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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Closes the gap between bioscience and mathematics-based process engineering This book presents the most commonly employed approaches in the control of bioprocesses. It discusses the role that control theory plays in understanding the mechanisms of cellular and metabolic processes, and presents key results in various fields such as dynamic modeling, dynamic properties of bioprocess models, software sensors designed for the online estimation of parameters and state variables, and control and supervision of bioprocesses Control in Bioengineering and Bioprocessing: Modeling, Estimation and the Use of Sensors is divided into three sections. Part I, Mathematical preliminaries and overview of the control and monitoring of bioprocess, provides a general overview of the control and monitoring of bioprocesses, and introduces the mathematical framework necessary for the analysis and characterization of bioprocess dynamics. Part II, Observability and control concepts, presents the observability concepts which form the basis of design online estimation algorithms (software sensor) for bioprocesses, and reviews controllability of these concepts, including automatic feedback control systems. Part III, Software sensors and observer-based control schemes for bioprocesses, features six application cases including dynamic behavior of 3-dimensional continuous bioreactors; observability analysis applied to 2D and 3D bioreactors with inhibitory and non-inhibitory models; and regulation of a continuously stirred bioreactor via modeling error compensation. * Applicable across all areas of bioprocess engineering, including food and beverages, biofuels and renewable energy, pharmaceuticals and nutraceuticals, fermentation systems, product separation technologies, wastewater and solid-waste treatment technology, and bioremediation * Provides a clear explanation of the mass-balance-based mathematical modelling of bioprocesses and the main tools for its dynamic analysis * Offers industry-based applications on: myco-diesel for implementing "quality" of observability; developing a virtual sensor based on the Just-In-Time Model to monitor biological control systems; and virtual sensor design for state estimation in a photocatalytic bioreactor for hydrogen production Control in Bioengineering and Bioprocessing is intended as a foundational text for graduate level students in bioengineering, as well as a reference text for researchers, engineers, and other practitioners interested in the field of estimation and control of bioprocesses.
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Table of Contents
Cover
Preface
Part I: Overview of the Control and Monitoring of Bioprocesses and Mathematical Preliminaries
1 Introduction
1.1 Overview of the Control and Monitoring of Bioprocesses
1.2 Improvements to Bioprocesses Productivity
1.3 Bioprocess Control
1.4 Process Measurements
1.5 Dynamic Bioprocess Models
1.6 Process Optimization
References
2 Mathematical Preliminaries
2.1 Systems of Ordinary Differential Equations
2.2 Linear Systems
2.3 Nonlinear Dynamical Systems and its Analysis
2.4 Stability Theory via Lyapunov Approach
2.5 Bifurcation Theory
2.6 Overview of Non-Smooth Dynamical Systems
References
Part II: Observability and Control Concepts
3 State Estimation and Observers
3.1 Observability
3.2 Observer Designs for Linear Structures
3.3 Observer Designs for Nonlinear Structures
References
4 Control of Bioprocess
4.1 The Control Idea
4.2 Controllers for Linear Systems
4.3 Nonlinear Controllers
References
Part III: Software Sensors and Observer-Based Control Schemes for Bioprocess
5 Dynamical Behavior of a 3-Dimensional Continuous Bioreactor
5.1 Introduction
5.2 Bioreactor Modeling
5.3 Main Results
5.4 Concluding Remarks
References
6 Observability Analysis Applied to 2D and 3D Bioreactors with Inhibitory and Non-inhibitory Kinetics Models
6.1 Introduction
6.2 Materials and Methods
6.3 Results and Discussion
6.4 Implementation of a Linear Observer to Check the Results of the Observability Analysis
6.5 Conclusion
References
7 Production System Myco-Diesel for Implementation of “Quality” of the Observability
7.1 Introduction
7.2 Methodology
7.3 Main Results
7.4 Conclusions
References
8 Regulation of a Continuously Stirred Bioreactor via Modeling Error Compensation
8.1 Introduction
8.2 Materials and Methods
8.3 Input–Output Identified Model
8.4 Control Design
8.5 Main Results
8.6 Concluding Remarks
References
9 Development of Virtual Sensor Based on the Just-In-Time Model for Monitoring of Biological Control Systems
9.1 Introduction
9.2 Materials and Methods
9.3 On-line Monitoring (Proposed Nonlinear Observer)
9.4 Such Approaches, Known as Proposed Just-in-Time Modeling “Hybrid Systems”
9.5 Results
9.6 Conclusions
References
10 Virtual Sensor Design for State Estimation in a Photocatalytic Bioreactor for Hydrogen Production
10.1 Introduction
10.2 Material and Methods
10.3 Mathematical Model Development
10.4 Virtual Sensor Design
10.5 Results and Discussion
10.6 Conclusions
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Bioprocess based sustainable production [34].
Table 1.2 The most common requirements for microorganism's growth [45].
Table 1.3 Most bioprocesses consist of some general phases that are conducted...
Table 1.4 Summary: model controllers applied in bioprocesses [59].
Table 1.5 Feedback control strategies with focus on the monitoring technique ...
Table 1.6 Advantages and disadvantages of different methods for software sens...
Table 1.7 Kinetic models of inhibition.
Table 1.8 Kinetic models of inhibition by product (the expression of the comp...
Table 1.9 Modified kinetic models.
Chapter 2
Table 2.1 Review of the basic theorem of Lyapunov [27].
Table 2.2 Properties for the Lyapunov theorem.
