*3.2.1. Microtubules*

Microtubules are the largest of the filamentous structures making up the cytoskeleton, for which the basic building block is tubulin heterodimers made up of α and β subunits. Structural analysis shows that the α and β tubulins alternately line up to form protofilaments, which are further laterally arranged into a small lattice and closed to form a 25 nm wide cylindrical structure [71]. The α subunit forms the end of the microtubule localized 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) bind and stabilize parallel arrayed microtubular filaments [75-77].

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 concentration and crosslinking.

#### *3.2.2. Intermediate filaments*

138 Viscoelasticity – From Theory to Biological Applications

the cell wall [43].

**3.2. Cell cytoskeleton** 

their contribution to cell mechanics.

*3.2.1. Microtubules* 

been few studies measuring their mechanical properties.

mechanical properties for cell walls of live fungal hyphae is challenging [60] and so there have

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

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 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.

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

Microtubules are the largest of the filamentous structures making up the cytoskeleton, for which the basic building block is tubulin heterodimers made up of α and β subunits. Structural analysis shows that the α and β tubulins alternately line up to form protofilaments, which are further laterally arranged into a small lattice and closed to form a 25 nm wide cylindrical structure [71]. The α subunit forms the end of the microtubule localized

significantly affect the surface nano-mechanical properties of *T. clypeatus* [61].

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

microfilaments [83,84]. Intermediate filaments are constructed by a group of related proteins, which have been divided into five subgroups according to their sequence identity. All of the proteins associated with type I, II, III, and IV immediate filaments are localized to the cytoplasm, while those of type V (*e.g.* lamins) localize to the cell nucleus and form a network underneath the nuclear membrane. Similar to microtubules, intermediate filaments are composed of protein dimers, but in this case elongated ones.

Viscoelasticity in Biological Systems: A Special Focus on Microbes 141

**Figure 7.** Schematic of a cytoskeleton as a dynamic 3-dimensional scaffold made up of actin filaments,

Actin filaments are the thinnest (≈ 8nm) and most plentiful among all the components of the eukaryotic cytoskeleton [101]. Under physiological conditions, actin filaments grow by polymerization of the ATP-bound actin monomers, addition of monomers to the end of the severed filament fragments, or by branching out of the existing filaments. Actin filaments are polar fibers, with helically arranged actin monomers all pointed in the same direction, which can form a cortex underneath the cytoplasmic membrane to support cell movement. More than 100 proteins promote the formation of a single actin filament, filament crosslinking, networks and bundle formation. Actin filaments are continuously assembled and

F-actin exhibits viscoelasticity as a semi-flexible polymer with linear and nonlinear responses to external forces [102,103]. To quantitatively evaluate the contribution of Factins to cytoskeleton mechanics, such networks have been reconstituted *in vitro* with purified protein. The reconstituted F-actin forms a gel-like network in which the mesh size is dependent on the F-actin concentration [104]. Under a low applied force, semiflexible networks only composed of F-actins deform in a manner proportional to the force load, but under a larger force which affects F-actin filament contour length, the deformation can be described as strain-stiffening [95]. The mechanical properties of F-

intermediate filaments and microtubules.

disassembled in response to cell signaling.

*3.2.3. Actin filaments* 

Intermediate filaments have been discovered in diverse cell types, with more than 60 associated genes coded in humans [85,86]. They are found to be highly extensible compared to filamentous actin (F-actin) and microtubules, which are able to retain enormous strains while sustaining the intact filament structure [87,88]. Their unique extensibility implies their it could play a special role in cell mechanics, which would set it apart from other cytoskeletal elements. Since most genes associated with intermediate filaments are responsible for coding keratins, keratin-based intermediate filaments are considered an important player in cellular mechanics [89,90], regulating viscoelastic properties and the motility of cancer cells. The architecture of the keratin filament is regulated by phosporylation, accounting for the viscoelastic responses of carcinoma cells during large deformations, and the actin network is also regulated by phosphorylation under the regulation of kinases [91-93], phosphatases and other regulatory proteins [89,94].

