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.     

Morphology and physiology of an alpha-amylase producing strain of Aspergillus oryzae during batch cultivations

The microscopic morphology, that is, total hyphal length and total number of tips, has been characterized during batch cultivations of Aspergillus oryzae. The specific growth rate estimated by measuring the total hyphal length (mu(h)) corresponds well with the specific growth rate estimated from dry weight measurements during cultures grown as free hyphal elements. The average tip extension rate can be described with a saturation type kinetics with respect to the average total hyphal length, and the branching frequency is closely related to the total hyphal length. For the applied strain of A. oryzae, pellet formation occurs by coagulation of spores. The agglomeration process is pH dependent and pellets are formed at pH values higher than 5, whereas low pH (<3.5) results in growth as freely dispersed hyphal elements. The maximum specific growth rate has a broad pH optimum between 3 and 7, whereas the alpha-amylase production has a sharper maximum at about pH 6. During batch cultivation with pellets the growth is described well by the cube-root law when pellet fragmentation can be neglected. The kinetic parameter k in the cube-root law is derived from the growth kinetics with no mass transfer limitation, k = mu(h)/3. Based on an oxygen balance, the active growth layer in the pellet is estimated to be 200 to 325 mum and, consequently, up to 50% of the biomass is limited by oxygen for large pellets. Ethanol production (up to 1 g L(-1)) was observed during batch cultivations with pellets, suggesting that ethanol is produced in the oxygen limited part of the biomass. A constitutive, low alpha-amylase production was observed at high glucose concentration. The specific alpha-amylase production was significantly higher for filamentous growth than for pellets and oxygen appears to be necessary for production of alpha-amylase. (c) 1996 John Wiley & Sons, Inc.     

A stochastic model of neuronal growth cone guidance regulated by multiple sensors

Neuronal growth cones migrate directionally under the control of axon guidance molecules, thereby forming synapses in the developing brain. The signal transduction system by which a growth cone detects surrounding guidance molecules, analyzes the detected signals, and then determines the overall behavior remains undetermined. In this study, we describe a novel stochastic model of this behavior that utilizes multiple sensors on filopodia to respond to guidance molecules. Overall growth cone behavior is determined by using only the concentration gradients of guidance molecules in the immediate vicinity of each sensor. The detected signal at each sensor, which is treated as a vector quantity, is sent to the growth cone center and then integrated to determine axonal growth in the next step by means of a simple vector operation. We compared the results of computer simulations of axonal growth with observations of actual axonal growth from co-culture experiments using olfactory bulb and septum. The probabilistic distributions of axonal growth generated by the computer simulation were consistent with those obtained from the culture experiments, indicating that our model accurately simulates growth cone behavior. We believe that this model will be useful for elucidating the as yet unknown mechanisms responsible for axonal growth in vivo.     

Adding talc microparticles to Aspergillus terreus ATCC 20542 preculture decreases fungal pellet size and improves lovastatin production

Changing fungal morphology with the use of morphological engineering techniques leads to improving the production of metabolites by filamentous fungi in the submerged culture. Adding mineral microparticles is one such simple method to change fungal pellet size. Here, it was studied for a lovastatin producer, Aspergillus terreus ATCC 20542. The experiments were conducted in shake flasks and 10 μm talc microparticles were added to the preculture. Intrapellet oxygen concentration profiles were determined by an oxygen microprobe. Talc microparticles caused a decrease of A. terreus pellets diameter from about 2000 to 900 μm, dependent on their concentration in the preculture. Smaller pellets produced more lovastatin, whose titre exceeded then 120 mg L^?1, utilising more lactose. The decrease in pellet size resulted in changes of oxygen concentration profiles in the pellets. The estimated critical pellet diameter, at which the non‐oxygenated zone was observed in the centre of the pellets, was 1700 μm. Smaller pellets were fully penetrated by oxygen. To conclude, facilitated diffusion of oxygen into the pellets of smaller diameter and their less dense structure made lactose utilisation by A. terreus more efficient, which ultimately increased lovastatin production in the runs with talc microparticles added, compared to the control runs.     

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%.     

Effective diffusivity of oxygen in microbial pellets

In a typical submerged aerobic fermentation with microbial pellets, the effective diffusivity of oxygen in the pellets is probably the most important, yet most difficult transport property to characterize experimentally. Its values directly indicate the efficiency or deficiency of oxygen to individual cells, and thus the biological activity of the microorganisms. In the past, it was not possible to assess reliably the effective diffusivity of oxygen in pellets due to several reasons. Firstly, most oxygen electrodes available were coarse, and hence not suitable for in situ measurements. Secondly, there was a lack of methods rigorous enough to characterize the structure of the microbial pellets. A state-of-the-art review of the literature relating to the feature subject is presented. Emphasis is laid upon development and evolution of the means for quantitative characterization of the effective diffusivity of oxygen in microbial pellets.     