Table 2.3 Local stability R
2
[49].
Table 2.4 Parameters used in modeling and their meaning.
Chapter 4
Table 4.1 Review and applications of the properties the controllability and o...
Table 4.2 Control techniques actually applied to real bioprocesses [29].
Chapter 5
Table 5.1 Kinetic rates and coefficient yields definitions.
Table 5.2 Kinetic models for substrate and product inhibition.
Table 5.3 Kinetic parameters estimated for
Desulfovibrio alaskensis
6SR.
Table 5.4 Correlation coefficients R
2
.
Table 5.5 Variability of the internal dynamics of each model with respect to ...
Chapter 6
Table 6.1 Kinetic models of inhibition.
Table 6.2 Overall results of the observability analysis applied to 2D and 3D ...
Chapter 7
Table 7.1 Kinetic parameters for
Mortierella isabellina
growth.
Chapter 8
Table 8.1 Parameters of the proposed model.
Table 8.2 Correlation coefficients
Chapter 9
Table 9.1 Parameters of model proposed.
Table 9.2 Correlation coefficients.
Chapter 10
Table 10.1 Procedure for the adjustment of kinetic parameters of the proposed...
Table 10.2 Hydrogen productivities reported in literature works.
Table 10.3 Kinetic parameters for the mathematical model.
Table 10.4 Correlation coefficients and model efficiency.
Table 10.5 Local properties: stability and observability.
List of Illustrations
Chapter 1
Figure 1.1 Opportunities for control by topics [3–12].
Figure 1.2 Comparison of: (a) experimental sulfate, (b) experimental biomass...
Figure 1.3 Comparison of: (a) experimental lactate, and (b) experimental ace...
Figure 1.4 Comparison of experimental Cd
2+
with predictions of the model...
Figure 1.5 Simple metabolic model with feedback.
Figure 1.6 Temporal evolution of the variables described by Eqs. (1.7 and 1....
Figure 1.7 The figure shows phase-plane, we see that the trajectories are at...
Figure 1.8 Temporal evolution of the variables described by Eqs. (1.7 and 1....
Figure 1.9 The figure shows Phase-plane, we see that the trajectories are at...
Figure 1.10 Temporal evolution of the variables concentration of the system ...
Figure 1.11 The figure shows a phase-plane, we see that the trajectories are...
Figure 1.12 Schematic representing the current improvements to bioprocesses ...
Figure 1.13 Bioprocess operations [43].
Figure 1.14 Illustrative example for bioprocess monitoring and control.
Figure 1.15 Efficient fermentation process.
Figure 1.16 Concept of stability.
Figure 1.17 Scheme of stability and unstable of equilibrium.
Figure 1.18 Overall scheme of bioprocesses and basic control structures.
Figure 1.19 On-line measurements for monitoring bioprocess [83–89].
Figure 1.20 Balance equation based methods.
Figure 1.21 Observer based on mathematical model.
Figure 1.22 Kalman filter.
Figure 1.23 Neural networks.
Figure 1.24 Fuzzy reasoning.
Figure 1.25 Conceptual scheme explaining the principle of a bioreactor.
Figure 1.26 Comparison of experimental data (symbol) and predictions of the ...
Figure 1.27 Ethanol concentration, and productivity in continuous processes.
Chapter 2
Figure 2.1 Schematic diagram of the activated-sludge process.
Figure 2.2 Temporal evolution of the variable's concentration described by E...
Figure 2.3 Phase diagram of the open-loop system of output variables, the ef...
Figure 2.4 Dynamical system.
Figure 2.5 Showing initial condition (
x
0
,
y
0
) enclosed in neighborhoods R and...
Figure 2.6 Geometry stability concept.
Figure 2.7 Stability Lyapunov.
Figure 2.8 The Goodwin oscillator. Phase portrait showing convergence to a l...
Figure 2.9 Dynamics evolution of the concentrations described by Eqs. (2.98)...
Chapter 3
Figure 3.1 A general estimation scheme (
x
: state variables, π: parameters,
y
Chapter 4
Figure 4.1 The control idea in bioprocess.
Figure 4.2 Schematic of the nonlinear PI controller.
Figure 4.3 Stabilization by state feedback.
Chapter 5
Figure 5.1 Open-loop and closed-loop dynamics of the four proposed model for...
Figure 5.2 Open-loop and closed-loop dynamics of the four proposed model for...
Figure 5.3 Open-loop and closed-loop dynamics of the four proposed model for...
Figure 5.4 Open-loop and closed-loop dynamics of the four proposed model vs ...
Figure 5.5 Open-loop and closed-loop dynamics for performance index.
Figure 5.6 Open-loop and closed-loop dynamics of the four proposed model in ...
Figure 5.7 The zero dynamics performance of the uncontrolled states.
Chapter 6
Figure 6.1 Results of (symbols) actual values, (lines) Luenberger observer. ...
Figure 6.2 Results of (symbols) actual values, (lines) Luenberger observer. ...
Chapter 7
Figure 7.1 Bioreactor scheme for continuous culture system.
Figure 7.2 Bifurcation diagram of the four state variables: hydrolyzed sugar...
Figure 7.3 Bifurcation diagram of the sugar consumption (PS) and lipid produ...
Figure 7.4 Variations in the singular values of the observability matrix wit...
Figure 7.5 Condition number for the observability matrix (logarithmic scale)...
Figure 7.6 Simulation of a continuous bioreactor that produces mycodiesel an...
