Modelling of aerobic growth of Saccharomyces cerevisiae in a pH-auxostat

A model for growth and overflow metabolism of Saccharomyces cerevisiae was applied to simulate continuous cultivations in a pH-auxostat. The concentrations of glucose, biomass and ethanol are controlled by the flow ratio r between fresh medium and titrant solution, both of which are pH-regulated. A critical value of r could be derived, below which the culture becomes substrate depleted, resulting in a stop-flow condition with retained biomass but without growth. At r-values slightly above the critical value the pH-auxostat is substrate limited and unstable. Further increase of the r value results in a stable continuous culture growing at w_max. Thus, the pH-auxostat complements the chemostat in the growth range at or close to w_max. Even at w_max conditions, the ethanol concentration can be controlled at a low level.     

Estimation of specific growth rate from cell density measurements

For modelling purposes it is of great importance to derive the specific growth rate as a function of time from biomass measurements. Traditional methods such as exponential or polynomial fitting do not give satisfactory results nor do these methods take the noise characteristics of the biomass measurements into account. Standard recursive techniques, such as Kalman filtering, use only the data up to the time under consideration and are dependent of a good initial estimation. This paper describes a technique based on combining subsequent backward and forward extended Kalman filtering to give a smoothing estimator for the specific growth rate. The estimator does not need an initial value and is shown to have a single tuning parameter. The applicability of the estimator is demonstrated on batch and fed-batch cultivations of two organisms: Bordetella pertussis and Neisseria meningitidis.     

Nonlinear feedforward control of bioreactors with input multiplicities

A steady-state nonlinear feedforward controller (FFC) for measurable disturbances is designed for a continuous bioreactor, which is represented by Hammerstein type nonlinear model wherein the nonlinearity is a polynomial with input multiplicities. The manipulated variable is the feed substrate concentration (S_f) and the disturbance variable is the dilution rate (D). The productivity (Q=DP) is considered as the controlled variable. The desired value of Q=3.73 gives two values of feed substrate concentration. The nonlinearity in the gain is considered for relating output to the manipulated variable and separately for the relation between output to disturbance variable. The FFC is also designed for the overall linearized system. The performance of the FFC is evaluated on the nonlinear differential equation model. The FFC is also designed for the model based on a single nonlinear steady-state equation containing both D and S_f. This nonlinear FFC gives the best performance. The nonlinear FFC is also designed by using only linear gain for the disturbance and nonlinear gain for the manipulated variable. Similarly, nonlinear FFC is also designed by using linear gain for the manipulated variable and the nonlinear gain for the disturbance variable. The performances of these FFC schemes are compared.     

Application of artificial neural networks to modelling of starch hydrolysis by glucoamylase

The applicability of neural networks to the dynamic modelling of starch hydrolysis by Aspergillus niger glucoamylase is studied. The advantage of this technique is the possibility of predicting the reaction curves without a detailed kinetic model. Two independent neural models were proposed to predict the concentration of the products and conversion degree of the substrate at the end of the reaction (Model 1) as well as the reaction courses in the first stage when the sharp changes in the reaction rate are observed (Model 2). The results of simulations prove the ability of neural-network models to describe the complex kinetics of starch hydrolysis by glucoamylase.     

Phenol utilization by filamentous yeast Trichosporon cutaneum

The investigated strain Trichosporon cutaneum shows well expressed capability for metabolizing high concentrations of phenol, up to 1 g/l, utilizing it as the sole carbon source for the growth and development of the population. The data reported, prove the good perspectives for its application in protecting the environment from phenol pollution. No data about modelling the process of cultivation of Trichosporon cutaneum in phenol media is available in scientific literature up to now. The mathematical model, reported here, consists of two nonlinear differential equations, describing cell growth and substrate consumption. The unknown parameters are estimated following the method of Hooke and Jeeves. A number of simulation investigations are carried out. They prove the adequacy of the model and its applicability in further studies on the processes of growth and phenol uptake of Trichosporon cutaneum.     

