Table Of ContentDeveloping Synthetic Transport Systems
Alexey Melkikh Maria Sutormina
•
Developing Synthetic
Transport Systems
123
Alexey Melkikh Maria Sutormina
Instituteof Physicsand Technology Instituteof Physicsand Technology
UralFederal University UralFederal University
Yekaterinburg Yekaterinburg
Russia Russia
ISBN 978-94-007-5892-6 ISBN 978-94-007-5893-3 (eBook)
DOI 10.1007/978-94-007-5893-3
SpringerDordrechtHeidelbergNewYorkLondon
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(cid:2)SpringerScience?BusinessMediaDordrecht2013
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Contents
1 Biological Cybernetics and the Optimization Problem
of Transport of Substances in Cells . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Methods of Optimization and Living Systems. . . . . . . . . . . . . 4
1.2.1 Control Theory and Biosystems. . . . . . . . . . . . . . . . . . 4
1.2.2 Optimality and Living Systems. . . . . . . . . . . . . . . . . . 9
1.2.3 Compartmental Models of Living Systems
in Biological Cybernetics . . . . . . . . . . . . . . . . . . . . . . 10
1.2.4 Biological Cybernetics, Synthetic Biology
and the ‘‘Minimal Cell’’. . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Transport of Ions Through Cell Membranes:
Models and Methods of Optimization. . . . . . . . . . . . . . . . . . . 13
1.3.1 Active and Passive Transport of Ions,
Resting Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Osmotic Pressure of Solutions Inside and
Outside the Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.3 Classification of Models of Ion Transport,
Two-Level Model, Algorithm ‘‘One Ion-One
Transport System’’. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.4 Methods of Optimizations and Transport
of Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.3.5 Two Transport Systems for One Substance. . . . . . . . . . 27
1.3.6 An Optimization of the Transport System
of a Cell as a Game Problem . . . . . . . . . . . . . . . . . . . 31
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 Models of Ion Transport in Mammalian Cells. . . . . . . . . . . . . . . . 35
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
v
vi Contents
2.2 Cardiac Cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Model of Transport Systems. . . . . . . . . . . . . . . . . . . . 38
2.2.2 Regulation of Ion Transport . . . . . . . . . . . . . . . . . . . . 43
2.3 Neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.3.1 Model of Transport Systems. . . . . . . . . . . . . . . . . . . . 48
2.3.2 Model of Ion Transport with a Restriction
of Deviation from the Experimental Data. . . . . . . . . . . 53
2.3.3 Regulation of Ion Transport . . . . . . . . . . . . . . . . . . . . 56
2.4 Erythrocytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.1 Model of Ion Transport . . . . . . . . . . . . . . . . . . . . . . . 59
2.4.2 Model of Regulation of Ion Transport:
Efficiency or Robustness?. . . . . . . . . . . . . . . . . . . . . . 63
2.5 Hepatocytes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.5.1 Model for Ion Transport. . . . . . . . . . . . . . . . . . . . . . . 67
2.5.2 Regulation of Ion Transport . . . . . . . . . . . . . . . . . . . . 70
2.6 Regulation of Ion Transport in Compartments
of a Mammalian Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.6.1 Mitochondria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.6.2 Sarcoplasmic and Endoplasmic Reticulum . . . . . . . . . . 77
2.6.3 Synaptic Vesicles. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
2.7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3 Models of Ion Transport and Regulation in Plant
Cells and Unicellular Organisms. . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.2 Archaea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.3 Diatomei. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4 E. coli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.4.1 A Transport Model of Basic Ions in E. coli . . . . . . . . . 103
3.4.2 Calculation of the Osmotic Pressure
Differences in Bacteria. . . . . . . . . . . . . . . . . . . . . . . . 111
3.5 Regulation of Ion Transport in Select Microorganisms. . . . . . . 112
3.6 Possible Regulatory Strategies for Bacterial Transport
of Heavy Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
3.7 Plant Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.8 Vacuoles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.9 Thylakoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Contents vii
4 Optimization of the Transport of Substances in Cells . . . . . . . . . . 131
4.1 Optimization Methods Used for Models of Transport
Subsystems of Living and Artificial Cells. . . . . . . . . . . . . . . . 131
4.1.1 Effectiveness of the Energy Conversion in the Transport
of Substances Through Biomembranes. . . . . . . . . . . . . 132
4.1.2 Synthesis of the Transport System of an Artificial
Cell Based on the Method of Dynamic Programming. . . 137
4.1.3 Ideal Transport System: Simultaneous Optimization
of Robustness and Effectiveness . . . . . . . . . . . . . . . . . 142
4.1.4 Method of the Critical Point. . . . . . . . . . . . . . . . . . . . 145