Figure 7.7 Performance index (ITSE) of the observer for the nitrogen concent...
Chapter 8
Figure 8.1 Dynamics of biomass, sulfate and sulfide concentrations.
Figure 8.2 Dynamics of acetate, lactate and biomass concentrations.
Figure 8.3 Open-loop and closed-loop dynamics of acetate, lactate, and sulfa...
Figure 8.4 Open-loop and closed-loop dynamics of sulfide and biomass.
Figure 8.5 Control effort.
Figure 8.6 Performance index.
Chapter 9
Figure 9.1 Virtual sensor based on JIT model for monitoring of biological co...
Figure 9.2 Software sensor coupled to the JIT approach in real time.
Figure 9.3 Simulation of mycoparasitism. Dynamic behavior of the experimenta...
Figure 9.4 Simulation of mycoparasitism. Dynamic behavior of the experimenta...
Figure 9.5 Simulation of mycoparasitism. Dynamic behavior of the experimenta...
Figure 9.6 Simulation of mycoparasitism. Dynamic behavior of the experimenta...
Figure 9.7 Simulation of mycoparasitism. Dynamic behavior of the experimenta...
Figure 9.8 Simulation of mycoparasitism. Dynamic behavior of the experimenta...
Figure 9.9 Simulation of mycoparasitism. Dynamic behavior of the experimenta...
Figure 9.10 The integral time absolute error. Numerical simulations (extende...
Chapter 10
Figure 10.1 The bio-hydrogen production in microorganism “strategies”.
Figure 10.2 Conceptual model.
Figure 10.3 Schematic representation of virtual sensor design.
Figure 10.4 Sulfate reduction and cadmium removal, the comparison between ba...
Figure 10.5 Biomass, acetate, cadmium sulfide and carbon dioxide, the compar...
Figure 10.6 Hydrogen production, the comparison between batch experimental d...
Figure 10.7 Sulfate reduction and cadmium removal, a comparison between batc...
Figure 10.8 Biomass, acetate, cadmium sulfide and carbon dioxide, a comparis...
Figure 10.9 Hydrogen production, a comparison between batch experimental dat...
Guide
Cover
Table of Contents
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Control in Bioprocessing
Modeling, Estimation and the Use of Soft Sensors
Pablo Antonio López Pérez
Escuela Superior de Apan, Universidad Autónoma del Estado de Hidalgo, México.
Ricardo Aguilar Lopez
Department of Biotechnology and Bioengineering, Center for Research and Advanced Studies (Cinvestav), México
Alejandro Ricardo Femat Flores
Department of Applied Mathematics, Institute for Scientific and Technological Research of San Luis Potosi (IPICYT), México
This edition first published 2020
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Library of Congress Cataloging-in-Publication Data Applied for
HB ISBN: 9781119295990
Cover Design: Wiley
Cover Image: © Reptile8488/Getty Images
Preface
The purpose of this book is to present the different approaches most commonly employed in the control of bioprocesses. It aims to develop in some detail the bases and concepts of bioprocesses related to the control theory introduced in basic principles of mathematical modeling in bioprocesses. From this viewpoint, the systems approach to bioengineering and bioprocessing, with its current focus on the development of mathematical models and their analysis, is a logical sequel that the control theory that will play a relevant role in understanding the mechanisms of cellular and metabolic processes. It concerns specifically applications in modeling, estimation, and control of bioprocesses. Consequently, this book presents key results in various fields, including: dynamic modeling, dynamic properties of bioprocess models, software sensors designed for the online estimation of parameters and state variables, and control and supervision of bioprocesses. The book is divided into three sections.
Part I: Overview of the Control and Monitoring of Bioprocesses and Mathematical Preliminaries, contains Chapters 1 and 2. Chapter 1 is a general overview of the control and monitoring of biotechnological processes. Chapter 2 introduces the mathematical framework necessary for the analysis and characterization of bioprocess dynamics. In other words, Chapter 2 deals with the mathematical approach we follow to describe the evolution in time of the bioprocess under consideration. Therefore, understanding and formalizing the role of nonlinearity is indeed one of the greatest challenges in the study of living systems, mainly in bioprocesses. In engineering practice two of the most important sources of modeling error are the presence of nonlinearities in the system and a lack of exact knowledge of some of the system parameters, therefore, it is necessary to describe the properties of the state of the dynamics of the nominal model under the theory of systems.
Part II: Observability and control concepts, contains Chapter 3 on state estimation and observers and Chapter 4 focusses on control of bioprocess. Chapter 3 introduces the reader to the observability concepts that are the basis to designing online estimation algorithms (software sensor) for bioprocess. The observability conditions for bioprocess models from local linearization, differential geometric and algebraic differential approaches are established. Chapter 4 reviews the controllability concepts that are the basis for designing automatic feedback control schemes for bioprocesses. A clear explanation is developed from the classical linear schemes to advanced robust algorithms with application in bioprocess systems. However, performance may degrade when they are applied to highly nonlinear processes, which are the fact rather than the exception in the chemical and biochemical process industry.