Neural network modelling of fermentation processes. Microorganisms cultivation model

In the present paper the problem of chemostat modelling using the neural networks techniques is considered. A feedforward neural network with time delay feedback connections from and to the output neurons, which take into account the culture memory is proposed. A model of the growth of a strain Saccharomyces cerevisiae on a glucose limited medium is developed. Simulation investigations are carried out. The results are discussed.     

The use of structural dynamic models to explain successes and failures of biomanipulation

A development of a structural dynamic model, i.e. a model with current change of the most important parameters according to a goal function, is presented with the aim to explain the structural changes observed in lakes, when the nutrient concentration is increased or decreased. This type of models may be important in lake management as it may be possible qualitatively to predict the success or failure of biomanipulation. The answer to the crucial question: àt which phosphorus level will the success of biomanipulation be most probable?' will probably require the development of model which takes into account site specific processes and properties, i.e., a more complicated model. As goal function is proposed the thermodynamic function, exergy, which is defined as the work content of the system (model) compared with the system at thermodynamic equilibrium. It is shown that the structural dynamic modelling approach has been able to explain the shift from large to small zooplankton species at a certain level of phosphorus concentration, accompanied by a shifts from a dominance of zooplankton, and predatory fish to a system dominated by planktivorous fish and phytoplankton. The shift in zooplankton species cannot be explained by application of catastrophe theoretical models, which have been used to explain the hysteresis reaction. The results show that the shift should be expected at approximately 0.12 mg P l-1 and that a typical hysteresis reaction occurs at this concentration in accordance with the expectations. These results are consistent with many observations but should be interpreted with great caution, as the model is simple and general and don't account for a number of processes which may influence the results significantly in specific lake studies. The structural dynamic approach has previously been used in ten case studies with good agreement with the observations, but more case studies are needed before a general recommendation of the use of this type of models can be given. The results from this study point toward to apply this type of models for lake management where biomanipulation is involved, although it should be recommended to improve the presented general model with introduction of site specific properties for a considered lake study.     

The mathematical modelling of population dynamics taking into account the adaptive behavior of individuals

The general approach for modelling of abundance dynamic of biological populations and communities is offered. The mechanisms of individual adaptation in changing environment are considered. The approach is detailed for population models without structure and with age structure. The property of solutions are investigated. As examples the author studies the concrete definitions of general models by analogy with models of Ricker and May. Theoretical analysis and calculations shows that survival of model population in extreme situation increases if adaptive behaviour is taking into account.     

Assessment of cell alignment by fibronectin multi-fibre cables capable of large scale production

The repair of damaged human tissue will be enhanced greatly by a capacity to organise the arrangement of the cells. We have demonstrated an approach to quantifying the capacity of fibronectin multi-fibre cables to align human cells. It is based on staining and subsequent image analysis of cells in the neighbourhood of the cables, and the application of an Orientation Index (S), to give a quantitative measure of alignment of the cells. Alignment of human dermal fibroblasts, parallel to the fibronectin cable axis, was observed by light microscopy after 3 days in culture. At 7 days, alignment was determined by image analysis after hematoxylin and eosin staining. This showed that the lateral extent of cell alignment i.e. the number of cell layers lined up beside a cable, termed the cell docking band width, was independent of cable diameter. Scanning electron microscopy confirmed cell alignment and the deposition of fine collagen fibrils by the cells. Orientation of cells to the cable, as measured by an orientation index (S), was S = 0.97 - 0.05 in cell docking bands denoting almost perfect alignment. Cell seeding levels ranging from 14 K cells/cm² up to 54 K cells/cm² resulted in cell docking band widths of aligned cells from 335 wm to 890 wm respectively, increasing as a function of cell seeding levels. This method represents a quantitative measure of quality for potential contact guidance materials. The guidance system is capable of large-scale manufacture.     

