A hybrid computational model for collective cell durotaxis

Prevented Cell Clusters' Migration Via Microdot Biomaterials for Inhibiting Scar Adhesion

Cluster-like collective cell migration of fibroblasts is one of the main factors of adhesion in injured tissues. In this research, a microdot biomaterial system is constructed using α-helical polypeptide nanoparticles and anti-inflammatory micelles, which are prepared by ring-opening polymerization of α-amino acids-N-carboxylic anhydrides (NCAs) and lactide, respectively. The microdot biomaterial system slowly releases functionalized polypeptides targeting mitochondria and promoting the influx of extracellular calcium ions under the inflammatory environment, thus inhibiting the expression of N-cadherin mediating cell-cell interaction, and promoting apoptosis of cluster fibroblasts, synergistically inhibiting the migration of fibroblast clusters at the site of tendon injury. Meanwhile, the anti-inflammatory micelles are celecoxib (Cex) solubilized by PEG/polyester, which can improve the inflammatory microenvironment at the injury site for a long time. In vitro, the microdot biomaterial system can effectively inhibit the migration of the cluster fibroblasts by inhibiting the expression of N-cadherin between cell-cell and promoting apoptosis. In vivo, the microdot biomaterial system can promote apoptosis while achieving long-acting anti-inflammation effects, and reduce the expression of vimentin and α-smooth muscle actin (α-SMA) in fibroblasts. Thus, this microdot biomaterial system provides new ideas for the prevention and treatment of tendon adhesion by inhibiting the cluster migration of fibroblasts.

Extracellular vesicles derived from paclitaxel-sensitive nasopharyngeal carcinoma cells deliver miR-183-5p and impart paclitaxel sensitivity through a mechanism involving P-gp

Paclitaxel treatment has been applied for late-stage nasopharyngeal carcinoma (NPC), but therapy failure usually occurs due to paclitaxel resistance. Besides, microRNAs (miRs) delivered by extracellular vesicles (EVs) have been demonstrated as promising biomarkers affecting cancer development. Our work clarified the role of bioinformatically predicted miR-183-5p, which could be delivered by EVs, in the paclitaxel resistance of NPC. Downstream targets of miR-183-5p were predicted in publicly available databases, followed by GO enrichment analysis. A confirmatory dual-luciferase reporter assay determined the targeting relationship between miR-183-5p and P-glycoprotein (P-gp). The shuttling of extracellular miR-183-5p was identified by immunofluorescence. EVs transferred miR-183-5p from paclitaxel-sensitive NPC cells to paclitaxel-resistant NPC cells. Furthermore, overexpression of miR-183-5p and under-expression of P-gp occurred in clinical samples and cells of NPC. High expression of miR-183-5p corresponded to better survival of paclitaxel-treated patients. The effects of manipulated expression of miR-183-5p on NPC cell activities, tumor growth, and paclitaxel resistance were investigated in vitro and in vivo. Its effect was achieved through negatively regulating drug transporters P-gp. Ectopically expressed miR-183-5p enhanced the cancer-suppressive effects of paclitaxel by targeting P-gp, corresponding to diminished cell viability and tumor growth. Taken together, this work goes to elucidate the mechanical actions of miR-183-5p delivered by EVs and its significant contribution towards paclitaxel sensitivity to NPC. 1. This study provides mechanistic insight into the role of miR-183-5p-containing EVs in NPC. 2. The intercellular transportation of miR-183-5p is mediated by EVs in NPC. 3. Overexpressing miR-183-5p facilitates the anti-tumor effects of paclitaxel in NPC. 4. miR-183-5p suppresses paclitaxel resistance of NPC cells by inhibiting P-gp.

Mathematical model of mechano-sensing and mechanically induced collective motility of cells on planar elastic substrates