Part III: Software sensors and observer-based control schemes for bioprocess. This last part deals with application cases in Chapters 5–10. Chapter 5 covers the dynamical behavior of a three-dimensional continuous bioreactor. The dynamic behavior of a two-dimensional model of a continuous bioreactor was studied in this chapter. The objective of the analysis under the control of feedback allows the most suitable regions to be found and to model where the best performance of the bioreactor operates. Chapter 6 reviews observability analysis applied to 2D and 3D bioreactors with inhibitory and non-inhibitory kinetics models. The results indicate that the proposed model can be applied for simulation in different conditions of operation for possible instrumentation, estimation and control from laboratory scale up to semi-pilot scale. Chapter 7 introduces the production system myco-diesel for implementation of "quality" of the observability. Myco-diesel is a new alternative and, compared to traditional fossil fuels, an environmentally sustainable biofuel source due to reduced gas emission. It is made from renewable bioprocess sources such as vegetable oils, animal fats, and microorganism culture. Chapter 8 is about the regulation of continuously stirred bioreactors via modeling error compensation. The aim of this chapter is to control the nonlinear behavior of a class of continuously stirred bioreactors with regulation purposes. From the above, a linearized representation of the state space bioreactor's model is obtained via standard identification processes employing a step disturbance in the control input. Chapter 9 reviews the development of virtual sensors based on the just-in-time model for monitoring of biological control systems. Real-time monitoring of physiological characteristics during a cultivation process is of great importance in bioprocesses. Biological control involves the use of beneficial organisms for metabolite production that reduces the negative effects of plant pathogens disease suppression. Finally, chapter 10 discusses virtual sensor design for state estimation in a photocatalytic bioreactor for hydrogen production. This chapter is focused on the design of a virtual sensor for a class of continuous bioreactors to estimate the production of hydrogen. The proposed mathematical model is suitable for predicting concentrations of biomass, acetate, cadmium in liquid, sulfate, lactate, carbon dioxide, sulfide, and cadmium sulfide, as well as hydrogen production.
Bioprocess modeling and control still offers interesting perspectives to obtain automatization solutions for the aerobic and anaerobic bioprocesses.
Part IOverview of the Control and Monitoring of Bioprocesses and Mathematical Preliminaries
1Introduction
This chapter aims to develop in some detail the basis and concepts of the bioprocesses related to the control theory introduced in the basic principles of mathematical modeling in bioprocesses. From this viewpoint, the systems approach bioengineering and bioprocessing, with a current focus on the development of mathematical models and their analysis, which logically results in the control theory playing a relevant role in the understanding of the mechanisms of cellular and metabolic processes. It concerns specifically applications in modeling, estimation, and control of bioprocesses. Consequently, there are many exciting opportunities for control experts who want to shift their interest to bioprocesses.
1.1 Overview of the Control and Monitoring of Bioprocesses
1.1.1 Why Nonlinear Control in Bioprocesses?
Nowadays, many proteins and metabolites are produced by genetically modified microorganisms applied to bioprocesses. Since the physical, biochemical, and genetic properties of the bacterium Escherichia coli are the best known, it is the most generic host microorganism used for the production of bio-products.
The success of this process is ensured by appropriate control of the feeding rate. In other words, under-feeding causes productivity loss and starvation whereas over-feeding leads to carbon nutrient accumulation or by-product formation, such as acetate [1, 2].
Current bioprocess control technology and opportunities include biotherapeutics, specialty chemicals, and reagents such as diagnostics, biochemicals for research, and enzymes for the food and consumer markets.
Products and services that depend on bioprocessing can be grouped broadly into antibiotics, therapeutic proteins, polysaccharides, vaccines and diagnostics, value-added food, and agricultural products, as well as fuels, specialty products and industrial chemicals, and fibers from renewable resources (see Figure 1.1) [13].
Of course, any bioprocess may be considered as a system, being built up of large numbers of individual organisms or cells, each of which may show a far simpler behavior than the whole system or may show a far more complex one.
Despite the diversity of organisms, they all possess the following specific features that must be taken into account in studying and designing the bioprocesses: cells self-organize, interaction between intra-cellular processes and inter/extra-cellular systems, metabolic processes, signaling, and regulatory bioprocesses at different molecular levels, organized and regulated interplay between different pathways or network modules, structured and non-structured models (metabolic or genetic level), inorganic, and organic matter for the biosynthesis of biological macromolecules, homogeneous and heterogeneous systems, flows of matter and energy, for example, of inorganic ions and organic molecules. An outline of these topics is shown in Figure 1.1.
Figure 1.1 Opportunities for control by topics [3–12].
Achievements in modern biology have revealed numerous facts related to the structure and regulation of many intracellular systems. Schemes of bioprocesses are complex, they have nonlinear kinetics, a chemical structure and, in most cases, the molecular structures of the components of processes are examined, including the bio-regulators. This makes it possible to construct mathematical computer models that allow formalization of the knowledge of complex biological objects. The degree of specification of models can be different depending on the goal of modeling and on the degree of completeness of the examination of the objects. If the modeling is aimed at control, for example, an efficiency increase in the output of a biotechnological process is desired, and then it is often sufficient to consider individual blocks as components and examine stationary states of a system. They are modeled by “constructors”, that is, programs that automatically write differential equations according to a prescribed scheme of processes and expressions for the rates of individual reactions. In investigating such complex systems, the theory of metabolic control has a deserved good reputation. If an object is thoroughly examined, mathematical models become an effective method of fundamental research. By solving inverse problems, they allow the estimation of kinetic and physical parameters of a holistic system, which is impossible in experimentation without fractionating a system. In complex biological systems, the latter leads to the modification of the functional activity [14].
Control of bioprocesses is a complicated task for, at least, the following three reasons:
The process' complexity, nonlinearity and non-stationarity which make modeling and parameter estimation particularly difficult.