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.     

Nikkomycin production in pellets of Streptomyces tendae.

In previous submerged fermentation experiments mycelial suspensions of Streptomyces tendae were viscous and availability of oxygen limited the yield of nikkomycins (Nk), a complex of secondary metabolites which includes nucleoside-peptides with antibiotic activity. Increasing agitation improved oxygen transfer but consumed considerable power and shear-damaged cells. In this paper, cellular aggregates (pellets) were used to reduce viscosity and protect cells from shear. Under the conditions tested, specific productivity of S. tendae pellets increased with increasing size up to 1.4 mm diameter and then decreased. The maximal specific productivity of S. tendae pellets (44 mg Nk/g dry weight/h) occurred at a very low cell concentration. Pellet formation or high biomass concentration was required for the production of bioactive dipeptide and tripeptide Nks. It is speculated that accumulation of intermediates in large pellets activates the production of mature secondary metabolites.     

Nikkomycin production in pellets of Streptomyces tendae

S.E. VECHT-LIFSHITZ, Y. SASSON AND S. BRAUN. 1992. In previous submerged fermentation experiments mycelial suspensions of Streptomyces tendae were viscous and availability of oxygen limited the yield of nikkomycins (Nk), a complex of secondary metabolites which includes nucleoside-peptides with antibiotic activity. Increasing agitation improved oxygen transfer but consumed considerable power and shear-damaged cells. In this paper, cellular aggregates (pellets) were used to reduce viscosity and protect cells from shear. Under the conditions tested, specific productivity of S. tendae pellets increased with increasing size up to 1.4 mm diameter and then decreased. The maximal specific productivity of S. tendae pellets (44 mg Nk/g dry weight/h) occurred at a very low cell concentration. Pellet formation or high biomass concentration was required for the production of bioactive dipeptide and tripeptide Nks. It is speculated that accumulation of intermediates in large pellets activates the production of mature secondary metabolites.     

Modelling of hexadecane degradation in continuous-flow cultures

Microorganisms of Wadden Sea sediments are able to degrade hydrocarbons in suspensions. (Berthe-Corti, L., Bruns, A., Hulsch, R., 1997. J. Microb. Methods 29, 129-137) have observed in continuous culture experiments that the growth rate of microorganisms increases roughly proportional to the dilution rate. The growth rate is nearly independent of the oxygen saturation down to about 0.5%. Even at very low oxygen supply, corresponding to an oxygen saturation far below 0.1%, growth takes place at a reduced rate. In this paper, a model is presented which can reproduce the results of these experiments. The model treats the following processes, selection of the active fraction of microorganisms growing on hexadecane, uptake of hexadecane and transformation into palmitate as a first metabolic step, synthesis of biomass, respiration and exudation. The processes are regulated by the substrate concentration, the internal palmitate quota, the exudates' concentration and an inhibiting factor. For the experiments under very low oxygen conditions, the observed growth with reduced O(2)-consumption and CO(2)-production is modelled by assuming an anoxic metabolic pathway.     

灵芝胞外多糖分批发酵非结构动力学模型

在２Ｌ搅拌发酵罐上提出了描述了灵芝胞外多糖分批发酵过程中菌球生长、底物消耗和胞外多糖形成的非结构动力学模型。首先研究了灵芝分批发酵特性,结果表明该发酵过程属菌体生长和产物形成相偶联型。然后在总结文献的基础上,运用动力学模型,经过非线性回归,得到了模型中的参数值。通过计算机模拟,证明模型预测值与实际实验值具有良好的拟合性。     

Continuous production of a hybrid antibiotic by Streptomyces lividans TK21 pellets in a three-phase fluidized-bed bioreactor

The continuous production of a hybrid antibiotic by a transformed strain of Streptomyces lividans TK21 in a three-phase fluidized bed is studied. Cell aggregates, known as pellets, are used as immobilized cell particles in the bioreactor. A methodology to prepare pellets of a suitable size and morphology is developed. The continuous production of the antibiotic is studied on the basis of decoupling cell growth and antibiotic production, by means of phosphate limitation in the growth medium. The best results are achieved at D = 0.021 h(1), with alternate feeding of 0 and 0.05 m M phosphate media. Continuous production of the antibiotic can be maintained at satisfactory levels for periods of 60 days, and stable operation of the bioreactor is achieved during 85 days. Finally, the evolution of the internal structure of the pellets during continuous fermentation is studied. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 601-610, 1997.     

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.     

