A time-dependent phenomenological model for cell mechano-sensing

Active viscoelastic models for cell and tissue mechanics

Living cells are out of equilibrium active materials. Cell-generated forces are transmitted across the cytoskeleton network and to the extracellular environment. These active force interactions shape cellular mechanical behaviour, trigger mechano-sensing, regulate cell adaptation to the microenvironment and can affect disease outcomes. In recent years, the mechanobiology community has witnessed the emergence of many experimental and theoretical approaches to study cells as mechanically active materials. In this review, we highlight recent advancements in incorporating active characteristics of cellular behaviour at different length scales into classic viscoelastic models by either adding an active tension-generating element or adjusting the resting length of an elastic element in the model. Summarizing the two groups of approaches, we will review the formulation and application of these models to understand cellular adaptation mechanisms in response to various types of mechanical stimuli, such as the effect of extracellular matrix properties and external loadings or deformations.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

An Energetic Approach to Modeling Cytoskeletal Architecture in Maturing Cardiomyocytes

Through a variety of mechanisms, a healthy heart is able to regulate its structure and dynamics across multiple length scales. Disruption of these mechanisms can have a cascading effect, resulting in severe structural and/or functional changes that permeate across different length scales. Due to this hierarchical structure, there is interest in understanding how the components at the various scales coordinate and influence each other. However, much is unknown regarding how myofibril bundles are organized within a densely packed cell and the influence of the subcellular components on the architecture that is formed. To elucidate potential factors influencing cytoskeletal development, we proposed a computational model that integrated interactions at both the cellular and subcellular scale to predict the location of individual myofibril bundles that contributed to the formation of an energetically favorable cytoskeletal network. Our model was tested and validated using experimental metrics derived from analyzing single-cell cardiomyocytes. We demonstrated that our model-generated networks were capable of reproducing the variation observed in experimental cells at different length scales as a result of the stochasticity inherent in the different interactions between the various cellular components. Additionally, we showed that incorporating length-scale parameters resulted in physical constraints that directed cytoskeletal architecture toward a structurally consistent motif. Understanding the mechanisms guiding the formation and organization of the cytoskeleton in individual cardiomyocytes can aid tissue engineers toward developing functional cardiac tissue.

A mechanobiological model to study upstream cell migration guided by tensotaxis

Cell migration is a process of crucial importance for the human body. It is responsible for important processes such as wound healing and tumor metastasis. Migration may occur in response to stimuli of chemical, physical and mechanical nature occurring in the cellular microenvironment. The interstitial flow (IF) can generate mechanical stimuli in cells that influence the cell behavior and interactions of the cells with the extracellular matrix (ECM). One of the phenomena is upstream migration, which is observed in some tumors. In this work, we present a new approach to study the adherent cell migration in a porous medium using a mechanobiological model, attempting to understand if upstream migration can be generated exclusively by mechanical factors. The influence of IF on the behavior of cells and the extracellular matrix was considered. The model is based on a system of coupled nonlinear differential equations solved by the finite element method. Several simulations were performed to study the upstream cell migration and evaluate the effects of pressure, permeability, ECM stiffness and cellular concentration variations on the cell velocity. The results indicated that upstream migration can occur in the presence of mechanical stimuli generated by IF and that the tested parameters have a direct influence on the cellular velocity, especially the pressure and the permeability.

Exploring cardiac form and function: A length-scale computational biology approach

The ability to adequately pump blood throughout the body is the result of tightly regulated feedback mechanisms that exist across many spatial scales in the heart. Diseases which impede the function at any one of the spatial scales can cause detrimental cardiac remodeling and eventual heart failure. An overarching goal of cardiac research is to use engineered heart tissue in vitro to study the physiology of diseased heart tissue, develop cell replacement therapies, and explore drug testing applications. A commonality within the field is to manipulate the flow of mechanical signals across the various spatial scales to direct self-organization and build functional tissue. Doing so requires an understanding of how chemical, electrical, and mechanical cues can be used to alter the cellular microenvironment. We discuss how mathematical models have been used in conjunction with experimental techniques to explore various structure-function relations that exist across numerous spatial scales. We highlight how a systems biology approach can be employed to recapitulate in vivo characteristics in vitro at the tissue, cell, and subcellular scales. Specific focus is placed on the interplay between experimental and theoretical approaches. Various modeling methods are showcased to demonstrate the breadth and power afforded to the systems biology approach. An overview of modeling methodologies exemplifies how the strengths of different scientific disciplines can be used to supplement and/or inspire new avenues of experimental exploration. This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

A minimal mechanics model for mechanosensing of substrate rigidity gradient in durotaxis

Durotaxis refers to the phenomenon in which cells can sense the spatial gradient of the substrate rigidity in the process of cell migration. A conceptual two-part theory consisting of the focal adhesion force generation and mechanotransduction has been proposed previously by Lo et al. to explain the mechanism underlying durotaxis. In the present work, we are concerned with the first part of the theory: how exactly is the larger focal adhesion force generated in the part of the cell adhering to the stiffer region of the substrate? Using a simple elasticity model and by assuming the cell adheres to the substrate continuously underneath the whole cell body, we show that the mechanics principle of static equilibrium alone is sufficient to account for the generation of the larger traction stress on the stiffer region of the substrate. We believe that our model presents a simple mechanistic understanding of mechanosensing of substrate stiffness gradient at the cellular scale, which can be incorporated in more sophisticated mechanobiochemical models to address complex problems in mechanobiology and bioengineering.

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.

A phenomenological cohesive model for the macroscopic simulation of cell-matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell-matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell-matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell-matrix adhesions.

ALIGNMENT OF CELLULAR FOCAL CONTACTS AND THEIR SHAPES BY SUBSTRATE ANISOTROPY

Cell adhesion to the extracellular matrix is accomplished by the clustering of receptor–ligand bonds into focal contacts on the cell-substrate interface. The contractile forces applied onto these focal contacts lead to elastic deformation of the surrounding, which results into a cellular mechanosensory capability that plays a key role in cell adhesion, spreading, and migration, among many others. The mechanosensitivity can be manipulated by the substrate anisotropy, by which focal contacts may align into certain directions so to minimize the total mechanical potential energy. Using the elastic anisotropic contact analysis, this work systematically analyzes the dependence of the alignment on the elastic anisotropy, and more importantly, the direction of the inclined contractile forces. The contact displacement fields are a complex function of the elastic constants, so simple analysis based on tensile or shear softest direction cannot properly predict the alignment orientation. It is also proved that if these focal contacts are of elongated shape, the major axis will be parallel to the alignment direction.