The scarcity of on-line measurements of the component concentrations (essential substrates, biomass, and products of interest) [
14
].
Furthermore, almost all such bioprocesses are nonlinear systems. Because of the large number of interactions in such systems, some are bound to be nonlinear. Given the large number of species, strains, and consortia, they are almost certain to show chaotic behaviors under a wide range of conditions. Complex systems may show roughly four types of behavior:
steady state,
periodic,
complex, and
chaotic.
steady state is the simplest; the system is unmoving into a particular state. Though there may be some initial oscillations, these die out and the system settles down into its final state [15].
A dynamical system is a simple system that can be characterized by
a set of parameters the values of which define its state at a given point in time, and
a set of mathematically specified rules defining the change of state of the system with time.
The rules of dynamical systems can be specified as differential equations, defining the rate of change of each of the parameters describing the system, as a function of the current state of the system. This definition is broad indeed, and many systems in biotechnology, bioengineering, medicine, bio-economics, and the social sciences may be described and studied as dynamical systems. The extracellular and intracellular metabolite concentrations from industrial bacteria, either strain [16, 17], mixed cultures (consortia) [18], or ecosystems [19] can be described in terms of dynamical systems. The key feature of the dynamics of these systems is that they show autocatalytic or inhibitory loops: the presence of a biomass is needed to make more of that kind of biomass.
Furthermore:
some species may inhibit other species by secretion of toxins by competition;
some species might also enhance growth by producing metabolites that serve as food for other species by cooperation;
or may remove or reduce concentrations of toxic substances by symbiosis.
In systems that are far from the thermodynamical equilibrium, such autocatalytic and inhibitory loops produce just the type of nonlinear dynamics that can produce highly complicated and chaotic behaviors [15].
In practice, all ecosystems are far from thermodynamic equilibrium, since large fluxes of energy or food pass through them; only death (a point attractor of any ecosystem) corresponds to thermodynamic equilibrium.
For these reasons it may be assumed that techniques for analysis and modeling of nonlinear dynamical systems are, in general, appropriate tools for the study of bioprocesses including bacterial, fungal, mammalian cells, or insect or plant cells. The following examples are developed (modeling and simulation) to represent the diversity and complexity of some bioprocesses:
Example 1.1 A Mathematical Model for Cadmium Removal Via Sulfate-Reducing Process
Sulfate reducing bacteria (SRB) have been used to solve a number of environmental problems, e.g. removal of metals from wastewater through the production of biogenic sulfides, followed by metal precipitation. A mathematical model was developed to describe the kinetics of cadmium (Cd2+) removal in a batch bioreactor. The classical growth with reduction of sulfate to H2S is described by Eqs. (1.1–1.6). The Levenspiel inhibition model was modified to describe the reduction of sulfate. The model considers the inhibitory effect of sulfide (H2S) on microbial growth [20–22]. The mass balance of the various concentrations gives the following set of equations:
Sulfate (S) mass balance:
Sulfide (P) mass balance:
Biomass (X) balance:
Lactate (L) mass balance:
Acetate (A) mass balance:
The mass balance describing the removal of Cd2+:
In addition, the model showed that the H2S production rate and initial concentration of Cd2+ are key operating variables in a bioreactor. Desulfovibrio alaskensis 6SR was able to remove more than 99.9% of cadmium in a batch process (see Figures 1.2 and 1.3), where the initial concentration was 170 mg l−1(see Figure 1.4).
Figure 1.2 Comparison of: (a) experimental sulfate, (b) experimental biomass, and (c) experimental sulfide with predictions of the model (—).
Figure 1.3 Comparison of: (a) experimental lactate, and (b) experimental acetate.
Figure 1.4 Comparison of experimental Cd2+ with predictions of the model (—).
Example 1.2 Simple Metabolic Model
As an example, we consider a simple metabolic model, illustrated by the Figure 1.5 [23]. Both types of feedback loop are important in biological systems, and both can produce chaos, the mathematical complexity of which often produces strange, beautiful, and totally unexpected patterns that have only begun to be explored using the computational capabilities of modem electronic computers. Examples of such systems are found in catabolic pathways in which the first step involves coupling of adenosine triphosphate (ATP) hydrolysis to activation of a substrate [24, 25].
Figure 1.5 Simple metabolic model with feedback.
Figure 1.6 Temporal evolution of the variables described by Eqs. (1.7 and 1.8). It is demonstrated, that increasing the nonlinearity in the model leads to the sustained oscillatory behavior.
This scheme is motivated by the “turbocharged” positive feedback aspect of the glycolytic chain in which the ATP output is used to produce more ATP. The potential for oscillations can be inferred from the model structure: the concentration of species S2 builds up, causing further buildup until the pool of S1 is depleted. The S2 level then crashes until more S1 is available, and so on. Although this intuitive argument indicates the potential for oscillatory behavior, it cannot predict the conditions under which oscillations will occur (see, Figures 1.6–1.9). Positive feedback tends to reinforce the effects of changes in the input signal, producing instability, oscillation, and even catastrophic destruction of the system [26].
Figure 1.7 The figure shows phase-plane, we see that the trajectories are attracted to a cyclic track, called a limit cycle, the parameter values used are π0 = 8, r1 = 1, r2 = 5, r3 = 1, and n = 2.
