A method to evaluate the isothermal effectiveness factor for dynamic oxygen into mycelial pellets in submerged cultures

Several models have been developed simulating O2 transfer in bioreactors, but three limitations are often found: (i) an inadequate kinetic representation of O2 consumption or wrong boundary conditions, (ii) unrealistic parameter values, and (iii) inadequate experimental systems. In our study we minimized those possible sources of error. Oxygen uptake rate, void fraction of the pellet, and external O2 mass transfer coefficient were experimentally obtained from bioreactor studies in which pellets of Gibberella fujikuroi were naturally formed. Michaelis-Menten kinetics and diffusion equations were used to describe the O2 consumption rate and to evaluate the effectiveness factor in dynamic mode. The nonlinear mathematical model proposed was solved by the orthogonal collocation technique. The O2 consumption rate in pellets of G. fujikuroi of 1.7-2.0 mm is only marginally inhibited by diffusion constraints under conditions tested. Simulation analysis showed that the effectiveness factor decreased as the Thiele modulus and pellet diameter increased. The proposed model was applied to experimental data reported for other fungal pellets and allowed to predict optimal conditions for O2 transfer into mycelial pellets.     

Development and experimental evaluation of a steady-state, multispecies biofilm model

A steady-state model for quantifying the space competition in multispecies biofilms is developed. The model includes multiple active species, inert biomass, substrate utilization and diffusion within the biofilm, external mass transport, and detachment phenomena. It predicts the steady-state values of biofilm thickness, species distribution, and substrate fluxes. An experimental evaluation is carried out in completely mixed biofilm reactors in which slow-growing nitrifying bacteria compete with acetate-utilizing heterotrophs. The experimental results show that the model successfully describes the space competition. In particular, increasing acetate concentrations causes NH(4) (+)-N fluxes to decrease, because nitrifiers are forced deeper into the biofilm, where they experience greater mass-transport resistance.     

Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study

A two-dimensional model for quantitative evaluation of the effect of convective and diffusive substrate transport on biofilm heterogeneity was developed. The model includes flow computation around the irregular biofilm surface, substrate mass transfer by convection and diffusion, biomass growth, and biomass spreading. It was found that in the absence of detachment, biofilm heterogeneity is mainly determined by internal mass transfer rate of substrates and by the initial percentage of carrier-surface colonization. Model predictions show that biofilm structures with highly irregular surface develop in the mass transfer-limited regime. As the nutrient availability increases, there is a gradual shift toward compact and smooth biofilms. A smaller fraction of colonized carrier surface leads to a patchy biofilm. Biofilm surface irregularity and deep vertical channels are, in this case, caused by the inability of the colonies to spread over the whole substratum surface. The maximum substrate flux to the biofilm was greatly influenced by both internal and external mass transfer rates, but not affected by the inoculation density. In general, results of the present model were similar to those obtained by a simple diffusion-reaction-growth model.     

A theoretical study on the effect of surface roughness on mass transport and transformation in biofilms

This modeling study evaluates the influence of biofilm geometrical characteristics on substrate mass transfer and conversion rates. A spatially two-dimensional model was used to compute laminar fluid flow, substrate mass transport, and conversion in irregularly shaped biofilms. The flow velocity above the biofilm surface was varied over 3 orders of magnitude. Numerical results show that increased biofilm roughness does not necessarily lead to an enhancement of either conversion rates or external mass transfer. The average mass transfer coefficient and Sherwood numbers were found to decrease almost linearly with biofilm area enlargement in the flow regime tested. The influence of flow, biofilm geometry and biofilm activity on external mass transfer could be quantified by Sh-Re correlations. The effect of biofilm surface roughness was incorporated in this correlation via area enlargement. Conversion rates could be best correlated to biofilm compactness. The more compact the biofilm, the higher the global conversion rate of substrate. Although an increase of bulk fluid velocity showed a large effect on mass transfer coefficients, the global substrate conversion rate per carrier area was less affected. If only diffusion occurs in pores and channels, then rough biofilms behave as if they were compact but having less biomass activity. In spite of the fact that the real biofilm area is increased due to roughness, the effective mass transfer area is actually decreased because only biofilm peaks receive substrate. This can be explained by the fact that in the absence of normal convection in the biofilm valleys, the substrate gradients are still largely perpendicular to the carrier. Even in the cases where convective transport dominates the external mass transfer process, roughness could lead to decreased conversion rates. The results of this study clearly indicate that only evaluation of overall conversion rates or mass fluxes can describe the correct biofilm conversion, whereas interpretation of local concentration or flow measurements as such might easily lead to erroneous conclusions.     

