# Finite Element Modeling of Cells Adhering to a Substrate: An Overview
## 1 Introduction
### Theoretical Background (Principles) of Cell Adhesion and Mechanotransduction Mechanism
At the cytoplasmatic side of the cell, integrins link to the FA intracellular domain consisting of a multiprotein complex which, in turn, links to the actin bundles, thus ensuring the connection between integrins and cytoskeleton structure. The components that constitute the FA intracellular domain are vinculin, talin, zyxin, paxillin, focal adhesion kinase, vasodilator-stimulated phosphoprotein, and adaptor protein p130 Cas. Abbreviations in the figure are VCL (vinculin), TLN (talin), ZYX (zyxin), PAX (paxillin), FAK (focal adhesion kinase), and VASP (vasodilator-stimulated phosphoprotein). Reprinted with permission from [35], 2018 Frontiers. filaments compared to the surrounding cytoskeleton domain. Therefore, stiffness variations in the cell structure effectively canalize mechanical signals to the nucleus along stiffer paths that prevent quick stress wave energy dissipation. Moreover, the tensional state characterizing cytoskeleton architecture allows the cell to auto-support its constantly evolving structure, in which bundles of cytoskeletal filaments polymerize and depolymerize continually, thus adapting cell conformation to the external environment [36]. Simulation of cell adhesion phenomena requires careful consideration of all these issues related to cell structure and behavior. The cell adhesion process is the main interest of the many researchers who try to design and optimize the surface of biodevices, such as scaffolds for bone tissue engineering. The analysis of the current state of the art indicates that extensive research was conducted to determine the optimal scaffold architecture [37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52]; however, rather few studies focused on the identification of the optimal surface micro-geometry favoring the most extended adhesion of mesenchymal stem cells (MSCs) to the scaffold walls and their subsequent differentiation in the osteoblastic sense [53]. Figure 2: Schematization of the linker of nucleoskeleton and cytoskeleton (LINC) complexes binding cytoskeleton structures to the nucleoskeleton. LINC complexes consist of SUN and negrin protein isoforms. SUN proteins span the inner nuclear membrane (INM) and bind to negrin isoforms in the perinuclear space (PS). Nesprin isoforms, in turn, pass through the outer nuclear membrane (ONM) and connect to the cytoskeleton structures. In particular, negrin-1/2 isoform connects directly to actin filaments, negin-3 isoform connects to intermediate filaments (IFs) through pectin, and negrin-4 isoform connects to microtubules (MTs) through kinesin. At the nucleoskeleton side, SUN proteins bind to the lamina of the nucleus through lamin A, which interacts with chromatin both directly and through emerin protein. Therefore, thanks to LINC complexes, the stimulus detected by FAs at the cell-substrate interface and canalized through cytoskeletal transferring channels can reach the intranuclear domain, thus resulting in chromatin reorganization and transcription program activation that affect cell behavior. Abbreviations in the figure are MTs (microtubules), IFs (intermediate filaments), PS (perinuclear space), NPC (nuclear pore complex), INM (inner nuclear membrane), and ONM (outer nuclear membrane). Reprinted with permission from [35], 2018 Frontiers.