Modeling Confined Cell Migration Mediated by Cytoskeleton Dynamics

Cell migration is an important biological process that has generated increasing interest during the last several years. This process is based on three phases: protrusion at the front end of the cell, de-adhesion at the rear end and contraction of the cell body, all of them coordinated due to the polymerization/depolymerization of certain cytoskeletal proteins. The aim of this work is to present a mathematical model to simulate the actin polymerization/depolymerization process that regulates the final outcome of cell migration process, considering all the above phases, in a particular case: when the cell is confined in a microfluidic channel. Under these specific conditions, cell migration can be approximated by using one-dimensional simulations. We will propose a system of reaction-diffusion equations to simulate the behavior of the cytoskeletal proteins responsible for protrusion and contraction in the cell, coupled with the mechanical response of the cell, computing its deformations and stresses. Furthermore, a numerical procedure is presented in order to simulate the whole process in a moving and deformable domain corresponding to the cell body

Mechanical modeling of collective cell migration: An agent-based and continuum material approach

We develop a novel modeling approach that combines a discrete agent-based model and a continuum material model to simulate collective cell migration in epithelial layers. In this approach, cells are represented as particles located at their geometrical center, but also as a polygonal body derived from the Voronoi diagram. Furthermore, we model the tissue as a continuum medium with different spatial domains that represent cell and substrate materials. In fact, the mechanical behavior of each domain is affected by the presence of cells from the discrete model. Moreover, we solve this mechanical problem using the finite element method (FEM). The forces generated by cells are projected to the FE mesh, that is created dynamically during the simulation from the discrete cell representation. After the FE resolution, we use the mesh displacements to determine the new cell positions in the agent-based model. Finally, to demonstrate the potential of this approach to model epithelial tissue mechanics, we simulate two well-studied cases of collective cell migration: durotaxis and gap closure. We use the experimental data from the literature to validate our numerical results. Therefore, the modeling strategy here presented offers a new perspective for a deeper understanding of tissue mechanics that emerge from cell dynamics in epithelial layers

A discrete approach for modeling cell-matrix adhesions

During recent years the interaction between the extracellular matrix and the cytoskeleton of the cell has been object of numerous studies due to its importance in cell migration processes. These interactions are performed through protein clutches, known as focal adhesions. For migratory cells these focal adhesions along with force gener- ating processes in the cytoskeleton are responsible for the for- mation of protrusion structures like lamellipodia or filopodia. Much is known about these structures: the different proteins that conform them, the players involved in their formation or their role in cell migration. Concretely, growth-cone filopo- dia structures have attracted significant attention because of their role as cell sensors of their surrounding environment and its complex behavior. On this matter, a vast myriad of math- ematical models has been presented to explain its mechan- ical behavior. In this work, we aim to study the mechani- cal behavior of these structures through a discrete approach. This numerical model provides an individual analysis of the proteins involved including spatial distribution, interaction between them, and study of different phenomena, such as clutches unbinding or protein unfolding

A time-dependent phenomenological model for cell mechano-sensing

Adherent cells normally apply forces as a generic means of sensing and responding to the mechanical nature of their surrounding environment. How these forces vary as a function of the extracellular rigidity is critical to understanding the regulatory functions that drive important phenomena such as wound healing or muscle contraction. In recognition of this fact, experiments have been conducted to understand cell rigidity-sensing properties under known conditions of the extracellular environment, opening new possibilities for modeling this active behaviour. In this work, we provide a physics-based constitutive model taking into account the main structural components of the cell to reproduce its most significant contractile properties such as the traction forces exerted as a function of time and the extracellular stiffness. This model shows how the interplay between the time-dependent response of the acto-myosin contractile system and the elastic response of the cell components determine the mechano-sensing behaviour of single cells

A time-dependent phenomenological model for cell mechano-sensing

Adherent cells normally apply forces as a generic means of sensing and responding to the mechanical nature of their surrounding environment. How these forces vary as a function of the extracellular rigidity is critical to understanding the regulatory functions that drive important phenomena such as wound healing or muscle contraction. In recognition of this fact, experiments have been conducted to understand cell rigidity-sensing properties under known conditions of the extracellular environment, opening new possibilities for modeling this active behaviour. In this work, we provide a physics-based constitutive model taking into account the main structural components of the cell to reproduce its most significant contractile properties such as the traction forces exerted as a function of time and the extracellular stiffness. This model shows how the interplay between the time-dependent response of the acto-myosin contractile system and the elastic response of the cell components determine the mechano-sensing behaviour of single cells

