Determination of pollutant diffusion coefficients in naturally formed biofilms using a single tube extractive membrane bioreactor

A novel technique has been used to determine the effective diffusion coefficients for 1,1,2-trichloroethane (TCE), a nonreacting tracer, in biofilms growing on the external surface of a silicone rubber membrane tube during degradation of 1,2-dichloroethane (DCE) by Xanthobacter autotrophicus GJ10 and monochlorobenzene (MCB) by Pseudomonas JS150. Experiments were carried out in a single tube extractive membrane bioreactor (STEMB), whose configuration makes it possible to measure the transmembrane flux of substrates. A video imaging technique (VIT) was employed for in situ biofilm thickness measurement and recording. Diffusion coefficients of TCE in the biofilms and TCE mass transfer coefficients in the liquid films adjacent to the biofilms were determined simultaneously using a resistances-in-series diffusion model. It was found that the flux and overall mass transfer coefficient of TCE decrease with increasing biofilm thickness, showing the importance of biofilm diffusion on the mass transfer process. Similar fluxes were observed for the nonreacting tracer (TCE) and the reactive substrates (MCB or DCE), suggesting that membrane-attached biofilm systems can be rate controlled primarily by substrate diffusion. The TCE diffusion coefficient in the JS150 biofilm appeared to be dependent on biofilm thickness, decreasing markedly for biofilm thicknesses of >1 mm. The values of the TCE diffusion coefficients in the JS150 biofilms <1-mm thick are approximately twice those in water and fall to around 30% of the water value for biofilms >1-mm thick. The TCE diffusion coefficients in the GJ10 biofilms were apparently constant at about the water value. The change in the diffusion coefficient for the JS150 biofilms is attributed to the influence of eddy diffusion and convective flow on transport in the thinner (<1-mm thick) biofilms.     

Measurement of local mass transfer coefficient in biofilms

Local mass transfer rates for an electrochemically formed microsink in an aerobic biofilm was measured by a mobile microelectrode using limiting current technique. Mass transfer coefficients varied both horizontally and vertically in the biofilm. The results implied the existence of an irregular biofilm structure consisting of microbial cell clusters surrounded by tortuous water channels. An unexpected increase of the local mass transfer coefficient just above the biofilm surface suggested the existence, of local flow instability in this region. As expected, the influence of bulk flow velocity on the local mass transfer rate decreased with increasing depth into the biofilm. Mass transfer coefficients fluctuated significantly inside microbial cell clusters, suggesting the existence of internal channels through which liquid could flow. A new conceptual model of biofilm microbial cluster structure is proposed to account for such biofilm microstructure irregularities. (c) 1995 John Wiley & Sons, Inc.     

Measurement of local diffusion coefficients in biofilms by microinjection and confocal microscopy

A new technique for the determination of local diffusion coefficients in biofilms is described. It is based on the microinjection of fluorescent dyes and quantitative analysis of the subsequent plume formation using confocal laser microscopy. The diffusion coefficients of fluorescein (MW 332), TRITC-IgG (MW 150000) and phycoerythrin (MW 240000) were measured in the cell clusters and interstitial voids of a heterogeneous biofilm. The diffusivities measured in the voids were close to the theoretical values in water. Fluorescein had the same diffusivity in cell clusters, voids, and sterile medium. TRITC-IgG did not diffuse in cell clusters, presumably due to binding to the cell cluster matrix. After treatment of the biofilm with bovine serum albumin, binding capacity decreased and the diffusion coefficient could be measured. The diffusivity of phycoerythrin in cell clusters was impeded by 41%, compared to interstitial voids. From the diffusion data of phycoerythrin it was further calculated that the cell cluster matrix had the characteristics of a gel with 0.6 nm thick fibers and pore diameters of 80 nm. (c) 1997 John Wiley & Sons, Inc.     

