Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures
Abstract and Figures
One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.
![Diversity dynamic behaviors emerge in the simple dissipative metabolic subsystem. ( a ) Periodic pattern. ( b ) Hard excitation, the integral solutions depending on the initial conditions settle on two regimens: a stable steady state and a stable periodic oscillation. ( c ) Chaotic oscillations. ( d ) Complex periodic behaviors. The substrate concentration is represented as a function of the time in seconds. Reproduced with permission from PNAS [198].](https://www.researchgate.net/publication/47460044/figure/fig1/AS:306108083261450@1449993262809/Diversity-dynamic-behaviors-emerge-in-the-simple-dissipative-metabolic-subsystem-a_Q320.jpg)
![Molecular processes for M-phase control in eukaryotic cells. ( a ) Cdc2 protein kinase monomers combine with cyclin subunits to form dimers. Subunits of kinase Cdc2 can be phosphorylated and desphosphorylated at an activatory threonine (Thr) residue or/and an inhibitory tyrosine (Tyr) residue. All cyclin subunits can be degraded by an ubiquitin pathway. ( b ) Active MPF stimulates its own production, which is positive feedback. ( c ) But active MPF also stimulates the destruction of cyclin, which is negative feedback. Reproduced with permission from the Company of Biologistd Ltd. [218].](https://www.researchgate.net/publication/47460044/figure/fig2/AS:306108083261451@1449993262832/Molecular-processes-for-M-phase-control-in-eukaryotic-cells-a-Cdc2-protein-kinase_Q320.jpg)
![Quantitative analysis of the M-phase control system showing spontaneous periodic oscillations in the metabolic intermediaries. The total cyclin concentrations (blue), active form of MPF (red), tyrosine-phosphorylated dimers, YP, (green) and total phosphorylated cdc2 monomers (orange) are represented as a function of the time in minute. The bar graphs indicate the periods during which the active forms exceed 50% of the total amount. Reproduced with permission from the Company of Biologists Ltd. [218].](https://www.researchgate.net/publication/47460044/figure/fig3/AS:306108083261452@1449993262859/Quantitative-analysis-of-the-M-phase-control-system-showing-spontaneous-periodic_Q320.jpg)
![A limit cycle attractor governs the cell cycle. The cell cycle is controlled by a dynamical structure called ―limit cycle‖ which is a closed orbit corresponding to the oscillations with a period of 80 minutes. The numbers along the limit cycle represent time in minutes after exit from mitosis. Reproduced with permission from the Company of Biologists Ltd. [218].](https://www.researchgate.net/publication/47460044/figure/fig4/AS:306108083261453@1449993262880/A-limit-cycle-attractor-governs-the-cell-cycle-The-cell-cycle-is-controlled-by-a_Q320.jpg)
![Numerical oscillatory responses of glycolysis under periodic substrate input flux showing a transition sequence to chaos through quasiperiodicity. In the first column are represented the corresponding attractors (projections in two dimensions for the concentration, x-axis, and the concentrations, y-axis), power spectra in the second column and Poincaré sections in the , plane (third column). Reproduced with permission from Elsevier [283].](https://www.researchgate.net/publication/47460044/figure/fig5/AS:306108083261454@1449993262903/Numerical-oscillatory-responses-of-glycolysis-under-periodic-substrate-input-flux-showing_Q320.jpg)
Figures - available via license: Creative Commons Attribution 3.0 Unported
Content may be subject to copyright.
... This is particularly true in the umbrella field of computational biology and bioinformatics that deals with computational applications of mathematical and statistical methods in the study of biological systems and processes. In this domain, information theory is widely used for model development and data analysis for a variety of biologically derived data types ranging from molecular, sequence and phenotypic data in genomics and genetics to gene expression, protein and spectral data in transcriptomics, proteomics and metabolomics, respectively [4][5][6][7][8][9][10][11]. ...
