Electrical synapses between neurons in the mammalian CNS are predominantly formed of the connexin36 (Cx36) gap junction (GJ) channel protein. Unique among GJs formed of a number of other members of the Cx gene family, Cx36 GJs possess a high sensitivity to intracellular Mg that can robustly act to modulate the strength of electrical synaptic transmission. Although a putative Mg binding site was previously identified to reside in the aqueous pore in the first extracellular (E1) loop domain, the involvement of the N-terminal (NT) domain in the atypical response of Cx36 GJs to pH was shown to depend on intracellular levels of Mg. In this study, we examined the impact of amino acid substitutions in the NT domain on Mg modulation of Cx36 GJs, focusing on positions predicted to line the pore funnel, which constitutes the cytoplasmic entrance of the channel pore. We find that charge substitutions at the 8th, 13th, and 18th positions had pronounced effects on Mg sensitivity, particularly at position 13 at which an A13K substitution completely abolished sensitivity to Mg. To assess potential mechanisms of Mg action, we constructed and tested a series of mathematical models that took into account gating of the component hemichannels in a Cx36 GJ channel as well as Mg binding to each hemichannel in open and/or closed states. Simultaneous model fitting of measurements of junctional conductance, g, and transjunctional Mg fluxes using a fluorescent Mg indicator suggested that the most viable mechanism for Cx36 regulation by Mg entails the binding of Mg to and subsequent stabilization of the closed state in each hemichannel. Reduced permeability to Mg was also evident, particularly for the A13K substitution, but homology modeling of all charge-substituted NT variants showed only a moderate correlation between a reduction in the negative electrostatic potential and a reduction in the permeability to Mg ions. Given the reported role of the E1 domain in Mg binding together with the impact of NT substitutions on gating and the apparent state-dependence of Mg binding, this study suggests that the NT domain can be an integral part of Mg modulation of Cx36 GJs likely through the coupling of conformational changes between NT and E1 domains.