**3. Viscoelastic cellular components and super structures**

134 Viscoelasticity – From Theory to Biological Applications

response, and η2 is viscosity.

the experimentally obtained creep response data:

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Vadillo-Rodrigue et al. (2009) [19] explained the viscoelastic properties of bacterial cell walls using a standard solid model which describes both an instantaneous and a delayed elastic deformation. Based on this model they have derived the following equation that describes

where, ሺሻ is the position of the z piezoelectric transducer as a function of time t, K1 is the spring constant that represents initial deformation, K2 is the spring constant after creep

The contribution of elastic and viscous components can be determined from the force-time curve taken at the center of cells when applying a constant force, F0, for at least a 10 second period. Cantilever deflection is determined and using equation 1 is converted to force and then to an indentation-time curve, which is also called creep response. The indention of the cell over time at a constant force can be theoretically determined from equation 4 and fitted to the indentation-time curve shown in Figure 5. The experimentally determined data fit very well with the theoretical data obtained from the model. Microbial cells in particular exhibit two types of responses when a force is exerted on their surface. The first is the instantaneous linear relationship of the force versus distance curve, attributed to whole cell turgor pressure, while

the non-linear region is thought to correspond to the response of the cell envelope.

**Figure 5.** A typical creep deformation of an *Escherichia coli* cell at a constant force as a function of

time. Adapted from [45] with permission.

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Although several methods have been developed to quantify cellular responses to deformation during locomotion, adhesion and mitosis, reliable tools are not available to quantify the distribution of mechanical forces between the various sub-cellular components [26]. Biological cells range in size between 1-100 μm and are comprised of constituents that provide mechanical strength, such as the cell envelope composed of multiple complex and distinct structures, cell walls composed primarily of polysaccharides interspersed with proteins, the cell membrane composed of phospholipid bilayers and membrane proteins, complex cell organelles of different sizes and shapes made of a variety of macromolecules, the cytoskeleton composed of microtubule networks, actin and intermediate filaments, other proteins and macromolecules such as DNA and RNA. The structure and function of each of these constituents may vary depending upon cell type. For instance, fungi are encased in cell walls, whereas bacteria have more elaborate cell envelopes with a peptidoglycan (polysaccharides cross-linked with peptides) layer and one or more cell membranes. Human cells, generally by virtue of being part of more elaborate structures, have only a cell membrane. It is not well understood how cells and their associated components sense mechanical forces or deformation, and convert such signals into biological responses [46].

The small size of prokaryotes, in comparison with larger eukaryotic cells, was a considerable obstacle in the development of methods for directly measuring their mechanical properties [47], solved largely by FS methods now routinely used. Cellular mechanical strength mainly relies on the outermost layers, such as the cell wall, envelope, or membrane, in addition to internal structural components such as the cytoskeleton. Extracellular components, such as those used to help form elaborate community structures (*e.g*. biofilms) also contribute to viscoelasticity and mechanical strength. There has been a major focus on the viscoelastic properties imbued to the cell by its cytoskeleton, which has been highly conserved

throughout evolution and influences not only internal cell dynamics but overall function. Nonetheless, external cellular components also play a significant role in mechanics despite their limited study.

Viscoelasticity in Biological Systems: A Special Focus on Microbes 137

viscoelasticity [19]. A micromanipulation study using optical fiber probes to test bursting strength also showed *E. coli* to have a weaker envelope than the Gram-positive *Staphylococcus epidermis*, more susceptible to mechanical stress [47]. Researchers thus attribute the elastic component of the cell envelope to the peptidoglycan layer and the viscous component to the liquid phase of the membranes [19,45]. The viscoelasticity of the bacterial cell envelope has also been shown to depend on its degree of hydration [19] and is thought to play an important role during cell division. During cell division, polymerization−depolymerization reactions in the FtsZ assembly cause softening and fluidization, reducing viscoelasticity and reflecting the more dynamic and active motion of individual FtsZ filaments in the lipid membrane [54].

**Figure 6.** Simple models of (A) Gram-positive and (B) Gram-negative bacteria.

Earlier work on several fungi showed that the viscoelasticity of cell wall components allow for growth, cell division and spore germination [55-57]. The mechanical strength of fungal cells is largely attributed to their rigid but flexible cell walls which contain four major structural components: β-(1,3)-glucan, β-(1,6)-glucan, chitin (N-acetylglucosamine) and glycoproteins. The β-[1, 3]-glucan and β-[1,6]-glucan are more fibrous components whereas glycoproteins form a gel-like matrix, thought to impart viscoelasticity to the fungal cell wall. The mature cell wall has covalent cross-links formed between the chitin and glucan residues to provide the wall with sufficient strength and viscoelasticity. A study of the fungi *A. nidulans* showed that the immature hyphal wall region, having less well ordered wall components, and those devoid the cell wall component β-galactofuranose have lower viscoelasticity than wild type mature regions [58, 59] and this was conjectured to relate to reduced cross-linking. Determining the