... Cellular metabolic systems form self-assembled aggregates and the activities of cellular enzymes can also exhibit spontaneous spatial-temporal functional structures. Entropy is a useful concept in the study of these dynamical systems [11]. In particular, Kolmogorov-Sinai entropy, which can be estimated from a finite number of observations using a family of statistics named Approximate Entropy (ApEn), provides a good measure of the complexity and information for the study of attractors in biochemical systems. ...
... Nykter et al. [168] Studied network structure-dynamics relationships, using Kolmogorov complexity as a measure of distance between pairs of network structures and between their associated dynamic state trajectories Grimbs et al. [169] Stoichiometric analysis to parameterize the metabolic states, assessed the effect of enzyme-kinetic parameters on the stability properties of a metabolic state using MI and Kolmogorov-Smirnov test Fuente et al. [11]. Studied properties of dissipative metabolic structures at different organizational levels using entropy De Martino et al. [170] Introduced a generalization of FBA to single-cell level based on maximum entropy principle Saccenti et al. [163] Investigated the associations and the interconnections among different metabolites by means of network modeling using maximum entropy ensemble null model ...
“A Mathematical Theory of Communication” was published in 1948 by Claude Shannon to address the problems in the field of data compression and communication over (noisy) communication channels. Since then, the concepts and ideas developed in Shannon’s work have formed the basis of information theory, a cornerstone of statistical learning and inference, and has been playing a key role in disciplines such as physics and thermodynamics, probability and statistics, computational sciences and biological sciences. In this article we review the basic information theory based concepts and describe their key applications in multiple major areas of research in computational biology—gene expression and transcriptomics, alignment-free sequence comparison, sequencing and error correction, genome-wide disease-gene association mapping, metabolic networks and metabolomics, and protein sequence, structure and interaction analysis.
... Irreversible processes generate entropy, which is conventionally associated with disorder increase; but they can also produce DS with self-organizing ability [13]. The DS provides a thermodynamic framework to unify metabolic processes that can lead to self-organization in all biological living organisms [14], which are biological DS. Glansdorff and Prigogine [15] showed that possibilities exist for application of non-equilibrium thermodynamics based on entropy production in a system in the highly non-linear range. ...
... When mass-energy interactions are slowed-down or momentarily paused, sufficient negentropy-debt is not paid by complex DS to their surroundings. When mass-energy interactions are paused, DS enters gradual decay phase; in which Eq. (14) holds and S DS,org (disorder of DS) builds-up. Thus, growing complex DS have lesser ability (relative to simple DS) to divert unused Ṡ gen as negentropy debt, for increasing the disorder of surroundings. ...
Dissipative structures (DS) exist at all scales, systems, and at different levels of complexity. A thermodynamic theory integrating simple and complex DS is introduced, which addresses existence of growing/decaying DS based on their entropy analysis. Two entropy-based dimensionless ratios are introduced, which explain negentropy-debt payment and existence of DS with growth or decay. It is shown that excess negentropy debt payment is needed and beneficial for growing DS; but for decaying DS, it hastens its approach to perish and is counter-productive. Growing complex DS tend to pay lower negentropy debt to their surroundings, due to involvement in other activities enabled by complexity; e.g. mediation for survival that is linked to their mortality. Hence, disorder of complex DS increases, due to which, their growth can be un-sustained, leading to entry in decay-phase in spite of availability of adequate mass-energy in-flows. Proper handling or reduction of complexity enables growth in the direction of ideal growth (without increase in disorder of DS), which is limited only by availability of adequate mass-energy in-flows.
... Enzymes are responsible for molecular recycling processes shaping multienzyme complexes (reversible structures formed by several enzymes of a metabolic pathway), which carry out their activity with autonomy between them playing distinctive and essential roles in cellular physiology. When a multienzyme complex operates far enough from equilibrium dissipative selforganization can emerge (Goldbeter, 2007;De la Fuente, 2010. ...
