Predrag Horvat

Engineering approach to mixing quantification in bioreactors

Abstract“Homogeneity-time” is defined and introduced as the criterion for mixing quality in bioreactors. The criterion could replace the mixing time, in the case, when more than one measuring point (sensors) is included in the measuring system. Results based on the homogeneity-time and the temperature pulse method, achieved in stirred tank reactors under aerated conditions as well as in a jet-mixed tank, are presented.

Mathematical modeling of poly((R)-3-hydroxyalkanoate) synthesis by Cupriavidus necator DSM 545 on substrates stemming from biodiesel production

Two low structured mathematical models for fed-batch production of polyhydroxybutyrate and poly[hydroxybutyrate-co-hydroxyvalerate] by Cupriavidus necator DSM 545 on renewable substrates (glycerol and fatty acid methyl esters-FAME) combined with glucose and valeric acid, were established. The models were used for development/optimization of feeding strategies of carbon and nitrogen sources concerning PHA content and polymer/copolymer composition. Glycerol/glucose fermentation featured a max. specific growth rate of 0.171 h(-1), a max. specific production rate of 0.038 h(-1) and a PHB content of 64.5%, whereas the FAME/valeric acid fermentation resulted in a max. specific growth rate of 0.046 h(-1), a max. specific production rate of 0.07 h(-1) and 63.6% PHBV content with 4.3% of 3-hydroxyvalerate (3HV) in PHBV. A strong inhibition of glycerol consumption by glucose was confirmed (inhibition constant ki,G=4.28×10(-4) g L(-1)). Applied concentration of FAME (10-12 g L(-1)) positively influenced on PHBV synthesis. HV/PHBV ratio depends on applied VA concentration.

Mathematical Modelling as a Tool for Optimized PHA Production

The potential of poly(hydroxyalkanoates) (PHAs) to replace conventional plastic materials justifies the increasing attention they have drawn both at lab-scale and in industrial biotechnology. The improvement of large-scale productivity and biochemical/genetic properties of producing strains requires mathematical modeling and process/strain optimization procedures. Current models dealing with structurally diversified PHAs, both structured and unstructured, can be divided into formal kinetic, low-structured, dynamic, metabolic (high-structured), cybernetic, neural networks and hybrid models; these attempts are summarized in this review. Characteristic properties of specific groups of models are stressed in light of their benefit to the better understanding of PHA biosynthesis, and their applicability for enhanced productivity. Unfortunately, there is no single type of mathematical model that expresses exactly all the characteristics of producing strains and/or features of industrial-scale plants; in addition, the different requirements for modelling of PHA production by pure cultures or mixed microbial consortia have to be addressed. Therefore, it is crucial to sophisticatedly adapt and fine-tune the modelling approach accordingly to actual processes, as the case arises. For “standard microbial cultivations and everyday practices”, formal kinetic models (for simple cases) and “low-structured” models will be appropriate and of great benefit. They are relatively simple and of low computational demand. To overcome the specific weaknesses of different established model types, some authors use hybrid models. Here, satisfying compromises can be achieved by combining mechanistic, cybernetic, and neural and computational fluid dynamics (CFD) models. Therefore, this hybrid modelling approach appears to constitute the most promising solution to generate a holistic picture of the entire PHA production process, encompassing all the benefits of the original modelling strategies. Complex growth media require a higher degree of model structuring. For scientific purposes and advanced development of industrial equipment in the future, real systems will be modelled by highly organized hybrid models. All solutions related to modelling PHA production are discussed in this review.

Mixing-models applied to industrial batch bioreactors

Mixing models for bioreactors on the basis of the tanks-in-series concept are presented and a suitable parameter-estimation method is introduced. The Monte-Carlo-optimization procedure with the inhomogeneity-curve included in the objective function is used. Results of the parameter optimization procedure are given for stirred-tank-bioreactors equipped with one and three Rushton turbines under aerated conditions. The model designed for the stirredtank with three Rushton turbines is capable to describe the mixing properties, while in case of the stirred-tank with one Rushton turbine the simulated radial circulation time does not correlate with the measured one.

Whey Lactose as a Raw Material for Microbial Production of Biodegradable Polyesters

Whey, a by-product of diary and cheese industry, constitutes the watery portion after the separation of fat and caseins from whole milk. Cheese whey is a surplus material produced in volumes almost equal to the milk processed in cheese manufactories, therefore its disposal as a waste causes serious pollution problems in the surrounding environment where it s discarded. This is due to its enormous biochemical oxygen demand that is mainly caused by its high lactose content; as a consequence a large amount of industrial capital is requested for whey disposal. During the last years, the amounts of whey increased to such an extent that they cannot be simply used as animal feed as the most common application. To overcome these problems a sustainable alternative is to upgrade whey and its derivates to a resource for many value added industrial products, making whey not only a waste but also a valuable resource.

