Three-Dimensional Numerical Model of Cell Morphology during Migration in Multi-Signaling Substrates

Abstract

Cell Migration associated with cell shape changes are of central importance in many biological processes ranging from morphogenesis to metastatic cancer cells. Cell movement is a result of cyclic changes of cell morphology due to effective forces on cell body, leading to periodic fluctuations of the cell length and cell membrane area. It is well-known that the cell can be guided by different effective stimuli such as mechanotaxis, thermotaxis, chemotaxis and/or electrotaxis. Regulation of intracellular mechanics and cell’s physical interaction with its substrate rely on control of cell shape during cell migration. In this notion, it is essential to understand how each natural or external stimulus may affect the cell behavior. Therefore, a three-dimensional (3D) computational model is here developed to analyze a free mode of cell shape changes during migration in a multi-signaling micro-environment. This model is based on previous models that are presented by the same authors to study cell migration with a constant spherical cell shape in a multi-signaling substrates and mechanotaxis effect on cell morphology. Using the finite element discrete methodology, the cell is represented by a group of finite elements. The cell motion is modeled by equilibrium of effective forces on cell body such as traction, protrusion, electrostatic and drag forces, where the cell traction force is a function of the cell internal deformations. To study cell behavior in the presence of different stimuli, the model has been employed in different numerical cases. Our findings, which are qualitatively consistent with well-known related experimental observations, indicate that adding a new stimulus to the cell substrate pushes the cell to migrate more directionally in more elongated form towards the more effective stimuli. For instance, the presence of thermotaxis, chemotaxis and electrotaxis can further move the cell centroid towards the corresponding stimulus, respectively, diminishing the mechanotaxis effect. Besides, the stronger stimulus imposes a greater cell elongation and more cell membrane area. The present model not only provides new insights into cell morphology in a multi-signaling micro-environment but also enables us to investigate in more precise way the cell migration in the presence of different stimuli.

The Mechanics of Single Cell and Collective Migration of Tumor Cells

“…Despite the frequency with which they have and continue to be utilized for migration studies, 2D models have significant limitations, primarily owing to the fact that migration in vivo typically occurs in a 3D space. More recent work has shown that topography and dimensionality, among other parameters [25,39], play a critical role in determining migratory phenotype and the mechanical responses of cells. Micromolded and micromachined 2D surfaces [40] as well as tunably compliant 2D substrates such as polyacrylamide (PA) [39,41] or collagen gels [42][43][44] partially resolve the limitations of 2D systems by allowing for tuning of topography and stiffness, but still do not entirely account for dimensional cues from the environment.…”

Role of Mechanical Cues in Cell Differentiation and Proliferation: A 3D Numerical Model

“…This force drives the cell body forward and is directly proportional to the cell stress, σ cell . Representing the cell by a connected group of finite elements, the nodal traction force of the cell can be represented as [ 24 , 25 ] where e i denotes a unit vector passing through the i th node of the cell membrane towards the cell centroid ( Fig 1-a ). S represents the cell membrane area and ζ is a dimensionless parameter named “adhesivity” which is directly proportional to the concentration of the ligands at the leading edge of the cell, ψ , the total number of available receptors, n r , and the binding constant of the cell integrins, k .…”

“…To migrate, cells extend local protrusions by exerting a protrusion force to evaluate their surrounding substrate. This refers to the actin polymerization and differs from the cytoskeletal contractile force transmitted to the substrate [ 22 , 25 , 31 ]. It is a random force that causes cells to move along a directed random path towards the effective cue.…”

A hemidesmosomal protein regulates actin dynamics and traction forces in motile keratinocytes

“…Thus, we performed TF microscopy on cells plated onto a fluorescent bead-impregnated gel substrate as describedp r e v i o u s l y( 2 9 ) .W et h e n compared net and total TF magnitudes and their localization. Based on both experimental and computational definitions used by others, we define net TF magnitude as the magnitude of the sum of cellular TF vectors and total TF magnitude as the sum of the magnitudes of cellular TF vectors (4,40,41).…”