The role of nuclear mechanics in cell deformation under creeping flows

Unravelling cell migration: defining movement from the cell surface

Cell motility is essential for life and development. Unfortunately, cell migration is also linked to several pathological processes, such as cancer metastasis. Cells' ability to migrate relies on many actors. Cells change their migratory strategy based on their phenotype and the properties of the surrounding microenvironment. Cell migration is, therefore, an extremely complex phenomenon. Researchers have investigated cell motility for more than a century. Recent discoveries have uncovered some of the mysteries associated with the mechanisms involved in cell migration, such as intracellular signaling and cell mechanics. These findings involve different players, including transmembrane receptors, adhesive complexes, cytoskeletal components , the nucleus, and the extracellular matrix. This review aims to give a global overview of our current understanding of cell migration.

A mechanistic protrusive-based model for 3D cell migration

Cell migration is essential for a variety of biological processes, such as embryogenesis, wound healing, and the immune response. After more than a century of research-mainly on flat surfaces-, there are still many unknowns about cell motility. In particular, regarding how cells migrate within 3D matrices, which more accurately replicate in vivo conditions. We present a novel in silico model of 3D mesenchymal cell migration regulated by the chemical and mechanical profile of the surrounding environment. This in silico model considers cell's adhesive and nuclear phenotypes, the effects of the steric hindrance of the matrix, and cells ability to degradate the ECM. These factors are crucial when investigating the increasing difficulty that migrating cells find to squeeze their nuclei through dense matrices, which may act as physical barriers. Our results agree with previous in vitro observations where fibroblasts cultured in collagen-based hydrogels did not durotax toward regions with higher collagen concentrations. Instead, they exhibited an adurotactic behavior, following a more random trajectory. Overall, cell's migratory response in 3D domains depends on its phenotype, and the properties of the surrounding environment, that is, 3D cell motion is strongly dependent on the context.

Fluid shear stress-induced mechanotransduction in myoblasts: Does it depend on the glycocalyx?

Muscle stem cells (MuSCs) are involved in muscle maintenance and regeneration. Mechanically loaded MuSCs within their native niche undergo tensile and shear deformations, but how MuSCs sense mechanical stimuli and translate these into biochemical signals regulating function and fate is still poorly understood. We aimed to investigate whether the glycocalyx is involved in the MuSC mechanoresponse, and whether MuSC morphology affects mechanical loading-induced pressure, shear stress, and fluid velocity distribution. FSS-induced deformation of active proliferating MuSCs (myoblasts) with intact or degraded glycocalyx was assessed by live-cell imaging. Glycocalyx-degradation did not significantly affect nitric oxide production, but reduced FSS-induced myoblast deformation and modulated gene expression. Finite-element analysis revealed that the distribution of FSS-induced pressure, shear stress, and fluid velocity on myoblasts was non-uniform, and the magnitude depended on myoblast morphology and apex-height. In conclusion, our results suggest that the glycocalyx does not play a role in NO production in myoblasts but might impact mechanotransduction and gene expression, which needs further investigation. Future studies will unravel the underlying mechanism by which the glycocalyx affects FSS-induced myoblast deformation, which might be related to increased drag forces. Moreover, MuSCs with varying apex-height experience different levels of FSS-induced pressure, shear stress, and fluid velocity, suggesting differential responsiveness to fluid shear forces.

Porous Geometry Guided Micro-mechanical Environment Within Scaffolds for Cell Mechanobiology Study in Bone Tissue Engineering

Mechanobiology research is for understanding the role of mechanics in cell physiology and pathology. It will have implications for studying bone physiology and pathology and to guide the strategy for regenerating both the structural and functional features of bone. Mechanobiological studies in vitro apply a dynamic micro-mechanical environment to cells via bioreactors. Porous scaffolds are commonly used for housing the cells in a three-dimensional (3D) culturing environment. Such scaffolds usually have different pore geometries (e.g. with different pore shapes, pore dimensions and porosities). These pore geometries can affect the internal micro-mechanical environment that the cells experience when loaded in the bioreactor. Therefore, to adjust the applied micro-mechanical environment on cells, researchers can tune either the applied load and/or the design of the scaffold pore geometries. This review will provide information on how the micro-mechanical environment (e.g. fluid-induced wall shear stress and mechanical strain) is affected by various scaffold pore geometries within different bioreactors. It shall allow researchers to estimate/quantify the micro-mechanical environment according to the already known pore geometry information, or to find a suitable pore geometry according to the desirable micro-mechanical environment to be applied. Finally, as future work, artificial intelligent - assisted techniques, which can achieve an automatic design of solid porous scaffold geometry for tuning/optimising the micro-mechanical environment are suggested.