The mechanical properties of intermediate filament networks have been studied by applying classical models to homogeneous and isotropical samples, which link the elastic shear modulus to the mean mesh size of the cytoskeleton [95]. This means that the viscoelastic response of the network is dependent upon its subcellular organization, filament composition, and overall protein concentration. The nonlinear relationship between the mesh size of these networks and the elastic shear modulus [96] underscores whole cell mechanical properties, elasticity and viscoelasticity of the network, which can be significantly changed by small perturbations [97]. In the non-polar network, the intermediate filaments branch in an attempt to adapt to the cellular demands of the microenvironment [98].

The crosslinking interactions between proteins making up intermediate filaments are postulated to be vital for cell mechanics, inspiring the study of the associated protein tail. Mutation of the desmin proteins at the filament tail causes slight changes in network flexibility, but does not have a significant effect on the mesh size or shear modulus [99]. The crosslinking interaction may be expected to rely on electrostatic interactions between filament proteins, and by extension the salt concentration in their local micro-environment. Indeed, an increase in cations enhances the stiffness of the intermediate filament network. In the case of small external stresses, the elasticity of the network shifts from the linear to nonlinear state as a function of stress magnitude. On the other hand, under greater stress the network has a modified nonlinear elasticity [100]. Intermediate filament networks with a greater number of bundles have higher persistence lengths and flexural stiffness, in contrast to those with a lower number of bundles, demonstrating the importance of bundle number and thus protein type on cell elasticity.

**Figure 7.** Schematic of a cytoskeleton as a dynamic 3-dimensional scaffold made up of actin filaments, intermediate filaments and microtubules.

## *3.2.3. Actin filaments*

140 Viscoelasticity – From Theory to Biological Applications

environment [98].

and thus protein type on cell elasticity.

are composed of protein dimers, but in this case elongated ones.

microfilaments [83,84]. Intermediate filaments are constructed by a group of related proteins, which have been divided into five subgroups according to their sequence identity. All of the proteins associated with type I, II, III, and IV immediate filaments are localized to the cytoplasm, while those of type V (*e.g.* lamins) localize to the cell nucleus and form a network underneath the nuclear membrane. Similar to microtubules, intermediate filaments

Intermediate filaments have been discovered in diverse cell types, with more than 60 associated genes coded in humans [85,86]. They are found to be highly extensible compared to filamentous actin (F-actin) and microtubules, which are able to retain enormous strains while sustaining the intact filament structure [87,88]. Their unique extensibility implies their it could play a special role in cell mechanics, which would set it apart from other cytoskeletal elements. Since most genes associated with intermediate filaments are responsible for coding keratins, keratin-based intermediate filaments are considered an important player in cellular mechanics [89,90], regulating viscoelastic properties and the motility of cancer cells. The architecture of the keratin filament is regulated by phosporylation, accounting for the viscoelastic responses of carcinoma cells during large deformations, and the actin network is also regulated by phosphorylation under the

regulation of kinases [91-93], phosphatases and other regulatory proteins [89,94].

The mechanical properties of intermediate filament networks have been studied by applying classical models to homogeneous and isotropical samples, which link the elastic shear modulus to the mean mesh size of the cytoskeleton [95]. This means that the viscoelastic response of the network is dependent upon its subcellular organization, filament composition, and overall protein concentration. The nonlinear relationship between the mesh size of these networks and the elastic shear modulus [96] underscores whole cell mechanical properties, elasticity and viscoelasticity of the network, which can be significantly changed by small perturbations [97]. In the non-polar network, the intermediate filaments branch in an attempt to adapt to the cellular demands of the micro-

