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Models of Ion Transport in Mammalian Cells

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Models of Ion Transport in Mammalian Cells Chapter 1 Biological Cybernetics and the Optimization Problem of Transport of Substances in Cells The methods of biological cybernetics are used to observe living systems. The models of transport of substances through the biomembrane are discussed. Com- partmental models of living systems in control theory are considered. The problem of the ‘‘minimal cell’’ is discussed. The place and role of models of the transport of substances in synthetic and systems biology are discussed. The ‘‘one ion—a transport system’’ algorithm and the game approach, which were previously pro- posed by the authors to model the transport of ions in cells, are described. 1.1 Introduction Living systems are optimal. This statement, of course, needs to be clarified. In what sense do we understand optimality? To what extent are they optimal? If they are not fully optimal, why not? These issues of living systems also pertain to biological cybernetics. Biological cybernetics is the application of cybernetics to living systems. Cybernetics is traditionally composed of the following components: information theory, automata theory, control theory, operations research, pattern recognition and algorithms theory. At present, cybernetics also includes other sciences, but only the aforementioned six parts have a special mathematical apparatus that is inherent to only this science. Biological cybernetics is the fundamental basis of systems biology. Biological cybernetics objects are living organisms, their populations, and subsystems of organisms and cells. One of the objects of biological cybernetics is the transport subsystem of the cell. Processes involved in the transport of substances across the biomembranes of cells are important for vital cellular functions. For example, many cells (bacteria, archaebacteria, cyanobacteria, and yeast) survive considerable changes in the concentration of ions in the environment. It is necessary to understand the A. Melkikh and M. Sutormina, Developing Synthetic Transport Systems, 1 DOI: 10.1007/978-94-007-5893-3_1, Ó Springer Science+Business Media Dordrecht 2013 2 1 Biological Cybernetics and the Optimization Problem mechanisms by which cells resist such changes. The transport of ions is controlled, to a certain extent, in all cells. The purpose of the regulation of transport of substances is, in most cases, the maintenance of the constancy of the intracellular environment. Moreover, transport systems have one more important property: their efficiency in characterizing the ability of the cell to perform various types of useful work. However, these two properties have almost never been treated together in the context of a transport subsystem. The goal of systems biology is a comprehensive description of a cell (or an organism) through mathematical methods by the use of computers. At present, systems biology is concerned mainly with the gene and metabolic networks of cells. However, the transport subsystem of the cell has not been studied sufficiently in systems biology. Additionally, advancing synthetic biology requires a general approach to sim- ulating cell processes. In particular, it is necessary to understand the general principles according to which the transport subsystem of the cell is constructed. In the future, such an understanding will help to answer why the transport subsystem of a cell is arranged exactly the way it is. Although there are a great number of papers devoted to the application of control theory to biosystems, there has not been much discussion of the optimi- zation of transport processes in cells. In addition to other subsystems, the transport subsystem of a cell is within the purview of systems biology [see, e.g. (Jamshidi and Palsson 2006, El-Shamad et al. 2002)]. However, optimization methods have rarely been applied to the system of the transport of substances in the cell. This is most likely because the processes of the transport of substances are assumed to be secondary to gene or metabolic processes in many respects. The cell transport subsystem is connected with other subsystems. For example, the processes of transcription and translation are related to the transport of nucleotides and proteins through the nuclear membrane. The functioning of genetic and metabolic networks is related to the transport of proteins and metabolites within the cell and through the membranes of intracellular compart- ments (mitochondria, chloroplasts, nucleus and others). On the one hand, transport processes in turn depend on metabolism and other subsystems. Thus, considering the transport subsystem independently of the rest of a cell is an approximation. On the other hand, the consideration of the transport subsystem alone allows a better understanding of the other subsystems with which it interacts. Ultimately, a sep- arate description of the transport subsystem contributes to an understanding of the laws of cellular functioning as a whole. In addition, the construction of models for the optimization of the transport system is topical because at the early stages of evolution, the transport of sub- stances might be one of the few functions of a protocell. An understanding of the mechanisms by which transport is optimized in elementary cells would be helpful in the creation of artificial cells. This book is a study at the intersection of the three sciences: physics, cyber- netics, and biology (Fig. 1.1). 