## 1 Introduction  
Tooth eruption is a biological process induced by the interaction between bone resorption, bone formation, and dental hard tissue formation [1]. The latter helps the tooth to move in the alveolar bone due to the force of root formation in the pre-emergent and post-emergent eruptive stages [2].  
The incisors of rodents erupt continuously due to the constant formation of dental hard tissue to compensate for dental attrition [3].  
Many molecules related to bone resorption, bone formation, and dental hard tissue formation are known to control the process of tooth eruption [4]. Transforming growth factor-beta 1 (TGF-\(\beta\)1) plays an important role in cell proliferation and differentiation related to bone metabolism and tooth formation [5]. While bone morphogenic protein-2 (BMP-2) is a key molecule for osteogenesis, runt-related transcription factor 2 (Runx2) [6; 7; 8] and osterix (OSX) [8; 9; 10] are involved in osteoblast, odontoblast, and amelblast differentiation, eventually leading to bone and teeth formation. Dentin sialophosphoprotein (DSPP) is important for dentin formation, which in turn, is critical for root formation [8].  
When proper molecular regulations are inhibited, normal eruption of teeth can also be inhibited or delayed. Some endocrine disorders, including hypothyroidism, hypopituitarism, and hypoparathyroidism, are associated with delayed tooth eruption due to abnormal calcium metabolism [11; 12]. Cleidocranial dysplasia is a genetic disease that shows many impacted teeth, caused by mutations in the _RUNX2_ gene [13]. In the absence of parathyroid hormone-related protein (PTHrP) expression, tooth eruption and root formation do not occur normally [14]. Primary failure of eruption (PFE) [15], a rare condition that inhibits the eruption of particular teeth nonsyndromically, was found to be related to a mutation of the _PTHIR_ (Parathyroid Hormone 1 Receptor) gene [16; 17]. Tooth eruption can also be delayed or inhibited in conditions in which proper dental hard tissue formation does not occur, such as amelogenesis imperfeta or dentin dysplasia [12].  
In rat incisors, the odontogenic region with the enamel organ, dental papilla, and dental follicle is maintained even after the eruption of a tooth, resulting in the continuous formation of enamel and dentin. Therefore, rat incisors are good models to study the mechanism of dental hard tissue formation, which plays an important role in the regulation of the eruption process [3]. A few studies have previously reported the effects of several methods, in which molecular reactions caused a change in the eruption rate of rat incisors. Medications known to inhibit bone resorption, such as bisphosphonate [18] and alendronate [19], resulted in delayed tooth eruption; high-dose radiotherapy also slowed the rate of eruption with histologic alterations in the odontogenic region [20]. However, studies reporting an increased eruption rate due to the effect of chemicals are rare.  
4-Hexylrescorcinol (4 HR) is a multifunctional organic molecule that has been studied actively in tissue engineering [21]. In bone biology, 4 HR suppresses the nuclear factor kappa B (NF\(\kappa\)B) signaling pathway, consequently increasing new bone formation [22]; a recent study has shown the administration of 4 HR to accelerate orthodontic tooth movement by increasing bone turnover rate in ovariectomized rats [23]. Tooth eruption may have features similar to those in orthodontic tooth movement, in which bone turnover is required. However, there are differences as well, since bone turnover during the tooth eruption process is orchestrated genetically, whereas that in orthodontics is regulated by mechanical force [24]. Another critical difference is that both dental hard tissue formation and bone turnover are required for tooth eruption.  
This study aimed to evaluate the effects of 4 HR administration on dental hard tissue formation along with the eruption rate in rat incisors.