Nonlinear control of bioreactors with input multiplicities in dilution rate

Control problems of continuous bioreactors having two input multiplicities in dilution rate on the productivity are analyzed. The nonlinear system is represented by a unity gain linear subsystem cascaded with a nonlinear gain subsystem. A conventional PI controller designed for the linear subsystem followed by the solution of the nonlinear gain equation gives a nonlinear controller. The performance of the nonlinear controller is compared with that of the conventional PI controller and also of the nonlinear controller [1] designed based on the output equation. The present nonlinear PI controller gives a superior performance. A single set of controller settings can be used for both the operating points. Whereas the linear PI controller and the nonlinear controller proposed by Henson and Seborg [1] destabilize the system.     

Nonlinear control of bioreactors with input multiplicities

Control of bioreactors exhibiting two input multiplicities, i.e., steady-state gains having opposite sign, is theoretically analyzed. The nonlinear system is represented by a unity gain linear system cascaded with a nonlinear gain. A conventional PI controller designed for the linear portion of the system followed by the solution of the nonlinear gain equation gives a nonlinear controller. The performance of the nonlinear controller is compared with that of the linear PI controller designed for the overall linear system. The nonlinear PI controller performance is superior to that of the linear PI controller.     

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.     

Identification of Hammerstein model for bioreactors with input multiplicities

A closed loop identification method of Hammerstein model for continuous bioreactor with input multiplicity is proposed. Hammerstein model consists of nonlinear steady-state gain followed by a unity gain linear system. The method consists of first getting local first order plus time delay (FOPTD) models around the two input multiplicity values of the substrate feed concentration. The model parameters of the FOPTD is identified by a least square optimization method. The initial guess for the model parameters are obtained from the settling time, the initial delay in the closed loop servo response and using a simple proportional controller formula. From the local process gain values obtained for the several step changes around the two operating conditions, the nonlinear gain portion of the Hammerstein is then obtained. The actual nonlinear gain and the identified nonlinear gain is compared.     

Control of the specific growth rate of Bacillus subtilis for the production of biosurfactant lipopeptides in bioreactors with foam overflow

This paper formulates a feeding law for a bioprocess dedicated to the production of an antibiotic surfactant using Bacillus subtilis. The specificity of the process relies on the use of the surface active property of the product to extract it by foaming. The control law is designed to maintain a constant specific biomass growth rate while taking into account the particularity of the process. This law can be regarded as a generalization of the conventional exponential feeding strategy and is generic enough to encompass the case of continuous processes with partial recycling. Conventional exponential feeding strategies indeed fail to account for the loss of biomass induced by the foaming. Previous experiments have provided a model of the process and values for its parameters. From this information, a feeding rate law was computed using the feeding strategy proposed in this paper and applied to an experimental culture. This experiment allows discussion of the modeling of the biomass extraction method used in this study. The results on the estimated specific growth rate highlight the complete agreement between the expected and experimental features. Further process optimization studies can now be performed on the basis of the constant specific biomass growth rate.     

Impact of periodic nutrient input rate on trophic chain properties

Marine ecosystems are characterized by a strong influence of hydrodynamics on biological processes. The associated models involve the coupling of physical to biological models and therefore require a large number of state variables. The consequent high complexity limits our capacity to perform a complete and detailed study and even prevents any complete mathematical study of these models. It is also difficult to disentangle among all the processes involved, which ones actually drive the system at any moment. Hydrodynamics, among other consequences, affect the way under which the nutrients are supplied to marine ecosystems. The variability of nutrient input rate in marine systems generally results from runs-off in coastal systems and from physical processes (wind forcing and hydrodynamics) in open ocean. This paper is devoted to the study of the effects of the nutrient input rate variability on the dynamics and the functioning of trophic chains. In this context, we aim to provide an understandable study, based on simplified system models. We consider a periodic nutrient input rate and analyze how this variability modifies some system properties: its dynamics, its functioning and its structure. The dynamics is obtained by numerical simulations and when possible, enlighten by already published mathematical results. The functioning is measured by the time averaged state variables during the simulation period, and their variability. The structure concerns the number of surviving populations, a proxy of specific biodiversity. We show how these properties can be affected and provide some conditions under which the modifications can occur. We also highlight that, even if the physical process is the main driving force in the global dynamics, the choice of the biological model is important to understand the biological response of the system to physical forcing.     

Fed-batch operation of recombinant Escherichia coli containing trp promoter with controlled specific growth rate

A feb-batch operation for the production of bovine somatotropin (bST) under the control of tryptophan promoter in Escherichia coli was investigated. The plasmid used contains a two-cistron system and altered codon usage for higher expression of bST. Specific growth rate is an important parameter in the fermentation, because it affects the production of growth-inhibitory organic acids and the expression of recombinant protein. The feeding rate was adjusted to keep the specific growth rate constant in this study. The variable growth yield expressed as a function of time was used for the calculation of the feeding rate. The growth yield decreases during the fermentation as product expression is induced. The specific growth rate was well controlled; however, intracellular bST concentration decreased at high cell concentrations. This is considered to be due to degradation by proteases. The decrease was prevented by an exponential feeding of the yeast extract as an organic nitrogen source. (c) 1994 John Wiley & Sons, Inc.     