... Dissipative multienzyme complexes can also be considered fundamental modular networks (De la Fuente et al., 2008;De la Fuente, 2010. In this respect, the Metabolic Subsystem concept was suggested in 1999 to define dissipatively structured enzyme complexes in which autonomous catalytic processes with complex quasi-steady-state patterns and molecular rhythms spontaneously emerge (De la Fuente et al., 1999b). ...
One of the main aims of current biology is to understand the origin of the molecular organization that underlies the complex dynamic architecture of cellular life. Here, we present an overview of the main sources of biomolecular order and complexity spanning from the most elementary levels of molecular activity to the emergence of cellular systemic behaviors. First, we have addressed the dissipative self-organization, the principal source of molecular order in the cell. Intensive studies over the last four decades have demonstrated that self-organization is central to understand enzyme activity under cellular conditions, functional coordination between enzymatic reactions, the emergence of dissipative metabolic networks (DMN), and molecular rhythms. The second fundamental source of order is molecular information processing. Studies on effective connectivity based on transfer entropy (TE) have made possible the quantification in bits of biomolecular information flows in DMN. This information processing enables efficient self-regulatory control of metabolism. As a consequence of both main sources of order, systemic functional structures emerge in the cell; in fact, quantitative analyses with DMN have revealed that the basic units of life display a global enzymatic structure that seems to be an essential characteristic of the systemic functional metabolism. This global metabolic structure has been verified experimentally in both prokaryotic and eukaryotic cells. Here, we also discuss how the study of systemic DMN, using Artificial Intelligence and advanced tools of Statistic Mechanics, has shown the emergence of Hopfield-like dynamics characterized by exhibiting associative memory. We have recently confirmed this thesis by testing associative conditioning behavior in individual amoeba cells. In these Pavlovian-like experiments, several hundreds of cells could learn new systemic migratory behaviors and remember them over long periods relative to their cell cycle, forgetting them later. Such associative process seems to correspond to an epigenetic memory. The cellular capacity of learning new adaptive systemic behaviors represents a fundamental evolutionary mechanism for cell adaptation.
... f) The simulated glycolytic oscillations of ( Figure 4-B-C), (that is FDP and F6P species) are similar to the experimentally recorded dynamics by [104,105], and also similar to the dynamic simulations of [89,52,106,107]. Figure 4(A-E) display an incipient phase of the oscillation occurrence, when the species oscillation amplitude grows. However, over a longer time domain (not shown here), the oscillations stabilize and become stationary. ...
In the 1-st part of this work the general chemical and biochemical engineering (CBE) concepts and rules are briefly reviewed, together with the rules of the control theory of nonlinear systems (NSCT), all in the context of deriving deterministic modular structured cell kinetic models (MSDKM) and of hybrid structured modular dynamic (kinetic) models (HSMDM) (with continuous variables, based on cellular metabolic reaction mechanisms). In such HSMDM, the cell-scale model (including nano-level state variables) is linked to the biological reactor macro-scale state variables for improving the both model prediction quality and its validity range. By contrast, the current (classical/default) approach in biochemical engineering and bioengineering practice for solving design, optimization and control problems based on the math models of industrial biological reactors is to use unstructured Monod (for cell culture reactor) or Michaelis-Menten (if only enzymatic reactions are retained) global kinetic models by ignoring detailed representations of metabolic cellular processes. The applied engineering rules to develop MSDKM and HSMDM dynamic math models presented in the 1-st and 2-nd parts of this paper are similar to those used in the CBE, and in the NSCT. As exemplified in the 3&4 parts of this work, the MSDKM models can adequately represent the dynamics of cell-scale CCM (central carbon metabolism) key-modules, and of Genetic Regulatory Circuits (GRC) / networks (GRN) that regulate the CCM-syntheses. As reviewed in the 2-nd part of this paper, an accurate and realistic math modelling of individual GERMs (gene expression regulatory module) kinetic models, but also various genetic regulatory circuits (GRC) / networks (GRN). (e.g. toggle-switch, amplitude filters, modified operons, etc.) can be done by only using the novel holistic 'whole-cell of variable-volume' (WCVV) modelling framework introduced and promoted by the author. Also, special attention was paid in the 2-nd part to the conceptual and numerical rules used to construct various individual GERMs kinetic models, but also various GRC-s / GRN-s modular kinetic models from linking individual GERMs of desired regulatory properties, quantitatively expressed by their performance indices (P.I.