# Biofilms as complex fluids

Entry by Emily Redston, AP 225, Fall 2011

Work in progress

## 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

Bacterial biofilms can be found on nearly every surface as long as there is 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 bioflim can be seen as a composite of colloids (bacterial cells) embedded in a cross-linked polymer gel (extracellular matrix -- ECM).

## Biofilm Structure

Bacterial cells are rigid and 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 integrety.

Unfortunately, it is difficult to get a full picture of the 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 is able to control the water content in the biofilm. To maximize its entropy, an entangled polymer placed 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 the entropic costs. The mechanical properties of the biofilm are directly related to the water content since $\Pi$ ≈ $G_{E}$ at equilibrium. In this manner, the biofilm can control its mechanics.

## 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 non-Brownian spheres (left) and rods (right). At low ϕ, neither system exhibits an elastic response. An onset of elasticity occurs at intermediate ϕ = ϕ* when the bare surfaces of the colloids touch. This onset occurs at higher ϕ for anisotropic particles, as the colloids can rotate to accommodate a higher ϕ. At very high ϕ, the elasticity of the packing is set by the elasticity of the individual colloids (dashed line).

As most soft materials, biofilms are viscoelastic, so they exhibit a time-dependednt 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). Robust biofilms are difficult to deform and do not flow rapidly when deformed; robust biofilms will have large $G_{E}$ and long $t_{c}$.

The viscoelastic properties of systems like colloidal pastes and polymer gels depend uniquely on the fraction of liquid in the material. The manner of this dependence is contigent upon the physical properties and interactions of the colloids or polymer. The relevant paramter for soft, micron-scale colloids is the colloidal volume fraction,ϕ. A qualitative depiction of $G_{E}$ (ϕ) for a disorded system of repulsive soft sphers is shown in Figure 2bl this behavior is relavant for bacteria with spherical shapes, such as cocci. There is an onset of elasticity at an intermediate volume fraction ϕ*. At high ϕ, the elastic modulus is set by the elasticity of the individual colloids. At ϕ < ϕ*, the material is a liquid suspension, and the stress relaxes immediately. At ϕ > ϕ*, the material is a solid paste that exhibits stress relaxation. This stress relaxation is logarithmic in time, so residual strain can remain in the system for very long times.