Advances in Cell Mechanics

A phenomenological discrete model for the dynamics of growing cell clusters is presented. Each cell is modeled as a growing deformable solid which can interact mechanically with its neighbors by means of adhesion and repulsion forces. By defining simple behavior rules based on the age and the mechanical state of the cells, simple cluster dynamics can be reproduced. The framework is far from complete, but describes the essential features required for more complete mechanical simulations of cell ensembles.

A multiscale cell model has been developed to study the mechanotransduction of pluripotent stem cells in an attempt to explain the mechanical information exchange between the cells and their extracellular environment leading to a biologic response. In the model, the macroscale cell is modeled as liquid crystal with a hyperelastic nucleus. A nanoscale adhesive model was introduced to describe the interaction between receptors and ligands. We have developed and implemented a Lagrange type meshfree Galerkin formulation and related computational algorithms for the described cell and adhesive contact model. A comparison study with experimental data was conducted to validate the parameters of the cellular computational model. By using a soft matter physics modeling approach, we have simulated the adhesive contact process between cells and different extracellular matrix substrates. The simulation shows that the cell can sense substrate elasticity by responding via cell spreading, altered cell contact configurations, and altered molecular conformations.

Sickle cell anemia is the first disease whose cause was pinpointed at a genetic level. Hydrophobic interaction is the main cause for sickle hemoglobin (hemoglobin S) sticking to itself. Interaction of water with hydrophobic objects plays a major role in molecular self-assembly processes[1-3], as well in the process of aggregation of hemoglobin S. In this chapter, slow motion analysis and model reduction methods were employed for the study of hemoglobin-hemoglobin interaction. Through this study, a new computational framework was presented for calculating the normal modes and interactions of proteins, macromolecular assemblies, and surrounding solvents. The framework employs a combination of Molecular Dynamics (MD) simulation and Principal Component Analysis (PCA). It enables the capture and visualization of the molecules’ normal modes and interactions over time scales that are computationally challenging, providing a starting point for experimental and further computational studies of protein conformational changes. We hope that the modeling protocols or procedures established for this known pathology will eventually shed some light on other complex biological systems that are not well known.

Living systems have developed effective strategies in adapting to the environment during the last 3.5 billion years. Here we review joint experimental, computational and theoretical multiscale studies of the mechanical properties of intermediate filament (IF) proteins, an important component in the cell’s cytoskeleton and a key player in cell mechanics, migration and disease processes including cancer. We review the general field of intermediate filament mechanics, highlight recent advances, challenges, and explain the opportunities that now exist at the interface of engineering and biology. A general theme of our discussion is the consideration of how material properties change at different structural scales and how this relates to biological function, from a bottom-up perspectively that link the nano- to the macroscale.

Cells are basic functional units of life and control a wide range of intra- and extra-cellular activities. They are highly complex structures with unique biomechanical properties to withstand the physiological environment as well as mechanical stimuli. Studies related to the mechanics of single cells are aimed at describing the molecular mechanisms responsible for the physical integrity of the cells as well as their biological functions. These studies have significant implications for biotechnology and human health. Recent advanced and innovative experimental techniques for measuring forces at piconewton resolutions and displacements over nano-meter scales have greatly facilitated this area of research. Moreover, tremendous research efforts have been devoted to the development of multiscale multiphysics computational models for the mechanical properties and functions of cells. This chapter reviews recent numerical and experimental studies in the area of cytoskeletal mechanics and rheology. For this purpose, basic modeling techniques for the mechanics of semiflexible actin filaments as well as various experimental and computational methods for measuring the mechanical behavior of cells are discussed.

Tissue functions and properties are determined by the interactions between cells and their extra-cellular matrix. Cells, which are the active component of tissues, can sense mechanical stimuli provided by their surrounding matrix and respond by generating mechanical forces. These forces may then influence the reorganization of the matrix and begin a sequence of cell/matrix crosstalks that feedback onto themselves. Our understanding of these interactions and their influence on the evolution of soft tissue is thus critical to understand many phenomena in biological tissues, such as wound healing, or tissue morphogenesis. Experimental observations tell us that cell shape and size are intrinsically linked to its function, properties and motion. For instance, cell spreading area is known to control the expression of mitogen agents, and thus cell division. Inversely, cell elongation and orientation are linked to the properties and deformation of the surrounding extracellular matrix. The origins of these behavior can be traced down to the multiphasic nature of cytoplasm and the rich spectrum of chemo-mechanical processes occurring within it, including stress-fiber polymerization, structural deformation and mass transport. Such multiphasic media have traditionally been very well described by mixture theory based on a continuum representation of interpenetrating phases and their interactions. The objective of this chapter is to introduce such a formulation of cell mechanics in order to capture the fundamental mechanisms of cell contractility and its interaction with an underlying elastic substrate. As such, the cell is considered as a mixture of four different phases including a passive cytoskeleton, a distribution of contractile stress-fibers, the cytosol and a population of globular actin monomers dissolved in the cytosol. After discussing the general formalism based on balance laws and constitutive relation, the chapter introduces a numerical strategy, based on the extended finite element, to capture the contraction of cells on compliant substrate. Model prediction and comparison with experiments are finally provided and discussed.

Mechanical stiffness of bio-adhesive substrates is one of the major regulators of the cell adhesion and migration. In this contribution, we propose a theoretical model for the spontaneous growth of focal adhesion sites on compliant elastic substrates at the early stages of cellular adhesion. Using a purely thermodynamic approach, we demonstrate that the rate of membrane-substrate association decreases with increasing the compliance of the substrate. This can be considered as a reason for smaller spread area of the focal adhesion points after the stabilization of adhesion on compliant substrates, as reported by experiments. We also show that the extent to which the compliance of the substrate modulates the growth rate of adhesion site depends on the areal density of cell-adhesive ligands on the substrate.

In this chapter, a unique experimental platform is described for singlecell biomechanics. An optical tweezer with minimal applied laser power has successfully suspended biologic cells at the geometric center of a microfluidic crossjunction. The resulting flow environment creates a unique multiaxial load application to isolated cells with site-specific normal and shear stresses resulting in a physically extended state. Computational fluid dynamics combined with multiphysics modeling has characterized the fluid environment and solid cellular strain response in three-dimensions to accompany experimental cell stimulation. These models will guide future microfluidic experiments as well as provide a framework for characterizing cytoskeletal structures influencing the stress on strain response.

A version of nonlocal elasticity theory is employed to develop a nonlocal shear deformable shell model. The governing equations are based on higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity and include small scale effects. These equations are then used to solve buckling problems of microtubules (MTs) embedded in an elastic matrix of cytoplasm subjected to bending. The surrounding elastic medium is modeled as a Pasternak foundation. The thermal effects are also included and the material properties are assumed to be temperature-dependent. The small scale parameter e0a is estimated by matching the buckling curvature of MTs observed from measurements with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling loads are decreased with the increasing small scale parameter e0a. The results reveal that the lateral constraint has a significant effect on the buckling moments of a microtubule when the foundation stiffness is sufficiently large.