Human cystathionine β-synthase (hCBS) is a Heme-containing, unique pyridoxal 5’-phosphate (PLP) dependent enzyme. CBS catalyzes the bio-chemical condensation reactions in the transsulfuration pathway. The role of Heme in the catalytic activities of the hCBS enzyme is still unknown, even though various experimental studies indicated its participation in the bi-directional electronic communication with the PLP center. The hypothesis is, Heme acts as an electron density reservoir for the catalytic reaction center rather than a redox electron source. In this work, we have investigated In Silico dynamical aspects of the bi-directional communications by performing classical molecular dynamics (MD) simulations upon developing the necessary force field parameters for the cysteine and histidine bound hexa-coordinated Heme. The comparative aspects, of electron density overlap across the communicating pathways, were investigated adopting the Density Functional Theory (DFT) in conjunction with the hybrid exchange-correlation functional for the CBS^WT (wild-type) and CBS^R266K (mutated) enzymes. The molecular dynamics simulations and subsequent explorations of the electronic structures confirm the reported observations. It also provides an in-depth mechanistic understanding of how the non-covalent hydrogen bonding interactions with Cys52 control such long-distance communication. Our study also provides a convincing answer to the reduced enzymatic activities in the R266K mutated hCBS compared to the wild-type enzymes. The difference in hydrogen-bonding patterns and salt-bridge interactions play the pivotal roles in such long distant bi-directional communications.