**1. Introduction**

122 Viscoelasticity – From Theory to Biological Applications

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Over billions of years of evolution, living organisms have developed into complex biosystems, of which the basic unit is the cell. Cells have a complex molecular structure with a certain level of rigidity. Living cells, whether isolated or part of a larger collective, live under constant mechanical stress from their external environments. Cells have developed adaptive mechanisms to maintain homeostasis and viability, which interestingly follow the basic principles of classical mechanics.

Cell mechanical properties have myriad biological significance and so there has been significant interest in the past decade to measure the response of cells to external mechanical signals. Cellular mechanics and rheological properties (*e.g.* stress-strain relationships) are known to play a role in biological processes such as cell growth, stem cell differentiation, cell crawling, wound healing, protein regulation, cell malignancy and even apoptosis (programmed cell death) [1,2].

A living cell is a complex dynamic system, far from static, which constantly undergoes remodeling to adapt to varying environmental conditions. The mechanical changes in cells under normal conditions and in response to external signals are highly complex and extremely difficult to measure *in vitro*. The interplay of cellular constituents enables adaptation to changing demands of mechanical strength and stability. The field of rheological science deals with the mechanical behavior of biological materials and over the past decade several rheological methods have been developed to quantify the mechanical behavior of cells in response to external conditions and forces.

To understand cell mechanics we first need an appreciation of how cells operate in a mechanical context. Firstly, how do cells maintain their shape and flexibility to accommodate cellular requirements? Cell surface layers are strong, playing a crucial

<sup>© 2012</sup> Bhat et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

mechanical role in maintaining cellular shape and resisting turgor pressure, yet at the same time flexible enough to allow cell growth and division. Multi-cellular eukaryotes are arranged into specialized structures of varied composition (*e.g.* tissues) which protect them from harsh environments. Single-celled prokaryotes or eukaryotes can also form sophisticated structures, such as biofilms or mycelia, but even as single cells they are able to bear mechanical stress and maintain integrity which is quite astonishing. Cells range from soft mammalian tissue cells to those with very firm plant cellulosic fibers, so understanding how different cellular components provide diverse mechanical properties is of great interest. Further, how do mechanical properties support locomotion? Active movements depend on cell type and ultimate function within tissues or the greater environment, and their associated mechanical properties change according to environmental demands. Another question relates to how external factors, such as temperature, pH, aridity and xenobiotics affect cell mechanical properties. Further, what is the role of cell mechanics in processes such as active and passive diffusion, adhesion, community formation and evolution of complex tissues in higher eukaryotes, and how do the mechanics of isolated components work in concert within dynamic live systems that are far from equilibrium?

Viscoelasticity in Biological Systems: A Special Focus on Microbes 125

and movement of subcellular macromolecules (such as DNA and proteins), elasticity controls the response of the cytoplasm to mechanical stresses at shorter timescales (seconds), organelles and cytoskeleton elements over long timescales (minutes), and the contractile

The quantitative characterization of elastic material is the elastic modulus, described as the ratio of stress to strain, but the deformation (strain) of a fluid under an external stress changes as a function of time and is referred to as strain rate. Thus fluid viscosity is the ratio of stress to strain rate. The mechanical responses of biopolymers fall into a category between

In this chapter we will describe the methods to measure viscoelasticity in biological systems and their significance. We generalize the mechanical properties of prokaryotic and eukaryotic cells since it has been argued that viscoelastic properties are universal across cell types and species, however the mechanistic basis of this phenomenon is not well understood [4]. This chapter is organized into four main sections: (i) a brief summary of various rheological methods used for cell micromanipulation and the novel application of atomic force microscopy to measure cell mechanical properties, (ii) the main mechanical load bearing components of cells and associated studies that have helped to establish a consensus understanding of cell mechanical properties, (iii) a survey of the various factors that affect cell viscoelastic properties, but which currently lack clear interpretation, and