1.1 Introduction 3 Fig. 1.1 Systems biology are the intersection of the three sciences Biology provides information about the structure and functions of an organism (or cell); physics provides the laws, which allow us to build a model of transport processes; and cybernetics provides methods for the optimization of those pro- cesses and systems. Our goal is to present the algorithms and models of the transport subsystem of cells. These algorithms and models can maximize both the energy efficiency of transport processes and the independence of the internal environment of cells from the external environment. The book is organized as follows. This chapter provides an overview of the methods of cybernetics as they are applied to biological systems. We discuss the place of the transport subsystem in an integrated model of the cell in terms of systemic and synthetic biology. Some of the models of ion transport in biological membranes of cells are also considered. The Chap. 2 is devoted to models of ion transport in some mammalian cells and their compartments. These models include the first approximation (without regu- lation) and the regulation of ion transport at changing the composition of the environment. The Chap. 3 is devoted to models of ion transport in the cells of protozoa, plants, bacteria, and some of the compartments of these cells. We consider the behavioral strategy of cells in response to a substantial change in environmental conditions, such as salt stress. The Chap. 4 is devoted to models of ion transport in artificial cells. Particular attention is given to the application of optimization techniques to the transport subsystem of cells. The systems of transport of protocells in the early stages of evolution are discussed. The conditions under which various forms of energy 4 1 Biological Cybernetics and the Optimization Problem conversion (including directed movement) would be beneficial in a protocell are discussed. Note also that in the book, we have focused on models of the transport of substances, but models of the gene regulation associated with the transport sub- system of the cell are not considered. 1.2 Methods of Optimization and Living Systems Among the various optimization techniques applied to biological systems, control theory plays a special role. Historically, control theory began with the mathe- matical modeling of the optimization of the properties of living organisms. Let us consider the basic laws of control theory in the application of biological systems, bearing in mind that they are largely common to biological cybernetics as a whole. 1.2.1 Control Theory and Biosystems The essence of control theory is that the analyzed system is represented as a control system—the connection of individual elements in a configuration that provides the specified characteristics. The control system consists of a control device and the object of control. Control actions are aimed at achieving a certain result—the objective of control. For biological systems, this definition means that the work of organs, tissues, and cells is conveniently represented as a separate control system and control device. Because of the large amount of feedback regulating the activity and rate of synthesis of enzymes, the concentration of their final products remains almost unchanged even when faced with a fairly wide range of external perturbations. These mechanisms are incorporated into a regulated system; thus, the term ‘‘internal control’’ is used [see, for example (Novoseltsev 1978)]. Internal control is considered passive. This means that the existing system, which maintains the steady state of equilibrium (or the appearance of it) as a characteristic response of the system to an external perturbation, does not require any metabolic work (Waterman 1968). Passive mechanisms of regulation are not unique to the biochemical level of organization of biosystems. For example (Novoseltsev 1978), the maintenance of the normal spatial orientation of fish provides a passive mechanism of regulation: the center of buoyancy and the center of gravity do not coincide. Thus, when a deviation of an axial plane of the fish occurs because of vertical torque, the body returns to its normal position. Passive control of the system occurs as a result of the interaction of the elements that make up ‘‘the system itself’’. Bertalanffy (1973) suggested the term ‘‘dynamic interac- tion’’ or ‘‘primary regulation’’ for this type of control. 1.2 Methods of Optimization and Living Systems 5 Fig. 1.2 Homeostatic curve. Here, x—is an internal parameter of an organism, and y—is an external parameter In control theory, the decision of whether this system is a controllable system shall be made on the basis of the presence in the description of the feedback system. If feedback exists, the system is controllable.
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