Computational model of mesenchymal migration in 3D under chemotaxis

Subcellular mechano-regulation of cell migration in confined extracellular microenvironment

Cell migration is a highly coordinated cellular event that determines diverse physiological and pathological processes in which the continuous interaction of a migrating cell with neighboring cells or the extracellular matrix is regulated by the physical setting of the extracellular microenvironment. In confined spaces, cell migration occurs differently compared to unconfined open spaces owing to the additional forces that limit cell motility, which create a driving bias for cells to invade the confined space, resulting in a distinct cell motility process compared to what is expected in open spaces. Moreover, cells in confined environments can be subjected to elevated mechanical compression, which causes physical stimuli and activates the damage repair cycle in the cell, including the DNA in the nucleus. Although cells have a self-restoring system to repair damage from the cell membrane to the genetic components of the nucleus, this process may result in genetic and/or epigenetic alterations that can increase the risk of the progression of diverse diseases, such as cancer and immune disorders. Furthermore, there has been a shift in the paradigm of bioengineering from the development of new biomaterials to controlling biophysical cues and fine-tuning cell behaviors to cure damaged/diseased tissues. The external physical cues perceived by cells are transduced along the mechanosensitive machinery, which is further channeled into the nucleus through subcellular molecular linkages of the nucleoskeleton and cytoskeleton or the biochemical translocation of transcription factors. Thus, external cues can directly or indirectly regulate genetic transcriptional processes and nuclear mechanics, ultimately determining cell fate. In this review, we discuss the importance of the biophysical cues, response mechanisms, and mechanical models of cell migration in confined environments. We also discuss the effect of force-dependent deformation of subcellular components, specifically focusing on subnuclear organelles, such as nuclear membranes and chromosomal organization. This review will provide a biophysical perspective on cancer progression and metastasis as well as abnormal cellular proliferation.

Computational modeling of multiple myeloma interactions with resident bone marrow cells

The interaction of multiple myeloma with bone marrow resident cells plays a key role in tumor progression and the development of drug resistance. The tumor cell response involves contact-mediated and paracrine interactions. The heterogeneity of myeloma cells and bone marrow cells makes it difficult to reproduce this environment in in-vitro experiments. The use of in-silico established tools can help to understand these complex problems. In this article, we present a computational model based on the finite element method to define the interactions of multiple myeloma cells with resident bone marrow cells. This model includes cell migration, which is controlled by stress-strain equilibrium, and cell processes such as proliferation, differentiation, and apoptosis. A series of computational experiments were performed to validate the proposed model. Cell proliferation by the growth factor IGF-1 is studied for different concentrations ranging from 0-10 ng/mL. Cell motility is studied for different concentrations of VEGF and fibronectin in the range of 0-100 ng/mL. Finally, cells were simulated under a combination of IGF-1 and VEGF stimuli whose concentrations are considered to be dependent on the cancer-associated fibroblasts in the extracellular matrix. Results show a good agreement with previous in-vitro results. Multiple myeloma growth and migration are shown to correlate linearly to the IGF-1 stimuli. These stimuli are coupled with the mechanical environment, which also improves cell growth. Moreover, cell migration depends on the fiber and VEGF concentration in the extracellular matrix. Finally, our computational model shows myeloma cells trigger mesenchymal stem cells to differentiate into cancer-associated fibroblasts, in a dose-dependent manner.

A novel integrated experimental and computational approach to unravel fibroblast motility in response to chemical gradients in 3D collagen matrices

Fibroblasts play an essential role in tissue repair and regeneration as they migrate to wounded areas to secrete and remodel the extracellular matrix. Fibroblasts recognize chemical substances such as growth factors, which enhance their motility towards the wounded tissues through chemotaxis. Although several studies have characterized single-cell fibroblast motility before, the migration patterns of fibroblasts in response to external factors have not been fully explored in 3D environments. We present a study that combines experimental and computational efforts to characterize the effect of chemical stimuli on the invasion of 3D collagen matrices by fibroblasts. Experimentally, we used microfluidic devices to create chemical gradients using collagen matrices of distinct densities. We evaluated how cell migration patterns were affected by the presence of growth factors and the mechanical properties of the matrix. Based on these results, we present a discrete-based computational model to simulate cell motility, which we calibrated through the quantitative comparison of experimental and computational data via Bayesian optimization. By combining these approaches, we predict that fibroblasts respond to both the presence of chemical factors and their spatial location. Furthermore, our results show that the presence of these chemical gradients could be reproduced by our computational model through increases in the magnitude of cell-generated forces and enhanced cell directionality. Although these model predictions require further experimental validation, we propose that our framework can be applied as a tool that takes advantage of experimental data to guide the calibration of models and predict which mechanisms at the cellular level may justify the experimental findings. Consequently, these new insights may also guide the design of new experiments, tailored to validate the variables of interest identified by the model.