-s). As exemplified in the Parts 3 and 4 of this work, the use of MSDKM and of HSMDM models (developed under the novel WCVV modelling framework) to simulate the dynamics of the bioreactor and, implicitly, the dynamics of the cellular metabolic processes occurring in the bioreactor biomass, presents multiple advantages, such as: a) A higher degree of accuracy and of the prediction detailing for the bioreactor dynamic parameters (at a macro-and nano-scale level) and, b) The prediction of the biomass metabolism adaptation over tens of cell cycles to the variation of the operating conditions in the bioreactor; c) Prediction of the ccm key-species dynamics, by also including the metabolites of interest for the industrial biosynthesis.; d) Prediction of the ccm stationary reaction rates (i.e. Metabolic fluxes) allow to in-silico design gmo of desired characteristics. As proved by Maria [1-5], and Yang, et al. [176], the modular structured kinetic models can reproduce the dynamics of complex metabolic syntheses inside living cells. This is why, the modular GRC dynamic models, of an adequate mathematical representation, seem to be the most comprehensive mean for a rational design of the regulatory GRC with desired behaviour [178]. Once experimentally validated, such extended structured cellular kinetic models MSDKM including nano-scale state variables are further linked to those of the bioreactor dynamic models (including macro-scale state variables), thus resulting HSMDM models that can satisfactorily simulate, on a deterministic basis, the self-regulation of cell metabolism and its rapid adaptation over dozens of cell cycles to the changing bioreactor reaction environment, by means of complex GRC-s, which include chains of individual GERMs. In a HSMDM, the cell-scale model (including nano-level state variables) is linked to the biological reactor macro-scale state variables for improving the both model prediction quality and its validity range. Due to such particulars, as exemplify here, the immediate applications of such MSDKM and HSMDM kinetic models are related to solving various difficult bioengineering problems, such as: a) In-silico off-line optimize the operating policy of various types of bioreactors, and b) In-silico design/check some gmo-s of industrial use able to improve the performances of several bioprocess/bioreactors. Note: a) In the absence of these papers (parts 1& 2), the reader is asked to consult the references [4,5]. Keywords: Biochemical engineering concepts applied in bioinformatics; Deterministic modular structured cell kinetic model (MSDKM); Hybrid structured modular dynamic (kinetic) models (HSMDM); Whole cell variable cell volume (WCVV) modelling framework; Whole cell constant cell volume (WCCV) modelling framework; Individual gene expression regulatory module (GERM); Genetic regulatory circuits (GRC), or networks (GRN); Chemical and biochemical engineering principles (CBE); Rules of the control theory of nonlinear systems (NSCT); Kinetic model of glycolysis in E. coli; Glycolytic oscillations; GRC of mercury-operon expression regulation in modified E. coli cells; Three-phase fluidized bioreactor (TPFB) for mercury uptake by cloned E. coli cells; Fed-batch bioreactor (FBR) for tryptophan (TRP) production using in-silico design E. coli GMO cells; Tryptophan production maximization in a FBR; Design GRC of a genetic switch (GS) type, with the role of a biosensor in GMO E. coli cells; Pareto optimal front to maximize both biomass and succinate production by using design GMO E. coli cells based on the in-silico tested gene knockout strategies; Optimal operating policies of a fed-batch bioreactor (FBR) used for monoclonal antibodies (mAbs) production maximization; Mercury-operon expression regulation in modified E. coli cells; Cloned E. coli cells with mercury-plasmids; Gene knockout strategies to design optimized GMO E. coli for succinate production maximization; Pareto optimal front to maximize both biomass and succinate production in batch bioreactors (BR) using GMO E. coli cells
Directional motility is an essential property of cells. Despite its enormous relevance in many fundamental physiological and pathological processes, how cells control their locomotion movements remains an unresolved question. Here we have addressed the systemic processes driving the directed locomotion of cells. Specifically, we have performed an exhaustive study analyzing the trajectories of 700 individual cells belonging to three different species ( Amoeba proteus , Metamoeba leningradensis and Amoeba borokensis ) in four different scenarios: in absence of stimuli, under an electric field (galvanotaxis), in a chemotactic gradient (chemotaxis), and under simultaneous galvanotactic and chemotactic stimuli. All movements were analyzed using advanced quantitative tools. The results show that the trajectories are mainly characterized by coherent integrative responses that operate at the global cellular scale. These systemic migratory movements depend on the cooperative non-linear interaction of most, if not all, molecular components of cells.