Diffusion coefficients of metabolites in active biofilms

Diffusion coefficients of actual metabolites in completely active biofilms can be determined by applying a new concept that is based on a constant local activity in the entire biofilm. In that case, a concentration step will be transmitted unattenuated. Subsequently, the diffusion coefficient can be calculated from the response monitored with a microelectrode positioned in the biofilm without quantitative knowledge of the local microbial kinetics. The conditions required for such a constant microbial biofilm activity were formulated in terms of the Thiele modulus and the substrate concentration in the bulk liquid. This proposed method was successfully applied to determine diffusion coefficients of oxygen and glucose in agar gels containing various fractions of active immobilized microorganisms. The values obtained were compared to experimental results from well-defined inert systems. The transient response of oxygen was far more affected by the presence of the immobilized cells than glucose. This can be explained by partition of the diffusing solute between the microbial cells and the aqueous phase.     

A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms

Experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms are reviewed. Effective diffusive permeabilities, the parameter appropriate to the analysis of reaction-diffusion interactions, depend on solute type and biofilm density. Three categories of solute physical chemistry with distinct diffusive properties were distinguished by the present analysis. In order of descending mean relative effective diffusive permeability (De/Daq) these were inorganic anions or cations (0.56), nonpolar solutes with molecular weights of 44 or less (0.43), and organic solutes of molecular weight greater than 44 (0.29). Effective diffusive permeabilities decrease sharply with increasing biomass volume fraction suggesting a serial resistance model of diffusion in biofilms as proposed by Hinson and Kocher (1996). A conceptual model of biofilm structure is proposed in which each cell is surrounded by a restricted permeability envelope. Effective diffusion coefficients, which are appropriate to the analysis of transient penetration of nonreactive solutes, are generally similar to effective diffusive permeabilities in biofilms of similar composition. In three studies that examine diffusion of very large molecular weight solutes (>5000) in biofilms, the average ratio of the relative effective diffusion coefficient of the large solute to the relative effective diffusion coefficient of either sucrose or fluorescein was 0.64, 0.61, and 0.36. It is proposed that large solutes are effectively excluded from microbial cells, that small solutes partition into and diffuse within cells, and that ionic solutes are excluded from cells but exhibit increased diffusive permeability (but decreased effective diffusion coefficients) due to sorption to the biofilm matrix.     

A multiscale theoretical model for diffusive mass transfer in cellular biological media

An integrated methodology is developed for the theoretical analysis of solute transport and reaction in cellular biological media, such as tissues, microbial flocs, and biofilms. First, the method of local spatial averaging with a weight function is used to establish the equation which describes solute conservation at the cellular biological medium scale, starting with a continuum-based formulation of solute transport at finer spatial scales. Second, an effective-medium model is developed for the self-consistent calculation of the local diffusion coefficient in the cellular biological medium, including the effects of the structural heterogeneity of the extra-cellular space and the reversible adsorption to extra-cellular polymers. The final expression for the local effective diffusion coefficient is: D(Abeta)=lambda(beta)D(Aupsilon), where D(Aupsilon) is the diffusion coefficient in water, and lambda(beta) is a function of the composition and fundamental geometric and physicochemical system properties, including the size of solute molecules, the size of extra-cellular polymer fibers, and the mass permeability of the cell membrane. Furthermore, the analysis sheds some light on the function of the extra-cellular hydrogel as a diffusive barrier to solute molecules approaching the cell membrane, and its implications on the transport of chemotherapeutic agents within a cellular biological medium. Finally, the model predicts the qualitative trend as well as the quantitative variability of a large number of published experimental data on the diffusion coefficient of oxygen in cell-entrapping gels, microbial flocs, biofilms, and mammalian tissues.     