Dynamics of oxygen transport in erythrocytes

Distribution dynamics of oxygen tension throughout the erythrocyte volume was calculated by means of a mathematical model describing the dynamics of oxygen transport in the erythrocyte, its shape, diffusion resistance of hemoglobin solution. The pattern of the dissociation curve of oxyhemoglobin being taken into account. The model is presented as a system of differential equations in partial derivatives. Its solution was performed on an electron computer by a net method. Sharp jumps of pO2 inside the erythrocyte at its fast movements in the media with different partial pressure of O2 were shown. A quantitative relationship was found between the rate of physico-chemical reactions of oxygen binding and yield by hemoglobin and the level of hemoglobin saturation with oxygen.     

Influence of dissolved oxygen concentration on the oxygen kinetics of Gluconobacter oxydans

Summary As shown in earlier studies in production scale bioreactors oxygen limited zones occur. Microorganisms in these reactors are therefore subjected to concentrations of oxygen varying with time. To simulate these conditions, the effect of low oxygen concentrations upon product formation and kinetics of oxygen of Gluconobacter oxydans are studied at laboratory scale.Under these oxygen limited conditions comparable kinetic parameters for oxygen are observed as under normally aerated conditions.So, a saturation constant for oxygen K _{O 2}=6.9 mol/l is observed, which is equivalent to a DOT value of about 3% of air saturation.For optimization purposes of production scale conditions, gassing with oxygen enriched air or with pure oxygen is one of the possibilities.To study the effect of high oxygen concentrations upon kinetics and product formation, the organisms are also cultivated under these extreme conditions. Although at oxygen concentrations larger then 60% saturation with pure oxygen, still growth was observed, the growth rate and also the product formation rate were strongly diminished.From these experiments it can be concluded that gassing with pure oxygen to achieve higher oxygen transfer rates at production scale will be restricted.     

Influence of age and structure of Pencillium chrysogenum pellets on the internal concentration profiles

Pellets of Penicillium chrysogenum which were spontaneously formed after a certain stage of a batch fermentation, displayed a considerable structural change in course of their lifetime. Microelectrode studies showed the internal mass transport properties of these pellets (diameter 1–3 mm) to be highly effected by their morphological structure. Relatively young pellets, in an early stage of the batch fermentation, possessed a homogeneous and dense structure. These pellets were only partly penetrated by oxygen (ca. 70 μm) at air saturated bulk conditions. Older pellets, in a final stage of the batch fermentation, were stratified and fluffy. They were completely penetrated by oxygen due to a decreased activity and a higher diffusivity. Investigations with glucose microelectrodes revealed that glucose consumption inside pellets of all lifetimes exclusively occurred in the periphery, indicating that growth was restricted to these regions only.     

No Magic Number: an Examination of the Herd-Size Threshold in Pastoral Systems Using Agent-Based Modeling

Pastoralists who depend on their herds for their livelihoods need a minimum number of animals to support their household. Due to the dynamics of herd growth, pastoralists may find themselves at times below that minimum number. Previous studies have shown that there is a herd-size threshold below which households are unlikely to escape poverty. We explore the concept of a herd-size threshold using an agent-based model to examine the role of scale and stochasticity in family herd dynamics. The model was parametrized with data from the literature. The results from the computer simulations show (1) that offtake rates significantly limit herd growth; and (2) that herd-size threshold is better understood as a range of probabilities. We discuss the methodological and conceptual advantages of using agent-based modeling to examine demographic dynamics, including the possibility of conducting multiple experiments in silico to examine the dynamics of herd growth.     

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.     

Comparative chondrogenesis of human cells in a 3D integrated experimental–computational mechanobiology model

We present an integrated experimental–computational mechanobiology model of chondrogenesis. The response of human articular chondrocytes to culture medium perfusion, versus perfusion associated with cyclic pressurisation, versus non-perfused culture, was compared in a pellet culture model, and multiphysic computation was used to quantify oxygen transport and flow dynamics in the various culture conditions. At 2 weeks of culture, the measured cell metabolic activity and the matrix content in collagen type II and aggrecan were greatest in the perfused+pressurised pellets. The main effects of perfusion alone, relative to static controls, were to suppress collagen type I and GAG contents, which were greatest in the non-perfused pellets. All pellets showed a peripheral layer of proliferating cells, which was thickest in the perfused pellets, and most pellets showed internal gradients in cell density and matrix composition. In perfused pellets, the computed lowest oxygen concentration was 0.075 mM (7.5% tension), the maximal oxygen flux was 477.5 nmol/m²/s and the maximal fluid shear stress, acting on the pellet surface, was 1.8 mPa (0.018 dyn/cm²). In the non-perfused pellets, the lowest oxygen concentration was 0.003 mM (0.3% tension) and the maximal oxygen flux was 102.4 nmol/m²/s. A local correlation was observed, between the gradients in pellet properties obtained from histology, and the oxygen fields calculated with multiphysic simulation. Our results show up-regulation of hyaline matrix protein production by human chondrocytes in response to perfusion associated with cyclic pressurisation. These results could be favourably exploited in tissue engineering applications.