4.1.5 Controllability and Paradox of Ions Transport. . . . . . . . 148
4.1.6 Cascades and Networks of the Transport
Molecular Machines. . . . . . . . . . . . . . . . . . . . . . . . . . 151
4.1.7 Regulation of the Pressure in Generalized Cells, Cells
in Fresh and Distilled Water, Transport of Water . . . . . 156
4.1.8 Transport of Ions with a Lack of Energy
and Diffusion of ATP. . . . . . . . . . . . . . . . . . . . . . . . . 160
4.2 Protocells at the Early Stages of Evolution. . . . . . . . . . . . . . . 162
4.2.1 Early Stages of Evolution and Origin
of the First Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
4.2.2 A Model of the Simplest Transport System
in a Minimal Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.2.3 A Model of the Simplest System for the Control
of Transport Processes in a Cell . . . . . . . . . . . . . . . . . 166
4.2.4 Physico-Chemical Models of Cellular Movement . . . . . 169
4.2.5 Sunlight as a Possible Source of Energy
for Movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
4.2.6 The Energy Balance in Protocells . . . . . . . . . . . . . . . . 177
4.2.7 The Problem of Control and Reception of Information:
Strategies Used by Protocells for Directed Motion. . . . . 178
4.3 The Transport of Large Molecules in Living
and Artificial Cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
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-
partmentalmodelsoflivingsystemsincontroltheoryareconsidered.Theproblem
ofthe‘‘minimalcell’’isdiscussed.Theplaceandroleofmodelsofthetransportof
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
whatsensedoweunderstandoptimality?Towhatextentaretheyoptimal?Ifthey
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.MelkikhandM.Sutormina,DevelopingSyntheticTransportSystems, 1
DOI:10.1007/978-94-007-5893-3_1,(cid:2)SpringerScience+BusinessMediaDordrecht2013
2 1 BiologicalCyberneticsandtheOptimizationProblem
mechanismsbywhichcellsresistsuchchanges.Thetransportofionsiscontrolled,
to a certain extent, in all cells. The purpose of the regulation of transport of
substances is, in mostcases, the maintenance of the constancy of the intracellular
environment.Moreover,transportsystemshaveonemoreimportantproperty:their
efficiencyincharacterizingtheabilityofthecelltoperformvarioustypesofuseful
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,thetransportsubsystemofthecellhasnotbeenstudiedsufficiently
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
principlesaccordingtowhichthetransportsubsystemofthecellisconstructed.In
thefuture,suchanunderstandingwillhelptoanswerwhythetransportsubsystem
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-
zationoftransportprocessesincells.Inadditiontoothersubsystems,thetransport
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
rarelybeenappliedtothesystemofthetransportofsubstancesinthecell.Thisis
mostlikelybecausetheprocessesofthetransportofsubstancesareassumedtobe
secondary to gene or metabolic processes in many respects.
Thecelltransportsubsystemisconnectedwithothersubsystems.Forexample,
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,nucleusandothers).Ontheonehand,transport
processes in turn depend on metabolism and other subsystems. Thus, considering
thetransportsubsystemindependentlyoftherestofacellisanapproximation.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-
aratedescriptionofthetransportsubsystemcontributestoanunderstandingofthe
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 ofthe few functions of a protocell. An understanding of the
mechanismsbywhichtransportisoptimizedinelementarycellswouldbehelpful
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 Systemsbiologyare
theintersectionofthethree
sciences
Biologyprovides information about thestructureandfunctionsofanorganism
(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
transportsubsystemofcells.Thesealgorithmsandmodelscanmaximizeboththe
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 iontransport inbiological
membranes of cells are also considered.
TheChap.2isdevotedtomodelsofiontransportinsomemammaliancellsand
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 BiologicalCyberneticsandtheOptimizationProblem
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 thevariousoptimization techniques applied tobiologicalsystems,control
theory plays a special role. Historically, control theory began with the mathe-
matical modelingoftheoptimizationofthepropertiesoflivingorganisms.Letus
consider the basic laws of control theory in the application of biological systems,
bearinginmindthattheyarelargelycommontobiologicalcyberneticsasawhole.
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.Becauseofthelargeamountoffeedbackregulatingtheactivityandrateof
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
providesapassivemechanismofregulation:thecenterofbuoyancyandthecenter
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
controlofthesystemoccursasaresultoftheinteractionoftheelementsthatmake
up ‘‘the system itself’’. Bertalanffy (1973) suggested the term ‘‘dynamic interac-
tion’’ or ‘‘primary regulation’’ for this type of control.
