RNA-binding protein that affects the localization and the translation of a subset of mRNA. May play a role in adipogenesis through binding to the 3'-UTR of CEBPA mRNA and regulation of its translation. Targets ITPR1 mRNA to dendrites in Purkinje cells, and may regulate its activity-dependent translation. With ELAVL1, binds the 3'-UTR of p53/TP53 mRNAs to control their nuclear export induced by CDKN2A. Hence, may regulate p53/TP53 expression and mediate in part the CDKN2A anti-proliferative activity. May also bind CCNB1 mRNA. Alternatively, may also regulate p53/TP53 activity through direct protein-protein interaction. Interacts with p53/TP53 and promotes cell-cycle arrest over apoptosis enhancing preferentially the DNA binding and transactivation of p53/TP53 on cell-cycle arrest target genes over proapoptotic target genes. May also regulate the ubiquitination and stability of CDKN1A promoting DNA damage-induced cell cycle arrest. Also plays a role in megakaryocytes differentiation. Interacts with ELAVL1; the interaction is indirect, mRNA-dependent and may regulate p53/TP53 expression (By similarity). Interacts with p53/TP53; the interaction is direct and enhances p53/TP53 transactivation functions on cell-cycle arrest target genes, resulting in growth arrest. Detected in dendrites of Purkinje cells and hippocampal neurons. Expressed predominantly in the retina. Up-regulated by p53/TP53 in response to DNA damage and oxidative stress. Ubiquitinated upon prolonged exposure to genotoxic stress, which leads to proteasomal degradation of ZNF385A and releases p53/TP53 from cell-cycle arrest target gene promoters.