Cell biophysical stimuli in lobodopodium formation: a computer based approach

Different cell migration modes have been identified in 3D environments, e.g., modes incorporating lamellopodia or blebs. Recently, a new type of cellular migration has been investigated: lobopodia-based migration, which appears only in three-dimensional matrices under certain conditions. The cell creates a protrusion through which the nucleus slips, dividing the cell into two parts (front and rear) with different hydrostatic pressures. In this work, we elucidate the mechanical conditions that favour this type of migration. One of the hypotheses about this type of migration is that it depends on the mechanical properties of the extracellular matrix. That is, lobopodia-based migration is dependent on whether the extracellular matrix is linearly elastic or non-linearly elastic. To determine whether the mechanical properties of the extracellular matrix are crucial in the choice of cell migration mode and which mechanotransduction mechanism the cell might use, we develop a finite element model. From our simulations, we identify two different possible mechanotransduction mechanisms that could regulate the cell to switch from a lobopodial to a lamellipodial migration mode. The first relies on a differential pressure increase inside the cytoplasm while the cell contracts, and the second relies on a change in the fluid flow direction in non-linearly elastic extracellular matrices but not in linearly elastic matrices. The biphasic nature of the cell has been determined to mediate this mechanism and the different behaviours of cells in linearly elastic and non-linearly elastic matrices

Cell Cytoskeleton Dynamics: Mechano-Sensing Properties

`The actin cytoskeleton network is the dominant structure of eukaryotic cells. It is highlydynamic and plays a central role in a wide range of mechanical and biological functions.Cytoskeleton is composed mainly of actin filaments (F-actin) resulting from the self-assemblyof monomeric actin (G-actin) and cross-linked by actin cross-linking proteins (ACPs) whosenature and concentration determine the morphological and rheological properties of thenetwork. These actin filaments are reversibly coupled to membrane proteins (critical to theresponse of cells to external stress) and in conjunction with motor proteins from the myosinfamily, are able to generate contractile force during cell migration. Knowledge of actincytoskeleton and its rheological properties is therefore indispensable for understanding theunderlying mechanics and various biological processes of cells. Here, we present a 3-DBrownian dynamics (BD) computational model in which actin monomers polymerize andbecome cross-linked by two types of ACPs, forming either parallel filament bundles ororthogonal networks. Also, the active and dynamic behaviour of motors is included. In thissimulation, actin monomers, filaments, ACPs, and motors experience thermal motion andinteract with each other with binding probabilities and defined potentials. Displacements aregoverned by the Langevin equation, and positions of all elements are updated using the Eulerintegration scheme.In this first part of the work, the mechano-sensing properties of active networks are investigatedby evaluating stress and strain rate in response to different substrate stiffness

Finite Element Simulation of the Deformation of a Cell Driven by Creeping Flow

The purpose of this work is to calculate the deformation undergone by a cell in function of its nucleus size and mechanical properties. The cell immersed in a fluid go through a variable section channel and it is deformed by fluid forces.Cell deformation into the channel causes changes at the fluid velocity profile. This fluid configuration change results in diferent normal and viscous forces around the cell. Due to strong correlation between cell deformation and fluid velocity profile, a fluidsolid interacción (FSI) is required

Degradation of extracellular matrix regulates osteoblast migration: A microfluidic-based study

Bone regeneration is strongly dependent on the capacity of cells to move in a 3D microenvironment, where a large cascade of signals is activated. To improve the understanding of this complex process and to advance in the knowledge of the role of each specific signal, it is fundamental to analyze the impact of each factor independently. Microfluidic-based cell culture is an appropriate technology to achieve this objective, because it allows recreating realistic 3D local microenvironments by taking into account the extracellular matrix, cells and chemical gradients in an independent or combined scenario. The main aim of this work is to analyze the impact of extracellular matrix properties and growth factor gradients on 3D osteoblast movement, as well as the role of cell matrix degradation. For that, we used collagen-based hydrogels, with and without crosslinkers, under different chemical gradients, and eventually inhibiting metalloproteinases to tweak matrix degradation. We found that osteoblast''s 3D migratory patterns were affected by the hydrogel properties and the PDGF-BB gradient, although the strongest regulatory factor was determined by the ability of cells to remodel the matrix

Microfluidic model of monocyte extravasation reveals the role of hemodynamics and subendothelial matrix mechanics in regulating endothelial integrity

Extravasation of circulating cells is an essential process that governs tissue inflammation and the body's response to pathogenic infection. To initiate anti-inflammatory and phagocytic functions within tissues, immune cells must cross the vascular endothelial barrier from the vessel lumen to the subluminal extracellular matrix. In this work, we present a microfluidic approach that enables the recreation of a three-dimensional, perfused endothelial vessel formed by human endothelial cells embedded within a collagen-rich matrix. Monocytes are introduced into the vessel perfusate, and we investigate the role of luminal flow and collagen concentration on extravasation. In vessels conditioned with the flow, increased monocyte adhesion to the vascular wall was observed, though fewer monocytes extravasated to the collagen hydrogel. Our results suggest that the lower rates of extravasation are due to the increased vessel integrity and reduced permeability of the endothelial monolayer. We further demonstrate that vascular permeability is a function of collagen hydrogel mass concentration, with increased collagen concentrations leading to elevated vascular permeability and increased extravasation. Collectively, our results demonstrate that extravasation of monocytes is highly regulated by the structural integrity of the endothelial monolayer. The microfluidic approach developed here allows for the dissection of the relative contributions of these cues to further understand the key governing processes that regulate circulating cell extravasation and inflammation