Significance
Cellular migration is a cornerstone issue in many human physiological and pathological processes. For years, the scientific attention has been focused on the individualized study of the diverse molecular parts involved in directional motility; however, locomotion movements have never been regarded as a systemic process that operates at a global cellular scale. In our quantitative experimental analysis essential systemic properties underlying locomotion movements were detected. Such emergent systemic properties are not found specifically in any of the molecular parts, partial mechanisms, or individual processes of the cell. Cellular displacements seem to be regulated by integrative processes operating at systemic level.
Directional motility is an essential property of cells. Despite its enormous relevance in many fundamental physiological and pathological processes, how cells control their locomotion movements remains an unresolved question. Here we have addressed the systemic processes driving the directed locomotion of cells. Specifically, we have performed an exhaustive study analyzing the trajectories of 700 individual cells belonging to three different species (Amoeba proteus, Metamoeba leningradensis and Amoeba borokensis) in four different scenarios: in absence of stimuli, under an electric field (galvanotaxis), in a chemotactic gradient (chemotaxis), and under simultaneous galvanotactic and chemotactic stimuli. All movements were analyzed using advanced quantitative tools. The results show that the trajectories are mainly characterized by coherent integrative responses that operate at the global cellular scale. These systemic migratory movements depend on the cooperative non-linear interaction of most, if not all, molecular components of cells.
One of the most important goals of the post-genomic era is to understand the different sources of molecular information that regulate the functional and structural architecture of cells. In this regard, Prof. K. Baverstock underscores in his recent article “The gene: An appraisal” (Baverstock, 2021) that genes are not the leading elements in cellular functionality, inheritance and evolution. As a consequence, the theory of evolution based on the Neo-Darwinian synthesis, is inadequate for today's scientific evidence. Conversely, the author contends that life processes viewed on the basis of thermodynamics, complex system dynamics and self-organization provide a new framework for the foundations of Biology. I consider it necessary to comment on some essential aspects of this relevant work, and here I present a short overview of the main non-genetic sources of biomolecular order and complexity that underline the molecular dynamics and functionality of cells. These sources generate different processes of complexity, which encompasses from the most elementary levels of molecular activity to the emergence of systemic behaviors, and the information necessary to sustain them is not contained in the genome.
