Transport limitation of chlorine disinfection of Pseudomonas aeruginosa entrapped in alginate beads

An artificial biofilm system consisting of Pseudomonas aeruginosa entrapped in alginate and agarose beads was used to demonstrate transport limitation of the rate of disinfection of entrapped bacteria by chlorine. Alginate gel beads with or without entrapped bacteria consumed chlorine. The specific rate of chlorine consumption increased with increasing cell loading in the gel beads and decreased with increasing bead radius. The value of an observable modulus comparing the rates of reaction and diffusion ranged from less than 0.1 to 8 depending on the bead radius and cell density. The observable modulus was largest for large (3-mm-diameter) beads with high cell loading (1.8 x 10(9) cfu/cm(3)) and smallest for small beads (0.5 mm diameter) with no cells added. A chlorine microelectrode was used to measure chlorine concentration profiles in agarose beads (3.0 mm diameter). Chlorine fully penetrated cell-free agarose beads rapidly; the concentration of chlorine at the bead center reached 50% of the bulk concentration within approximately 10 min after immersion in chlorine solution. When alginate and bacteria were incorporated into an agarose bead, pronounced chlorine concentration gradients persisted within the gel bead. Chlorine did gradually penetrate the bead, but at a greatly retarded rate; the time to reach 50% of the bulk concentration at the bead center was approximately 46 h. The overall rate of disinfection of entrapped bacteria was strongly dependent on cell density and bead radius. Small beads with low initial cell loading (0.5 mm diameter, 1.1 x 10(7) cfu/cm(3)) experienced rapid killing; viable cells could not be detected (<1.6 x 10(5) cfu/cm(3)) after 15 min of treatment in 2.5 mg/L chlorine. In contrast, the number of viable cells in larger beads with a higher initial cell density (3.0 mm diameter, 2.2 x 10(9) cfu/cm(3)) decreased only about 20% after 6 h of treatment in the same solution. Spatially nonuniform killing of bacteria within the beads was demonstrated by measuring the transient release of viable cells during dissolution of the beads. Bacteria were killed preferentially near the bead surface. Experimental results were consistent with transport limitation of the penetration of chlorine into the artificial biofilm arising from a reaction-diffusion interaction. The methods reported here provide tools for diagnosing the mechanism of biofilm resistance to reactive antimicrobial agents in such applications as the treatment of drinking and cooling waters. (c) 1996 John Wiley & Sons, Inc.     

Gel beads composed of collagen reconstituted in alginate

Spherical gel beads of collagen/alginate were prepared by discharging droplets of a mixture containing collagen (1.07-1.9 mg/ml) and alginate (1.2-1.5% w/v) into 1.5% w/v CaCl2 solution at 4°C. Collagen in the gel beads was reconstituted by raising the temperature to 37°C after alginate was liquefied by citrate. Scanning electron microscopy of the beads revealed the characteristic fibrous structure of collagen. To demonstrate the application of this new technique in cell culture, GH3 rat pituitary tumor cells were entrapped and grown in the gel beads. The immobilized cells proliferated to a density of 1.95 x 106 cell/ml which is about an order of magnitude higher than that grown in the alginate beads.     

Optimization of alpha-amylase immobilization in calcium alginate beads

alpha-Amylase enzyme was produced by Aspergillus sclerotiorum under SSF conditions, and immobilized in calcium alginate beads. Effects of immobilization conditions, such as alginate concentration, CaCl(2) concentration, amount of loading enzyme, bead size, and amount of beads, on enzymatic activity were investigated. Optimum alginate and CaCl(2) concentration were found to be 3% (w/v). Using a loading enzyme concentration of 140 U mL(-1), and bead (diameter 3 mm) amount of 0.5 g, maximum enzyme activity was observed. Beads prepared at optimum immobilization conditions were suitable for up to 7 repeated uses, losing only 35% of their initial activity. Among the various starches tested, the highest enzyme activity (96.2%) was determined in soluble potato starch hydrolysis for 120 min at 40 degrees C.     