Figure 1.8 Temporal evolution of the variables described by Eqs. (1.7 and 1.8). The parameter values used are v0 = 8, k1 = 1, k2 = 5, k3 = 1, and q = 2.
Figure 1.9 The figure shows Phase-plane, we see that the trajectories are attracted to a cyclic track, called a limit cycle, the parameter values used are v0 = 8, k1 = 1, k2 = 5, k3 = 1, and q = 2.
The equations describing the system are given by
The qualitative behavior of the system changes as the parameter values shift [23].
Example 1.3 Glucose Regulatory System
Diabetes is a dysfunction of the equilibrium in the blood glucose homeostasis. This is caused by an autoimmune attack on beta cells secreted by the pancreas (Type 1) or by the inadequate supply or function of β-cells in counteracting the fluctuations of high and low blood glucose within the body (Type 2) [27, 28]. The experimental data suggests that multiple defects are required for the onset of type 2 diabetes [29]. Glucose dynamics is released into the blood by the liver and kidneys, removed from the interstitial fluid by all the cells of the body, and distributed into many physiological compartments (e.g. arterial blood, venous blood, interstitial fluid). Experimental studies have shown that despite such a complex distribution, slow glucose dynamics (on a time scale of hours and larger) can be modeled using a one-compartment approximation [30, 31]. Mathematical modeling of diabetes has focused predominantly on the dynamics of a single variable, usually glucose or insulin level [30]. Those models were usually used for measuring either rates (glucose, insulin production/uptake) or sensitivities (insulin sensitivity, glucose effectiveness) [31]. The model introduced by Topp et al. [29] incorporates β-cell mass, insulin, and glucose dynamics, and gives rises to a stiff system of ordinary differential equations (ODEs). The resulting system has two stable sink type equilibrium points and a saddle point. The description of the model presented in this section follows the original paper of Topp et al. [29].
Although simplistic, the systemic reduced-order model allows us to show how it is possible to study a biosystem in the context of this book. The mathematical model studied gives the following set of equations:
: The amount of insulin in the plasma with respect to time.
f
1
: The pancreatic insulin production controlled by the glucose concentration. E: A constant transfer rate for exchange of insulin between plasma and remote compartments. Ip: The amount of insulin in the plasma. Ii: The amount of insulin in the intracellular space. vp: The distribution volume for insulin in the plasma. vi: The effective volume of the intracellular space. tp: The insulin in the plasma as a time constant.
: The amount of glucose in the body with respect to time.
G
in
: The influx of glucose in the plasma and intracellular space at an exogenously controlled rate.
f
2
: The insulin-glucose independent utilization (uptake by the brain and nerve cells).
f
3
: The glucose utilization by the muscle and fat cells.
f
4
: The relationship between the plasma insulin concentration and the cellular glucose uptake.
: The inhibition of hepatic glucose production via the insulin stimulating pancreatic insulin production.
: Physiological action of insulin on the utilization of glucose correlated with the concentration of insulin in a slowly equilibrating intercellular compartment rather than with the concentration of insulin in the plasma.
: Time lag between the appearance of insulin in the plasma and its inhibitory effect on the hepatic glucose production.
t
d
: The response of the hepatic glucose production to changes in the plasma insulin concentration involves a time delay.
x
1
,
x
2
,
x
3
: Represents the relationship between the time delays of insulin in plasma and its effect on the hepatic glucose production.
R
m
: The rate of glucose metabolism within the cell.
C
1
: A given parametric value attained by experimental tests that pertains to the process within the function.
G
: Glucose.
V
g
: The volume of Glucose b
α
1
: A given parametric value attained by experimental tests that pertains to the process within the function.
U
b
C
2
: Are given parametric values attained by experimental tests that pertains to the process within the function.
V
g
: The Volume of Glucose.
C
3
: A given parametric value attained by experimental tests that pertains to the process within the function.
U
o
t
i
C
4
β
V
i
U
m
: Are all given parametric values attained by experimental tests that pertain to the process within the function.
R
g
: A given parametric value that denotes rate of glucose.
α
: A given constant transfer rate.
C
5
: A given parametric value attained by experimental tests that pertains to the process within the function.
The effect of the frequency of the oscillations on the extent of the inhibition of the hepatic glucose production needs further experimental investigation. Such experiments should be designed so that only the frequency is varied, whilst the mean value of the plasma insulin remains constant (see, Figure 1.10). Furthermore, it may be desirable to replace the variables for the time delay between the insulin in plasma and its effect on the hepatic glucose production by physiologically meaningful state variables.
Such a mechanism could result from effects of insulin on the pancreatic alpha cells, adipocytes, and muscle cells. In adipocytes insulin inhibits lipolysis, thus decreasing the level of glycerol and free fatty acids that reach the liver (see, Figure 1.11). The decreased concentration of glycerol reduces gluconeogenesis, whereas the lower concentration of free fatty acids suppresses the glycogen degradation into glucose [32, 33].
1.2 Improvements to Bioprocesses Productivity
Advances in genetic engineering have, over the past three decades, generated a wealth of novel molecules that have redefined the role of microbes, and plant–microbial consortium systems, in solving pharmaceutical, environmental, industrial, and agricultural problems. While some products have entered the marketplace, the difficulties of doing so and of complying with federal mandates of: safety, purity, potency, and efficacy have shifted the focus from the term genetic to the term engineering [34].