Mathematical modeling of mixing in a horizontal rotating tubular bioreactor: "Spiral flow" model

A horizontal rotating tubular bioreactor (HRTB) was designed as a combination of a “thin-layer bioreactor” and a “biodisc” reactor whose interior was divided by O-ring shaped partition walls. For the investigation of mixing in HRTB the temperature step method was applied. Temperature changes in the bioreactor were monitored by six Pt-100 sensors (t90 response time 0.08 s and resolution 0.002 °C) which were connected with an interface unit and a personal computer. In this work a modified “tank in series” concept was used to establish a mathematical model. The heat balance of the model compartments was established according to the physical model and the “spiral flow” pattern. Numerical integration was done by the Runge-Kutta-Fehlberg method. The mathematical mixing model called “spiral flow” model contained four adjustable parameters (N1, Ni, Fcrand Fp) and five parameters which characterized the plant and experimental conditions. The “spiral flow” model was capable to describe the mixing in HRTB properly, and its applicability was much better than with the “simple flow” model, presented earlier.

Footprint area analysis of binary imaged Cupriavidus necator cells to study PHB production at balanced, transient, and limited growth conditions in a cascade process

Statistical distribution of cell and poly[3-(R)-hydroxybutyrate] (PHB) granule size and number of granules per cell are investigated for PHB production in a five-stage cascade (5CSTR). Electron microscopic pictures of cells from individual cascade stages (R1–R5) were converted to binary pictures to visualize footprint areas for polyhydroxyalkanoate (PHA) and non-PHA biomass. Results for each stage were correlated to the corresponding experimentally determined kinetics (specific growth rate μ and specific productivity π). Log-normal distribution describes PHA granule size dissimilarity, whereas for R1 and R4, gamma distribution best reflects the situation. R1, devoted to balanced biomass synthesis, predominately contains cells with rather small granules, whereas with increasing residence time τ, maximum and average granule sizes by trend increase, approaching an upper limit determined by the cell’s geometry. Generally, an increase of intracellular PHA content and ratio of granule to cell area slow down along the cascade. Further, the number of granules per cell decreases with increasing τ. Data for μ and π obtained by binary picture analysis correlate well with the experimental results. The work describes long-term continuous PHA production under balanced, transient, and nutrient-deficient conditions, as well as their reflection on the granules size, granule number, and cell structure on the microscopic level.

In silico optimization and low structured kinetic model of poly[(R)-3-hydroxybutyrate] synthesis by Cupriavidus necator DSM 545 by fed-batch cultivation on glycerol.

Glycerol was utilized by Cupriavidus necator DSM 545 for production of poly-3-hydroxybutyrate (PHB) in fed-batch fermentation. Maximal specific growth rates (0.12 and 0.3h(-1)) and maximal specific non-growth PHB production rate (0.16 g g(-1)h(-1)) were determined from two experiments (inocula from exponential and stationary phase). Saturation constants for nitrogen (0.107 and 0.016 g L(-1)), glycerol (0.05 g L(-1)), non-growth related PHB synthesis (0.011 g L(-1)) and nitrogen/PHB related inhibition constant (0.405 g L(-1)), were estimated. Five relations for specific growth rate were tested using mathematical models. In silico performed optimization procedures (varied glycerol/nitrogen ratio and feeding) has resulted in a PHB content of 70.9%, shorter cultivation time (23 h) and better PHB yield (0.347 g g(-1)). Initial concentration of biomass 16.8 g L(-1) and glycerol concentration in broth between 3 and 5 g L(-1) were decisive factors for increasing of productivity.

Study of metabolic network of Cupriavidus necator DSM 545 growing on glycerol by applying elementary flux modes and yield space analysis

A metabolic network consisting of 48 reactions was established to describe intracellular processes during growth and poly-3-hydroxybutyrate (PHB) production for Cupriavidus necator DSM 545. Glycerol acted as the sole carbon source during exponential, steady-state cultivation conditions. Elementary flux modes were obtained by the program Metatool and analyzed by using yield space analysis. Four sets of elementary modes were obtained, depending on whether the pair NAD/NADH or FAD/FADH2 contributes to the reaction of glycerol-3-phosphate dehydrogenase (GLY-3-P DH), and whether 6-phosphogluconate dehydrogenase (6-PG DH) is present or not. Established metabolic network and the related system of equations provide multiple solutions for the simultaneous synthesis of PHB and biomass; this number of solutions can be further increased if NAD/NADH or FAD/FADH2 were assumed to contribute in the reaction of GLY-3-P DH. As a major outcome, it was demonstrated that experimentally determined yields for biomass and PHB with respect to glycerol fit well to the values obtained in silico when the Entner–Doudoroff pathway (ED) dominates over the glycolytic pathway; this is also the case if the Embden–Meyerhof–Parnas pathway dominates over the ED.

Mathematical models for mixing in deep jet bioreactors: analysis

A mathematical model for single and multi step deep-jet bioreactors is presented. A stagewise approach based on macroscopic mechanistic model which divides the reactor into compartments with good quality of mixing and plug flow regions (macromixer), was used. For the mathematical representation of this model a system of differential equations, describing the concentration of tracer in structural elements based on mass balance, and the Runge-Kutta-Fehlberg numerical method of integration, was applied. The mixing time in a 300 dm3 tank was determined by conductivity method with NaCl as tracer.