**3.1. Cell envelopes, walls and membranes**

The bacterial (prokaryotic) envelope is a structurally remarkable cell component that defines a cell from its external environment and serves a protective function. The envelope also helps maintain cell shape and mechanical integrity and is responsible for important biological functions, such as the selective transfer of material in and out of the cell, and necessary changes accommodating cell growth and division. The envelope has a multilayer geometry which withstands positive turgor pressure exerted by the cytoplasmic fluid from the cell interior, and so protects the cell from osmotic swelling and burst. Thus quantifying the cell envelope mechanical properties of prokaryotes that contribute to their mechanical strength is of interest.

The mechanical properties of the cell envelope relate to its structural composition, comprised of distinct layers made up of polysaccharides, lipids and proteins (Figure 6). Structural differences in the two different types of prokaryotic cell envelopes led to the classification of two distinct groups of bacteria namely, Gram-positive and Gram-negative. The former is named for the Gram stain retained by the thick peptidoglycan layer outside the cytoplasmic membrane (Figure 6A), while the latter having a relatively thin peptidoglycan layer sandwiched between inner cytoplasmic and outer membranes (Figure 6B) does not retain Gram stain. Many researchers have studied the flexibility of the bacterial cell envelope [48-50], for which the majority of its viscoelastic nature is attributed to the peptidoglycan layer.

Cell stiffness, required to maintain bacterial shape, is dependent on the cell envelope. When the peptidoglycan layer is removed from rod-shaped whole cells by chemical treatment, soft, highly deformable and osmotically sensitive spherical cells (spheroplasts) are the result, indicating that the elastic response of cells is largely dominated by the peptidoglycan matrix [51,52]. In isolation, peptidoglycan is very flexible, exhibiting purely elastic properties with a modulus of 25 MPa [53]. However, bacterial cell envelopes show a time dependent response to externally applied forces, meaning that their overall mechanical properties are more accurately described as viscoelastic [45].

Cell envelope composition makes a major contribution to viscoelasticity. The cell envelope of the Gram-positive bacterium *Bacillus subtilis* is significantly stiffer than the Gram-negative *E. coli*, attributed to the difference in their peptidoglycan layer thickness. FS measurements of local viscoelasticity for live bacterial cells show that the time required for *B. subtilis* to reach asymptotic creep deformation is higher than that of the Gram-negative *E. coli* and that covalent crosslinking increases cell envelope stiffness. The same study also showed a difference in the deformability of wild type *E. coli* (*lpp+*) and its Lpp mutant *lpp-* (Lpp a major peptidoglycanassociated lipoprotein and one of the most abundant outer membrane proteins in *E. coli* cells). Thus lipopolysaccharides, peptidoglycan thickness, the bound form of the peptidoglycan– lipoprotein complex and stabilizing cations all play an important role in maintaining 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].

136 Viscoelasticity – From Theory to Biological Applications

**3.1. Cell envelopes, walls and membranes** 

their limited study.

strength is of interest.

peptidoglycan layer.

accurately described as viscoelastic [45].

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

The bacterial (prokaryotic) envelope is a structurally remarkable cell component that defines a cell from its external environment and serves a protective function. The envelope also helps maintain cell shape and mechanical integrity and is responsible for important biological functions, such as the selective transfer of material in and out of the cell, and necessary changes accommodating cell growth and division. The envelope has a multilayer geometry which withstands positive turgor pressure exerted by the cytoplasmic fluid from the cell interior, and so protects the cell from osmotic swelling and burst. Thus quantifying the cell envelope mechanical properties of prokaryotes that contribute to their mechanical

The mechanical properties of the cell envelope relate to its structural composition, comprised of distinct layers made up of polysaccharides, lipids and proteins (Figure 6). Structural differences in the two different types of prokaryotic cell envelopes led to the classification of two distinct groups of bacteria namely, Gram-positive and Gram-negative. The former is named for the Gram stain retained by the thick peptidoglycan layer outside the cytoplasmic membrane (Figure 6A), while the latter having a relatively thin peptidoglycan layer sandwiched between inner cytoplasmic and outer membranes (Figure 6B) does not retain Gram stain. Many researchers have studied the flexibility of the bacterial cell envelope [48-50], for which the majority of its viscoelastic nature is attributed to the

Cell stiffness, required to maintain bacterial shape, is dependent on the cell envelope. When the peptidoglycan layer is removed from rod-shaped whole cells by chemical treatment, soft, highly deformable and osmotically sensitive spherical cells (spheroplasts) are the result, indicating that the elastic response of cells is largely dominated by the peptidoglycan matrix [51,52]. In isolation, peptidoglycan is very flexible, exhibiting purely elastic properties with a modulus of 25 MPa [53]. However, bacterial cell envelopes show a time dependent response to externally applied forces, meaning that their overall mechanical properties are more

Cell envelope composition makes a major contribution to viscoelasticity. The cell envelope of the Gram-positive bacterium *Bacillus subtilis* is significantly stiffer than the Gram-negative *E. coli*, attributed to the difference in their peptidoglycan layer thickness. FS measurements of local viscoelasticity for live bacterial cells show that the time required for *B. subtilis* to reach asymptotic creep deformation is higher than that of the Gram-negative *E. coli* and that covalent crosslinking increases cell envelope stiffness. The same study also showed a difference in the deformability of wild type *E. coli* (*lpp+*) and its Lpp mutant *lpp-* (Lpp a major peptidoglycanassociated lipoprotein and one of the most abundant outer membrane proteins in *E. coli* cells). Thus lipopolysaccharides, peptidoglycan thickness, the bound form of the peptidoglycan– lipoprotein complex and stabilizing cations all play an important role in maintaining

**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

mechanical properties for cell walls of live fungal hyphae is challenging [60] and so there have been few studies measuring their mechanical properties.