The crosslinking interactions between proteins making up intermediate filaments are postulated to be vital for cell mechanics, inspiring the study of the associated protein tail. Mutation of the desmin proteins at the filament tail causes slight changes in network flexibility, but does not have a significant effect on the mesh size or shear modulus [99]. The crosslinking interaction may be expected to rely on electrostatic interactions between filament proteins, and by extension the salt concentration in their local micro-environment. Indeed, an increase in cations enhances the stiffness of the intermediate filament network. In the case of small external stresses, the elasticity of the network shifts from the linear to nonlinear state as a function of stress magnitude. On the other hand, under greater stress the network has a modified nonlinear elasticity [100]. Intermediate filament networks with a greater number of bundles have higher persistence lengths and flexural stiffness, in contrast to those with a lower number of bundles, demonstrating the importance of bundle number Actin filaments are the thinnest (≈ 8nm) and most plentiful among all the components of the eukaryotic cytoskeleton [101]. Under physiological conditions, actin filaments grow by polymerization of the ATP-bound actin monomers, addition of monomers to the end of the severed filament fragments, or by branching out of the existing filaments. Actin filaments are polar fibers, with helically arranged actin monomers all pointed in the same direction, which can form a cortex underneath the cytoplasmic membrane to support cell movement. More than 100 proteins promote the formation of a single actin filament, filament crosslinking, networks and bundle formation. Actin filaments are continuously assembled and disassembled in response to cell signaling.

F-actin exhibits viscoelasticity as a semi-flexible polymer with linear and nonlinear responses to external forces [102,103]. To quantitatively evaluate the contribution of Factins to cytoskeleton mechanics, such networks have been reconstituted *in vitro* with purified protein. The reconstituted F-actin forms a gel-like network in which the mesh size is dependent on the F-actin concentration [104]. Under a low applied force, semiflexible networks only composed of F-actins deform in a manner proportional to the force load, but under a larger force which affects F-actin filament contour length, the deformation can be described as strain-stiffening [95]. The mechanical properties of F-

actin filaments are affected by thermal fluctuations, which cause transverse bending, decreasing its end to end distance [105]. When an F-actin filament is under strain, fluctuations in the F-actin filament cause straightening with an associated consumption of energy. Thus, F-actin filaments exhibit an entropic elastic response. The magnitude of Factin deformation reflects the reduction in the number of fluctuations in the actin filament [106].

Viscoelasticity in Biological Systems: A Special Focus on Microbes 143

**Figure 8.** A model of biofilm growth and their dynamic behaviors.

Several attempts have been made to study the rheological properties of biofilms, yet they remain understudied, likely for the following reasons: (i) biofilms are extremely complex and heterogeneous with no defined geometry, making the use of conventional techniques difficult, (ii) their size and diverse nature make sample handling difficult and underscore the need to study biofilms in the natural environment to best represent their complexity (Figure 8). Studies have shown that biofilms formed under low shear conditions (laminar flow) are characterized by spherical micro-colonies divided by water channels [109]. It has also been shown that biofilms formed under higher detachment forces (*e.g.* shaking) produce more EPS to increase mechanical strength and to withstand shear stress [113].

A decade ago it was demonstrated that biofilms are effectively viscoelastic, a property that plays a major role in the various stages of biofilm growth [109,112,114-117]. Biofilms, all of which exhibit classic viscoelastic behaviours [109,115,116,118,119], can grow in a wide variety of environments including laboratory conditions, under flow and even in hot springs, demonstrating their ability to absorb elevated changes in shear stresses. Biofilms are elastic for shorter periods, can resist shear stresses and detachment, and over longer periods of time they flow as viscous fluids and become streamlined [109,112,114]. Viscoelasticity of the biofilm matrix has been shown to determine its structural integrity, resistance to stress, and ease of dispersion [120]. Simple stress-strain and creep tests of mixed culture and single species biofilms showed that the deformation of individual cell