Autonomous oscillations of species levels in the glycolysis express the self-control of this essential cellular pathway belonging to the central carbon metabolism (CCM), and this phenomenon takes place in a large number of bacteria. Oscillations of glycolytic intermediates in living cells occur according to the environmental conditions and to the cell characteristics, especially the adenosine triphosphate (ATP) recovery system. Determining the conditions that lead to the occurrence and maintenance of the glycolytic oscillations can present immediate practical applications. Such a model-based analysis allows in silico (model-based) design of genetically modified microorganisms (GMO) with certain characteristics of interest for the biosynthesis industry, medicine, etc. Based on our kinetic model validated in previous works, this paper aims to in silico identify operating parameters and cell factors leading to the occurrence of stable glycolytic oscillations in the Escherichia coli cells. As long as most of the glycolytic intermediates are involved in various cellular metabolic pathways belonging to the CCM, evaluation of the dynamics and average level of its intermediates is of high importance for further applicative analyses. As an example, by using a lumped kinetic model for tryptophan (TRP) synthesis from literature, and its own kinetic model for the oscillatory glycolysis, this paper highlights the influence of glycolytic oscillations on the oscillatory TRP synthesis through the PEP (phosphoenolpyruvate) glycolytic node shared by the two oscillatory processes. The numerical analysis allows further TRP production maximization in a fed-batch bioreactor (FBR).
Autonomous oscillations of glycolytic intermediate concentrations reflect the dynamics of the control and regulation of this major catabolic pathway, and this phenomenon has been reported in a broad range of bacteria. Understanding glycolytic oscillations might therefore prove crucial for the general understanding of the regulation of cell metabolism with immediate practical applications, allowing in silico design of modified cells with desirable ‘motifs’ of practical applications in the biosynthesis industry, environmental engineering, and medicine. By using a kinetic model from literature, this paper is aiming at in silico (model-based) identification of some conditions leading to the occurrence of stable glycolytic oscillations in the E. coli cells.
Fluctuations in rates of gene expression can produce highly erratic time patterns of protein production in individual cells and wide diversity in instantaneous protein concentrations across cell populations. When two independently produced regulatory proteins acting at low cellular concentrations competitively control a switch point in a pathway, stochastic variations in their concentrations can produce probabilistic pathway selection, so that an initially homogeneous cell population partitions into distinct phenotypic subpopulations. Many pathogenic organisms, for example, use this mechanism to randomly switch surface features to evade host responses. This coupling between molecular-level fluctuations and macroscopic phenotype selection is analyzed using the phage λ lysis-lysogeny decision circuit as a model system. The fraction of infected cells selecting the lysogenic pathway at different phage:cell ratios, predicted using a molecular-level stochastic kinetic model of the genetic regulatory circuit, is consistent with experimental observations. The kinetic model of the decision circuit uses the stochastic formulation of chemical kinetics, stochastic mechanisms of gene expression, and a statistical-thermodynamic model of promoter regulation. Conventional deterministic kinetics cannot be used to predict statistics of regulatory systems that produce probabilistic outcomes. Rather, a stochastic kinetic analysis must be used to predict statistics of regulatory outcomes for such stochastically regulated systems.
In this review, we summarize the main structural and functional data on the role of the
phosphocreatine (PCr) – creatine kinase (CK) pathway for compartmentalized energy
transfer in cardiac cells. Mitochondrial creatine kinase, MtCK, fixed by cardiolipin
molecules in the vicinity of the adenine nucleotide translocator, is a key enzyme in this
pathway. Direct transfer of ATP and ADP between these proteins has been revealed both
in experimental studies on the kinetics of the regulation of mitochondrial respiration
and by mathematical modelling as a main mechanism of functional coupling of PCr
production to oxidative phosphorylation. In cells in vivo or in permeabilized cells in
situ, this coupling is reinforced by limited permeability of the outer membrane of the
mitochondria for adenine nucleotides due to the contacts with cytoskeletal proteins. Due
to these mechanisms, at least 80% of total energy is exported from mitochondria by
PCr molecules. Mathematical modelling of intracellular diffusion and energy transfer
shows that the main function of the PCr – CK pathway is to connect different pools
(compartments) of ATP and, by this way, to overcome the local restrictions and diffusion
limitation of adenine nucleotides due to the high degree of structural organization of