Here are some examples of some of the industrially efficient tools now coming from the application of bioprocesses and biotechnology (Table 1.1):
The bio-production systems allow major improvements in both economic profitability and environmental performance reducing its environmental impact. This transition from the laboratory to production is the basis of bioprocess engineering and involves a careful understanding of the conditions most favored for optimal production, and the duplication of these conditions during scaled- up production [34].
In biotechnology aimed at improving productivity three approaches are considered:
Biochemical/microbiological approach
selection of microorganisms/nutrients
genetic modifications.
Bioprocess engineering approach
operating modes/conditions
efficient techniques/bioprocesses.
Bioprocess control/instrumentation approach
productivity maximization via an on-line optimizing operation of the bioprocess (on the basis of a dynamical model of the process).
Figure 1.10 Temporal evolution of the variables concentration of the system described by Eqs. (1.9–1.19). Results from the improved model [29]. Plasma glucose and plasma insulin concentrations during a simulated constant glucose infusion with the rate of 216 mg min−1.
Source: Reproduced with permission of Elsevier.
Figure 1.11 The figure shows a phase-plane, we see that the trajectories are attracted to a cyclic track, called a limit cycle, the parameter values used are: C1 = 2000 mgl−1, C2 = 144 mgl−1, C3 = 1000 mgl−1, C4 = 80 mUl−1, C5 = 26 mUl−1.
Table 1.1 Bioprocess based sustainable production [34].
Bio-product
Application
Improvement
Extracted enzymes (micro-organisms, plants and animals)
Catalyze chemical reactions
High efficiency and specificity
Microreactor
Metabolic engineering
High yield
Biomass
Chemicals, fuels and materials that are renewable
No net emissions of greenhouse gases
Biopolymers and bioplastics
Plastics, food, medicine, waste water
Reduce environmental impacts.
Biofertilizer
Agriculture sector
Reduce environmental impacts
The aim of bioprocesses is to apply and improve natural systems by genetical manipulation of cells and their environment to produce them industrially and of high quality [35].
Systems used include:
virus
prokaryotes (bacteria, blue- green algae, cyanobacteria)
eukaryotes (yeasts, molds, animal cells, plant cells, whole plants, whole animals, transgenic organisms).
Examples
agrofood
: food/beverages
organic acids and alcohols
flavors and fragrances
DNA for gene therapy and transient infection
antibiotics
proteins (mAbs, tPA, hirudin, Interleukins, Interferons, Enzymes)
hormones (insulin, human growth hormone, erythropoietin, follicle-stimulating hormone, etc.).
Improvements to bioprocess productivity generally come from the following sources: (i) cell lines and (ii) bioprocess control (unit operation, few real-time direct measurements) [36]. The current rather expensive system bioprocesses need to be improved significantly.
Innovation in technological development as well as in production bioprocesses is to be pursued [37]. On the other hand, development in upstream processing (USP) includes various parts: cell line development and engineering, cell clone selection, media and feed development, bioprocess development and scale up [38, 39]. Bioreactor design, process control and monitoring, cell harvesting and the corresponding analytics can be part of the optimization bioprocess as well [37, 38]. These areas are optimized individually and focus on a stable product, high productivity and high quality [37]. Figure 1.12 schematically the different optimization areas and lists the most important variables. These include the establishment of platform technologies, high-through-put methods with approaches based on Quality by Design (QbD) and Design of Experiments (DoE) based on experimental optimizations. Additionally, an integration of modeling and simulation of unit operations as well as the use of mini-plant facilities is applied in bioprocess development [37]. Key steps in upstream process development are
Construct cell line
. Genetically engineer a host organism (mammalian cell line,
E. coli
, etc.) to produce the desired bio-product.
Clone selection
. Select from many hundreds of clones the most appropriate production cell line based on product quality and productivity.
Process development
. Optimize production process parameters to maximize productivity, obtain acceptable product quality, and scale-up process to production.
Process transfer
. Enable information transfer (process and equipment) between process development and production groups to minimize process issues and speed-up commercialization.
Development in downstream processing (DSP) focuses on yield and productivity as well as on purity and bioprocess capacities. An increase in separation (product sources, primary recovery, and purification) efficiency of single unit operations is achieved by expansion of existing facilities and by optimization of existing and alternative processes [37].
1.2.1 Cell Lines
The selection of the expression system is determined by its ability to ensure a high productivity and defined quality criteria. The expression system that is commonly used for the production of monoclonal antibodies or recombinant proteins is Chinese hamster ovary (CHO) cells [38]. The first proteins produced by CHO-derived cell lines were recombinant interferons and tissue-type plasminogen activator (tPA). In 2010, approximately 70% of all recombinant proteins had been produced in CHO cells [39].
High productivity and post-translational processing are the criteria for cell line selection after cell transfection. Other factors, such as growth behavior, stable production, cultivation in serum-free suspension media, amplification, clone selection, and possible risk assessment are taken into account as well [40]. Provide a robust manufacturing cell culture/fermentation process that has the following performance capabilities
Figure 1.12 Schematic representing the current improvements to bioprocesses productivity [37].
Source: Gronemeyer 2014, https://www.mdpi.com/2306-5354/1/4/188. Used under CC-By4.0 https://creativecommons.org/licenses/by/4.0/.
steady product quality
stable process yield
regular level of process impurities
host cell protein, DNA, and product variants
reliable broth conditions for predictable downstream unit operations performance
clarification and primary capture column.
1.2.1.1 Cell Culture Process General
Requirements
Phenotypic Stability
The cells grow, metabolize, and produce with a predictable profile from batch to batch.
