# Matrix Stiffness Influences Tubular Formation in Renal Tissue Engineering
## 1 Introduction  
Tissue engineering aims to generate functional cell-based composites that are analogous to native structures or tissues to replace or improve injured tissues or organs. Attempts have been made to create various tissues and organs, from tissue-engineered oral mucosa [1] to engineered heart valves [2] and lymphoid organs [3].  
Tubular structures are the central elements within a tissue that enable the function of organs such as the lung, the mammary gland, blood vessels, and components of the urogenital- and digestive systems. During tube formation, epithelial cells polarize and connect via tight- and adherence junctions to form tube-like structures that contain a lumen [4]. Evolution gave rise to various mechanisms to form tubular structures that have a continuous lumen. For example, the vertebrate neural tube is generated by the invagination of a sheet of polarized cells, while the heart tube in Drosophila is formed by the entrapment of extracellular space by non-polarized cells [5]. In mammary glands, the lumen is generated by the apoptosis of centrally located cells [5]. In the kidney, the lumencontaining the ureteric bud, and its subsequent branches, are formed by a mesenchymal-to-epithelial transition (MET) driven invagination of the mesonephric duct (Wolfrian duct) [6]. Lumen formation in nephrons, which develop from the metanephric mesenchyme, seems to follow a cord hollowing mechanism, where the lumen is formed de novo within a cord of cells [7].  
Micropatterned molds have been used to provide spatial cues to generate structures and tissue analogs from a wide variety of cells [8]. For example, [PERSON] et al. used a micropatterned gel to induce tube formation in mammary epithelial cells and control the tubes' branching geometry [9]. Using micropatterned gels, tubular structures can be generated in different diameters, as [PERSON] et al. reported [10]. In a previous study, we reported the controlled formation of tubes using ureteric bud cells in combination with a micropatterned gel [11].  
Developmental tissue engineering approaches the generation of tissues and organs by mimicking the processes of organogenesis and morphogenesis using the embryo's functional and morphological clues [12]. Studies have demonstrated that tube formation can be facilitated by extracellular matrix components and physical cues such as micropatterned molds [13]. While PDMS is commonly used as a first-choice polymer to generate micropatterned molds or microfluidic devices, the hydrophobic surface makes it difficult to handle small volumes of liquid outside of a microfluidic system. Therefore, for tubular formation, we aimed to find a better suited substrate. For example, the basement membrane component collagen is processed and used by seeded cells, enabling tubular lumen formation [14]. Alginate-based hydrogels commonly maintain progenitor stem cells and lineage-specific cells [15]. Cells do not form a cell-substrate interaction with alginate, which can be beneficial to help with the polarization of cells during tubular and lumen formation. Agarose-based hydrogels have been used in tissue engineering approaches to support the formation of the vascular tissue with morphological similarity to in vivo tissue [16]. In addition, a collagen and agarose composite has been shown to promote the formation of tubular vascular networks [17].  
An essential factor besides extracellular components and geometric cues are the physical properties of the materials used, such as stiffness [18]. For example, [PERSON] and colleagues demonstrated the effect of matrix stiffness on lymphatic tube formation [19]. In this study, we aimed to elicit the influence of matrix stiffness on the tube formation of ureteric bud-derived tubular cells in PDMS or agarose-based micropatterned molds.