Since the elastic response of F-actin filaments is length dependent, the concentration of actin and crosslinking proteins are closely related to the magnitude of the filament elastic modulus. The characterization of F-actin filament mechanical properties is also convoluted with actin concentration, the type and concentration of crosslinking protein, and the magnitude of the applied force. If the fluctuations are deconvoluted, the inherent elastic modulus of the filament dominates its mechanical response [106]. Crosslinking proteins covalently link individual subunits, allowing the actin filament to form a bundled structure with a larger diameter. Therefore, F-actin networks in combination with cross-linking proteins could behave differently from networks formed by only Factins, the mechanical properties of which are more akin to the properties of cells. Once the actin filament becomes stiffer with the addition of crosslinkers, its elasticity dominates, and contributions from thermal fluctuations play a smaller role in the total mechanical response [106]. The entropic elasticity is reduced as actin and cross linker concentrations increase. In this case, the deformation of the actin filament depends on the bending and stretching of the filament itself [106]. The rigidly cross-linked actin filament has a more linear response and tends to break under small strains [107,108], and such filaments can sustain much larger stresses compared to pure F-actin networks, providing a reasonable explanation for their ability to resist a broad range of external stresses or internal tension.

## **3.3. Biofilms contribute to viscoelasticity**

Biofilms have serious implications in industry, medicine and environmental systems making the study of their physical properties imperative to shed light on their growth mechanisms and adhesion properties, key factors in biofilm control. A biofilm is a surfaceassociated three dimensional consortia of microbial communities, surrounded by a matrix of protective biopolymers, macromolecular debris, sediment and precipitate, making it a highly complex mechanical, compliant, and viscoelastic structure. Biofilms can also be highly heterogeneous consisting of mixed populations of bacteria, fungi, protozoa [112] with interspersed pores and channels. Biofilms exhibit enormous resistance to external stress factors, with exopolysaccharides (EPS) contributing to their overall mechanical stability and enabling them to withstand external forces. Hydrodynamic forces can have a strong influence on biofilm formation, structure and thickness, EPS production, mass and metabolic activities [109-111]. Their dynamic structure ultimately affects how we view, model and study their mechanical behaviour. A schematic presentation of biofilm dynamic behavior is depicted in Figure 8.

**Figure 8.** A model of biofilm growth and their dynamic behaviors.

[106].

internal tension.

**3.3. Biofilms contribute to viscoelasticity** 

behavior is depicted in Figure 8.

actin filaments are affected by thermal fluctuations, which cause transverse bending, decreasing its end to end distance [105]. When an F-actin filament is under strain, fluctuations in the F-actin filament cause straightening with an associated consumption of energy. Thus, F-actin filaments exhibit an entropic elastic response. The magnitude of Factin deformation reflects the reduction in the number of fluctuations in the actin filament

Since the elastic response of F-actin filaments is length dependent, the concentration of actin and crosslinking proteins are closely related to the magnitude of the filament elastic modulus. The characterization of F-actin filament mechanical properties is also convoluted with actin concentration, the type and concentration of crosslinking protein, and the magnitude of the applied force. If the fluctuations are deconvoluted, the inherent elastic modulus of the filament dominates its mechanical response [106]. Crosslinking proteins covalently link individual subunits, allowing the actin filament to form a bundled structure with a larger diameter. Therefore, F-actin networks in combination with cross-linking proteins could behave differently from networks formed by only Factins, the mechanical properties of which are more akin to the properties of cells. Once the actin filament becomes stiffer with the addition of crosslinkers, its elasticity dominates, and contributions from thermal fluctuations play a smaller role in the total mechanical response [106]. The entropic elasticity is reduced as actin and cross linker concentrations increase. In this case, the deformation of the actin filament depends on the bending and stretching of the filament itself [106]. The rigidly cross-linked actin filament has a more linear response and tends to break under small strains [107,108], and such filaments can sustain much larger stresses compared to pure F-actin networks, providing a reasonable explanation for their ability to resist a broad range of external stresses or