Structural basis of stereoselectivity in Candida rugosa lipase-catalyzed hydrolysis of secondary alcohols

Lipases are widely used catalysts for highly enantioselective resolution of chiral secondary alcohols. While stereopreference is determined predominantly by the substrate structure, stereoselectivity (enantioselectivity and diastereoselectivity) depends on the atomic details of interactions between substrate and lipase. Experimentally obtained stereoselectivity and activity in the hydrolysis of butanoic acid esters of two secondary alcohols with two neighboring stereocenters by Candida rugosa lipase have been investigated by computer-aided molecular modeling of tetrahedral substrate intermediates in complex with the lipase. Breakdown of these intermediates is considered to be the rate-limiting step. Steric interactions of stereoisomers with the side chain of catalytic histidine led to different orientations of the imidazole. The distance d(H_N)-O_alc) between H_N) of the imidazole side chain of catalytic histidine and the alcohol oxygen of the substrate was identified to correlate with the experimentally determined reactivity order of the four stereoisomers. Modeled distances d(H_N)-O_alc) were short (=1.8 Å) for RR stereoisomers, which were also found to be hydrolyzed most rapidly experimentally; distances d(H_N)-O_alc) were about 2 Å for SS and SR stereoisomers, which were converted at similar rates but at a lower rate than RR stereoisomers; finally, distances d(H_N)-O_alc) for SR stereoisomers were greater than 4 Å, in accordance with very slow conversion of SR stereoisomers.     

An evaluation of the uniform stress hypothesis based on stem geometry in selected North American conifers

The uniform stress hypothesis of stem formation was evaluated by comparing stem taper of Abies balsamea, Abies lasiocarpa, Picea rubens, Pinus contorta, Pinus elliottii, Pinus palustris, Pinus ponderosa, Pinus taeda, and Pseudotsuga menziesii to the taper expected if stems develop to uniformly distribute bending stress. The comparison was conducted by regressing stem diameter at height h (D_h) against bending moment at h (M_h) using the model D_h=J (M_h)^' where J and ' are fitted coefficients, and testing for '=0.333, the hypothesized value. Twelve curves were fitted with the model. Seven of the fitted values of ' were significantly different from 0.333, but eight of the values were within ᆞ% of 0.333 and eleven values were within ᆣ% of 0.333. Where the fitted value of ' was >15% of 0.333, residuals were biased with height. Fit by relative height, values of ' were within ᆞ% of 0.333 for large portions of these stems. While most of the fitted values of ' support the uniform-stress hypothesis, the values of ' for Pseudotsuga menziesii trees clearly did not. Many of the fitted values of J were inversely related to the modulus of elasticity (E) of green wood reported for these species. With the exception of Pseudotsuga menziesii, growing conditions appeared to account for extraordinary values of J. Increases in J with stem height corresponded with reported decreases in E with height. The covariance between J and E suggests some regulation of bending curvature by adjustments in cross-sectional area. These results suggest that stems taper to maintain a uniform bending curvature and that when E is relatively constant within and among stems, diameter along the stem or across stems can be predicted from bending moment using a simple power function.     

Neuro-fuzzy prediction of uricase production

Recent biotechnology requires implementation of new modelling methods based on knowledge principles and learning structures, comprised in fuzzy knowledge-based systems (FKBS), neural networks (NN) and different hybrid methods. The intelligent modelling approaches solve sufficiently a very important problem - processing of scarce, uncertainty and incomplete numerical and linguistic information about multivariate non-linear and non-stationary systems as well as biotechnological processes. The paper deals with prediction of an enzyme oxidizing uric acid to alantoin - the uricase, produced by Candida utilis 90-12 employing neuro-fuzzy knowledge-based approach. The implemented predictive technique exploits the fact that the fuzzy model can be seen as a network structure, similar to artificial NN, which on computational level assure a high model accuracy. The predictors implemented are four different by nature variables. The developed predictive model shows that best predictors of uricase production are biomass and limiting substrate concentrations.     