Viscoelasticity in Biological Systems: A Special Focus on Microbes 139

to the centrosome, close to the center of the cell, and the microtubule grows out to peripheral regions of the cell ending with a β tubulin. The alternating α and β tubulins render the microtubule polar and its orientation guides the unidirectional movement of microtubule motor proteins from the kinesin and dynein families [72,73]. Microtubule aggregation is dependent on temperature and the relative amount of tubulin-GTP dimers [74]. The inherent dynamic instability caused by the hydrolysis of tubulin-GTP dimers puts microtubules in a state of continuous and rapid assembly and disassembly, depending on cell cycle phase. Given the limited generation of cellular microtubules, they are expected to play a minor role in cell mechanical responses and a major role in cell shape. Nevertheless, they do indirectly influence the mechanical properties of cells by regulating the actin network through myosin-II. In neural cells, axons, dendrites and microtubules play a more direct role in cell mechanics, because they form tight bundles in which microtubule-associated proteins (MAPs)

Experiments carried out on gels and cross-linked networks made of microtubules demonstrate that they exhibit the strongest bending stiffness among all the cytoskeletal components. Therefore, elasticity dominates over viscosity when microtubules are deformed under an external force. Under a low external load, microtubule network stiffness exhibits a linear elastic response as a function of microtubulin unit concentration [78], which closely relates to microtubule polymerization rate and the final microtubule length of tubulin dimers formed [79,80]. Fast growing microtubules are more likely to form short filaments, based on defects in the microtubule lattice that further influence the tubulin dimer bonds and make the microtubules more flexible. Microtubule viscoelasticity also depends on the intermolecular interactions between tubulin dimers, but their lateral and longitudinal interactions along the microtubule do not equally contribute to the total mechanical response. Both the shear and circumferential moduli of the longitudinal bonds in microtubule protofilaments are several orders of magnitude higher than those of lateral bonds. Since microtubules exhibit a mechanical response with enthalpic elasticity arising from the bending and stretching of microtubule filaments, factors influencing the tubulin spacings play a critical role in determining microtubule viscoelasticity [78]. Among these factors, the microtubule-associated proteins are an important contributor as they bind to the microtubule surface through electrostatic interactions. In the presence of MAPs, the spacing of adjacent microtubules is doubled creating a cushion against compression. There is also evidence to show that the elastic modulus increases with the addition of crosslinkers to the microtubule networks [81]. Factors affecting microtubule stiffness, such as taxol and GTP analogs, also influence their mechanical properties by stabilizing and preventing their depolymerization [82]. Therefore, microtubule viscoelasticity is a function of both subunit

Intermediate filaments are the non-polarized cylindrical fibrils of the cytoskeleton named for their size with a diameter of around 10 nm, intermediate to microtubules and

bind and stabilize parallel arrayed microtubular filaments [75-77].

concentration and crosslinking.

*3.2.2. Intermediate filaments* 

Cell wall mechanical properties of the budding yeast *Saccharomyces cerevisiae* were determined through compression in a micromanipulator. Individual cells were compressed between two parallel surfaces and elastic parameters extracted from the force-deformation data [52]. A FS study of *Termitomyces clypeatus* showed an increase in cell wall rigidity and elasticity until the organism reached the stationary phase, followed by a decrease in these parameters at the onset of the death phase. The adsorption of chromium was also found to significantly affect the surface nano-mechanical properties of *T. clypeatus* [61].

Spores, another morphological form of fungi, appear in several studies describing their surface morphology [56,62,63] and adhesive properties [3,64] however, little information is available regarding their mechanical properties. Changes in the cell wall mechanical properties are a key factor in the emergence of the germ tube [55,56]. Both rodlet-covered and rodlet-free spores of *A. nidulans* were subjected to nano-indentation measurements by FS in air, showing that the rodlet layer is significantly softer than the underlying portion of the cell wall [43].

The nano-mechanical properties of whole human cells has been a topic of great interest for the past few decades and the viscoelastic properties of epithelial cells [4,65], stem cells [66], red cells [67,68] and cancer cells [69,70] are well-studied but beyond the scope of this chapter. The microbial cytoskeleton is less well studied, so the next section highlights significant data from isolated cytoskeletal components and those in the context of human cells.

## **3.2. Cell cytoskeleton**

The filamentous network inside eukaryotic cells is a major contributor to the 3D morphology of a cell, acting as a scaffold to support the cell interior (Figure 7). This crosslinked biopolymer network has a role in cell mechanics, resisting deformation in response to external mechanical stresses. Besides being the determining factor for cellular shape, the cytoskeleton is involved in cell division, cell movement, adhesion and locomotion. Cellular viscoelastic responses can be largely dependent on the cytoskeleton, composed of three major groups of elements: microtubules, intermediate filaments and microfilaments. With the tremendous progress in biophysics, the structures of each cytoskeletal components are now well understood even at the molecular level, but we are just beginning to determine their contribution to cell mechanics.