Immobilization of the surfactant-degrading bacterium Pseudomonas C12B in polyacrylamide gel. II. Optimizing SDS-degrading activity and stability

Conditions were established for optimizing the surfactant (SDS)-degrading activity of Pseudomonas C12B immobilized in polyacrylamide gel beads. Optimum activity was obtained by using immobilized cells derived from stationary phase of batch cultures and incubating with SDS at 30°C at pH 6.5. Half-saturation of the degradation system was achieved at an SDS concentration of 0.23 m . Biocatalyst stability was highest for beads maintained in basal salts medium, retaining 91% of initial activity after 161 d. In Tris/HCl buffer or distilled water, the stability was much lower, although in all cases the stability of immobilized cells was higher than that of free cells under equivalent conditions. Biocatalyst beads “inactivated” by sequential incubation in three batches of distilled water containing only SDS could be reactivated by transferring beads to nutrient medium. Beads packed in a glass column and operated in a continuous up-flow mode using SDS/basal salts eluant produced 100% hydrolysis when run at retention times above 60 min. The system was highly stable in the continuous flow mode; when operated at a residence time of 55 min (initially giving 98% degradation), the extent of degradation decreased only slightly to 93% over a continuous operation period of 3 weeks.     

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited.     

Preparation of alginate-quaternary ammonium complex beads and evaluation of their antimicrobial activity

Alginate-quaternary ammonium complex beads with antimicrobial activity were prepared by the reaction of sodium alginate (SA) with 3-(trimethoxysilyl)propyl-octadecyldimethylammonium chloride (TSA) in acid solution, followed by crosslinking with CaCl(2). FTIR spectroscopy analysis showed that the resulting complex was formed mainly through covalent bonds between the hydroxyl groups of SA and the methoxysilyl groups of TSA. The complex beads exhibited a maximum swelling of 20% in water at 37 degrees C and were not hydrolyzed in water during experiments lasting for 30 days. The in vitro antimicrobial activity of the complex beads was evaluated against four species of bacteria and fungi. The test microorganisms were completely eliminated within 20 min when treated with 5% (v/v) complex beads, which showed a wide spectrum of excellent antimicrobial activity. The antimicrobial activity of the complex beads was retained after 10 cycles of washing and drying. The present results indicate that these SA-TSA complex beads are a new type of insoluble cationic polymer that can kill or remove microorganisms in water by mere contact without releasing the reactive agent.     

Isolation of human platelet plasma membranes with polylysine beads

Human platelet plasma membranes were isolated with polylysine beads according to the technique developed by Jacobson and Branton (1977, Science [Wash. D. C.] 195:302--304). Lactoperoxidase-catalyzed surface iodination revealed that ninefold greater 125I specific activity was associated with the membranes isolated on beads than with whole platelets. Enrichment in the bead membrane preparation of the activities of membrane marker enzymes, bis(p-nitrophenyl)phosphate phosphodiesterase and Na,K-ATPase, was 8.0 and 4.4, respectively. Contamination with enzymes of other organelles, cytochrome oxidase and beta-glucuronidase, was relatively low as compared with membranes isolated by sucrose gradient centrifugation. Analysis by SDS polyacrylamide gel electrophoresis showed that a full complement of surface glycoproteins was present on the membranes isolated with polylysine beads. The polylysine bead technique is a rapid, reproducible and efficient method for the preparation of relatively pure platelet plasma membranes.     

Counter-diffusion of lactose and lactic acid in kappa-carrageenan/locust bean gum gel beads with or without entrapped lactic acid bacteria.

The effective diffusion coefficient (De) and equilibrium partition factor (Kp) for lactose and lactic acid in k-carrageenan (2.75% w/w)/locust bean gum (0.25% w/w) (LBG) gel beads (1.5-2.0 mm diameter), with or without entrapped Lactobacillus casei subsp. casei (L. casei), were determined at 40 degrees C. Results were obtained from transient concentration changes in well-stirred solutions of finite volume in which the beads were suspended. Mathematical models of unsteady-state diffusion into and/or from a sphere and appropriate boundary conditions were used to calculate effective diffusion coefficients of lactose and lactic acid from the best fit of the experimental solute concentration changes. The effective diffusivities of lactose and lactic acid were 5.73 x 10(-10) and 9.96 x 10(-10) m2 s-1, respectively. Furthermore, lactic acid was found to modify gel structure since lactose diffusion characteristics (De and Kp) differed significantly from an earlier study and in the literature. In gel beads heavily colonized with L. casei, the effective diffusion coefficients of lactose and lactic acid were respectively 17% and 24% lower than for cell-free beads. Partition coefficients also confirmed the obstruction effect due to the cells, and decreased from 0.89 to 0.79, and from 0.98 to 0.87, for lactose and lactic acid, respectively. External mass transfer was estimated by an unsteady-state model in infinite volume using the Biot number. The effect of external mass transfer resistance on De results and the data reported in the literature are discussed.     

