The structure of oxygenated trHbN from Mycobacterium tuberculosis shows an extended heme distal hydrogen-bond network that includes Tyr33(B10), Gln58(E11), and the bound O(2). In addition, trHbN structure shows a network of hydrophobic cavities organized in two orthogonal branches. In the present work, the structure and the dynamics of oxygenated and deoxygenated trHbN in explicit water was investigated from 100 ns molecular dynamics (MD) simulations. Results show that, depending on the presence or the absence of a coordinated O(2), the Tyr33(B10) and Gln58(E11) side chains adopt two different configurations in concert with hydrogen bond network rearrangement. In addition, our data indicate that Tyr33(B10) and Gln58(E11) control the dynamics of Phe62(E15). In deoxy-trHbN, Phe62(E15) is restricted to one conformation. Upon O(2) binding, the conformation of Gln58(E11) changes and residue Phe62(E15) fluctuates between two conformations. We also conducted a systematic study of trHbN tunnels by analyzing thousands of MD snapshots with CAVER. The results show that tunnel formation is the result of the dynamic reshaping of short-lived hydrophobic cavities. The analyses indicate that the presence of these cavities is likely linked to the rigid structure of trHbN and also reveal two tunnels, EH and BE, that link the protein surface to the buried distal heme pocket and not present in the crystallographic structure. The cavities are sufficiently large to accomodate and store ligands. Tunnel dynamics in trHbN was found to be controlled by the side-chain conformation of the Tyr33(B10), Gln58(E11), and Phe62(E15) residues. Importantly, in contrast to recently published works, our extensive systematic studies show that the presence or absence of a coordinated dioxygen does not control the opening of the long tunnel but rather the opening of the EH tunnel. In addition, the data lead to new and distinctly different conclusion on the impact of the Phe62(E15) residue on trHbN tunnels. We propose that the EH and the long tunnels are used for apolar ligands storage. The trajectories bring important new structural insights related to trHbN function and to ligand diffusion in proteins.