The effective diffusive permeability of a nonreacting solute in microbial cell aggregates.

Aggregates of Escherichia coli confined within hollowfiber reactors were either formed in place by culturing cells within the reactors, or were prepared by injecting a cell suspension that had been concentrated by centrifugation. The effective diffusive permeability of an uncharged nonreacting tracer, nitrous oxide, within the cell aggregates was calculated from measurements of the tracer flux through the aggregates. Estimates of the hydraulic permeability were also obtained for the aggregates that were grown in place. The effective diffusive permeability was found to decrease with increasing cell volume fraction to a value, for aggregates comprising 95% cells, of ca. 30% that obtained for cell-free buffer solution. The dependence on the cell volume fraction was described adequately by the well-known HashinShtrikman bounds for a two-phase medium. The transport properties of aggregates cultivated in place were not significantly different from those of aggregates prepared by centrifugation. Furthermore, the effective diffusive permeabilities of the tracer in aggregates prepared from cells treated with detergent or disrupted by dehydration and grinding differed only slightly from the values obtained for aggregates formed from untreated cells. The results suggest that the method of formation of the cell aggregate and the details of the structure of the cells have little influence on the effective diffusive permeability. These findings should be applicable to the transport of other small uncharged solutes, such as oxygen, that can diffuse through cells. The hydraulic permeability estimates for the aggregates cultured in place were several orders of magnitude larger than the values predicted by a theory formulated with the assumption that the cells are impervious to flow and homogeneously distributed within the aggregates. Two possible reasons for this discrepancy are, first, that there is some flow through the cells themselves, and second, that the cells may form discrete clusters separated by relatively open regions.