Oxygen diffusivity in gel beads containing viable cells

This article proposes a simple steady-state method for measuring the effective diffusion coefficient of oxygen (D(e)) in gel beads entrapping viable cells. We applied this method to the measurement of D(e) in Ca- and Ba-alginate gel beads entrapping Saccharomyces cerevisiae and Pseudomonas ovalis. The diffusivity of oxygen through gel beads containing viable cells was measured within an accuracy of +/-7% and found not to be influenced by cell density (0-30 g/L gel), cell type, and cell viability in gel beads. The oxygen diffusivity in the Ca-alginate gel beads was superior to that of the Ba-alginate gel beads, and the D(e) in the Ca-alginate gel beads nearly equalled the molecular diffusion coefficient in the liquid containing the gel beads. The oxygen concentration profile in a single Ca-alginate gel bead was calculated and compared to the distribution of mycelia of Aspergillus awamori grown in that gel bead. This procedure indicated that the oxygen concentration profile is useful for the estimation of the thickness of the cell layer in a gel bead. Numerical investigation revealed that high effectiveness factors, greater than 0.8, could be obtained using microgel beads with a radius of 0.25 mm.     

Stabilization of alginate beads using radiation polymerized polyacrylamide.

A technique has been described for the stabilization of calcium alginate beads using radiation polymerized acrylamide. The technique involved dropping a mixture containing the cells (20%), sodium alginate (2%), acrylamide (2.5%) and N-N'-methylene-bis-acrylamide (0.1%) through a syringe needle into cold (-75 degrees C) toluene. The frozen beads obtained were exposed to 60Co gamma-rays (0.5 KGy) and were then thawed in 0.1 M CaCl2 solution. Unlike the calcium alginate beads the conjugate beads were not found to be dissolved when incubated in 3% trisodium citrate solution. Stabilized beads containing entrapped yeast cells could be reused for over 15 batches for the inversion of sucrose without loss in activity or chemical integrity of the beads.     

An assay for the measurement of the protein content of cells immobilized in carrageenan

A reliable and reproducible method for the estimation of the protein content of fungal cells immobilized in a carrageenan gel is described. The procedure depends upon the acid lability of the polysaccharide gel at 90 degrees C and on the acetone solubility of accumulated phenolics. Freeze-dried gel beads (2-3 mm) containing entrapped cells of Penicillium urticae were ground to a fine powder and samples of powder (approximately 20 mg) were sequentially extracted with hot 1 N HCl - 0.9% NaCl and acetone. The precipitated residue contained the cell protein, which was then solubilized with 1 N NaOH at 90 degrees C and quantitated by the Folin-Lowry method. Interferences from both carrageenan and phenols were thus eliminated. The presence of carrageenan (20-25 mg) did not affect the recovery of varying amounts (0-2500 micrograms) of bovine serum albumin. The recovery of radiolabeled protein from immobilized cells was parallel to that of Folin-Lowry positive material over a range of 0-60 beads (0-60 mg powder). Cycloheximide (0-100 micrograms/mL) was shown to progressively inhibit the incorporation of L-[U-14C]leucine so that the radioactivity present in the initial HCl-NaCl extract (i.e., [14C]leucine) increased as that in the final NaOH extract (i.e., 14C-labeled protein) decreased. Using this new assay for cell protein, free and immobilized cell cultures were found to exhibit virtually identical kinetics of glucose utilization, growth, and patulin production. In addition to providing a means of comparing the specific productivity of free versus immobilized cell preparations, this assay accurately measures the incorporation of [14C]leucine into cellular protein and could be used as a measure of cell viability.     