Effect of specific growth rates on productivity in continuous open and partial cell retention animal cell bioreactors.

A clonal derivative of a transfectant of the SP2/0 myeloma cell line producing a chimeric monoclonal antibody was cultivated in both continuous open and continuous partially-closed bioreactors. Using an open system for the determination of kinetic parameters, we showed that the production of this chimeric mAb was growth associated. As such, the volumetric productivity increased linearly with increasing dilution rate up to the maximum dilution rate. Three continuous cultivations employing partial cell retention were conducted. In agreement with mathematical predictions, the product titer and volumetric productivity were independent of the degree of cell retention when the total dilution was held constant. When cells were maintained at a low specific growth rate, the product titer was independent of dilution rate and the volumetric productivity increased with increasing dilution rate, again in agreement with mathematical predictions. Since the partially-closed bioreactor could be operated at dilution rates in excess of the maximum specific cellular growth rate, volumetric productivities were greater than those achievable in the open bioreactor. However, when cells were maintained at a high specific growth rate, cell accumulation was limited and product titers decreased at high dilution rates. Therefore, the volumetric productivity in this latter case did not increase at higher dilution rates.     

Osmotic effects on radial growth rate and specific growth rate of three soil fungi

The radial growth rate on osmotically adjusted agar medium and the relative specific growth rate in osmotically adjusted liquid medium were determined for Rhizoctonia solani, Pythium ultimum, and Verticillium dahliae. On basal medium, an isolate of P. ultimum and R. solani had similar radial growth rates of 0.52 and 0.47 mm/h, respectively, whereas V. dahliae grew at a rate of 0.08 mm/h. Radial growth rate was reduced 50% at osmotic potentials of -16, -27, and -32 bars for P. ultimum, R. solani, and V. dahliae, respectively. No growth occurred at -32 bars for P. ultimum, -56.2 bars for R. solani, and -100 bars for V. dahlia. Specific growth rates in liquid culture were 0.011 h-1 for P. ultimum, 0.008 h-1 for V. dahliae, and 0.026 h-1 for R. solani. Ratios of radial growth rate (Kr) to specific growth rate (alphas) were computed for each fungus growing at different osmotic potentials. There was not a constant relationship between Kr on agar and alphas in liquid medium, e.g., Kr/alphas ratios varied from 8-41% from a mean ratio for a particular species. The results indicated that radial growth rate on osmotic agar was not useful as a measure of relative specific growth rate of a fungus in osmotically adjusted liquid medium.     

Effect of mode of operation of bioreactors on the biosynthesis of penicillin amidase in Escherichia coli

Different operational mode of bioreactors influence the biosynthesis of the enzyme and related products as well as the growth of industrial microorganisms. This communication deals with the effect of mode of operation of various bioreactors with different geometric configurations, viz., batch (includes commercially available batch stirred tank, and custom-designed cylindrical and tapered reactors), batch-fed, continuous flow stirred tank reactors on the biosynthesis of penicillin amidase in Escherichia coli. Experimental findings show that the biosynthesis of penicillin amidase in E. coli show a little variation among batch reactor modes and significant variation on the continuous mode of operation. Further analysis show that the different reactor modes also influence periplasmic localization of the enzyme in the cell.     

Effect of weaning time on the growth rate and food intake of the spiny mouse pup

The spiny mouse Acomys cahirinus produces well-developed pups although it is a relatively small mammal (45 g). We envisioned two opposing hypotheses on the effect of early weaning on the growth rate of pups. The first predicts little effect since the increase in energy intake of dams above non-reproducing females is relatively low, suggesting that pups consume a large portion of their energy as solid food, and the pups are very well developed at birth. The second predicts a substantial effect since the 'index of precociality', that is the energy intake for maintenance of a pup as a proportion of that predicted for a rodent of its body mass, falls within values for altricial rodents, suggesting an extended maternal dependence of the young. To test these hypotheses, we measured the growth rate and food intake of pups weaned after either 7, 14, 21 or 28 days. Only three of 12 pups weaned after 7 days survived and, consequently, the latter hypothesis was supported. All pups weaned at 14–28 days survived. There was a significant decrease in growth rate during the first day after weaning in pups weaned at 7, 14 and 21 days but not after 28 days, suggesting that pups did not require parental care by day 28. Peak growth rate in pups weaned at 14 days occurred in the second week but occurred in the third week in pups weaned at 21 and 28 days. In spite of these differences, pups in all treatments had similar body mass at 64 days, indicating compensatory growth. We concluded that pups of A. cahirinus are precocial from a morphological aspect in that they are well developed at birth but altricial from a nutritional aspect in that they require extended maternal support.     