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.

Enhanced Piezoelectric Fibered Extracellular Matrix to Promote Cardiomyocyte Maturation and Tissue Formation: A 3D Computational Model

Mechanical and electrical stimuli play a key role in tissue formation, guiding cell processes such as cell migration, differentiation, maturation, and apoptosis. Monitoring and controlling these stimuli on in vitro experiments is not straightforward due to the coupling of these different stimuli. In addition, active and reciprocal cell-cell and cell-extracellular matrix interactions are essential to be considered during formation of complex tissue such as myocardial tissue. In this sense, computational models can offer new perspectives and key information on the cell microenvironment. Thus, we present a new computational 3D model, based on the Finite Element Method, where a complex extracellular matrix with piezoelectric properties interacts with cardiac muscle cells during the first steps of tissue formation. This model includes collective behavior and cell processes such as cell migration, maturation, differentiation, proliferation, and apoptosis. The model has employed to study the initial stages of in vitro cardiac aggregate formation, considering cell-cell junctions, under different extracellular matrix configurations. Three different cases have been purposed to evaluate cell behavior in fibered, mechanically stimulated fibered, and mechanically stimulated piezoelectric fibered extra-cellular matrix. In this last case, the cells are guided by the coupling of mechanical and electrical stimuli. Accordingly, the obtained results show the formation of more elongated groups and enhancement in cell proliferation.

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.

Matrix degradation regulates osteoblast protrusion dynamics and individual migration

Protrusions are one of the structures that cells use to sense their surrounding environment in a probing and exploratory manner as well as to communicate with other cells. In particular, osteoblasts embedded within a 3D matrix tend to originate a large number of protrusions compared to other type of cells. In this work, we study the role that mechanochemical properties of the extracellular matrix (ECM) play on the dynamics of these protrusions, namely, the regulation of the size and number of emanating structures. In addition, we also determine how the dynamics of the protrusions may lead the 3D movement of the osteoblasts. Significant differences were found in protrusion size and cell velocity, when degradation activity due to metalloproteases was blocked by means of an artificial broad-spectrum matrix metalloproteinase inhibitor, whereas stiffening of the matrix by introducing transglutaminase crosslinking, only induced slight changes in both protrusion size and cell velocity, suggesting that the ability of cells to create a path through the matrix is more critical than the matrix mechanical properties themselves. To confirm this, we developed a cell migration computational model in 3D including both the mechanical and chemical properties of the ECM as well as the protrusion mechanics, obtaining good agreement with experimental results.

The role of actin protrusion dynamics in cell migration through a degradable viscoelastic extracellular matrix: Insights from a computational model

Actin protrusion dynamics plays an important role in the regulation of three-dimensional (3D) cell migration. Cells form protrusions that adhere to the surrounding extracellular matrix (ECM), mechanically probe the ECM and contract in order to displace the cell body. This results in cell migration that can be directed by the mechanical anisotropy of the ECM. However, the subcellular processes that regulate protrusion dynamics in 3D cell migration are difficult to investigate experimentally and therefore not well understood. Here, we present a computational model of cell migration through a degradable viscoelastic ECM. This model is a 2D representation of 3D cell migration. The cell is modeled as an active deformable object that captures the viscoelastic behavior of the actin cortex and the subcellular processes underlying 3D cell migration. The ECM is regarded as a viscoelastic material, with or without anisotropy due to fibrillar strain stiffening, and modeled by means of the meshless Lagrangian smoothed particle hydrodynamics (SPH) method. ECM degradation is captured by local fluidization of the material and permits cell migration through the ECM. We demonstrate that changes in ECM stiffness and cell strength affect cell migration and are accompanied by changes in number, lifetime and length of protrusions. Interestingly, directly changing the total protrusion number or the average lifetime or length of protrusions does not affect cell migration. A stochastic variability in protrusion lifetime proves to be enough to explain differences in cell migration velocity. Force-dependent adhesion disassembly does not result in faster migration, but can make migration more efficient. We also demonstrate that when a number of simultaneous protrusions is enforced, the optimal number of simultaneous protrusions is one or two, depending on ECM anisotropy. Together, the model provides non-trivial new insights in the role of protrusions in 3D cell migration and can be a valuable contribution to increase the understanding of 3D cell migration mechanics.