Transport of neutral solute in articular cartilage: effect of microstructure anisotropy

Due to the avascular nature of articular cartilage, solute transport through its extracellular matrix is critical for the maintenance and the functioning of the tissue. What is more, diffusion of macromolecules may be affected by the microstructure of the extracellular matrix in both undeformed and deformed cartilage and experiments demonstrate diffusion anisotropy in the case of large solute. However, these phenomena have not received sufficient theoretical attention to date. We hypothesize here that the diffusion anisotropy of macromolecules is brought about by the particular microstructure of the cartilage network. Based on this hypothesis, we then propose a mathematical model that correlates the diffusion coefficient tensor with the structural orientation tensor of the network. This model is shown to be successful in describing anisotropic diffusion of macromolecules in undeformed tissue and is capable of clarifying the effects of network reorientation as the tissue deforms under mechanical load. Additionally, our model explains the anomaly that at large strain, in a cylindrical plug under unconfined compression, solute diffusion in the radial direction increases with strain. Our results indicate that in cartilage the degree of diffusion anisotropy is site specific, but depends also on the size of the diffusing molecule. Mechanical loading initiates and/or further exacerbates this anisotropy. At small deformation, solute diffusion is near isotropic in a tissue that is isotropic in its unstressed state, becoming anisotropic as loading progresses. Mechanical loading leads to an attenuation of solute diffusion in all directions when deformation is small. However, loading, if it is high enough, enhances solute transport in the direction perpendicular to the load line, instead of inhibiting it.     

Red Cell Membrane Permeability Deduced from Bulk Diffusion Coefficients

The permeability coefficients of dog red cell membrane to tritiated water and to a series of[¹⁴C]amides have been deduced from bulk diffusion measurements through a "tissue" composed of packed red cells. Red cells were packed by centrifugation inside polyethylene tubing. The red cell column was pulsed at one end with radiolabeled solute and diffusion was allowed to proceed for several hours. The distribution of radioactivity along the red cell column was measured by sequential slicing and counting, and the diffusion coefficient was determined by a simple plotting technique, assuming a one-dimensional diffusional model. In order to derive the red cell membrane permeability coefficient from the bulk diffusion coefficient, the red cells were assumed to be packed in a regular manner approximating closely spaced parallelopipeds. The local steady-state diffusional flux was idealized as a one-dimensional intracellular pathway in parallel with a one-dimensional extracellular pathway with solute exchange occurring within the series pathway and between the pathways. The diffusion coefficients in the intracellular and extracellular pathways were estimated from bulk diffusion measurements through concentrated hemoglobin solutions and plasma, respectively; while the volume of the extracellular pathway was determined using radiolabeled sucrose. The membrane permeability coefficients were in satisfactory agreement with the data of Sha'afi, R. I., C. M. Gary-Bobo, and A. K. Solomon (1971. J. Gen. Physiol. 58:238) obtained by a rapid-reaction technique. The method is simple and particularly well suited for rapidly permeating solutes.     

Diffusion in Pseudomonas aeruginosa biofilms: a pulsed field gradient NMR study

A Pseudomonas aeruginosa biofilm is studied with pulsed field gradient echo nuclear magnetic resonance. Although not all spectral components are assigned yet, the experimental results show that a biofilm consists of components with very different diffusion coefficients. The various biofilm components that give motionally narrowed 1H NMR signals, can be grouped into five classes with diffusion coefficients, ranging from 2 x 10(-9) to 1 x 10(-13) m2 s-1. Investigation of the diffusion behavior of water in the biofilm shows three fractions with different diffusion coefficients. Besides the highly mobile bulk water at least two other fractions with much lower diffusion coefficients are detected. It is shown that one of the fractions with the low diffusion coefficient probably arises from intracellular water. Also for another component of the biofilm, glycerol, three fractions with diffusion coefficients that differ more than a factor ten are detected. Also a group of signals exists which result from practically immobile components.     

A model for sieving of macromolecules by the glomerular membrane of the kidney.

The transport of water and of macromolecules across the glomerular membrane of the kidney depends on the membrane parameters (radius, length and number of pores) as well as on the hydrostatic and oncotic pressures on either side of the membrane. The filtration pressure decreases along the capillary loops from afferent to efferent end. Water and solute flows are thus given by a system of two differential equations. The sieving coefficient of the macromolecules is the ratio of solute to water flow. In the program described the differential equations are solved by the Runge-Kutta method (fourth order). Rosenbrock's method of minimization is used to adjust the theoretical to the experimental sieving coefficients. The pore radius, total pore area per unit of path length and conductance of the membrane, as well as the intracapillary hydrostatic pressure and its gradient can thus be determined.     