Profile control of the specific growth rate in fed-batch experiments

Summary The aim of this paper is to apply a computer control scheme to a laboratory scale fermentor so that the specific growth rate in a baker's yeast fed-batch culture, which cannot be measured directly, will follow as accurately as possible the desired profile specified in advance. Using an extended Kalman filter and programmed controller/feedback compensator (PF) system proposed previously, profile control of the specific growth rate () was achieved experimentally in a baker's yeast fed-batch culture. Also, bang-bang type profile control of minimized the proportion of budding cells, which have a strong correlation with the fermentative activity in bread-making.     

Effects of preculturing conditions on lag time and specific growth rate of Enterobacter sakazakii in reconstituted powdered infant formula

Enterobacter sakazakii can be present, although in low levels, in dry powdered infant formulae, and it has been linked to cases of meningitis in neonates, especially those born prematurely. In order to prevent illness, product contamination at manufacture and during preparation, as well as growth after reconstitution, must be minimized by appropriate control measures. In this publication, several determinants of the growth of E. sakazakii in reconstituted infant formula are reported. The following key growth parameters were determined: lag time, specific growth rate, and maximum population density. Cells were harvested at different phases of growth and spiked into powdered infant formula. After reconstitution in sterile water, E. sakazakii was able to grow at temperatures between 8 and 47 degrees C. The estimated optimal growth temperature was 39.4 degrees C, whereas the optimal specific growth rate was 2.31 h(-1). The effect of temperature on the specific growth rate was described with two secondary growth models. The resulting minimum and maximum temperatures estimated with the secondary Rosso equation were 3.6 degrees C and 47.6 degrees C, respectively. The estimated lag time varied from 83.3 +/- 18.7 h at 10 degrees C to 1.73 +/- 0.43 h at 37 degrees C and could be described with the hyperbolic model and reciprocal square root relation. Cells harvested at different phases of growth did not exhibit significant differences in either specific growth rate or lag time. Strains did not have different lag times, and lag times were short given that the cells had spent several (3 to 10) days in dry powdered infant formula. The growth rates and lag times at various temperatures obtained in this study may help in calculations of the period for which reconstituted infant formula can be stored at a specific temperature without detrimental impact on health.     

Effect of oxygen on the growth, respiratory rate and morphology of Candida utilis cells in periodic and continuous cultures

The aim of this work was to study how the concentration of oxygen dissolved in the cultural broth influenced the respiration and morphology of the yeast Candida utilis in batch and continuous cultures. Highly effective respiration was registered in cells growing for a certain period of time at low oxygen concentrations limiting the growth; the respiration was characterized by low values of the Michaelis constant kc and the critical concentration of dissolved oxygen Ccr. When passing from the low oxygen concentration to a high one, the character of cellular respiration changed abruptly in the cells whose growth was limited with oxygen for a long time. The morphology of the culture limited with oxygen was characterized by an increase in the percentage of elongated forms in the population. The respiration of the cells cultivated at high oxygen concentrations, when their growth was either non-limited or limited by glucose, was distinguished by high Ccr values and slow respiration rates at small oxygen concentrations while the dependence of the respiration rate on the concentration of oxygen had an about S-shaped character.     

Effect of incorrectly estimated parameters on the control of specific growth rate inE. coli fed-batch fermentation

An exponential feeding strategy has been frequently used in fed-batch fermentation of recombinantE. coli. In this feeding scheme, growth yield and initial cell concentration, which can be erroneously determined, are needed to calculate the feed rate for controlling specific growth rate at the set point. The effect of the incorrect growth yield and initial cell concentration on the control of the specific growth rate was theoretically analyzed. Insignificance of the correctness of those parameters for the control of the specific growth rate was shown theoretically and experimentally.     

Effect of compost temperature on oxygen uptake rate, specific growth rate and enzymatic activity of microorganisms in dairy cattle manure

Investigations were carried out to find out the relationship between temperature and microbial activity in dairy cattle manure composting using oxygen uptake rate, specific growth rate and enzymatic activities during autothermal and isothermal composting experiments. In autothermal composting, oxygen uptake rate and specific growth rate were found to be most intensive in order of 43 degrees C, 60 degrees C and 54 degrees C. Isothermal composting at 54 degrees C resulted highest levels of enzymatic activity and promoted the volatile solids reduction. Based on the maximum enzymatic activity, specific growth rate appeared to be more closely linked with microbial activity in compost than with oxygen uptake rate. The enhancement of specific growth rate, enzymatic activity and volatile solids reduction were induced at 54 degrees C in cattle manure composting.