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.

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.

Mechanoreciprocity in cell migration

Cell migration is an adaptive process that depends on and responds to physical and molecular triggers. Moving cells sense and respond to tissue mechanics and induce transient or permanent tissue modifications, including extracellular matrix stiffening, compression and deformation, protein unfolding, proteolytic remodelling and jamming transitions. Here we discuss how the bi-directional relationship of cell-tissue interactions (mechanoreciprocity) allows cells to change position and contributes to single-cell and collective movement, structural and molecular tissue organization, and cell fate decisions.

Cell migration in microengineered tumor environments

Recent advances in microengineered cell migration platforms are discussed critically with a focus on how cell migration is influenced by engineered tumor microenvironments, the medical relevance being to understand how tumor microenvironments may promote or suppress the progression of cancer. We first introduce key findings in cancer cell migration under the influence of the physical environment, which is systematically controlled by microengineering technology, followed by multi-cues of physico-chemical factors, which represent the complexity of the tumor environment. Recognizing that cancer cells constantly communicate not only with each other but also with tumor-associated cells such as vascular, fibroblast, and immune cells, and also with non-cellular components, it follows that cell motility in tumor microenvironments, especially metastasis via the invasion of cancer cells into the extracellular matrix and other tissues, is closely related to the malignancy of cancer-related mortality. Medical relevance of forefront research realized in microfabricated devices, such as single cell sorting based on the analysis of cell migration behavior, may assist personalized theragnostics based on the cell migration phenotype. Furthermore, we urge development of theory and numerical understanding of single or collective cell migration in microengineered platforms to gain new insights in cancer metastasis and in therapeutic strategies.

Quantifying 3D chemotaxis in microfluidic-based chips with step gradients of collagen hydrogel concentrations

Cell migration is an essential process involved in crucial stages of tissue formation, regeneration or immune function as well as in pathological processes including tumor development or metastasis. During the last few years, the effect of gradients of soluble molecules on cell migration has been widely studied, and complex systems have been used to analyze cell behavior under simultaneous mechano-chemical stimuli. Most of these chemotactic assays have, however, focused on specific substrates in 2D. The aim of the present work is to develop a novel microfluidic-based chip that allows the long-term chemoattractant effect of growth factors (GFs) on 3D cell migration to be studied, while also providing the possibility to analyze the influence of the interface generated between different adjacent hydrogels. Namely, 1.5, 2, 2.5 and 4 mg ml^-1 concentrations of collagen type I were alternatively combined with 5, 10 or 50 ng ml^-1 concentrations of PDGF and VEGF (as a negative control). To achieve this goal, we have designed a new microfluidic device including three adjacent chambers to introduce hydrogels that allow the generation of a collagen concentration step gradient. This versatile and simple platform was tested by using dermal human fibroblasts embedded in 3D collagen matrices. Images taken over a week were processed to quantify the number of cells in each zone. We found, in terms of cell distribution, that the presence of PDGF, especially in small concentrations, was a strong chemoattractant for dermal human fibroblasts across the gels regardless of their collagen concentration and step gradient direction, whereas the effects of VEGF or collagen step gradient concentrations alone were negligible.

A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets

Cell migration, known as an orchestrated movement of cells, is crucially important for wound healing, tumor growth, immune response as well as other biomedical processes. This paper presents a cell-based model to describe cell migration in non-isotropic fibrin networks around pancreatic tumor islets. This migration is determined by the mechanical strain energy density as well as cytokines-driven chemotaxis. Cell displacement is modeled by solving a large system of ordinary stochastic differential equations where the stochastic parts result from random walk. The stochastic differential equations are solved by the use of the classical Euler–Maruyama method. In this paper, the influence of anisotropic stromal extracellular matrix in pancreatic tumor islets on T-lymphocytes migration in different immune systems is investigated. As a result, tumor peripheral stromal extracellular matrix impedes the immune response of T-lymphocytes through changing direction of their migration.