Cells mechanically interact with their environment to sense, for example, topography, elasticity and mechanical cues from other cells. Mechano-sensing has profound effects on cellular behaviour, including motility. The current study aims to develop a mathematical model of cellular mechano-sensing on planar elastic substrates and demonstrate the model's predictive capabilities for the motility of individual cells in a colony. In the model, a cell is assumed to transmit an adhesion force, derived from a dynamic focal adhesion integrin density, that locally deforms a substrate, and to sense substrate deformation originating from neighbouring cells. The substrate deformation from multiple cells is expressed as total strain energy density with a spatially varying gradient. The magnitude and direction of the gradient at the cell location define the cell motion. Cell-substrate friction, partial motion randomness, and cell death and division are included. The substrate deformation by a single cell and the motility of two cells are presented for several substrate elasticities and thicknesses. The collective motility of 25 cells on a uniform substrate mimicking the closure of a circular wound of 200 µm is predicted for deterministic and random motion. Cell motility on substrates with varying elasticity and thickness is explored for four cells and 15 cells, the latter again mimicking wound closure. Wound closure by 45 cells is used to demonstrate the simulation of cell death and division during migration. The mathematical model can adequately simulate the mechanically induced collective cell motility on planar elastic substrates. The model is suitable for extension to other cell and substrates shapes and the inclusion of chemotactic cues, offering the potential to complement in vitro and in vivo studies.

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.

A Stiff Extracellular Matrix Favors the Mechanical Cell Competition that Leads to Extrusion of Bacterially-Infected Epithelial Cells

Cell competition refers to the mechanism whereby less fit cells (“losers”) are sensed and eliminated by more fit neighboring cells (“winners”) and arises during many processes including intracellular bacterial infection. Extracellular matrix (ECM) stiffness can regulate important cellular functions, such as motility, by modulating the physical forces that cells transduce and could thus modulate the output of cellular competitions. Herein, we employ a computational model to investigate the previously overlooked role of ECM stiffness in modulating the forceful extrusion of infected “loser” cells by uninfected “winner” cells. We find that increasing ECM stiffness promotes the collective squeezing and subsequent extrusion of infected cells due to differential cell displacements and cellular force generation. Moreover, we discover that an increase in the ratio of uninfected to infected cell stiffness as well as a smaller infection focus size, independently promote squeezing of infected cells, and this phenomenon is more prominent on stiffer compared to softer matrices. Our experimental findings validate the computational predictions by demonstrating increased collective cell extrusion on stiff matrices and glass as opposed to softer matrices, which is associated with decreased bacterial spread in the basal cell monolayer in vitro. Collectively, our results suggest that ECM stiffness plays a major role in modulating the competition between infected and uninfected cells, with stiffer matrices promoting this battle through differential modulation of cell mechanics between the two cell populations.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

Collective durotaxis of cohesive cell clusters on a stiffness gradient

Many types of motile cells perform durotaxis, namely directed migration following gradients of substrate stiffness. Recent experiments have revealed that cell monolayers can migrate toward stiffer regions even when individual cells do not-a phenomenon known as collective durotaxis. Here, we address the spontaneous motion of finite cohesive cell monolayers on a stiffness gradient. We theoretically analyze a continuum active polar fluid model that has been tested in recent wetting assays of epithelial tissues and includes two types of active forces (cell-substrate traction and cell-cell contractility). The competition between the two active forces determines whether a cell monolayer spreads or contracts. Here, we show that this model generically predicts collective durotaxis, and that it features a variety of dynamical regimes as a result of the interplay between the spreading state and the global propagation, including sequential contraction and spreading of the monolayer as it moves toward higher stiffness. We solve the model exactly in some relevant cases, which provides both physical insights into the mechanisms of tissue durotaxis and spreading as well as a variety of predictions that could guide the design of future experiments.

Collective motility and mechanical waves in cell clusters

Epithelial cell clusters often move collectively on a substrate. Mechanical signals play a major role in organizing this behavior. There are a number of experimental observations in these systems which await a comprehensive explanation. These include: the internal strains are tensile even for clusters that expand by proliferation; the tractions on the substrate are often confined to the edges of the cluster; there can exist density waves within the cluster; and for cells in an annulus, there is a transition between expanding clusters with proliferation and the case where cells fill the annulus and rotate around it. We formulate a mechanical model to examine these effects. We use a molecular clutch picture which allows "stalling"-inhibition of cell contraction by external forces. Stalled cells are passive from a physical point of view and the un-stalled cells are active. By attaching cells to the substrate and to each other, and taking into account contact inhibition of locomotion, we get a simple picture for many of these findings as well as predictions that could be tested.

