Inhibits DNA replication by preventing the incorporation of MCM complex into pre-replication complex (pre-RC) (PubMed:12192004, PubMed:9635433). It is degraded during the mitotic phase of the cell cycle. Its destruction at the metaphase-anaphase transition permits replication in the succeeding cell cycle (PubMed:12192004, PubMed:9635433). Inhibits histone acetyltransferase activity of KAT7/HBO1 in a CDT1-dependent manner, inhibiting histone H4 acetylation and DNA replication licensing (By similarity). Inhibits the transcriptional activity of a subset of Hox proteins, enrolling them in cell proliferative control (By similarity). Homotetramer (By similarity). Interacts with CDT1; this inhibits binding of the MCM complex to origins of replication (PubMed:12192004, PubMed:15286659, PubMed:15811859). The complex with CDT1 exists in two forms, a 'permissive' heterotrimer and an 'inhibitory' heterohexamer (By similarity). Interacts (via coiled-coil domain) with IDAS (via coiled-coil domain); this targets GMNN to the nucleus (By similarity). The heterodimer formed by GMNN and MCIDAS has much lower affinity for CDT1 than the GMNN homodimer (By similarity). Interacts with a subset of Hox proteins, affinity increasing from anterior to posterior types, the strongest interaction being with HOXB1, HOXC9 and HOXD10 (By similarity). Interacts with LRWD1 from G1/S to mitosis (By similarity). Mainly cytoplasmic but can be relocalized to the nucleus. Absent during G1 phase, accumulates during S, G2, and M phases, and disappears at the time of the metaphase-anaphase transition. Phosphorylated during mitosis. Phosphorylation at Ser-181 by CK2 results in enhanced binding to Hox proteins and more potent inhibitory effect on Hox transcriptional activity. Belongs to the geminin family.