Investigations of oxygen transfer into Penicillium chrysogenum pellets by microprobe measurements

A microcoaxial needle sensor with a tip diameter of ca. 0.7 mum was used as a microprobe to measure profiles of dissolved oxygen tension (DOT) within fixed pellets of Penicillium chrysogenum as a function of the DOT level around the pellet, in the presence and absence of bulk convective flow and turbulence. The investigations indicate that the oxygen transfer mechanism is complex. The results were interpreted by assuming the penetration convective flow into the entire pellet and penetration of turbulence into the outer range. A model was developed which was able to describe the measured DOT profiles very well. The model takes into account molecular and turbulent diffusion as well as convective flow as transfer mechanisms inside of the pellet. Structures of pellets used for microprobe measurements were evaluated by histological investigations. Considerable variations of mycelial density with radius within the pellets were found.     

Strategies for penicillin fermentation in tower-loop reactors

Since it has not been possible to produce penicillin in tower-loop reactors with highly viscous filamentous molds of Penicillium chrysogenum which are employed in stirred-tank reactors, a new strategy has been developed to avoid the formation of this morphology and to use the pellet form of the fungi. When employing definite impeller speeds in the subculture in connection with definite inoculum amounts and substrate concentrations in the main culture (bubble column), it is possible to generate a suspension of isolated small pellets, which shows a low broth viscosity up to a sediment content of 45% over the entire fermentation time. Volumetric mass-transfer coefficients k(L)as are by a factor of 4 to 5 higher in these pellet suspensions than in filamentous broths. It was easy to maintain the necessary oxygen supply for penicillin production in these pellet suspensions. Under these conditions the specific penicillin productivities were higher with regard to power input (up to 90%), biomass, and consumed substrate than in the stirred-tank reactors with highly viscous filamentous morphology of the fungi. Under nonoptimized operating conditions the absolute penicillin production in the tower loop was 35% lower than in the stirred-tank reactor due to lower possible biomass concentrations. The separation of the biomass, and therefore the penicillin recovery, is much simpler when employing pellets. It is shown how the particular mass transfer resistances at the gas/liquid and liquid/pellet interfaces and within the pellets change with the pellet diameter. There should be a particular pellet diameter at which penicillin productivity has its maximum. These investigations indicate that the use of tower-loop reactors can, in the future, be an alternative for more economical penicillin production methods.     

A multispecies biofilm model

Using a continuum approach and observing conservation principles, an analytical mathematical model of microbial interaction in biofilms was developed. The model predicts changes in biofilm thickness and describes the dynamics and spatial distribution of microbial species and substrates in the film. It allows for biomass detachment due to shear stress and sloughing, external mass transfer limitations, as well as variations in substrate concentrations in the bulk liquid. A computer implementation of the model is provided using an example of heterotrophicautotrophic competition to illustrate how the observed phenomena can be numerically reproduced and indicating how they might affect overall biofilm performance.     

A semimechanistic mathematical model for growth of Rhizopus oligosporus in a model solid-state fermentation system

A Semimechanistic mathematical model is developed which describes the growth of Rhizopus oligosporus in a model solid-state fermentation system. Equations are presented for the release of glucoamylase, the diffusion of glucoamylase, the hydrolysis of starch, the generation and diffusion of glucose, and the uptake of glucose and conversion into new biomass. Good agreement of the model with the experimental data was obtained only after the glucoamylase diffusivity and the maximum specific glucose uptake rate were altered from their originally determined values. The model recognizes the distributed nature of the solid-state fermentation and therefore is able to predict the concentration profiles of the system components within the substrate. The model provides an insight into the possible rate-limiting steps in solid-state fermentation-the generation of glucose within the substrate and the resulting availability of glucose at the surface.     

A new method to solve a non-steady-state multispecies biofilm model

A transient multispecies model for quantifying microbial space competition in biofilm is derived from existing models, introducing a new approach to biomass detachment modelling. This model includes inert biomass, substrate diffusion and utilization rate within the biofilm and diffusional layers. It predicts the evolution of biofilm thickness, bulk substrate concentration, species distribution and substrate concentration within the biofilm. A zero-dimensional transient model is described. Its steady-state solution is used to set up initial conditions of the one-dimensional model and case computation towards steady-state solution. Some numerical tools have been developed, enabling fast computation on microcomputers. Simulations show the validity of a zero-dimensional model and perturbated systems are also simulated. Simulations with experimental data give acceptable results.     