Preparation and activity of carbonic anhydrase immobilized on porous silica beads and graphite rods

Techniques for the immobilization of bovine carbonic anhydrase (BCA) on porous silica beads and graphite are presented. Surface coverage on porous silica beads was found to be 1.5 x 10(-5) mmol BCA/m(2), and on graphite it was 1.7 x 10(-3) mmol BCA/m(2) nominal surface area. Greater than 97% (silica support) and 85% (graphite support) enzyme activity was maintained upon storage of the immobilized enzyme for 50 days in pH 8 buffer at 4 degrees C. After 500 days storage, the porous silica bead immobilized enzyme exhibited over 70% activity. Operational stability of the enzyme on silica at 23 degrees C and pH 8 was found to be 50% after 30 days. Catalytic activity expressed as an apparent second-order rate constant K'(Enz) for the hydrolysis of p-nitrophenyl acetate (p-NPA) catalyzed by BCA immobilized on silica beads and graphite at pH 8 and 25 degrees C is 2.6 x 10(2) and 5.6 x 10(2) M(-1)s(-1) respectively. The corresponding K(ENZ) value for the free enzyme is 9.1 x 10(2) M(-1)s(-1). Activity of the immobilized enzyme was found to vary with pH in such a manner that the active site pK, on the porous silica bead support is 6.75, and on graphite it is 7.41. Possible reasons for a microenvironmental influence on carbonic anhydrase pK(a), are discussed. Comparison with literature data shows that the enzyme surface coverage on silica beads reported here is superior to previously reported data on silica beads and polyacrylamide gels and is comparable to an organic matrix support. Shifts in BCA-active site pK(a) values with support material, a lack of pH dependent activity studies in the literature, and differing criteria for reporting enzyme activity complicate literature comparisons of activity; however, immobilized BCA reported here generally exhibits comparable or greater activity than previous reports for immobilized BCA.     

Diffusion of lactose in kappa-carrageenan/locust bean gum gel beads with or without entrapped growing lactic acid bacteria

Effective diffusion coefficients (De) of lactose in kappa-carrageenan (2.75% wt/wt)/locust bean gum (0.25% wt/wt) (LBG) gel beads (1.5-2.0-mm diameter)with or without entrapped lactic acid bacteria (LAB) were determined at 40 degrees C. The effects of lactose concentration, bacteria strain (Streptococcus salivarius subsp. thermophilus and Lactobacillus casei subsp. casei) and cell content at various steps of the fermentation process (after immobilization, pre-incubation of the beads and successive fermentations) were measured on De as a first step for process modelling. Results were obtained from transiend concentration changes n well-stirred lactose solutions in which the beads were suspended. A mathematical model of unsteady-state diffusion in a sphere was used, and De was obtained from the best fit of the experimental data. Diffusivity of lactose in cell-tree beads was significantly lower than in pure water mainly because of the obstruction effect of the polymer chains and the hydration region. Furthermore, effective diffusivity and equilibrium partition factor were independent of lactose concentration in the range from 12.5 to 50 g/L. No significant difference was found for De (effective diffusivity) and Kp (partition) coefficients between beads entrapping S. thermophilus (approximately 5 x 10(9) CFU/mL) and cell-free beads. On the other hand higher cell counts obtained with L. casei (close to 1.8 x 10(11) CFU/mL) increased mass transfer resistance resulting in lower effective diffusivities and Kp. Finally, the effects of the type of bacteria and their distribution in the beads on the diffusivity were also discussed.     

Cyclodextrin-linked alginate beads as supporting materials for Sphingomonas cloacae, a nonylphenol degrading bacteria

Calcium alginate beads covalently linked with alpha-cyclodextrin (alpha-CD-alginate beads) were prepared and examined for their ability to serve as a supporting matrix for bacterial degradation of nonylphenol, an endocrine disruptor. Column chromatographic experiment using alpha-CD-alginate beads with diameter of 657+/-82 microm and with degree of CD substitution of 0.16 showed a strong affinity for nonylphenol adsorption. Although addition of alpha-CD (2.7-27 mM) to the culture broth of Sphingomonas cloacae retarded nonylphenol degradation, the immobilized bacteria on the CD-alginate beads were effective for the degradation. Batch degradation tests using the immobilized bacteria on alpha-CD-alginate-beads showed 46% nonylphenol recovery after 10-day incubation at 25+/-2 degrees C, and the recovery reached to about 17% when wide and shallow incubation tubes were used to facilitate uptake of the viscous liquid of nonylphenol on the surface of the medium. Scanning electron microscopic photographs revealed that multiplicated bacteria was present both on the surface and inside the beads and the matrix of CD-alginate was stable and suitable during 10-day incubation.     