Wine vinasses treatments by ozone and an activated sludge system in continuous reactors

In this work wine vinasses have been treated separately by means of a chemical ozonation and a biological aerobic degradation in an activated sludge system, and later by means of a combined process which consisted of an aerobic pretreatment followed by an ozonation treatment, in continuous reactors in all cases. In the ozonation experiments, the hydraulic retention time and the ozone partial pressure were varied leading to substrate removals in the range 4.4-16%, with increases in this removal when both operating variables were increased. A kinetic study, which combines mixed flow reactor model for the liquid phase and plug flow reactor model for the gas phase, allows to determine the rate constant for the ozone reaction and the consumption ratio, which are k_O3 = 3.6 l/(g COD · h) and b = 22.5 g COD degraded/mol O₃ consumed. The aerobic degradation experiments were conducted in the activated sludge system with variations in the retention time and influent organic substrate concentration in the wastewater. A modified Contois model applied to the experimental results leads to the determination of the kinetic parameters of that model: K₁ = 5.43 l/g VSS and q_max = 6.29 g COD/(g VSS · h). Finally, the combined process reveals an improvement in the efficiency of the ozonation stage due to the previous aerobic treatment with increases in the substrate removal reached and in the rate constant obtained, the last one being k_O3 = 5.6 l/(g COD · h).     

Carbon isotope discrimination in photosynthetic bark

We developed and tested a theoretical model describing carbon isotope discrimination during photosynthesis in tree bark. Bark photosynthesis reduces losses of respired CO₂ from the underlying stem. As a consequence, the isotopic composition of source CO₂ and the CO₂ concentration around the chloroplasts are quite different from those of photosynthesizing leaves. We found three lines of evidence that bark photosynthesis discriminates against ¹³C. First, in bark of Populus tremuloides, the '¹³C of CO₂ efflux increased from -24.2‰ in darkness to -15.8‰ in the light. In Pinus monticola, the '¹³C of CO₂ efflux increased from -27.7‰ in darkness to -10.2‰ in the light. Observed increases in '¹³C were generally in good agreement with predictions from the theoretical model. Second, we found that '¹³C of dark-respired CO₂ decreased following 2-3 h of illumination (P<0.01 for Populus tremuloides, P<0.001 for Pinus monticola). These decreases suggest that refixed photosynthate rapidly mixes into the respiratory substrate pool. Third, a field experiment demonstrated that bark photosynthesis influenced whole-tissue '¹³C. Long-term light exclusion caused a localized increase in the '¹³C of whole bark and current-year wood in branches of P. monticola (P<0.001 and P<0.0001, respectively). Thus bark photosynthesis was shown to discriminate against ¹³C and create a pool of photosynthate isotopically lighter than the dark respiratory pool in all three experiments. Failure to account for discrimination during bark photosynthesis could interfere with interpretation of the '¹³C in woody tissues or in woody-tissue respiration.     

Origin of cytoplasm substituted rice cultivars found in Japan

Genetic variation of Japanese rice cultivars were examined. Five of 450 lowland cultivars and another five of 200 upland cultivars were determined as the indica type by using isozyme genotypes and the remainder were of the japonica type. The major characteristics of these indica cultivars, revealed a slender shape of grains, a short apiculus hair length, a positive allele for Ph reaction, and allele-3 for the Pgd1 locus. Three of these indica cultivars showed a non-deletion ORF100, which is essential to the japonica-type plastid. The plastid subtype identity (PS-ID) sequences of these plastids is 6C7A, which is also a japonica-specific repeat unit. Thus, these cultivars were concluded to be naturally generated cytoplasm substituted lines. These plastids were introduced into a indica genetic background from japonica cultivars grown elsewhere. The rest of the indica cultivars revealed a deletion-type ORF100 and plastid subtype 8C8A, both of which are indica-specific. These cultivars carried indica-type allelic constitutions for diagnostic isozyme loci. However, other characters were identical to the cytoplasm-substituted cultivars in Japan. In East and Southeast Asia, cultivars carrying a indica-type nuclear genotype with a japonica-type plastid are restricted to Aus cultivars in the Bengal region. Genetic and historical records suggest that Japanese indica cultivars and the Aus cultivars are closely related. The Aus cultivars acquire necessary genetic constitutions from both indica and japonica cultivars through naturally occurring out-crossing to adapt to a particular cultivation condition in the region. The wide adaptability enabled them to be introduced into a northern region like Japan.     