Biofilms have serious implications in industry, medicine and environmental systems making the study of their physical properties imperative to shed light on their growth mechanisms and adhesion properties, key factors in biofilm control. A biofilm is a surfaceassociated three dimensional consortia of microbial communities, surrounded by a matrix of protective biopolymers, macromolecular debris, sediment and precipitate, making it a highly complex mechanical, compliant, and viscoelastic structure. Biofilms can also be highly heterogeneous consisting of mixed populations of bacteria, fungi, protozoa [112] with interspersed pores and channels. Biofilms exhibit enormous resistance to external stress factors, with exopolysaccharides (EPS) contributing to their overall mechanical stability and enabling them to withstand external forces. Hydrodynamic forces can have a strong influence on biofilm formation, structure and thickness, EPS production, mass and metabolic activities [109-111]. Their dynamic structure ultimately affects how we view, model and study their mechanical behaviour. A schematic presentation of biofilm dynamic Several attempts have been made to study the rheological properties of biofilms, yet they remain understudied, likely for the following reasons: (i) biofilms are extremely complex and heterogeneous with no defined geometry, making the use of conventional techniques difficult, (ii) their size and diverse nature make sample handling difficult and underscore the need to study biofilms in the natural environment to best represent their complexity (Figure 8). Studies have shown that biofilms formed under low shear conditions (laminar flow) are characterized by spherical micro-colonies divided by water channels [109]. It has also been shown that biofilms formed under higher detachment forces (*e.g.* shaking) produce more EPS to increase mechanical strength and to withstand shear stress [113].

A decade ago it was demonstrated that biofilms are effectively viscoelastic, a property that plays a major role in the various stages of biofilm growth [109,112,114-117]. Biofilms, all of which exhibit classic viscoelastic behaviours [109,115,116,118,119], can grow in a wide variety of environments including laboratory conditions, under flow and even in hot springs, demonstrating their ability to absorb elevated changes in shear stresses. Biofilms are elastic for shorter periods, can resist shear stresses and detachment, and over longer periods of time they flow as viscous fluids and become streamlined [109,112,114]. Viscoelasticity of the biofilm matrix has been shown to determine its structural integrity, resistance to stress, and ease of dispersion [120]. Simple stress-strain and creep tests of mixed culture and single species biofilms showed that the deformation of individual cell

clusters was related to the fluid shear stress, and that both mixed species biofilms and those from pure cultures behaved like viscoelastic fluids [114]. It has been proposed that the viscoelasticity of biofilms allows them to resist detachment as demonstrated for *Staphylococcus aureus* biofilms [117]. Lieleg et al. [121] showed that high shear stress may transiently fragment the biofilm but does not cause it to detach from the surface. This resilience has been attributed to the viscoelastic behavior of the bacterial biofilm. Biofilms of various *Pseudomonas aeruginosa* strains subjected to physical deformations in fluid were shown to be viscoelastic fluids, which behave like elastic solids over periods of a few seconds but like linear viscous fluids over longer times. Therefore in several studies, bacterial biofilms have been reported to behave as viscoelastic materials [38,122,123], while in other studies they are described as elastic [124,125]. Chemical perturbations can reduce biofilm viscoelasticity and hence slow down recovery to their original state [126].

Viscoelasticity in Biological Systems: A Special Focus on Microbes 145

) was converted to a spherical shape from the wild

**4. Factors affecting viscoelasticity of biological materials** 

viscoelasticity and eventually germination [20, 136].

mutant of *B. subtilis* (indole- and thymine-

with increasing temperature.

in low ionic strength.

