Multiscale mechanobiology: computational models for integrating molecules to multicellular systems

Biomechanics of soft biological tissues and organs, mechanobiology, homeostasis and modelling

The human body consists of many different soft biological tissues that exhibit diverse microstructures and functions and experience diverse loading conditions. Yet, under many conditions, the mechanical behaviour of these tissues can be described well with similar nonlinearly elastic or inelastic constitutive relations, both in health and some diseases. Such constitutive relations are essential for performing nonlinear stress analyses, which in turn are critical for understanding physiology, pathophysiology and even clinical interventions, including surgery. Indeed, most cells within load-bearing soft tissues are highly sensitive to their local mechanical environment, which can typically be quantified using methods of continuum mechanics only after the constitutive relations are determined from appropriate data, often multi-axial. In this review, we discuss some of the many experimental findings of the structure and the mechanical response, as well as constitutive formulations for 10 representative soft tissues or organs, and present basic concepts of mechanobiology to support continuum biomechanical studies. We conclude by encouraging similar research along these lines, but also the need for models that can describe and predict evolving tissue properties under many conditions, ranging from normal development to disease progression and wound healing. An important foundation for biomechanics and mechanobiology now exists and methods for collecting detailed multi-scale data continue to progress. There is, thus, considerable opportunity for continued advancement of mechanobiology and biomechanics.

Engineering innovations in medicine and biology: Revolutionizing patient care through mechanical solutions

The overlap between mechanical engineering and medicine is expanding more and more over the years. Engineers are now using their expertise to design and create functional biomaterials and are continually collaborating with physicians to improve patient health. In this review, we explore the state of scientific knowledge in the areas of biomaterials, biomechanics, nanomechanics, and computational fluid dynamics (CFD) in relation to the pharmaceutical and medical industry. Focusing on current research and breakthroughs, we provide an overview of how these fields are being used to create new technologies for medical treatments of human patients. Barriers and constraints in these fields, as well as ways to overcome them, are also described in this review. Finally, the potential for future advances in biomaterials to fundamentally change the current approach to medicine and biology is also discussed.

MRTF may be the missing link in a multiscale mechanobiology approach toward macrophage dysfunction in space

Macrophages exhibit impaired phagocytosis, adhesion, migration, and cytokine production in space, hindering their ability to elicit immune responses. Considering that the combined effect of spaceflight microgravity and radiation is multiscale and multifactorial in nature, it is expected that contradictory findings are common in the field. This theory paper reanalyzes research on the macrophage spaceflight response across multiple timescales from seconds to weeks, and spatial scales from the molecular, intracellular, extracellular, to the physiological. Key findings include time-dependence of both pro-inflammatory activation and integrin expression. Here, we introduce the time-dependent, intracellular localization of MRTF-A as a hypothetical confounder of macrophage activation. We discuss the mechanosensitive MRTF-A/SRF pathway dependence on the actin cytoskeleton/nucleoskeleton, microtubules, membrane mechanoreceptors, hypoxia, oxidative stress, and intracellular/extracellular crosstalk. By adopting a multiscale perspective, this paper provides the first mechanistic answer for a three-decade-old question regarding impaired cytokine secretion in microgravity—and strengthens the connection between the recent advances in mechanobiology, microgravity, and the spaceflight immune response. Finally, we hypothesize MRTF involvement and complications in treating spaceflight-induced cardiovascular, skeletal, and immune disease.

Risky interpretations across the length scales: continuum vs. discrete models for soft tissue mechanobiology

Modelling and simulation in mechanobiology play an increasingly important role to unravel the complex mechanisms that allow resident cells to sense and respond to mechanical cues. Many of the in vivo mechanical loads occur on the tissue length scale, thus raising the essential question how the resulting macroscopic strains and stresses are transferred across the scales down to the cellular and subcellular levels. Since cells anchor to the collagen fibres within the extracellular matrix, the reliable representation of fibre deformation is a prerequisite for models that aim at linking tissue biomechanics and cell mechanobiology. In this paper, we consider the two-scale mechanical response of an affine structural model as an example of a continuum mechanical approach and compare it with the results of a discrete fibre network model. In particular, we shed light on the crucially different mechanical properties of the 'fibres' in these two approaches. While assessing the capability of the affine structural approach to capture the fibre kinematics in real tissues is beyond the scope of our study, our results clearly show that neither the macroscopic tissue response nor the microscopic fibre orientation statistics can clarify the question of affinity.

