# Difference between revisions of "Biofilms as complex fluids"

Entry by Emily Redston, AP 225, Fall 2011

## Reference

Biofilms as Complex Fluids by J. N. Wilking, T. E. Angelini, A. Seminara, M. P. Brenner, and D. A. Weitz. MRS Bulletin, 26, 385-391 (2011)

## Introduction

The goal of this paper was to present a method for analyzing biofilms using soft matter physics. Bacterial biofilms can be found on nearly every surface as long as there is sufficient moisture and nutrients. They can have a positive impact in areas such as water treatment and waste sequestration, but they also play a devastating role in many bacteria-related problems like tooth decay and hospital-acquired infections. A better understanding of the structure, mechanics, and dynamics of biofilms is necessary for both their removal and for the optimization of their properties.

Viewing biofilms as a complex fluid is a good starting point for analyzing their structure and properties. A biofilm can be seen as a composite of colloids (bacterial cells) embedded in a cross-linked polymer gel (extracellular matrix).

## Biofilm Structure

Bacterial biofilms are colonies of bacteria embedded in an extracellular matrix (ECM). Bacterial cells are rigid and typically have well-defined shapes like spheres or rods. Since the bacteria within a biofilm are mostly sessile and cannot generate forces outside of the cell, they control the structural and mechanical properties of the biofilm by regulating the composition of the ECM. The ECM is primarily composed of polysaccharides cross-linked by proteins and multivalent cations. This matrix is the scaffold that holds the bacteria together; it gives the biofilm its mechanical integrity.

Unfortunately, it is difficult to get a full picture of biofilm material properties due to the highly variably nature of the ECM. The ECM is often composed of multiple species, so it is poorly understood.

## Biofilm Mechanics

By exploiting the relation between biofilms and soft matter (specifically the polymer-like behavior of the ECM), one can understand a great deal about how the bacteria controls the water content in the biofilm. To maximize its entropy, an entangled polymer in contact with a reservoir of liquid will swell. If instead the polymer and reservoir are separated by a semi-permeable membrane that only allows water to pass through, the poymer will exert on osmotic pressure,$\Pi$, on the membrane. The polymer swells and strands between cross-links are stretched out. Eventually, $\Pi$ is balanced by the elastic shear modulus of the gel, $G_{E}$. Thus there is an equilibrium water content in the biofilm for a given polymer concentration and cross-link density in the ECM. Therefore, if the biofilm is in contact with an abundant water source, the cross-links will place a limit on the maximum amount of water absorbed by the biofilm. This will prevent complete dissolution of the biofilm. On the other extreme, dehydration of the biofilm is avoided due to high entropic costs associated with the loss of water. The mechanical properties of the biofilm are directly related to the water content since $\Pi$ ≈ $G_{E}$ at equilibrium. In this manner, the bacteria are able to control the mechanical properties of the biofilm by regulating the water content using the ECM.

## Viscoelasticity

Figure 1. (a) Material between parallel plates is deformed by the displacement of the upper plate, and strain $\gamma$ is defined as Δx/h. Stress induced in an elastic solid is proportional to the strain through the elastic modulus $G_{E}$. Stress induced in a viscous liquid is proportional to the strain rate $\dot{\gamma}$ through the viscosity $\eta$. Viscous dissipation in a viscoelastic material is characterized by a relaxation time, $t_{c}$. (b) Qualitative depictions (red lines) of $G_{E}$ as a function of ϕ for systems of spheres (left) and rods (right). At very high ϕ, the elasticity of the packing is set by the elasticity of the individual colloids (dashed line).

As most other soft materials, biofilms are viscoelastic, so they exhibit a time-dependent response to an imposed mechanical stress. The viscoelastic response of a material can be characterized by the linear elastic shear modulus, $G_{E}$ and the relaxation time, $t_{c}$ (Figure 1a). Strong biofilm formers are often referred to as "robust", meaning they are difficult to deform and do not flow rapidly when deformed; robust biofilms will have large $G_{E}$ and long $t_{c}$. One can understand the viscoelastic behavior of biofilms by considering the mechanics of other well-defined viscoelastic materials.

The viscoelastic properties of systems like soft colloids and polymer gels depend uniquely on the fraction of liquid in the material. The manner of this dependence is contingent upon the physical properties and the interactions of the colloids or polymer. The relevant parameter for soft, micron-scale colloids is the colloidal volume fraction, ϕ. Figure 1b shows qualitative depictions of $G_{E}$(ϕ) for disordered systems of repulsive soft spheres (left) and rods (right). These behaviors are relevant for bacteria like cocci, which are spherical, and bacilli, which have rod-like cells. At low ϕ, neither system exhibits an elastic response. There is an onset of elasticity at an intermediate volume fraction ϕ*, which is when the bare surfaces of the colloids touch. The rods have a higher onset of elasticity because they can rotate when packed. At high ϕ, the elastic modulus is set by the elasticity of the individual colloids. At ϕ < ϕ*, the material acts like a liquid suspension and the stress relaxes immediately. At ϕ > ϕ*, the material acts like a solid paste and exhibits stress relaxation. This stress relaxation is logarithmic in time, so residual strain can remain in the system for very long times.

Although biofilms are 80% or more water by volume, one must consider that a lot of this water is contained within the rigid bacterial cells. Thus it is often useful to consider a bacterial volume fraction $\phi_{b}$, which is analogous to the colloidal volume fraction. The high ϕ behavior of colloidal packing is likely relevant for biofilms with large $\phi_{b}$, like biofilms grown on infections in tissue wounds. However, most biofilms have a low $\phi_{b}$, particularly those in contact with reservoirs of liquid. In fact, $\phi_{b}$ is typically so low that the elasticity of the biofilm is determined predominantly by the properties of the ECM. A deeper understanding of biofilm mechanics is limited by their material and genetic complexity.

## Conclusion

Using soft matter physics to model bacterial biofilms as complex composite fluids gives us insight into their structure, mechanics, and dynamics.