Solute size effects on the diffusion in biofilms of Streptococcus mutans

The diffusion of poly(ethylene glycol) (PEG) (MW varying between 200 and 10,000), and of three different types of micelles was examined in Streptococcus mutans biofilms using infrared spectroscopy. PEGs were used because they show limited interactions with biological materials and their weight can be selected in order to cover a wide range of size. The study showed that a considerable fraction at the base of the biofilm was not accessible to the diffusing solute molecules and this inaccessible fraction was very dependent on the size of the diffusing molecules. In parallel, it was found that the diffusion coefficients of these solutes in the biofilms were less than those in water and this reduction was less pronounced for large macromolecules, an effect proposed to be related to their limited penetration. Triton X-100, a neutral detergent, forms micelles that behave like PEG, suggesting that the behaviour observed for neutral macromolecules can be extrapolated to neutral macroassemblies. However, the diffusion, as well as the penetration of sodium dodecylsulphate micelles (a negatively charged surfactant) and cetylpyridinium chloride micelles (positively charged), in the biofilms appeared to be significantly influenced by electrostatic interactions with biofilm components. The present findings provide useful insights associated with the molecular parameters required to efficiently penetrate bacterial biofilms. The study suggests a rationale for the limited bactericidal power of some antibiotics (the large ones). The restricted accessibility of macromolecules and macroassemblies to biofilms must be examined carefully in order to offer guidelines in the development of novel antibacterial treatments.     

Determination of glucose and ethanol effective diffusion coefficients in Ca-alginate gel.

Glucose and ethanol diffusion coefficients in 2% Ca-alginate gel were measured using the experimental technique based on solute diffusion into or out of gel beads in a well-stirred solution. The aim of the study was to make the measurements under typical conditions found in alcoholic fermentations, such as the concentrations of glucose (100 g l-1) and ethanol (50 g l-1), the simultaneous counter-diffusion of glucose and ethanol, and the presence of cells in the gel beads at a level of 10(9) cells g-1 of beads. Previously, an evaluation of the error associated with the methodology used indicated how the experimental procedure would minimize the error. The individual measurement of glucose and ethanol coefficients in 2% Ca-alginate with no cells gave values of 5.1 and 9.6 x 10(-6) cm2 s-1, respectively, which are lower than those in water. When the effect of counter-diffusion was investigated, both coefficients decreased: glucose by 14% and ethanol by 28%. When cells were incorporated into the beads, only the ethanol coefficient decreased significantly, while the glucose coefficient apparently increased its value to 6.9 10(-6) cm2 s-1.     

Diffusion of macromolecules in agarose gels: comparison of linear and globular configurations.

The diffusion coefficients (D) of different types of macromolecules (proteins, dextrans, polymer beads, and DNA) were measured by fluorescence recovery after photobleaching (FRAP) both in solution and in 2% agarose gels to compare transport properties of these macromolecules. Diffusion measurements were conducted with concentrations low enough to avoid macromolecular interactions. For gel measurements, diffusion data were fitted according to different theories: polymer chains and spherical macromolecules were analyzed separately. As chain length increases, diffusion coefficients of DNA show a clear shift from a Rouse-like behavior (DG congruent with N0-0.5) to a reptational behavior (DG congruent with N0-2.0). The pore size, a, of a 2% agarose gel cast in a 0.1 M PBS solution was estimated. Diffusion coefficients of the proteins and the polymer beads were analyzed with the Ogston model and the effective medium model permitting the estimation of an agarose gel fiber radius and hydraulic permeability of the gels. Not only did flexible macromolecules exhibit greater mobility in the gel than did comparable-size rigid spherical particles, they also proved to be a more useful probe of available space between fibers.     