Seven challenges in the multiscale modeling of multicellular tissues

The growth and dynamics of multicellular tissues involve tightly regulated and coordinated morphogenetic cell behaviors, such as shape changes, movement, and division, which are governed by subcellular machinery and involve coupling through short- and long-range signals. A key challenge in the fields of developmental biology, tissue engineering and regenerative medicine is to understand how relationships between scales produce emergent tissue-scale behaviors. Recent advances in molecular biology, live-imaging and ex vivo techniques have revolutionized our ability to study these processes experimentally. To fully leverage these techniques and obtain a more comprehensive understanding of the causal relationships underlying tissue dynamics, computational modeling approaches are increasingly spanning multiple spatial and temporal scales, and are coupling cell shape, growth, mechanics, and signaling. Yet such models remain challenging: modeling at each scale requires different areas of technical skills, while integration across scales necessitates the solution to novel mathematical and computational problems. This review aims to summarize recent progress in multiscale modeling of multicellular tissues and to highlight ongoing challenges associated with the construction, implementation, interrogation, and validation of such models. This article is categorized under: Reproductive System Diseases > Computational Models Metabolic Diseases > Computational Models Cancer > Computational Models.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

A mesoscale mechanical model of cellular interactions

Computational models of cell mechanics allow the precise interrogation of cell shape change. These morphological changes are required for cells to survive in diverse tissue environments. Here, we present a mesoscale mechanical model of cell-substrate interactions using the level set method based on experimentally measured parameters. By implementing a viscoelastic mechanical equivalent circuit, we accurately model whole-cell deformations that are important for a variety of cellular processes. To effectively model shape changes as a cell interacts with a substrate, we have included receptor-mediated adhesion, which is governed by catch-slip bond behavior. The effect of adhesion was explored by subjecting cells to a variety of different substrates including flat, curved, and deformable surfaces. Finally, we increased the accuracy of our simulations by including a deformable nucleus in our cells. This model sets the foundation for further exploration into computational analyses of multicellular interactions.

Mechanobiology of the female reproductive system

BACKGROUND

Mechanobiology in the field of human female reproduction has been extremely challenging technically and ethically.

METHODS

The present review provides the current knowledge on mechanobiology of the female reproductive system. This review focuses on the early phases of reproduction from oocyte development to early embryonic development, with an emphasis on current progress.

MAIN FINDINGS RESULTS

Optimal, well-controlled mechanical cues are required for female reproductive system physiology. Many important questions remain unanswered; whether and how mechanical imbalances among the embryo, decidua, and uterine muscle contractions affect early human embryonic development, whether the biomechanical properties of oocytes/embryos are potential biomarkers for selecting high-quality oocytes/embryos, whether mechanical properties differ between the two major compartments of the ovary (cortex and medulla) in normally ovulating human ovaries, whether durotaxis is involved in several processes in addition to embryonic development. Progress in mechanobiology is dependent on development of technologies that enable precise physical measurements.

CONCLUSION

More studies are needed to understand the roles of forces and changes in the mechanical properties of female reproductive system physiology. Recent and future technological advancements in mechanobiology research will help us understand the role of mechanical forces in female reproductive system disorders/diseases.