Perfusion cultures and modelling of oxygen uptake with three-dimensional chondrocyte pellets

Chondrocyte pellets were cultivated in a perfused flow chamber and supplied with medium by a constant flow rate from a conditioning vessel. In this conditioning vessel the medium was aerated and used medium was exchanged semi-continuously. The higher amount of DNA and glycosaminoglycane (GAG) in these pellets compared to control cultures under stationary conditions showed a positive effect of the reactor system, compared to standard culture conditions. A diffusion reaction model was applied to calculate the oxygen uptake of the cell pellet and to describe the oxygen profile within the pellet. The model included diffusion within the cell pellet and oxygen uptake of the cells. Calculated data were compared to experimental data obtained by tissue engineered chondrocyte cell pellets. Model calculations agreed rather well with experimental data.     

Optimization of fumaric acid production by Rhizopus delemar based on the morphology formation

The effects of temperature, agitation rate and medium composition, including concentrations of glucose, soybean peptone, and inorganic ions, on pellet formation and pellet diameter of Rhizopus delemar (Rhizopus oryzae) NRRL1526 during pre-culture were studied. Inorganic ions and soybean peptone had negative and positive effects on pellet formation, respectively. The initial glucose and soybean peptone concentrations directly affected pellet diameter. Within a certain range, pellet diameter decreased with increased initial substrate concentrations; however, above this range there was an opposite trend. Thus, optimal concentrations of substrate during pre-culture were beneficial for producing small pellets of R. delemar. Furthermore, dry cell mass and yield of fumaric acid tended to increase with decreased pellet diameter. Based on the pellet morphology optimization, the final fumaric acid concentration was improved by 46.13% when fermented in a flask and 31.82% in stirred bioreactor tank fermentation.     

Simulation of growth of a filamentous fungus in 3 dimensions

The tridimensional growth of a filamentous fungus was simulated, based on a model for the evolution of the microscopic morphology of Trichoderma reesei. When supplemented with a spatial representation of growth, the model correctly simulates the evolution from a single spore to a pellet. Diffusion of oxygen is included in the model. The simulated tridimensional structures have a fractal nature; and the fractal dimension, determined by a box-counting method, increases during growth. The fractal dimension only depends on the mass of the pellet and is not affected by model parameters such as tip extension rate and branching frequency. Realistic pictures are obtained and the radius of the pellet increases at a constant rate. The influence of model parameters (tip extension rate, branching frequency, minimum porosity) on dissolved oxygen concentration profiles, biomass concentration profiles, rate at which the pellet diameter increases, and the evolution of the fractal dimension was determined. The dissolved oxygen profiles were found to be very different from the profiles, obtained by assuming a homogenous biomass distribution within the pellet. Finally, the formation of pellets from spore aggregates is calculated and the size of the spore aggregate is found to only influence the time needed before the appearance of a pellet and not its morphology. (c) 1997 John Wiley & Sons, Inc.     

Abrasion of suspended biofilm pellets in airlift reactors: importance of shape, structure, and particle concentrations

The detachment of biomass from suspended biofilm pellets in three-phase internal loop airlift reactors was investigated under nongrowth conditions and in the presence of bare carrier particles. In different sets of experiments, the concentrations of biofilm pellets and bare carrier particles were varied independently. Gas hold-up, bubble size, and general flow pattern were strongly influenced by changes in volume fractions of biofilm pellets and bare carrier particles. In spite of this, the rate of biomass detachment was found to be linear with both the concentration of biofilm pellets and the bare carrier concentration up to a solids hold-up of 30%. This implies that the detachment rate was dominated by collisions between biofilm pellets and bare carrier particles. These collisions caused an on-going abrasion of the biofilm pellets, leading to a reduction in pellet volume. Breakage of the biofilm pellets was negligible. The biofilm pellets were essentially ellipsoidal, which made three-dimensional size determination necessary. Calculating particle volumes from two-dimensional image analysis measurements and assuming a spherical shape led to serious errors. The abrasion rate was not equal on all sides of the biofilm pellets, resulting in an increasing flattening of the pellets. This flattening was oriented with the basalt carrier inside the biofilm and independent of the absolute abrasion rate. These observations suggest that the collisions causing abrasion are somehow oriented. The internal structure of the biofilms showed two layers, a cell-dense outer layer and an interior with a low biomass density. Taking this density gradient into account, the washout of detached biomass matched observed changes in volume of the biofilm pellets. No gradient in biofilm strength with biofilm depth was indicated. (c) 1997 John Wiley & Sons, Inc.     