Genetic Stability
The cells retain the genetic code for the protein of interest over the population generations from the cell vial to the production vessel harvest.
Axenic Processing
The process is free of foreign growth.
The cell clones considered for final production have to fulfill the required product quality, bioprocesses ability and volumetric productivity [41]. Criteria for selection are:
cell-specific
growth
volumetric productivity
glycosylation profiles
development of charge variants
protein sequence heterogeneity
clone stability [
41
].
Especially product quality, productivity, and the metabolic profiles of the cells strongly depend on cell culture conditions that include a number of technological trends:
improved expression systems
cell lines and genetic engineering
culture media and media optimization
process analytical technologies
(
PAT
)
modeling software for process debottlenecking.
In manufacturing facilities, many of bioprocess parameters are being monitored and acquired automatically in real time throughout the entire production train [42].
1.2.2 Microorganism Growth Under Controlled Conditions
The key mission in industrial production bioprocesses is to increase yields and also ensure consistent product. To this end, strain phenotype improvement, bioprocesses optimization, and scale-up, the main topics of industrial bioprocesses are aimed at maintaining optimum and homogenous reaction conditions, minimizing microbial stress exposure and enhancing metabolic accuracy.
Figure 1.13 Bioprocess operations [43].
Microorganism growth is significantly influenced by the sensitivity of microorganisms to their environment. Traditionally variables like pH, dissolved oxygen, temperature, pressure, level, and flow are employed for monitoring, instrumentation, and controlling bioprocesses (see, Figure 1.13). Controlling only the culture parameters like dissolved oxygen (DO), pH, pressure, and temperature are not enough to reduce the variability in the process. In fact, factors like concentration of nutrients, growth balance, intracellular metabolic products, and energy charge are all relevant for understanding the process state [44]. Usually the goal is to make measurements that can be quantified in real time as shown in Figure 1.14.
Microorganisms grow in a wide range of environments:
some like hot environments while others like cold
grow in an acidic environment
some require high moisture
some can tolerate high-salt (saline) environments.
Many require the presence of oxygen, but some do not. The overall effect of the underlying mechanisms of cellular regulation dictates a nonlinear behavior in cell culture processes.
Nutrients – change during process:
high energy and N (protein) at first (rapid growth)
very precise conditions later, to maximize yield.
1.2.3 On the Environment for the Microorganism's Growth
The minimum growth temperature is the lowest temperature at which the species will grow, and the maximum is the highest. The optimum growth temperature is that at which it grows best (see Table 1.2). Any nutrient material prepared for the growth of bacteria in a laboratory is called a culture medium. Microbes growing in a container of culture medium are referred to as a culture. When microbes are added to initiate growth, they are an inoculum. To ensure that the culture will contain only the microorganisms originally added to the medium (and their offspring), the medium must initially be sterile (see Table 1.2). Two types of culture medium are available: a broth and a liquid nutrient medium without agar.
Figure 1.14 Illustrative example for bioprocess monitoring and control.
Table 1.2 The most common requirements for microorganism's growth [45].
Source: Richards 2014, https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0103548. Used under CC-BY 4.0 https://creativecommons.org/licenses/by/4.0/.
Requirements
Temperature
Organisms
Interval
Examples
Psychrophiles
−10 °C to 30 °C
Pseudoalteromonas
Mesophiles
25° to 40 °C
Escherichia coli
Thermophiles
50° to 60 °C
Alicyclobacillus
Hyperthermophiles (extreme thermophiles)
80 °C or higher
Calyptogena magnifica
pH
Acidophiles
< 6.5
Thiobacillus acidophilus
Neutrophiles
6.5 to 7.5
Salmonella
Alkaliphiles
> 7.5
Clostridium
Nutritional requirements
Carbon: all living things need a carbon source Sulfur: used in protein synthesis
Nitrogen: used in protein and nucleic acid synthesis
Cyanobacteria
Phosphorus: used in ATP and nucleic acids
Bradyrhizobium
Trace elements: (Fe, Zn, Cu, etc.) Co-factors and co-enzymes
Oxygen needs
Obligate anaerobes
O
2
= 0
Actinomyces
Facultative Anaerobes
O
2
≈ 0
Desulfovibrio alaskensis
Obligate aerobes
O
2
> 0
Staphylococcus species
Agar: a common solidifying agent for a culture medium. Most bacteria grow best in a narrow pH range near neutrality, between pH 6.5 and 7.5. Very few grow below pH 4.0 (see Table 1.2) bacteria (mostly) at pH = 3 to 8 yeast, pH = 3 to 6, plants pH = 5 to 6 animals pH = 6.5 to 7.5. Microbes that use molecular oxygen are aerobes; if oxygen is an absolute requirement, they are obligate aerobes. Facultative anaerobes use oxygen when it is present but continue growth by fermentation or anaerobic respiration when it is not available.
Facultative anaerobes grow more efficiently aerobically than they do anaerobically. Obligate anaerobes are bacteria totally unable to use oxygen for growth and usually find it toxic. Water is required to dissolve most cell substances that microorganisms use: minerals, ions, gases, and numerous organic compounds. Some bacteria can survive under extremely dry conditions by forming spores, most bacteria grow at aw 0.85–1.0. So, it is important that the operator understand how the following factors affect the growth of the bacterium:
oxygen utilization
sludge age
dissolved oxygen
mixing
pH
temperature
nutrients.