**5. Summary** 

Cell components imparting viscoelastic properties to the entire cell are well studied, but there are very few examples in the literature in which external factors are shown to affect cell viscoelasticity. The structural integrity of biological systems is partially dependent on the degree of hydration. Humidity affects the mechanical properties of biopolymers, but the intensity of this effect depends on the type of biopolymer. For example, effects of humidity on cellulose are much less severe than on peptidoglycan. Thwaites et al. [136] demonstrated that the viscoelastic behavior of *Bacillus subtilis* depends on humidity, which affects the viscoelasticity of the peptidoglycan layer. Increasing humidity gives rise to cell wall hydration, allowing water to form hydrogen bonds with peptides and other cell wall components, making the cell wall more pliable [136]. Bacterial and fungal spores are very rigid under dry conditions, but increased humidity leads to removal of the outer spore hydrophobic layer, making it softer than under dry conditions and leading to changes in

Cells also require optimal temperature conditions for their survival. Temperature affects the proper function and conformation of biomolecules, and hence indirectly affects cell mechanical properties. The rigidity of *E. coli* has been found to increase as a function of temperature, attributed to the folding of lipoproteins in the outer membrane leading to an increase in turgor pressure [136]. An earlier study showed that a temperature sensitive

type rod shape, attributed to loosening of the cell wall strength [137]. Hochmuth et al. [7] demonstrated that for red blood cells the time dependent viscoelastic behavior was reduced

The elastic behavior of the bacterial cell surface depends on the cell volume and ionic strength of the surrounding medium, which is related to its osmolarity. Abu-Lail and Camesano [138] observed that the elasticity of *E. coli* increased with reduced solvent polarity, and that bacteria in the least polar solvent have the highest Young's modulus [138]. Further, the spring constant of bacteria in a high ionic strength solvent of is higher than that

In summary, the viscoelastic properties of biological structures are responsible for their mechanical behavior which in turn is required for normal cell function. Viscoelasticity of whole biological cells is the combined contribution of cellular components, and several creative methods have been put forward to measure the associated parameters. Emerging experimental tools enable quantitative deformation studies of individual cells, biological polymers and macromolecules, which have led to understanding the relationship between mechanical properties and function. Nonetheless, studying the mechanical behavior of cellular components remains challenging. There are several theoretical models to determine the mechanical properties of cells and their components, but based on diverse findings and the different cell types used to determine viscoelastic parameters, it is difficult to compare

Several experimental models have been generated to help understand the rheology and mechanical behaviour of biofilms. Rheology of undisturbed dental plaque biofilms made up of *Streptococcus mutans* and those from pond water showed a linear viscoelastic behaviour for which the Burger model was successfully applied to study creep compliances [127]. There are a large number of studies in the literature that have used different techniques to measure various material properties of biofilms, each of which provide information about their mechanics. Some of the most common methods used to measure the tensile strength of biofilms include cone and plate rheometry [128] and later the centrifugation method [125]. Particle-tracking microrheology has been successfully used to measure the strength of single species biofilms of *S. aureus* and *P. aeruginosa* [129]. The strength and apparent viscoelastic modulus of *P. aeruginosa* biofilms grown on membrane filters has also been investigated using a uniaxial compression experimental device and a film rheometer [118]. Directly applied and controlled loading forces have been used to quantify various biofilm viscoelasticity parameters, usually without a hydrodynamic flow, for example microbead FS [120], the micro-cantilever technique [130,131], indenters [122] or T-shaped probes [75], which are used to pull (tensile testing under a normal load) or push (compression testing under a normal load) the biofilm (see review 38 and references therein). On the other hand, there are several methods that use hydrodynamic loading, where biofilms are subjected to a fluid flow in flow cells [109,112,132], or Couette–Taylor type reactors [133,134]. Real time monitoring of cell growth and proliferation corresponding to viscoelasticity changes within a biofilm have been investigated in *Streptococcus mutans* biofilms using a Quartz crystal microbalance with a dissipation monitoring device [135].

Although there have been a large number of techniques developed to measure various biofilm parameters, a fully effective method is pending. The diverse magnitude of viscoelasticity parameters might reflect diverse biofilm properties, growth environments and source organisms. The viscoelastic properties of biofilms are adaptations to stress factors and shear forces, and are achieved through modifications to the secreted EPS. A better understanding of biolfilm mechanical properties and viscoelastic behaviours may inform effective strategies for biofilm removal or control.