cardiac cells
Technological systems become organized by commands from outside, as when human intentions lead to the building of structures or machines. But many nat ural systems become structured by their own internal processes: these are the self organizing systems, and the emergence of order within them is a complex phe nomenon that intrigues scientists from all disciplines. Unfortunately, complexity is ill-defined. Global explanatory constructs, such as cybernetics or general sys tems theory, which were intended to cope with complexity, produced instead a grandiosity that has now, mercifully, run its course and died. Most of us have become wary of proposals for an "integrated, systems approach" to complex matters; yet we must come to grips with complexity some how. Now is a good time to reexamine complex systems to determine whether or not various scientific specialties can discover common principles or properties in them. If they do, then a fresh, multidisciplinary attack on the difficulties would be a valid scientific task. Believing that complexity is a proper scientific issue, and that self-organizing systems are the foremost example, R. Tomovic, Z. Damjanovic, and I arranged a conference (August 26-September 1, 1979) in Dubrovnik, Yugoslavia, to address self-organizing systems. We invited 30 participants from seven countries. Included were biologists, geologists, physicists, chemists, mathematicians, bio physicists, and control engineers. Participants were asked not to bring manu scripts, but, rather, to present positions on an assigned topic. Any writing would be done after the conference, when the writers could benefit from their experi ences there.
Thermodynamics is a rather old discipline of physics, however, it is not oldfashioned. On the contrary,such modern topics as the hot big bang model, the theory of black holes, as well as the theory of biological systems /1,2/, show that thermodynamics goes through a renaissance. Thermodynamics is also intimately related to information theory, a key discipline for the study of selforganization and evolution /3,4/. The very origin of this discipline is closely connected with thermodynamical reasoning, as shown in the fundamental papers of SZILARD (1929), SHANNON (1948) and BRILLOUIN (1956). Thus STRATONOVICH, one of the pioneers of several branches of modern information theory, writes that thermodynamics and statistical physics are the cement which hold together the disciplines forming modern information theory /5/. Besides the informational aspects also the direct consideration of thermodynamic functions and of the entropy production is of much interest for the study of selforganization processes /6,7/. The structures created in the process of selforgánization are often called “dissipative structures” /6-8/. Besides this term, which underlines the aspect of dissipation, we shall also use the term “autostructures”, which underlines the aspect autonomy /9/. The term autostructure is a generalization of well-known terms as “autooscillations” and “autowaves” /10/.
A cell's behavior is a consequence of the complex interactions between its numerous constituents, such as DNA, RNA, proteins and small molecules. Cells use signaling pathways and regulatory mechanisms to coordinate multiple processes, allowing them to respond to and adapt to an ever-changing environment. The large number of components, the degree of interconnectivity and the complex control of cellular networks are becoming evident in the integrated genomic and proteomic analyses that are emerging. It is increasingly recognized that the understanding of properties that arise from whole-cell function require integrated, theoretical descriptions of the relationships between different cellular components. Recent theoretical advances allow us to describe cellular network structure with graph concepts, and have revealed organizational features shared with numerous non-biological networks. How do we quantitatively describe a network of hundreds or thousands of interacting components? Does the observed topology of cellular networks give us clues about their evolution? How does cellular networks' organization influence their function and dynamical responses? This article will review the recent advances in addressing these questions.
The neurosciences deal with the various levels of nervous system from a single neuron, a highly nonlinear element, to the whole brain, a highly complex system. Consequently, when observing neural activities and/or the end-organ responses, one can easily find signals exhibiting irregular, complex, and seemingly random dynamics. Until recently, the common strategy to study these dynamics has been to use various types of stochastic models to deal with the randomness (Tuckwell 1989). The theory of nonlinear dynamics, especially that of (low-dimensional) chaos and fractals, is changing this traditional strategy.
In this first integrated view, practically each of the world's leading experts has contributed to this one and only authoritative resource on the topic. Bringing systems biology to cellular energetics, they address in detail such novel concepts as metabolite channeling and medical aspects of metabolic syndrome and cancer.