Cell biophysical stimuli in lobopodium 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.

Dual role of the nucleus in cell migration on planar substrates

Cell migration is essential to sustain life. There have been significant advances in the understanding of the mechanisms that control cell crawling, but the role of the nucleus remains poorly understood. The nucleus exerts a tight control of cell migration in 3D environments, but its influence in 2D migration on planar substrates remains unclear. Here, we study the role of the cell nucleus in 2D cell migration using a computational model of fish keratocytes. Our results indicate that the apparently minor role played by the nucleus emerges from two antagonist effects: While the nucleus modifies the spatial distributions of actin and myosin in a way that reduces cell velocity (e.g., the nucleus displaces myosin to the sides and front of the cell), its mechanical connection with the cytoskeleton alters the intracellular stresses promoting cell migration. Overall, the favorable effect of the nucleus-cytoskeleton connection prevails, which may explain why regular cells usually move faster than enucleated cells.

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

Numerical design of a microfluidic chip for probing mechanical properties of cells

Microfluidic chips have been widely used to probe the mechanical properties of cells, which are recognized as a promising label-free biomarker for some diseases. In our previous work (Ye et al., 2018), we have studied the relationships between the transit time and the mechanical properties of a cell flowing through a microchannel with a single constriction, which potentially forms a basis for a microfluidic chip to measure cell's mechanical properties. Here, we investigate this microfluidic chip design and examine its potential in performances. We first develop the simultaneous dependence of the transit time on both the shear and bending moduli of a cell, and then examine the chip sensitivity with respect to the cell mechanical properties while serializing a single constriction along the flow direction. After that, we study the effect of the flow velocity on the transit time, and also test the chip's ability to identify heterogeneous cells with different mechanical properties. The results show that the microfluidic chip designed is capable of identifying heterogeneous cells, even when only one unhealthy cell is included. The serialization of chip can greatly increase the chip sensitivity with respect to the mechanical properties of cells. The flow with a higher velocity helps in not only promoting the chip throughput, but also in providing more accurate transit time measurements, because the cell prefers a symmetric deformation under a high velocity.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

A phenomenological model for cell and nucleus deformation during cancer metastasis

Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing a phenomenological computational model. In our work, cells are attracted by a generic emitting source (e.g., a chemokine or stiffness signal), which is treated by using Green’s Fundamental solutions. We use an IMEX integration method where the linear parts and the nonlinear parts are treated by using an Euler backward scheme and an Euler forward method, respectively. We develop the numerical model for an obstacle-induced deformation in 2D or/and 3D. Considering the uncertainty in cell mobility, stochastic processes are incorporated and uncertainties in the input variables are evaluated using Monte Carlo simulations. This quantitative study aims at estimating the likelihood for invasion and the length of the time interval in which the cell invades the tissue through an obstacle. Subsequently, the two-dimensional cell deformation model is applied to simplified cancer metastasis processes to serve as a model for in vivo or in vitro biomedical experiments.

Relationship between transit time and mechanical properties of a cell through a stenosed microchannel

The changes in the mechanical properties of a cell are not only the cause of some diseases, but can also be a biomarker for some disease states. In recent times, microfluidic devices with built-in constrictions have been widely used to measure these changes. The transit time in such devices, defined as the time that a cell takes to pass through a constriction, has been found to be a crucial factor associated with the cell mechanical properties. Here, we use smoothed dissipative particle dynamics (SDPD), a particle-based numerical method, to explore the relationship between the transit time and mechanical properties of a cell. Three expressions of the transit time are developed from our simulation data, with respect to the stenosed size of constrictions, the shear modulus and bending modulus of cells, respectively. We show that a convergent constriction (the inlet is wider than the outlet), and a sharp-corner constriction (the constriction outlet is narrow) are better in identifying the differences in the transit time of cells. Moreover, the transit time increases and gradually approaches a constant as the shear modulus of cells increases, but increases first and then decreases as the bending modulus increases. These results suggest that the mechanical properties of cells can indeed be measured by analyzing their transit time, based on the recommended microfluidic device.