A constriction channel analysis of astrocytoma stiffness and disease progression

Studies have demonstrated that cancer cells tend to have reduced stiffness (Young's modulus) compared to their healthy counterparts. The mechanical properties of primary brain cancer cells, however, have remained largely unstudied. To investigate whether the stiffness of primary brain cancer cells decreases as malignancy increases, we used a microfluidic constriction channel device to deform healthy astrocytes and astrocytoma cells of grade II, III, and IV and measured the entry time, transit time, and elongation. Calculating cell stiffness directly from the experimental measurements is not possible. To overcome this challenge, finite element simulations of the cell entry into the constriction channel were used to train a neural network to calculate the stiffness of the analyzed cells based on their experimentally measured diameter, entry time, and elongation in the channel. Our study provides the first calculation of stiffness for grades II and III astrocytoma and is the first to apply a neural network analysis to determine cell mechanical properties from a constriction channel device. Our results suggest that the stiffness of astrocytoma cells is not well-correlated with the cell grade. Furthermore, while other non-central-nervous-system cell types typically show reduced stiffness of malignant cells, we found that most astrocytoma cell lines had increased stiffness compared to healthy astrocytes, with lower-grade astrocytoma having higher stiffness values than grade IV glioblastoma. Differences in nucleus-to-cytoplasm ratio only partly explain differences in stiffness values. Although our study does have limitations, our results do not show a strong correlation of stiffness with cell grade, suggesting that other factors may play important roles in determining the invasive capability of astrocytoma. Future studies are warranted to further elucidate the mechanical properties of astrocytoma across various pathological grades.

Adhesion strength and contractility enable metastatic cells to become adurotactic

Significant changes in cell stiffness, contractility, and adhesion, i.e., mechanotype, are observed during a variety of biological processes. Whether cell mechanics merely change as a side effect of or driver for biological processes is still unclear. Here, we sort genotypically similar metastatic cancer cells into strongly adherent (SA) versus weakly adherent (WA) phenotypes to study how contractility and adhesion differences alter the ability of cells to sense and respond to gradients in material stiffness. We observe that SA cells migrate up a stiffness gradient, or durotax, while WA cells largely ignore the gradient, i.e., adurotax. Biophysical modeling and experimental validation suggest that differences in cell migration and durotaxis between weakly and strongly adherent cells are driven by differences in intra-cellular actomyosin activity. These results provide a direct relationship between cell phenotype and durotaxis and suggest how, unlike other senescent cells, metastatic cancer cells navigate against stiffness gradients.

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.

Coupling of Fibrin Reorganization and Fibronectin Patterning by Corneal Fibroblasts in Response to PDGF BB and TGFβ1

We previously reported that corneal fibroblasts within 3D fibrin matrices secrete, bind, and organize fibronectin into tracks that facilitate cell spreading and migration. Other cells use these fibronectin tracks as conduits, which leads to the development of an interconnected cell/fibronectin network. In this study, we investigate how cell-induced reorganization of fibrin correlates with fibronectin track formation in response to two growth factors present during wound healing: PDGF BB, which stimulates cell spreading and migration; and TGFβ1, which stimulates cellular contraction and myofibroblast transformation. Both PDGF BB and TGFβ1 stimulated global fibrin matrix contraction (p < 0.005); however, the cell and matrix patterning were different. We found that, during PDGF BB-induced cell spreading, fibronectin was organized simultaneously with the generation of tractional forces at the leading edge of pseudopodia. Over time this led to the formation of an interconnected network consisting of cells, fibronectin and compacted fibrin tracks. Following culture in TGFβ1, cells were less motile, produced significant local fibrin reorganization, and formed fewer cellular connections as compared to PDGF BB (p < 0.005). Although bands of compacted fibrin tracks developed in between neighboring cells, fibronectin labeling was not generally present along these tracks, and the correlation between fibrin and fibronectin labeling was significantly less than that observed in PDGF BB (p < 0.001). Taken together, our results show that cell-induced extracellular matrix (ECM) reorganization can occur independently from fibronectin patterning. Nonetheless, both events seem to be coordinated, as corneal fibroblasts in PDGF BB secrete and organize fibronectin as they preferentially spread along compacted fibrin tracks between cells, producing an interconnected network in which cells, fibronectin and compacted fibrin tracks are highly correlated. This mechanism of patterning could contribute to the formation of organized cellular networks that have been observed following corneal injury and refractive surgery.