Studies on the structure of actin gels using time correlation spectroscopy of fluorescent beads.

Fluorescence correlation spectroscopy (FCS) has been used to measure the diffusion of fluorescently labeled beads in solutions of polymerized actin or buffer. The results, obtained at actin concentrations of 1 mg/ml, show that small beads (0.09 micron in diameter) diffuse nearly as rapidly in the actin gel as in buffer, whereas the largest beads tested (0.5 micron in diameter) are immobilized. Measured autocorrelation times for motions of beads with intermediate sizes show that the diffusion is retarded (relative to buffer) and that the time behavior cannot be represented as a single diffusive process. In addition to the retarded diffusion observed over distances > 1 micron, 0.23-micron beads also show a faster motion over smaller distances. Based on the measured rate of this faster motion, we estimate that the beads may be constrained within a cage approximately 0.67 micron on a side, equal to a filament length of approximately 250 subunits. Fluorescence correlation spectroscopy measurements made in the same small spot (radius of 1.4 microns) of the gel vary over time. From the variations of both the autocorrelation functions and the mean fluorescence, we conclude that, corresponding to a spatial scale of 1.4 microns, the actin gel is a dynamic structure with slow rearrangement of the gel occurring over periods of 20-50 s at 21-22 degrees C. This rearrangement may result from local reorganization of the actin matrix. Data for the retardation of beads by the actin gel are consistent with a detailed theory of the diffusion of particles through solutions of rigid rods that have longitudinal diffusion coefficients much less than that of the particles (Ogston, A. G., B. N. Preston, and J. D. Wells. 1973. Proc. R. Soc. Lond. A. 333:297-316).     

Hydrogen production by Rhodopseudomonas capsulata cells entrapped in carrageenan beads

Summary The photosynthetic bacteria Rhodopseudomonas capsulata strain B10 were immobilized in agar or in carrageenan beads (Ø = 1–3 mm). Beads containing 5.8 mg cell dry weight/mL of gel produced hydrogen from lactate at a rate of 54 mL/h.g dry weight; the efficiency of H₂ production by immobilized cells was comparable to that of free cells and was 60 to 65% that of the theoretical maximum from lactate. Carrageenan-entrapped cells produced H₂ steadily over a 16-day period.     

Low-temperature electron microscopy for the study of polysaccharide ultrastructures in hydrogels. II. Effect of temperature on the structure of Ca2+-alginate beads

Calcium alginate beads were thermally treated at temperatures ranging from 25 degrees C to 130 degrees C for periods of up to 30 minutes. Important modifications to the structure of the alginate beads were shown to be a function of the temperature and period of incubation at each temperature. Modifications to the alginate beads included reduction in size, mechanical resistance, and molecular weight cut-off with increasing temperature and incubation period. Thus, heating 700 microm calcium alginate beads for 20 min at 130 degrees C resulted in a 23% reduction in diameter, 70% increase in mechanical resistance, and 67% reduction in molecular weight cut-off.Incubation of calcium alginate beads containing 2 x 10(6) kDa blue dextran for 20 min at 130 degrees C resulted in no detectable loss of either dye or alginate. This indicates the shrinkage of the beads was due to re-arrangement of the alginate chains within the beads, coupled with loss of water. This hypothesis was verified by direct visual observation of calcium alginate beads before and after thermal treatment using cryo-scanning electron microscopy (cryo-SEM). Unlike other microscopy methods cryo-SEM offers the advantage of extremely rapid freezing which preserves the original structure of the alginate network. As a result cryo-SEM is a powerful tool for studies of hydrogel and capsule structure and formation.Differential scanning calorimetry (DSC) showed that the water entrapped in 2% alginate beads was present in a single state, irrespective of the thermal treatment. This result is attributed to the low alginate concentration used to form the beads.     