Mechanical competition triggered by innate immune signaling drives the collective extrusion of bacterially infected epithelial cells

Intracellular pathogens alter their host cells' mechanics to promote dissemination through tissues. Conversely, host cells may respond to the presence of pathogens by altering their mechanics to limit infection. Here, we monitored epithelial cell monolayers infected with intracellular bacterial pathogens, Listeria monocytogenes or Rickettsia parkeri, over days. Under conditions in which these pathogens trigger innate immune signaling through NF-κB and use actin-based motility to spread non-lytically intercellularly, we found that infected cell domains formed three-dimensional mounds. These mounds resulted from uninfected cells moving toward the infection site, collectively squeezing the softer and less contractile infected cells upward and ejecting them from the monolayer. Bacteria in mounds were less able to spread laterally in the monolayer, limiting the growth of the infection focus, while extruded infected cells underwent cell death. Thus, the coordinated forceful action of uninfected cells actively eliminates large domains of infected cells, consistent with this collective cell response representing an innate immunity-driven process.

Protein nanomechanics in biological context

How proteins respond to pulling forces, or protein nanomechanics, is a key contributor to the form and function of biological systems. Indeed, the conventional view that proteins are able to diffuse in solution does not apply to the many polypeptides that are anchored to rigid supramolecular structures. These tethered proteins typically have important mechanical roles that enable cells to generate, sense, and transduce mechanical forces. To fully comprehend the interplay between mechanical forces and biology, we must understand how protein nanomechanics emerge in living matter. This endeavor is definitely challenging and only recently has it started to appear tractable. Here, I introduce the main in vitro single-molecule biophysics methods that have been instrumental to investigate protein nanomechanics over the last 2 decades. Then, I present the contemporary view on how mechanical force shapes the free energy of tethered proteins, as well as the effect of biological factors such as post-translational modifications and mutations. To illustrate the contribution of protein nanomechanics to biological function, I review current knowledge on the mechanobiology of selected muscle and cell adhesion proteins including titin, talin, and bacterial pilins. Finally, I discuss emerging methods to modulate protein nanomechanics in living matter, for instance by inducing specific mechanical loss-of-function (mLOF). By interrogating biological systems in a causative manner, these new tools can contribute to further place protein nanomechanics in a biological context.

Durotaxis: the mechanical control of directed cell migration

Directed cell migration is essential for cells to efficiently migrate in physiological and pathological processes. While migrating in their native environment, cells interact with multiple types of cues, such as mechanical and chemical signals. The role of chemical guidance via chemotaxis has been studied in the past, the understanding of mechanical guidance of cell migration via durotaxis remained unclear until very recently. Nonetheless, durotaxis has become a topic of intensive research and several advances have been made in the study of mechanically guided cell migration across multiple fields. Thus, in this article we provide a state of the art about durotaxis by discussing in silico, in vitro and in vivo data. We also present insights on the general mechanisms by which cells sense, transduce and respond to environmental mechanics, to then contextualize these mechanisms in the process of durotaxis and explain how cells bias their migration in anisotropic substrates. Furthermore, we discuss what is known about durotaxis in vivo and we comment on how haptotaxis could arise from integrating durotaxis and chemotaxis in native environments.

In situ continuously monitoring of cancer cell invasion process based on impedance sensing

Activation of invasion and metastasis is recognized as one of the hallmarks of cancer. There are 90% of cancer-related deaths due to metastasis and given that it is worthy of note to study cancer progression and metastasis. Owing to restricted tools used to underpin the study of tumor invasion process, an on-site platform was developed to monitor this event in vitro. We used interdigital gold electrodes to monitor the dynamic process of cancer cells invading into extracellular matrix in situ continuously. Influences of collagen concentration and number of cancer cells on the measured impedance was exhibited. In addition, the parameters used to demonstrate the experiment results were optimized. The change of impedance magnitude indicated the cell-matrix interaction during invasion process. The potential further use of this platform would be complementary in cell studies when concerning metastasis.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

Durotaxis: The Hard Path from In Vitro to In Vivo

Durotaxis, the process by which cells follow gradients of extracellular mechanical stiffness, has been proposed as a mechanism driving directed migration. Despite the lack of evidence for its existence in vivo, durotaxis has become an active field of research, focusing on the mechanism by which cells respond to mechanical stimuli from the environment. In this review, we describe the technical and conceptual advances in the study of durotaxis in vitro, discuss to what extent the evidence suggests durotaxis may occur in vivo, and emphasize the urgent need for in vivo demonstration of durotaxis.

Bridging from single to collective cell migration: A review of models and links to experiments

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.

