a novel normal mode-based method to quantitatively delineate what and how breathing motions open ligand migration channels in Mb and its mutants. The motivation behind this work springs from the observation that normal mode motions are closely linked to the breathing motions that are thought to open ligand migration channels. In addition, the method provides a direct and detailed depiction of the motions of each and every residue that lines a channel and can identify key residues that play a dominating role in regulating the channel. The all-atom model and the full force-field employed in the method provide a realistic energetics on the work cost required to open a channel, and as a result, the method can be used to efficiently study the effects of mutations on ligand migration channels and on ligand entry rates. Our results on Mb and its mutants are in excellent agreement with MD simulation results and experimentally determined ligand entry rates.