Interpretation of the stokes radius of macromolecules determined by gel filtration chromatography

From a comparison of the gel chromatographic properties of large randomly-coiled polypeptides in 6 M guanidine hydrochloride and of large globular proteins, we found that the distribution coefficient was more closely correlated with the intrinsic viscosity-based Stokes radius than with the translational frictional coefficient-based Stokes radius. This means that the effect of the hydrodynamic flow of dissolved molecules during gel chromatography should be considered. The ratio of transport of solute by bulk flow as compared with that by net diffusion (i.e., Brownian motion) is large under some conditions. On the other hand, we consider that the distribution coefficient obtained in static equilibrium experiments should be determined by the translational frictional coefficient-based Stokes radius, since the solvent does not flow. On this basis, we discuss the meaning of the Stokes radius and the separation mechanism of macromolecules by gel filtration.     

Solute transport in orthorhombic lysozyme crystals: a molecular simulation study

Long-time equilibrium molecular dynamics simulations were performed to study the passage of a substrate, l-arabinose, through nanopores of orthorhombic hen egg white lysozyme crystals. Cross-linked protein crystals (CLPC), as novel biological nanoporous media, consist of an extensive regular matrix of chiral solvent-filled nanopores via which ions and solutes, e.g. sugars and amino acids, travel in and out. We studied the diffusive motion of arabinose inside protein channels. The computed diffusion coefficients within the crystal were orders of magnitudes lower relative to the diffusion coefficient of the solute in water. This study is valuable for understanding the nature of solute–protein interactions and transport phenomena in CLPCs and provides an understanding of biocatalytic and bioseparation processes using CLPC.     

Standing-gradient osmotic flow. A mechanism for coupling of water and solute transport in epithelia

At the ultrastructural level, epithelia performing solute-linked water transport possess long, narrow channels open at one end and closed at the other, which may constitute the fluid transport route (e.g., lateral intercellular spaces, basal infoldings, intracellular canaliculi, and brush-border microvilli). Active solute transport into such folded structures would establish standing osmotic gradients, causing a progressive approach to osmotic equilibrium along the channel's length. The behavior of a simple standing-gradient flow system has therefore been analyzed mathematically because of its potential physiological significance. The osmolarity of the fluid emerging from the channel's open end depends upon five parameters: channel length, radius, and water permeability, and solute transport rate and diffusion coefficient. For ranges of values of these parameters encountered experimentally in epithelia, the emergent osmolarity is found by calculation to range from isotonic to a few times isotonic; i.e., the range encountered in epithelial absorbates and secretions. The transported fluid becomes more isotonic as channel radius or solute diffusion coefficient is decreased, or as channel length or water permeability is increased. Given appropriate parameters, a standing-gradient system can yield hypertonic fluids whose osmolarities are virtually independent of transport rate over a wide range, as in distal tubule and avian salt gland. The results suggest that water-to-solute coupling in epithelia is due to the ultrastructural geometry of the transport route.     

Magnetic Resonance Imaging of Mass Transport and Structure Inside a Phototrophic Biofilm

The aim of this study was to utilize magnetic resonance imaging (MRI) to image structural heterogeneity and mass transport inside a biofilm which was too thick for photon based imaging. MRI was used to map water diffusion and image the transport of the paramagnetically tagged macromolecule, Gd-DTPA, inside a 2.5 mm thick cyanobacterial biofilm. The structural heterogeneity of the biofilm was imaged at resolutions down to 22 × 22 μm, enabling the impact of biofilm architecture on the mass transport of both water and Gd-DTPA to be investigated. Higher density areas of the biofilm correlated with areas exhibiting lower relative water diffusion coefficients and slower transport of Gd-DTPA, highlighting the impact of biofilm structure on mass transport phenomena. This approach has potential for shedding light on heterogeneous mass transport of a range of molecular mass molecules in biofilms.     