Computational models of migration modes improve our understanding of metastasis

Tumor cells migrate through changing microenvironments of diseased and healthy tissue, making their migration particularly challenging to describe. To better understand this process, computational models have been developed for both the ameboid and mesenchymal modes of cell migration. Here, we review various approaches that have been used to account for the physical environment's effect on cell migration in computational models, with a focus on their application to understanding cancer metastasis and the related phenomenon of durotaxis. We then discuss how mesenchymal migration models typically simulate complex cell–extracellular matrix (ECM) interactions, while ameboid migration models use a cell-focused approach that largely ignores ECM when not acting as a physical barrier. This approach greatly simplifies or ignores the mechanosensing ability of ameboid migrating cells and should be reevaluated in future models. We conclude by describing future model elements that have not been included to date but would enhance model accuracy.

All Roads Lead to Directional Cell Migration

Directional cell migration normally relies on a variety of external signals, such as chemical, mechanical, or electrical, which instruct cells in which direction to move. Many of the major molecular and physical effects derived from these cues are now understood, leading to questions about whether directional cell migration is alike or distinct under these different signals, and how cells might be directed by multiple simultaneous cues, which would be expected in complex in vivo environments. In this review, we compare how different stimuli are spatially distributed, often as gradients, to direct cell movement and the mechanisms by which they steer cells. A comparison of the downstream effectors of directional cues suggests that different external signals regulate a common set of components: small GTPases and the actin cytoskeleton, which implies that the mechanisms downstream of different signals are likely to be closely related and underlies the idea that cell migration operates by a common set of physical principles, irrespective of the input.

The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration

The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.

Cellogram: On-the-Fly Traction Force Microscopy

Traction force microscopy (TFM) derives maps of cell-generated forces, typically in the nanonewton range, transmitted to the extracellular environment upon actuation of complex biological processes. In traditional approaches, force rendering requires a terminal, time-consuming step of cell deadhesion to obtain a reference image. A conceptually opposite approach is provided by reference-free methods, opening to the on-the-fly generation of force maps from an ongoing experiment. This requires an image processing algorithm keeping the pace of the biological phenomena under investigation. Here, we introduce an integrated software pipeline rendering force maps from single reference-free TFM images seconds to minutes after their acquisition. The algorithm tackles image processing, reference image estimation, and finite element analysis as a single problem, yielding a robust and fully automatic solution. The method's capabilities are demonstrated in two applications. First, the mechanical annihilation of cancer cells is monitored as a function of rising environmental temperature, setting a population threshold at 45 °C. Second, the fast temporal correlation of forces produced across individual cells is used to map physically connected adhesion points, yielding typical lengths that vary as a function of the cell cycle phase.

Role of Substrate Stiffness in Tissue Spreading: Wetting Transition and Tissue Durotaxis

Living tissues undergo wetting transitions: On a surface, they can either form a dropletlike cell aggregate or spread as a monolayer of migrating cells. Tissue wetting depends not only on the chemical but also on the mechanical properties of the substrate. Here, we study the role of substrate stiffness in tissue spreading, which we describe by means of an active polar fluid model. Taking into account that cells exert larger active traction forces on stiffer substrates, we predict a tissue wetting transition at a critical substrate stiffness that decreases with tissue size. On substrates with a stiffness gradient, we find that the tissue spreads faster on the stiffer side. Furthermore, we show that the tissue can wet the substrate on the stiffer side while dewetting from the softer side. We also show that, by means of viscous forces transmitted across the tissue, the stiffer-side interface can transiently drag the softer-side interface toward increasing stiffness, against its spreading tendency. These two effects result in directed tissue migration up the stiffness gradient. This phenomenon-tissue durotaxis-can thus emerge both from dewetting on the soft side and from hydrodynamic interactions between the tissue interfaces. Overall, our work unveils mechanisms whereby substrate stiffness impacts the collective migration and the active wetting properties of living tissues, which are relevant in development, regeneration, and cancer.

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.

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.

Mechanical and Systems Biology of Cancer

Mechanics and biochemical signaling are both often deregulated in cancer, leading toincreased cell invasiveness, proliferation, and survival. The dynamics and interactions of cytoskeletal components control basic mechanical properties, such as cell tension, stiffness, and engagement with the extracellular environment, which can lead to extracellular matrix remodeling. Intracellular mechanics can alter signaling and transcription factors, impacting cell decision making. Additionally, signaling from soluble and mechanical factors in the extracellular environment, such as substrate stiffness and ligand density, can modulate cytoskeletal dynamics. Computational models closely integrated with experimental support, incorporating cancer-specific parameters, can provide quantitative assessments and serve as predictive tools toward dissecting the feedback between signaling and mechanics and across multiple scales and domains in tumor progression.