A hybrid representation approach for modelling complex dynamic bioprocesses

This paper considers the use of hybrid models to represent the dynamic behaviour of biotechnological processes. Each hybrid model consists of a set of non linear differential equations and a neural model. The set of differential equations attempts to describe as much as possible the phenomenology of the process whereas neural networks model predict some key parameters that are an essential part of the phenomenological model. The neural model is obtained indirectly, that is, using the prediction errors of one or more state variables to adjust its weights instead of successive presentations of input-output data of the neural network. This approach allows to use actual measurements to derive a suitable neural model that not only represents the variation of some key parameters but it is also able to partly include dynamic behaviour unaccounted for by the phenomenological model. The approach is described in detail using three test cases: (1) the fermentation of glucose to gluconic acid by the micro-organism Pseudomonas ovalis, (2) the growth of filamentous fungi in a solid state fermenter, and (3) the propagation of filamentous fungi growing on a 2-D solid substrate. Results for the three applications clearly demon- strate that using a hybrid model is a viable alternative for modelling complex biotechnological bioprocesses.     

Reactor kinetics for submerged aerobic biofilms

Sclerotium rolfsii ATCC 15205 was cultivated in continuous culture (48 l reactor volume) for scleroglucan production. The maximum volumetric productivity (Q_Pvmax) amounted to 7.2 g/ld and was more than twice as high as in comparable batchwise cultivations. In addition, the relation between (a) volumetric productivity (Q_P [g/ld]) and product yield (Y_{Glucan/Glucose} [1]), (b) volumetric productivity and product quality (M_W [g/mol]), and (c) product quality and impeller tip speed (Nd [m/s]) was studied in continuous culture. It was found, that an increase in volumetric productivity led to a decline in product yield and product quality. Furthermore, an impeller tip speed of >0.7 m/s decreased the attainable product quality considerably. Based on these results, the impact of the operational setpoint of the process in terms of oxygen supply and reactor scale on the economics of scleroglucan production was discussed. In contrast to batchwise cultivation, scleroglucan production in continuous culture proved to be not feasible under non-aseptic conditions.     

Bifurcation of periodic oscillations due to delays in single species growth models

Summary Theorems are given which guarantee the bifurcation of non-constant, periodic solutions (of fixed period) of a scalar functional equation with two independent parameters. These results are applied to a single, isolated species growth model of general form with a general Volterra (Stieltjes) delay using the ‘magnitudes’ of the instantaneous and delayed growth rate responses as the independent bifurcation parameters. The case of linear growth rate responses (i.e. delay logistic models) is considered in more detail, particularly the often studied single lag logistic equation.     

Joint aerobic biodegradation of wastewater from table olive manufacturing industries and urban wastewater

Wastewater generated in the elaboration of table olives has been treated using activated sludge from a municipal wastewater plant after adequate acclimation. To avoid bactericide properties of some chemical structures present in this type of effluents, synthetic urban wastewater has been used to dilute the original wastewater. The main parameters affecting efficiency of biological processes have been studied. Thus, initial biomass concentration, temperature up to 303 K (upper working temperature limit = 313 K) and initial substrate concentration exerted a positive influence on COD degradation rate. The optimum pH was found to be around 7, experiencing a slight inhibition on cell activity at pH 4. Under the experimental conditions investigated other parameters like polyphenol content, absorbance at 254 nm and total organic carbon were also reduced to some extent. Only nitrates amount was increased after the biological process took place. A kinetic model based on Monod equation was proposed and applied to experimental results. The maximum specific growth rate was calculated by means of the aforementioned kinetic model. The value of this parameter as a function of temperature was fitted to an Arrhenius expression, w_max = 9.43 2 10¹⁰ exp(72021/RT) h^у (R in J mol^у K^у283 K < T < 303 K, pH , 7-10).