Tissue dynamics with permeation (original) (raw)

Fluidization of tissues by cell division and apoptosis

2010

During the formation of tissues, cells organize collectively by cell division and apoptosis. The multicellular dynamics of such systems is influenced by mechanical conditions and can give rise to cell rearrangements and movements. We develop a continuum description of tissue dynamics, which describes the stress distribution and the cell flow field on large scales. In the absence of division and apoptosis, we consider the tissue to behave as an elastic solid. Cell division and apoptosis introduce stress sources that, in general, are anisotropic. By combining cell number balance with dynamic equations for the stress source, we show that the tissue effectively behaves as a viscoelastic fluid with a relaxation time set by the rates of division and apoptosis. If the system is confined in a fixed volume, it reaches a homeostatic state in which division and apoptosis balance. In this state, cells undergo a diffusive random motion driven by the stochasticity of division and apoptosis. We calculate the expression for the effective diffusion coefficient as a function of the tissue parameters and compare our results concerning both diffusion and viscosity to simulations of multicellular systems using dissipative particle dynamics.

Relating cell and tissue mechanics: Implications and applications

Developmental Dynamics, 2008

The Differential Adhesion Hypothesis (DAH) posits that differences in adhesion provide the driving force for morphogenetic processes. A manifestation of differential adhesion is tissue liquidity and a measure for it is tissue surface tension. In terms of this property, DAH correctly predicts global developmental tissue patterns. However, it provides little information on how these patterns arise from the movement and shape changes of cells. We provide strong qualitative and quantitative support for tissue liquidity both in true developmental context and in vitro assays. We follow the movement and characteristic shape changes of individual cells in the course of specific tissue rearrangements leading to liquid-like configurations. Finally, we relate the measurable tissue-liquid properties to molecular entities, whose direct determination under realistic three-dimensional culture conditions is not possible. Our findings confirm the usefulness of tissue liquidity and provide the scientific underpinning for a novel tissue engineering technology. Developmental Dynamics 237:2438 -2449, 2008.

Mechanical formalism for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progress in experimental techniques that provide access to cell-scale, quantitative information both on the shapes of cells within tissues and on the genes being expressed. This information suggests that our understanding of the respective contributions of gene expression and mechanics, and of their crucial entanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assist the design and interpretation of experiments, point out the main ingredients and assumptions, and can ultimately lead to predictions. The newly accessible local information thus urges for a reflection on how to select suitable classes of mechanical models. We review both mechanical ingredients suggested by the current knowledge of tissue behaviour, and modelling methods that can help generate a constitutive equation. We also recall the mathematical framework developped for continuum materials and how to transform a constitutive equation into a system of partial differential equations amenable to numerical resolution. The present article thus groups together mechanical elements and theoretical methods that are ready to enhance the significance of the data extracted from recent or future high throughput biomechanical experiments.

A Sub-Cellular Viscoelastic Model for Cell Population Mechanics

PLoS ONE, 2010

Understanding the biomechanical properties and the effect of biomechanical force on epithelial cells is key to understanding how epithelial cells form uniquely shaped structures in two or three-dimensional space. Nevertheless, with the limitations and challenges posed by biological experiments at this scale, it becomes advantageous to use mathematical and 'in silico' (computational) models as an alternate solution. This paper introduces a single-cell-based model representing the cross section of a typical tissue. Each cell in this model is an individual unit containing several sub-cellular elements, such as the elastic plasma membrane, enclosed viscoelastic elements that play the role of cytoskeleton, and the viscoelastic elements of the cell nucleus. The cell membrane is divided into segments where each segment (or point) incorporates the cell's interaction and communication with other cells and its environment. The model is capable of simulating how cells cooperate and contribute to the overall structure and function of a particular tissue; it mimics many aspects of cellular behavior such as cell growth, division, apoptosis and polarization. The model allows for investigation of the biomechanical properties of cells, cell-cell interactions, effect of environment on cellular clusters, and how individual cells work together and contribute to the structure and function of a particular tissue. To evaluate the current approach in modeling different topologies of growing tissues in distinct biochemical conditions of the surrounding media, we model several key cellular phenomena, namely monolayer cell culture, effects of adhesion intensity, growth of epithelial cell through interaction with extra-cellular matrix (ECM), effects of a gap in the ECM, tensegrity and tissue morphogenesis and formation of hollow epithelial acini. The proposed computational model enables one to isolate the effects of biomechanical properties of individual cells and the communication between cells and their microenvironment while simultaneously allowing for the formation of clusters or sheets of cells that act together as one complex tissue.

Differences in cell death and division rules can alter tissue rigidity and fluidization

2022

Tissue mechanical properties such as rigidity and fluidity, and changes in these properties driven by jammingunjamming transitions (UJT), have come under recent highlight as mechanical markers of health and disease in various biological processes including cancer. However, most analysis of these mechanical properties and UJT have sidestepped the effect of cellular death and division in these systems. Cellular apoptosis (programmed cell death) and mitosis (cell division) can drive significant changes in tissue properties. The balance between the two is crucial in maintaining tissue function, and an imbalance between the two is seen in situations such as cancer progression, wound healing and necrosis. In this work we investigate the impact of cell death and division on tissue mechanical properties, by incorporating specific mechanosensitive triggers of cell death and division based on the size and geometry of the cell within in silico models of tissue dynamics. Specifically, we look a...

Multi-scale models of cell and tissue dynamics

Philosophical Transactions of The Royal Society A: Mathematical, Physical and Engineering Sciences, 2009

Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. Early development of multicellular organisms involves individual and collective cell movement, leukocytes must migrate toward sites of infection as part of the immune response, and in cancer directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell-or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumor growth in which each cell is treated individually, and a hybrid continuum-discrete model of later stages of tumor growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.

Biomedical Modeling: The Role of Transport and Mechanics

Bulletin of Mathematical Biology, 2013

Multi-scale modeling • Computer simulation • Physiological systems • Mechanics • Normal and abnormal tissue • Adaptive mechanism This issue contains a series of papers that were invited following a workshop held in July 2011 at the University of Notre Dame London Center. The goal of the workshop was to present the latest advances in theory, experimentation, and modeling methodologies related to the role of mechanics in biological systems. Growth, morphogenesis, and many diseases are characterized by time dependent changes in the material properties of tissues-affected by resident cells-that, in turn, affect the function of the tissue and contribute to, or mitigate, the disease. Mathematical modeling and simulation are essential for testing and developing scientific hypotheses related to the physical behavior of biological tissues, because of the complex geometries, inhomogeneous properties, rate dependences, and nonlinear feedback interactions that it entails.

Non-Maxwellian velocity distribution and anomalous diffusion of { it in vitro} kidney cells

Eprint Arxiv Q Bio 0503013, 2005

This manuscript uses a statistical mechanical approach to study the effect of the adhesion, through MOCA protein, on cell locomotion. The MOCA protein regulates cell-cell adhesion, and we explore its potential role in the cell movement. We present a series of statistical descriptions of the motion in order to characterize the cell movement, and found that MOCA affects the statistical scenario of cell locomotion. In particular, we observe that MOCA enhances the tendency of joint motion, inhibits super-diffusion, and decreases overall cell motion. These facts are compatible with the hypothesis that the cells move faster in a less cohesive environment.