Effects of dissolved oxygen tension and mechanical forces on fungal morphology in submerged fermentation

The effects of dissolved oxygen tension and mechanical forces on fungal morphology were both studied in the submerged fermentation of Aspergillus awamori. Pellet size, the hairy length of pellets, and the free filamentous mycelial fraction in the total biomass were found to be a function of the mechanical force intensity and to be independent of the dissolved oxygen tension provided that the dissolved oxygen tension was neither too low (5%) nor too high (330%). When the dissolved oxygen concentration was close to the saturation concentration corresponding to pure oxygen gas, A. awamori formed denser pellets and the free filamentous mycelial fraction was almost zero for a power input of about 1 W/kg. In the case of very low dissolved oxygen tension, the pellets were rather weak and fluffy so that they showed a very different appearance. The amount of biomass per pellet surface area appeared to be affected only by the dissolved oxygen tension and was proportional to the average dissolved oxygen tension to the power of 0.33. From this it was concluded that molecular diffusion was the dominant mechanism for oxygen transfer in the pellets and that convection and turbulent flow in the pellets were negligible in submerged fermentations. The biomass per wet pellet volume increased with the dissolved oxygen tension and decreased with the size of the pellets. This means that the smaller pellets formed under a higher dissolved oxygen tension had a higher intrinsic strength. Correspondingly, the porosity of the pellets was a function of the dissolved oxygen tension and the size of pellets. Within the studied range, the void fraction in the pellets was high and always much more than 50%.     

Kinetic studies of alpha-galactosidase-containing mold pellets on PNPG hydrolysis.

Little is known about techniques for applying untreated microbial cells containing enzymes directly to industrial processes as a biocatalyst. The kinetic behavior of alpha-galactosidase-containing spherical pellets which are formed naturally under given conditions in a submerged culture of Mortierella vinacea was studied on the hydrolysis of PNPG (p-nitrophenyl-alpha-D-galactopyranoside). The effect on intraparticle diffusion on the overall reaction rate was assessed by the use of an effectiveness factor, which was calculated by the approximate solution to the equation derived from the mass balance within a pellet. The experimental effectiveness factors were found to be represented as a single function of the modified Thiele modulus, including such parameters as pellet size, enzyme concentration in the pellet, and substrate concentration. As the diffusional effect became more significant, the marked substrate inhibition as seen for a free enzyme disappeared gradually. The effect of product inhibition on the pellets was much weaker than that for a free enzyme at a given substrate concentration. In the region of diffusion controlled reaction, it was found that the rate is proportional to the square root of the enzyme concentration in the pellet. In addition, similarly to what was reported previously for a free enzyme,the reaction in a batch system was found to be approximately representable as simple first-order kinetics in which the rate constant was dependent on the initial substrate concentration.     

Polyaniline nanofiber coated monolith reactor for enzymatic bioconversion

The monolith reactor has many advantages over other reactors including good mass transfer, low-pressure drop and high enzyme stability. In this study, an enzyme-coated monolith with high enzyme stability and activity was developed. The monolith surface was coated with polyaniline nanofibers containing glucose oxidase immobilized on its surface. The developed enzyme-coated monolith was used for the bioconversion of glucose to glucolactone at different residence times. The conversion ratio increased up to 83% at increasing residence time. In addition, the polyaniline-coated monolith showed excellent enzyme activity and long-term stability. The stability of the enzyme-coated monolith containing the polyaniline nanofibers showed almost 100% residual activities after 8 days operation, while rapid enzyme deactivation and detachment was observed when the enzymes were immobilized without the polyaniline nanofibers.     

Modeling and measurements of fungal growth and morphology in submerged fermentations

Generalizing results from fungal fermentations is difficult due to their high sensitivity toward slight variation in starting conditions, poor reproducibility, and difference in strains. In this study a mathematical model is presented in which oxygen transfer, agitation intensity, dissolved oxygen tension, pellet size, formation of mycelia, the fraction of mycelia in the total biomass, carbohydrate source consumption, and biomass growth are taken into account. Two parameters were estimated from simulation, whereas all others are based on measurements or were taken from literature. Experimental data are obtained from the fermentations in both 2 L and 100 L fermentors at various conditions. Comparison of the simulation with experiments shows that the model can fairly well describe the time course of fungal growth (such as biomass and carbohydrate source concentrations) and fungal morphology (such as pellet size and the fraction of pellets in the total biomass). The model predicts that a stronger agitation intensity leads to a smaller pellet size and a lower fraction of pellets in the total biomass. At the same agitation intensity, pellet size is hardly affected by the dissolved oxygen tension, whereas the fraction of mycelia decreases slightly with an increase of the dissolved oxygen tension in the bulk. All of these are in line with observations at the corresponding conditions.