Parameters affecting attachment ofBacillus thuringiensis var.israelensis toxin to latex beads

Summary Bacillus thuringiensis var.israelensis protein toxin radiolabeled with¹⁴C-iodoacetamide was bound to latex beads. The efficiency of attachment was not affected by the temperature or length of incubation or by the presence of several different buffers, salts, or organic solvents. However, attachment decreased dramatically at pH values >8.5 or in the presence of detergents (anionic, neutral, or cationic). Protein concentrations 2–3 mg/m² of bead surface led to a progressively decreasing efficiency of protein adsorption. With minor variations, these findings should also be applicable to the attachment of numerous other proteins of diagnostic significance.Abbreviations BSA bovine serum albumin - Bti Bacillus thuringiensis var.israelensis - EDTA ethylenediaminetetraacetic acid - HEPES N-2-hydroxyethyl-piperazine-N-2-ethanesulfonic acid - LAT latex agglutination test - PAGE polyacrylamide gel electrophoresis - SDS sodium dodecylsulfate - TCA trichloroacetic acid - Tris Tris(hydroxymethyl)aminomethane - TTAB tetradecyltrimethylammonium bromide     

Freeze-thaw immobilization of liposomes in chromatographic gel beads: evaluation by confocal microscopy and effects of freezing rate

Biological membranes immobilized in chromatographic gel beads constitute a multifunctional affinity matrix. Membrane protein-solute interactions and drug partitioning into the lipid bilayers can conveniently be studied. By the use of confocal laser-scanning microscopy (CLSM) the distribution of immobilized model membranes in the beads has been visualized for the first time. Freeze-thaw-immobilized liposomes in Superdex 200 gel beads were situated in a thick shell surrounding a liposome-free core. The amount of phospholipids immobilized by freeze-thawing was dependent on the temperature in the cooling bath and the type of test tube used. A bath temperature of -25 degrees C gave higher immobilization yield than freezing at -75 or -8 degrees C did. Freeze-thawing in the presence of liposomes did not affect the gel bead shape or the refractive index homogeneity of the agarose network of the beads, as shown by confocal microscopy.     

Fibronectin-mediated binding and phagocytosis of polystyrene latex beads by baby hamster kidney cells

The binding and phagocytosis of fibronectin (pFN)-coated latex beads by baby hamster kidney (BHK) cells was studied as a function of fibronectin concentration and bead diameter. Cells were incubated with radioactive pFN-coated beads, and total bead binding (cell surface or ingested) was measured as total radioactivity associated with the cells. Of the bound beads, those that also were phagocytosed were distinguished by their insensitivity to release from the cells by trypsin treatment. In continuous incubations, binding of pFN-coated beads to cells occurred at 4 degrees C or 37 degrees C, but phagocytosis was observed only at 37 degrees C. In addition, degradation of 3H-pFN from ingested beads occurred at 37 degrees C, as shown by the release of trichloroacetic acid-soluble radioactivity into the incubation medium. When the fibronectin density on the beads was varied, binding at 4 degrees C and ingestion at 37 degrees C were found to have the same dose-response dependencies, which indicated that pFN densities that permitted bead binding were sufficient for phagocytosis to occur. The fibronectin density for maximal binding of ingestion was approximately 250 ng pFN/cm2. When various sized beads (0.085-1.091 micron), coated with similar densities of pFN, were incubated with cells at 4 degrees C, no variation in binding as a function of bead size was observed. Under these conditions, the absolute amount of pFN ranged from less than 100 molecules on the 0.085-micron beads to greater than 15,000 molecules on the 1.091-micron beads. Based upon these results it can be concluded that the critical parameter controlling fibronectin-mediated binding of latex beads by BHK cells is the spacing of the pFN molecules on the beads. Correspondingly, it can be suggested that the spacing between pFN receptors on the cell surface that is optimal for multivalent interactions to occur is approximately 18 nM. When phagocytosis of various sized beads was compared, it was found that the largest beads were phagocytosed slightly better (two fold) than the smallest beads. This occurred both in continuous incubations of cells with beads and when the beads were prebound to the cells. Finally, the kinetic constants for the binding of 0.085 microM pFN-coated beads to the cells were analyzed. There appeared to be approximately 62,000 binding sites and the KD was 4.03 X 10(-9) M. Assuming a bivalent interaction, it was calculated that BHK cells have approximately 120,000 pFN receptors/cell and the binding affinity between pFN and its receptor is approximately 6 X 10(-5) M.