Opioid　receptors,　a　kind　of　G　protein-coupled　receptors　(GPCRs),　mainly　mediate　an　analgesic　response　via　allosterically　transducing　the　signal　of　endogenous　ligand　binding　in　the　extracellular　domain　to　couple　to　effector　proteins　in　the　intracellular　domain.　The　delta　opioid　receptor　(DOP)　is　associated　with　emotional　control　besides　pain　control,　which　makes　it　an　attractive　therapeutic　target.　However,　its　allosteric　mechanism　and　key　residues　responsible　for　the　structural　stability　and　signal　communication　are　not　completely　clear.　Here　we　utilize　the　Gaussian　network　model　(GNM)　and　amino　acid　network　(AAN)　combined　with　perturbation　methods　to　explore　the　issues.　The　constructed　fcfGNMMD,　where　the　force　constants　are　optimized　with　the　inverse　covariance　estimation　based　on　the　correlated　fluctuations　from　the　available　DOP　molecular　dynamics　(MD)　ensemble,　shows　a　better　performance　than　traditional　GNM　in　reproducing　residue　fluctuations　and　cross-correlations　and　in　capturing　function-ally　low-frequency　modes.　Additionally,　fcfGNM(MD)　can　consider　implicitly　the　environmental　effects　to　some　extent.　The　lowest　mode　can　well　divide　DOP　segments　and　identify　the　two　sodium　ion　(important　allosteric　regulator)　binding　coordination　shells,　and　from　the　fastest　modes,　the　key　residues　important　for　structure　stabilization　are　identified.　Using　fcfGNMMD　combined　with　a　dynamic　perturbation-response　method,　we　explore　the　key　residues　related　to　the　sodium　ion　binding.　Interestingly,　we　identify　not　only　the　key　residues　in　sodium　ion　binding　shells　but　also　the　ones　far　away　from　the　perturbation　sites,　which　are　involved　in　binding　with　DOP　ligands,　suggesting　the　possible　long-range　allosteric　modulation　of　sodium　binding　for　the　ligand　binding　to　DOP.　Furthermore,　utilizing　the　weighted　AAN　combined　with　attack　perturbations,　we　identify　the　key　residues　for　allosteric　communication.　This　work　helps　strengthen　the　understanding　of　the　allosteric　communication　mechanism　in　delta　opioid　receptor　and　can　provide　valuable　information　for　drug　design.