Hydrolase that deubiquitinates polyubiquitinated target proteins such as MDM2, MDM4 and CCND1 (By similarity). Isoform 1 and isoform 2 possess both ubiquitin-specific peptidase and isopeptidase activities (PubMed:12107281). Deubiquitinates MDM2 without reversing MDM2-mediated p53/TP53 ubiquitination and thus indirectly promotes p53/TP53 degradation and limits p53 activity (By similarity). Has no deubiquitinase activity against p53/TP53 (By similarity). Prevents MDM2-mediated degradation of MDM4 (By similarity). Plays a role in the G1/S cell-cycle progression in normal and cancer cells (By similarity). Regulates the circadian clock by modulating its intrinsic circadian rhythm and its capacity to respond to external cues (PubMed:23213472). Associates with clock proteins and deubiquitinates core clock component PER1 but does not affect its overall stability (PubMed:23213472). Regulates the nucleocytoplasmic shuttling and nuclear retention of PER1 and its repressive role on the clock transcription factors CLOCK and ARNTL/BMAL1 (By similarity). Plays a role in the regulation of myogenic differentiation of embryonic muscle cells (PubMed:12107281). Circadian clock output effector that regulates Ca(2+) absorption in the small intestine. Probably functions by regulating protein levels of the membrane scaffold protein NHERF4 in a rhythmic manner, and is therefore likely to control Ca(2+) membrane permeability mediated by the Ca(2+) channel TRPV6 in the intestine. Thiol-dependent hydrolysis of ester, thioester, amide, peptide and isopeptide bonds formed by the C-terminal Gly of ubiquitin (a 76-residue protein attached to proteins as an intracellular targeting signal). Cleavage is inhibited by ubiquitin in a dosage-dependent manner (By similarity). Cleavage is blocked by ubiquitin aldehyde. Homooligomer. Found in trimeric complex with MDM2 and MDM4 and USP2. Interacts with CCND1; the interaction is direct and promotes its stabilization by antagonizing ubiquitin-dependent degradation. Interacts (via N-terminus and C-terminus) with MDM2. Interacts with MDM4 (By similarity). Interacts with PER1. Interacts with KCNQ1; counteracts the NEDD4L-specific down-regulation of I(Ks) and restores plasma membrane localization of KCNQ1 (By similarity). Isoform 4: Interacts with PDZD3 and CLTC (By similarity). Localizes in the spermatid head in late-elongating spermatids in the thin area between the outer acrosomal membrane and the plasma membrane. Predominantly expressed at membranes. Expressed in mesangial cells of the kidney. Isoform 1 and isoform 2 are expressed in elongated spermatids; the shorter form appearing earlier than the longer form (at protein level). Isoform 1 and isoform 2 are expressed in early round spermatids of the testis. Isoform 1 is expressed in muscle and heart. Isoform 2 is expressed in muscle, lung, heart, brain, liver and ovary. During muscle differentiation, isoform 1 expression increases before the onset of membrane fusion and decreases as the myogenic processes proceeded; un counterpart, isoform 2 expression remains low until the burst of membrane fusion but increases thereafter. Up-regulated by IL-1. Isoform 1 is up-regulated with any signal for withdrawal from the cell cycle such as serum deprivation. The different N-terminus extensions of isoform 1 and isoform 2 determine their respective subcellular localization and differentiel effect on myoblast fusion and accumulation of muscle-specific proteins. The different N-terminus extensions of isoform 1 and isoform 2 are not essential for their catalytic activity. Stimulates both membrane fusion during myogenesis and accumulation of muscle-specific proteins. Inhibits both membrane fusion during myogenesis and accumulation of muscle-specific proteins. Belongs to the peptidase C19 family. USP2 subfamily.