Tumour Initiation: a Discussion on Evidence for a "Load-Trigger" Mechanism

Appropriate mechanical forces on cells are vital for normal cell behaviour and this review discusses the possibility that tumour initiation depends partly on the disruption of the normal physical architecture of the extracellular matrix (ECM) around a cell. The alterations that occur thence promote oncogene expression. Some questions, that are not answered with certainty by current consensus mechanisms of tumourigenesis, are elegantly explained by the triggering of tumours being a property of the physical characteristics of the ECM, which is operative following loading of the tumour initiation process with a relevant gene variant. Clinical observations are consistent with this alternative hypothesis which is derived from studies that have, together, accumulated an extensive variety of data incorporating biochemical, genetic and clinical findings. Thus, this review provides support for the view that the ECM may have an executive function in induction of a tumour. Overall, reported observations suggest that either restoring an ECM associated with homeostasis or targeting the related signal transduction mechanisms may possibly be utilised to modify or control the early progression of cancers. The review provides a coherent template for discussing the notion, in the context of contemporary knowledge, that tumourigenesis is an alliance of biochemistry, genetics and biophysics, in which the physical architecture of the ECM may be a fundamental component. For more definitive clarification of the concept there needs to be a phalanx of experiments conceived around direct questions that are raised by this paper.

Mechanical Interaction between Cells Facilitates Molecular Transport

In vivo, eukaryotic cells are embedded in a matrix environment, where they grow and develop. Generally, this extracellular matrix (ECM) is an anisotropic fibrous structure, through which macromolecules and biochemical signaling molecules at the nanometer scale diffuse. The ECM is continuously remodeled by cells, via mechanical interactions, which lead to a potential link between biomechanical and biochemical cell-cell interactions. Here, it is studied how cell-induced forces applied on the ECM impact the biochemical transport of molecules between distant cells. It is experimentally observed that cells remodel the ECM by increasing fiber alignment and density of the matrix between them over time. Using random walk simulations on a 3D lattice, elongated fixed obstacles are implemented that mimic the fibrous ECM structure. Both diffusion of a tracer molecule and the mean first-passage time a molecule secreted from one cell takes to reach another cell are measured. The model predicts that cell-induced remodeling can lead to a dramatic speedup in the transport of molecules between cells. Fiber alignment and densification cause reduction of the transport dimensionality from a 3D to a much more rapid 1D process. Thus, a novel mechanism of mechano-biochemical feedback in the regulation of long-range cell-cell communication is suggested.

A Biophysical Model for Curvature-Guided Cell Migration

The latest experiments have shown that adherent cells can migrate according to cell-scale curvature variations via a process called curvotaxis. Despite identification of key cellular factors, a clear understanding of the mechanism is lacking. We employ a mechanical model featuring a detailed description of the cytoskeleton filament networks, the viscous cytosol, the cell adhesion dynamics, and the nucleus. We simulate cell adhesion and migration on sinusoidal substrates. We show that cell adhesion on three-dimensional curvatures induces a gradient of pressure inside the cell that triggers the internal motion of the nucleus. We propose that the resulting out-of-equilibrium position of the nucleus alters cell migration directionality, leading to cell motility toward concave regions of the substrate, resulting in lower potential energy states. Altogether, we propose a simple mechanism explaining how intracellular mechanics enable the cells to react to substratum curvature, induce a deterministic cell polarization, and break down cells basic persistent random walk, which correlates with latest experimental evidences.

