Ryanodine receptors (RyRs) serve for excitation-contraction coupling in skeletal and cardiac muscle cells in a noticeably different way, not fully understood at the molecular level. We addressed the structure of skeletal (RyR1) and cardiac (RyR2) isoforms relevant to the gating by divalent ions (M2+). The bioinformatics analysis of 43 cryo-EM RyR structures ascertained the EF1 and EF2 loops as a moderate-affinity non-specific M2+binding site interacting with the S23 loop of neighbor monomer stronger in RyR1 than RyR2. The EF1/EF2 loops were allosterically coupled to the S6 gate by two parallel pathways. The intra-monomeric pathway uses the U-motif, ATP binding site, S45 linker, and S6 helix, shared with the Ca2+-activation pathway in both RyR isoforms. The inter-monomeric pathway, prominent in RyR1, passes through the S23* loop of the neighbor monomer (*) andviathe U-motif* to the S6* gate either directly or through the S45* linker or CFF* binding site. The structural pieces of evidence for the M2+-binding activation and inhibition sites and their interacting allosteric networks were implemented in the model of RyR operation based on statistical mechanics, MWC theorem, and Markov processes. This model defines allosterically coupled closed, open, and inactivated RyR macrostates common for both RyR isoforms and solves the relative occupancy of macrostates in dependence on cytosolic M2+concentrations. The model approximated the single-channel open probability data for RyR1 and RyR2 of several species obtained in the presence or absence of ATP and luminal calcium. The proposed platform of RyR operation interprets the structural and functional data of mammalian RyR channels on common grounds.