The　authors　regret　the　error　in　Fig.　3.　In　the　initially　published　version　of　Fig.　3,　the　p-AKT,　GSK3β,　and　β-Actin　bands　were　erroneously　pasted.　We　have　re-evaluated　the　original　bands　of　these　proteins　and　recalculated　the　correct　protein　expression　levels　for　all　these　proteins.　The　results　are　similar　to　the　result　of　our　previous　analysis.　The　corrected　Fig.　3　is　as　follows:[Figure　presented]　The　interpretation　of　the　results　are　as　follow:　As　shown　in　Fig.　3F–H,　p-JNK/JNK　expression　was　significantly　enhanced,　meanwhile,　both　p-ERK/ERK　and　p-AKT/AKT　were　decreased　in　the　HFD　and　HFD　+　AlCl3　+　D-gal　groups.　TG-Res-CS/TPP-NPs　intervention　reversed　the　altered　protein　expression　of　phosphorylated　JNK,　AKT　and　ERK　to　nearly　normal　levels,　thereby　improving　neuron　survival　in　obesity-related　AD　mice.　Moreover,　glycogen　synthase　kinase　3β　(GSK3β)　is　a　downstream　protein　present　in　the　AKT　signaling　pathway　(Hernandez　et　al.,　2012).　Inactivation　of　AKT　can　decrease　the　phosphorylation　of　GSK3β　(Liu　et　al.,　2017),　which　would　subsequently　promote　the　phosphorylation　of　Tau　(p-Tau)　and　lead　to　aggregation　of　p-Tau　in　AD　(Kim　et　al.,　2017).　Fig.　3I–J　demonstrates　that　p-GSK3β　was　reduced　in　the　HFD　and　HFD　+　AlCl3　+　D-gal　groups　compared　to　the　control.　This　reduction　resulted　in　accumulation　of　p-Tau　in　the　brain.　Administration　of　TG-Res-CS/TPP-NPs　up-regulated　the　protein　expression　of　p-GSK3β　and　reduced　expression　of　p-Tau　in　obesity-related　AD　mice.The　authors　would　like　to　apologise　for　any　inconvenience　caused.　©　2025　Elsevier　Ltd