Andrzej Kasperski

Nonlinear modelling of a synchronized chemostat with impulsive state feedback control

Bioreactor control is an active area of research on continuous microorganism cultivation. Control of the substrate concentration in the bioreactor medium is especially necessary because of the substrate inhibition phenomenon. Moreover in order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed a set level. To maintain the biomass concentration in the desired range the universal mathematical model of a continuous bioprocess with impulsive state feedback control is formulated in the article. By discussing the dynamic properties of the model including the existence and stability of the periodic solution, the choice of suitable operating conditions for continuous culture systems can be simplified, offering the possibility of establishing general and more systematic operations and control strategies based on the counteraction of the mechanisms underlying the adverse effects of the bioreactor dynamics. The article also presents and discusses aspects of the bioprocess optimization.

Modelling and simulation of a continuous process with feedback control and pulse feeding

Abstract This paper deals with feedback control of a microorganism continuous culture process with pulse dosage supply of substrate and removal of products. By the analysis of the dynamic properties and numerical simulation of the continuous process, the conditions are obtained for the existence and stability of positive period-1 solution of the system. It is also pointed out that there does not exist positive period-2 solution. The results simplify the choice of suitable operating conditions for continuous culture systems. It also gives the complete expression of the period of the positive period-1 solution, which provides the precise feeding period for a regularly continuous culture system to achieve the same stable output as a continuous culture system with feedback control in the same production environment.

Modelling of cells bioenergetics.

This paper presents an integrated model describing the control of Saccharomyces cerevisiae yeast cells bioenergetics. This model describes the oxidative and respirofermentative metabolism. The model assumes that the mitochondria of the Saccharomyces cerevisiae cells are charged with NADH during the tricarboxylic acid cycle, and NADH is discharged from mitochondria later in the electron transport system. Selected effects observed in the Saccharomyces cerevisiae eucaryotic cells, including the Pasteurs and Crabtree effects, are also modeled.

Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect.

This work presents the first mathematical model of a bioprocess with product inhibition and impulse effect. To begin with, an exemplary mathematical bioprocess model with product inhibition and impulse effect is formulated. Then, according to the model, the analysis of bioprocess stability is presented. The article expresses the product oscillation period, which provides the precise feeding time frame for the regulator bioprocess to achieve an equivalent stable output as that of a bioprocess with impulse effect in the same production environment. Moreover, in this work, the optimization of the production process with respect to the tunable parameters is investigated, and analytical expressions of their optimal values are provided. Numerical simulations using biological data are presented to illustrate the main results.

Nonlinear Modelling and Qualitative Analysis of a Real Chemostat with Pulse Feeding

The control of substrate concentration in the bioreactor medium should be due to the substrate inhibition phenomenon. Moreover, the oxygen demand in a bioreactor should be lower than the dissolved oxygen content. The biomass concentration is one of the most important factors which affect the oxygen demand. In order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed a critical level. Based on the design ideas, a mathematical model of a chemostat with Monod-type kinetics and impulsive state feedback control for microorganisms of any biomass yield is proposed in this paper. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions for the existence of period-1 solution of the system are obtained. The results simplify the choice of suitable operating conditions for continuous culture systems. It also points out that the system is not chaotic according to the analysis on the existence of period-2 solution. The results and numerical simulations show that the chemostat system with state impulsive control tends to a stable state or a period solution.

Universal modelling and qualitative analysis of an impulsive bioprocess

The work proves that in an impulsive bioprocess the stable oscillation period exists for any microorganisms – i.e. microorganisms of any characteristics of biomass yield and specific growth rate – pointing out the practical and scientific importance of the presented solution. Moreover, universal stability conditions of the impulsive bioprocess are presented. In order to obtain the universality of the solution, a sigmoid function is introduced for description of the biomass yield changes. Further, the universal mathematical model of the impulsive bioprocess is established, tested and discussed. This work shows among others that the impulsive bioprocess extends functionality of a simple continuous bioprocess providing in an easy way to control biomass concentration. The article also introduces a new objective function and then presents and discusses aspects of the impulsive bioprocess multi-criteria optimization. The analytical results presented in the work are validated by numerical simulations.

New Approach to the Nonlinear Analysis of a Chemostat with Impulsive State Feedback Control

Bioreactor control is an important area of research concerning continuous microorganism cultivation. The possible occurrence of the substrate inhibition phenomenon or substrate deficiency engenders the necessity to the control the substrate concentration. Moreover in order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed the set out level. To maintain the substrate and biomass concentration in certain desired ranges, a proposal of a new chemostat with pulse state feedback control is presented in the work. Then, a universal mathematical model of the chemostat is formulated, and the dynamic properties of the model including the existence and stability of the periodic solution are discussed. After this, in order to optimize the biomass production, two objective functions are introduced and the optimization is performed. The work shows that the proposed chemostat extends functionality of a chemostat providing in easy way the control of biomass and substrate concentration. The analytical results presented in the work are validated by numerical simulations.

Theoretical Study and Optimization of the Biochemical Reaction Process by Means of Feedback Control Strategy

The aim of this work is to present a theoretical analysis and optimization of a biochemical reaction process by means of feedback control strategy. To begin with, a mathematical model of the biochemical reaction process with feedback control is formulated. Then, based on the formulated model, the analysis of systems dynamics is presented. The optimization of the bioprocess is carried out, in order to achieve maximal biomass productivity. It is shown that during the optimization, the bioprocess with impulse effects loses the possibility of synchronization and strives for a simple continuous bioprocess. The analytical results presented in the work are validated by numerical simulations for the Tessier kinetics model.

Studies on generalized kinetic model and Pareto optimization of a product-driven self-cycling bioprocess

The aim of this study is the optimization of a product-driven self-cycling bioprocess and presentation of a way to determine the best possible decision variables out of a set of alternatives based on the designed model. Initially, a product-driven generalized kinetic model, which allows a flexible choice of the most appropriate kinetics is designed and analysed. The optimization problem is given as the bi-objective one, where maximization of biomass productivity and minimization of unproductive loss of substrate are the objective functions. Then, the Pareto fronts are calculated for exemplary kinetics. It is found that in the designed bioprocess, a decrease of emptying/refilling fraction and an increase of substrate feeding concentration cause an increase of the biomass productivity. An increase of emptying/refilling fraction and a decrease of substrate feeding concentration cause a decrease of unproductive loss of substrate. The preferred solutions are calculated using the minimum distance from an ideal solution method, while giving proposals of their modifications derived from a decision maker’s reactions to the generated solutions.

Bioenergetics of life, disease and death phenomena

In this article, some new aspects of unified cell bioenergetics are presented. From the perspective of unified cell bioenergetics certain subsequent stages of cancer development, from initiation stage, through transformation to metastasis, are analyzed. Here we show that after transformation, cancer cells are permanently exposed to reactive oxygen species, that causes continual random DNA mutations and as a result genome and chromosomal destabilizations. The modern cancer attractor hypothesis has been extended in explaining cancer development. Discussion is conducted in light of current cancerogenesis research, including bioenergetic cancer initiation, the somatic mutation theory and the tissue organization field theory. In the article reasons complicating the discovery of patterns of cancer genome changes and cancer evolution are presented. In addition certain cancer therapeutic aspects are given attention to.