Solute Size Effects on the Diffusion in Biofilms of Streptococcus mutans

The diffusion of poly(ethylene glycol) (PEG) (MW varying between 200 and 10,000), and of three different types of micelles was examined in Streptococcus mutans biofilms using infrared spectroscopy. PEGs were used because they show limited interactions with biological materials and their weight can be selected in order to cover a wide range of size. The study showed that a considerable fraction at the base of the biofilm was not accessible to the diffusing solute molecules and this inaccessible fraction was very dependent on the size of the diffusing molecules. In parallel, it was found that the diffusion coefficients of these solutes in the biofilms were less than those in water and this reduction was less pronounced for large macromolecules, an effect proposed to be related to their limited penetration. Triton X-100, a neutral detergent, forms micelles that behave like PEG, suggesting that the behaviour observed for neutral macromolecules can be extrapolated to neutral macroassemblies. However, the diffusion, as well as the penetration of sodium dodecylsulphate micelles (a negatively charged surfactant) and cetylpyridinium chloride micelles (positively charged), in the biofilms appeared to be significantly influenced by electrostatic interactions with biofilm components. The present findings provide useful insights associated with the molecular parameters required to efficiently penetrate bacterial biofilms. The study suggests a rationale for the limited bactericidal power of some antibiotics (the large ones). The restricted accessibility of macromolecules and macroassemblies to biofilms must be examined carefully in order to offer guidelines in the development of novel antibacterial treatments.     

Use of holographic laser interferometry to study the diffusion of polymers in gels

The aim of this study was to demonstrate the potential for holographic interferometry to be used for diffusion studies of large molecules in gels. The diffusion and partitioning of BSA (67,000 g/mol) and pullulans (5,900-112,000 g/mol) in agarose gel were investigated. The gel diffusion coefficients obtained for BSA were higher when distilled water was used as a solvent compared to those obtained with 0.1 M NaCl as the solvent. Furthermore, the gel diffusion coefficient increased with increasing BSA concentration. The same trend was found for liquid BSA diffusion coefficients obtained by DLS. BSA partition coefficients obtained at different agarose gel concentrations (2-6%, w/w) decreased slightly with increasing gel concentration. However, all BSA gel diffusion coefficients measured were significantly lower than those in pure solvent and they decreased with increasing agarose concentration. The gel diffusion coefficients obtained for pullulans decreased with increasing pullulan molecular weight. The same effect from increased molecular weight was seen in the liquid diffusion coefficients measured by DLS. The pullulan partition coefficients obtained decreased with increasing molecular weight. However, pullulans with a larger Stokes' radius than BSA had partition coefficients that were higher or approximately the same as BSA. This implied that the pullulan molecules were more flexible than the BSA molecules. The results obtained for BSA in this study agreed well with other experimental studies. In addition, the magnitude of the relative standard deviation was acceptable and in the same range as for many other methods. The results thereby obtained showed that holographic interferometry is a suitable method for studying diffusion of macromolecules in gels.     

Microelectrode measurements of local mass transport rates in heterogeneous biofilms

Microelectrodes were used to measure oxygen profiles and local mass transfer coefficient profiles in biofilm clusters and interstitial voids. Both profiles were measured at the same location in the biofilm. From the oxygen profile, the effective diffusive boundary layer thickness (DBL) was determined. The local mass transfer coefficient profiles provided information about the nature of mass transport near and within the biofilm. All profiles were measured at three different average flow velocities, 0.62, 1.53, and 2.60 cm sec-1, to determine the influence of flow velocity on mass transport. Convective mass transport was active near the biofilm/liquid interface and in the upper layers of the biofilm, independent of biofilm thickness and flow velocity. The DBL varied strongly between locations for the same flow velocities. Oxygen and local mass transfer coefficient profiles collected through a 70 micrometer thick cluster revealed that a cluster of that thickness did not present any significant mass transport resistance. In a 350 micrometer thick biofilm cluster, however, the local mass transfer coefficient decreased gradually to very low values near the substratum. This was hypothetically attributed to the decreasing effective diffusivity in deeper layers of biofilms. Interstitial voids between clusters did not seem to influence the local mass transfer coefficients significantly for flow velocities of 1.53 and 2.60 cm sec-1. At a flow velocity of 0.62 cm sec-1, interstitial voids visibly decreased the local mass transfer coefficient near the bottom.