## 1 Introduction  
Mesenchymal stem cells (MSCs) can be harvested from various human tissues, such as bone marrow, adipose tissue, and umbilical cord blood [1]. In addition, MSCs have been extracted from the periodontal ligaments of permanent teeth, primary teeth, and supernumerary teeth [2, 3, 4]. Periodontal ligament (PDL) represents a fibrous network, connecting the cementum of the tooth root and the alveolar bone [5]. It serves many functions, such as tooth support, nutrition, and protection. Periodontal ligament stem cells (PDLSCs) are easy to obtain and have a greater proliferation rate than bone marrow stem cells. PDLSCs are capable of differentiating into osteoblasts, cementoblasts, adipocytes, and chondrocytes, and can form a structure similar to periodontal ligaments in vitro [6, 7, 8, 9]. In 2011, PDLSCs were obtained from a supernumerary tooth (sPDLSCs) [4]. The sPDLSCs show a greater colony-forming ability than bone marrow stem cells, and can differentiate into adipocytes and osteoblasts [10]. Expendable dental tissue, such as supernumerary teeth, may be a source of stem cells. Therefore, studies of the biological properties of PDLSCs obtained from various dental tissue are needed to optimize their regenerative effects. Cell culture is essential for the study of MSCs. In conventional two-dimensional (2D) cell culture methods, cells are cultured on the bottom of a culture-compatible polystyrene plate. Such cultures create an environment for studying biological processes or cell mechanisms under specific experimental conditions, and maintain various types of proliferation [11]. However, in nature, cells grow three-dimensionally (3D) rather than in a 2D plane. Therefore, it is difficult to study cell-to-cell signal transduction and the functions of cells in a conventional 2D culture environment [12]. To overcome these limitations, cell research using 3D culture is under investigation. Three-dimensional cultures have the advantage of emulating the original characteristics of the cell's environment, so that the cell can display form, function, and activity as close to naturally as possible [13; 14]. In addition, 3D culture is an alternative to animal experimentation [15]. There are the following two general methods of 3D culture: scaffold and scaffold-free. The scaffold method involves creating a scaffold of microstructures that the cells can use to move, proliferate, differentiate, and remain in contact [15]. However, scaffolds have limitations that can negatively affect cell stability and behavior during incubation [16]. In the scaffold-free method, a pallet or centrifugation tube culture, low-adhesion plate culture, bioreactor, hanging drop culture, or pallet culture and liquid overlay are used to create 3D microstructures without scaffolding [11; 15; 16; 17]. In these methods, the cells assemble an endogenous extracellular matrix to form their own preferred microenvironment [18; 19]. Cells cultured in a 3D environment behave differently than those in a 2D environment [17]. For example, primary articular chondrocytes and hepatocytes cultured in a 2D culture rapidly lose their normal phenotypes, but in 3D cultures the normal phenotype is maintained [20]. In addition, 3D-cultured stem cells exhibit better osteoblastic, adipogenic, and neuronal differentiation [21]. Similarly, 3D-cultured human dental pulp cells show higher expression of osteoclastin, dentin sialophosphoprotein, and alkaline phosphatase [22]. The expression of these proteins is influenced by cell-cell and cell-matrix interactions, which are difficult to imitate in 2D culture. In addition, the expression of genes related to multi-lineage differentiation, such as Nanog and Oct4, as well as those related to pluripotency transcription factors, is higher in 3D-cultured cells. These studies demonstrate that cell culture conditions influence gene expression [17; 23]. However, previous studies have usually used microarrays and polymerase chain reaction, and few studies have analyzed genome-wide expression.