JOURNAL OF BACTERIOLOGY, Mar. 2003, p. 1485–1491 Vol. 185, No. 50021-9193/03/$08.00⫹0 DOI: 10.1128/JB.185.5.1485–1491.2003Copyright © 2003, American Society for Microbiology. All Rights Reserved.GUEST COMMENTARIESDiffusion in BiofilmsPhilip S. Stewart*Center for Biofilm Engineering and Department of Chemical Engineering, MontanaState University–Bozeman, Bozeman, Montana, 59717-3980Much of what makes life in a microbial biofilm differentfrom life in a free aqueous suspension can be explained byinvoking the phenomenon of diffusion. This article discussesthe profound influence of the physics of the diffusion processon the chemistry and biology of the biofilm mode of growth. Ihave framed the discussion in the form of answers to fiveimportant questions.WHY IS DIFFUSION AN IMPORTANT PROCESSIN BIOFILMS?When microorganisms are grown in planktonic culture, dif-fusion is usually of little consequence. There are two reasonsfor this. The first reason is that planktonic cultures are gener-ally agitated, and the resulting fluid flow transports solutesrapidly, resulting in a well-mixed system. Transport that occursas a solute is carried by the bulk flow of a fluid (convection) isgenerally much faster than the transport resulting from ran-dom molecular motion (diffusion). Of course, there is no netconvective flow of fluid into or out of the microbial cell. Atsome point close to the cell, diffusion becomes critical formoving the solute toward or away from the cell surface. Thereason that diffusion does not limit this step is that the diffusiondistance is small and diffusion is rapid over such short dis-tances.Diffusion limitation arises readily in biofilm systems becausefluid flow is reduced and the diffusion distance is increased inthe biofilm mode of growth. The biofilm and the substratum towhich it is anchored impede flow in the vicinity of the biofilm,throttling convective transport. Inside cell clusters, the locallyhigh cell densities and the presence of extracellular polymericsubstances arrest the flow of water. Diffusion is the predomi-nant transport process within cell aggregates (7, 36). Whereasthe diffusion distance for a freely suspended microorganism isof the order of magnitude of the dimension of an individualcell, the diffusion distance in a biofilm becomes the dimensionof multicellular clusters. This can easily represent an increasein the diffusion distance, compared to a single cell, of 2 ordersof magnitude. As is explained in the next section, diffusiveequilibration time scales as the square of the diffusion distance.In other words, a biofilm that is 10 cells thick will exhibit adiffusion time 100 times longer than that of a lone cell.HOW FAST DO SOLUTES DIFFUSE INTO OROUT OF A BIOFILM?Suppose a stain is added to the medium bathing a biofilm.How long will it take this dye to permeate, by diffusion, to theinterior of a cell cluster or to the bottom of the biofilm?Because I aspire in this article to avoid overwhelming thereader with mathematics, I will define a single, simple measureof diffusive penetration time. There are two versions of thismeasure, depending on the geometry of the system. The timerequired for a solute added to the fluid bathing a biofilm toattain 90% of the bulk fluid concentration at the base of flatslab (uniformly thick) biofilm is given very simply byt90⫽ 1.03L2De. (1)Here, L is the biofilm thickness, and Deis the effectivediffusion coefficient in the biofilm. The time required for asolute to attain 90% of the bulk fluid concentration at thecenter of a spherical biofilm cell cluster is given byt90⫽ 0.37R2De(2)where R is the cluster radius and Deis the effective diffusioncoefficient in the biofilm. The first step in performing thesecalculations is to estimate the effective diffusion coefficient inbiofilm.Biofilms are mostly water and the appropriate starting pointfor estimating a diffusion coefficient in a biofilm is to determinethe value of the diffusion coefficient in pure water (Daq). Someaqueous diffusion coefficients have been experimentally mea-sured and can be found in the literature. Others can be esti-mated from a predictive correlation such as the Wilke-Changcorrelation (22). Aqueous diffusion coefficients of selected sol-utes of interest in microbial systems are tabulated in Table 1.I have summarized elsewhere values of diffusion coefficients inwater of various biocides and antibiotics (32, 34).The diffusion coefficient in water depends on temperature,both directly and through the effect of temperature (T)onthesolution viscosity (␮). This temperature dependence of aque-ous diffusion coefficients can be calculated through the rela-tionship Daq␮/T ⫽ constant.The value of the effective diffusion coefficient in the biofilmwill be reduced compared to the diffusion coefficient in waterdue to the presence of microbial cells, extracellular polymers,and abiotic particles or gas bubbles that are trapped in thebiofilm. This reduction is described by the ratio De/Daq. Ex-* Mailing address: Center for Biofilm Engineering and Departmentof Chemical Engineering, Montana State University–Bozeman, Boze-man, Montana, 59717-3980. Phone: (406) 994-2890. Fax: (406) 994-6098. E-mail: [email protected] measurements of this ratio, termed the relativeeffective diffusivity, have been reviewed elsewhere (33) andthat article presents guidelines and formulae for estimatingDe/Daqin biofilms. There are also sophisticated approaches forcalculating this ratio (40). The relative effective diffusivity de-pends on the biomass density in the biofilm and the physio-chemical properties of the solute. De/Daqin biofilm rangesfrom ca. 0.2 to 0.8 with a mean value of ca. 0.4. Figure 1presents consensus values of De/Daqfor selected solutes. Isuggest using a value of De/Daqof 0.6 for light gases (e.g.,oxygen, nitrous oxide, carbon dioxide, or methane) and a valueof De/Daqof 0.25 for most organic solutes.Armed with an effective diffusion coefficient and an estimateof the biofilm thickness or cluster radius, the calculation ofdiffusive penetration times is straightforward. The best way toillustrate this is with some example calculations.Example calculation. A biofilm growing in a flow cell atroom temperature (22°C) is to be stained with a fluorescein-tagged probe. The biofilm consists of tightly packed mush-room-shaped clusters that are 100 ␮m tall. How long must thesample be incubated with this reagent to ensure that the stainreaches to the full