Towards personalized computational oncology: from spatial models of tumour spheroids, to organoids, to tissues

A main goal of mathematical and computational oncology is to develop quantitative tools to determine the most effective therapies for each individual patient. This involves predicting the right drug to be administered at the right time and at the right dose. Such an approach is known as precision medicine. Mathematical modelling can play an invaluable role in the development of such therapeutic strategies, since it allows for relatively fast, efficient and inexpensive simulations of a large number of treatment schedules in order to find the most effective. This review is a survey of mathematical models that explicitly take into account the spatial architecture of three-dimensional tumours and address tumour development, progression and response to treatments. In particular, we discuss models of epithelial acini, multicellular spheroids, normal and tumour spheroids and organoids, and multi-component tissues. Our intent is to showcase how these in silico models can be applied to patient-specific data to assess which therapeutic strategies will be the most efficient. We also present the concept of virtual clinical trials that integrate standard-of-care patient data, medical imaging, organ-on-chip experiments and computational models to determine personalized medical treatment strategies.

A stochastic algorithm for accurately predicting path persistence of cells migrating in 3D matrix environments

Cell mobility plays a critical role in immune response, wound healing, and the rate of cancer metastasis and tumor progression. Mobility within a three-dimensional (3D) matrix environment can be characterized by the average velocity of cell migration and the persistence length of the path it follows. Computational models that aim to predict cell migration within such 3D environments need to be able predict both of these properties as a function of the various cellular and extra-cellular factors that influence the migration process. A large number of models have been developed to predict the velocity of cell migration driven by cellular protrusions in 3D environments. However, prediction of the persistence of a cell's path is a more tedious matter, as it requires simulating cells for a long time while they migrate through the model extra-cellular matrix (ECM). This can be a computationally expensive process, and only recently have there been attempts to quantify cell persistence as a function of key cellular or matrix properties. Here, we propose a new stochastic algorithm that can simulate and analyze 3D cell migration occurring over days with a computation time of minutes, opening new possibilities of testing and predicting long-term cell migration behavior as a function of a large variety of cell and matrix properties. In this model, the matrix elements are generated as needed and stochastically based on the biophysical and biochemical properties of the ECM the cell migrates through. This approach significantly reduces the computational resources required to track and calculate cell matrix interactions. Using this algorithm, we predict the effect of various cellular and matrix properties such as cell polarity, cell mechanoactivity, matrix fiber density, matrix stiffness, fiber alignment, and fiber binding site density on path persistence of cellular migration and the mean squared displacement of cells over long periods of time.

A coupled approach for fluid saturated poroelastic media and immersed solids for modeling cell-tissue interactions

In this paper, we propose a finite element-based immersed method to treat the mechanical coupling between a deformable porous medium model (PM) and an immersed solid model (ISM). The PM is formulated as a homogenized, volume-coupled two-field model, comprising a nearly incompressible solid phase that interacts with an incompressible Darcy-Brinkman flow. The fluid phase is formulated with respect to the Lagrangian finite element mesh, following the solid phase deformation. The ISM is discretized with an independent Lagrangian mesh and may behave arbitrarily complex (it may, eg, be compressible, grow, and perform active deformations). We model two distinct types of interactions, namely, (1) the immersed fluid-structure interaction (FSI) between the ISM and the fluid phase in the PM and (2) the immersed structure-structure interaction (SSI) between the ISM and the solid phase in the PM. Within each time step, we solve both FSI and SSI, employing strongly coupled partitioned schemes. This novel finite element method establishes a main building block of an evolving computational framework for modeling and simulating complex biomechanical problems, with focus on key phenomena during cell migration. Cell movement is strongly influenced by mechanical interactions between the cell body and the surrounding tissue, ie, the extracellular matrix (ECM). In this context, the PM represents the ECM, ie, a fibrous scaffold of structural proteins interacting with interstitial flow, and the ISM represents the cell body. The FSI models the influence of fluid drag, and the SSI models the force transmission between cell and ECM at adhesions sites.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

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.