In microrheological studies, several experimental techniques and theoretical models are combined to accurately quantify cellular mechanics. Several methods that are routinely used for cell rheology are briefly reviewed in the following section. Micropipette aspiration, microplate rheometry, and optical stretching are used to probe whole cell mechanics, while probe- or particle-based techniques such as magnetic probes, optical tweezers and particle tracking cell rheology only measure local mechanical properties. The probes or particles within a structure are subjected to an external force and the subsequent response measured, usually by tracking their displacement, to characterize associated mechanical properties. Atomic force microscopy uses a probe, but attached to the end of a cantilever with welldefined rigidity able to the mechanics of whole cells and their surface layers. A schematic

The mechanical properties measured by a probe or particle technique are highly dependent on the strength of, and relationship between the particle/probe and the structure being studied. This relationship is highly complex, varies with cell type and can lead to significant misjudgement of the stiffness. Probes can be modified with different molecules such as antibodies, peptides and cadherins to target antigens, integrins and cytoskeletal components. However these measurements do not account for interactions between the probes and cells which can lead to confounding results [5]. Cells have a heterogeneous

mechanical regime governs responses at even longer time scales (minutes to hours).

finally (iv) a future perspective on the significance of cellular viscoelasticity.

that of an elastic solid and a fluid, defined as viscoelasticity.

**2. Methods of measuring cellular viscoelasticity** 

diagram of various devices is shown in Figure 1.

Several of these questions remain unanswered, however early success studying the rheological properties of non-living materials has provided a strong foundation for studying biological systems. Over the past decade, several obstacles have been overcome and thus a new perspective of cellular mechanics is emerging [2].

## **1.1. Viscoelasticity in biology**

If cellular metabolism could be frozen at any given moment, disrupting the production of metabolites and supra-molecular structures, the cell would simply become fluid-like with the associated mechanical properties. Living cells behave both as an elastic solid and as a viscous fluid, and so are considered viscoelastic. Such materials, including biological molecules and cells, cannot be fit using classical models of either elasticity or viscosity. Cellular viscoelasticity arises from the combination of high water content conflated with a polymerized structural matrix. On the one hand, the biopolymers which support cell shape provide strong enough mechanical properties to resist environmental pressures, but on the other hand their organization is highly dynamic and linked to metabolic conditions.

Cellular mechanical properties can be characterized using viscosity, elasticity and creep compliance. Herein we focus on viscoelasticity studies measuring either biological sample deformation induced by an external force or the force resulting from sample deformation. The cell cytosol, which contains the majority of cell fluid, can be treated as the coexistence of liquid and solid phases. The latter is composed of proteins, DNA, RNA and cytoskeleton filaments as well as organelles suspended in the viscous buffered saline, saturated with metabolites and proteins. The liquid component has a high compression modulus, meaning that without the structural components and macromolecules it would be very fluid (less viscous). In contrast, the solid phase has a lower compression modulus, exhibiting more elastic properties. In cells as a whole, the viscosity of the cytoplasm dominates the transport and movement of subcellular macromolecules (such as DNA and proteins), elasticity controls the response of the cytoplasm to mechanical stresses at shorter timescales (seconds), organelles and cytoskeleton elements over long timescales (minutes), and the contractile mechanical regime governs responses at even longer time scales (minutes to hours).

The quantitative characterization of elastic material is the elastic modulus, described as the ratio of stress to strain, but the deformation (strain) of a fluid under an external stress changes as a function of time and is referred to as strain rate. Thus fluid viscosity is the ratio of stress to strain rate. The mechanical responses of biopolymers fall into a category between that of an elastic solid and a fluid, defined as viscoelasticity.

In this chapter we will describe the methods to measure viscoelasticity in biological systems and their significance. We generalize the mechanical properties of prokaryotic and eukaryotic cells since it has been argued that viscoelastic properties are universal across cell types and species, however the mechanistic basis of this phenomenon is not well understood [4]. This chapter is organized into four main sections: (i) a brief summary of various rheological methods used for cell micromanipulation and the novel application of atomic force microscopy to measure cell mechanical properties, (ii) the main mechanical load bearing components of cells and associated studies that have helped to establish a consensus understanding of cell mechanical properties, (iii) a survey of the various factors that affect cell viscoelastic properties, but which currently lack clear interpretation, and finally (iv) a future perspective on the significance of cellular viscoelasticity.