In Vitro Modeling of Mechanics in Cancer Metastasis

In addition to a multitude of genetic and biochemical alterations, abnormal morphological, structural, and mechanical changes in cells and their extracellular environment are key features of tumor invasion and metastasis. Furthermore, it is now evident that mechanical cues alongside biochemical signals contribute to critical steps of cancer initiation, progression, and spread. Despite its importance, it is very challenging to study mechanics of different steps of metastasis in the clinic or even in animal models. While considerable progress has been made in developing advanced in vitro models for studying genetic and biological aspects of cancer, less attention has been paid to models that can capture both biological and mechanical factors realistically. This is mainly due to lack of appropriate models and measurement tools. After introducing the central role of mechanics in cancer metastasis, we provide an outlook on the emergence of novel in vitro assays and their combination with advanced measurement technologies to probe and recapitulate mechanics in conditions more relevant to the metastatic disease.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

The Nuclear Option: Evidence Implicating the Cell Nucleus in Mechanotransduction

Biophysical stimuli presented to cells via microenvironmental properties (e.g., alignment and stiffness) or external forces have a significant impact on cell function and behavior. Recently, the cell nucleus has been identified as a mechanosensitive organelle that contributes to the perception and response to mechanical stimuli. However, the specific mechanotransduction mechanisms that mediate these effects have not been clearly established. Here, we offer a comprehensive review of the evidence supporting (and refuting) three hypothetical nuclear mechanotransduction mechanisms: physical reorganization of chromatin, signaling at the nuclear envelope, and altered cytoskeletal structure/tension due to nuclear remodeling. Our goal is to provide a reference detailing the progress that has been made and the areas that still require investigation regarding the role of nuclear mechanotransduction in cell biology. Additionally, we will briefly discuss the role that mathematical models of cell mechanics can play in testing these hypotheses and in elucidating how biophysical stimulation of the nucleus drives changes in cell behavior. While force-induced alterations in signaling pathways involving lamina-associated polypeptides (LAPs) (e.g., emerin and histone deacetylase 3 (HDAC3)) and transcription factors (TFs) located at the nuclear envelope currently appear to be the most clearly supported mechanism of nuclear mechanotransduction, additional work is required to examine this process in detail and to more fully test alternative mechanisms. The combination of sophisticated experimental techniques and advanced mathematical models is necessary to enhance our understanding of the role of the nucleus in the mechanotransduction processes driving numerous critical cell functions.

Single-Cell Migration in Complex Microenvironments: Mechanics and Signaling Dynamics

Cells are highly dynamic and mechanical automata powered by molecular motors that respond to external cues. Intracellular signaling pathways, either chemical or mechanical, can be activated and spatially coordinated to induce polarized cell states and directional migration. Physiologically, cells navigate through complex microenvironments, typically in three-dimensional (3D) fibrillar networks. In diseases, such as metastatic cancer, they invade across physiological barriers and remodel their local environments through force, matrix degradation, synthesis, and reorganization. Important external factors such as dimensionality, confinement, topographical cues, stiffness, and flow impact the behavior of migrating cells and can each regulate motility. Here, we review recent progress in our understanding of single-cell migration in complex microenvironments.

Cellular adaptation to biomechanical stress across length scales in tissue homeostasis and disease

Human tissues are remarkably adaptable and robust, harboring the collective ability to detect and respond to external stresses while maintaining tissue integrity. Following injury, many tissues have the capacity to repair the damage - and restore form and function - by deploying cellular and molecular mechanisms reminiscent of developmental programs. Indeed, it is increasingly clear that cancer and chronic conditions that develop with age arise as a result of cells and tissues re-implementing and deregulating a selection of developmental programs. Therefore, understanding the fundamental molecular mechanisms that drive cell and tissue responses is a necessity when designing therapies to treat human conditions. Extracellular matrix stiffness synergizes with chemical cues to drive single cell and collective cell behavior in culture and acts to establish and maintain tissue homeostasis in the body. This review will highlight recent advances that elucidate the impact of matrix mechanics on cell behavior and fate across these length scales during times of homeostasis and in disease states.