Global self-organization of the cellular metabolic structure

Systemic cellular migration: The forces driving the directed locomotion movement of 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 nonlinear interaction of most, if not all, molecular components of cells.

Responses to commentaries on "The gene: An appraisal"

The central conclusions of "The Gene: An Appraisal" are that genetic variance does not underpin biological evolution, and, therefore, that genes are not Mendel's units of inheritance. In this response, I will address the criticisms I have received via commentaries on that paper by defending the following statements: 1. Epistasis does not explain the power-law fitness profile of the Long-Term Evolution Experiment (LTEE). The data from the evolution of natural systems displays the power-law form ubiquitously. Epistasis plays no role in evolution. 2. The common characteristics of living things (natural systems) are described by the principle of least action in de Maupertuis's original form, which is synonymous with the 2nd law of thermodynamics and Newton's 2nd law of motion in its complete form, i.e., F = dp/dt. Organisms strive to achieve free energy balance with their environments. 3. Based on an appraisal of the scientific environment between 1880 and 1911, I conclude that Johannsen's genotype conception was perhaps, the only option available to him. 4. The power-law fitness profile of the LTEE falsifies Fisher's Genetical Theory of Natural Selection, Johannsen's genotype conception, and the idea that 'Darwinian evolution' is an exception to the generic thermodynamic process of evolution in natural systems. 5. The use of the technique of genome-wide association to identify the causes and the likelihoods of inherited common diseases and behavioural traits is a 'wild goose chase' because genes are not the units of inheritance.

Assessing Protein Interactions for Clustering of Mitochondrial Urea Cycle Enzymes

Enzyme clustering is a phenomenon that involves partitioning of proteins that function together in a common subcellular or sub-organellar compartment. Traditional genetic, biochemical, and biophysical approaches for studying protein-protein interactions in complexes with defined stoichiometry yield inconclusive results when applied to clustered proteins. This chapter describes a combination of approaches to study clustered proteins including co-immunoprecipitation, biochemical co-localization in purified mitochondria, and super resolution imaging of endogenous proteins in situ. These approaches can be used to study interactions among proteins that form clusters. We will illustrate this approach by using the urea cycle enzymes that localize in the mitochondrial matrix, and form clusters at the inner mitochondrial membrane.

Correspondence insights into the role of genes in cell functionality. Comments on "The gene: An appraisal" by K. Baverstock

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.

Self-Organization, Entropy Generation Rate, and Boundary Defects: A Control Volume Approach

Self-organization that leads to the discontinuous emergence of optimized new patterns is related to entropy generation and the export of entropy. Compared to the original pattern that the new, self-organized pattern replaces, the new features could involve an abrupt change in the pattern-volume. There is no clear principle of pathway selection for self-organization that is known for triggering a particular new self-organization pattern. The new pattern displays different types of boundary-defects necessary for stabilizing the new order. Boundary-defects can contain high entropy regions of concentrated chemical species. On the other hand, the reorganization (or refinement) of an established pattern is a more kinetically tractable process, where the entropy generation rate varies continuously with the imposed variables that enable and sustain the pattern features. The maximum entropy production rate (MEPR) principle is one possibility that may have predictive capability for self-organization. The scale of shapes that form or evolve during self-organization and reorganization are influenced by the export of specific defects from the control volume of study. The control volume (CV) approach must include the texture patterns to be located inside the CV for the MEPR analysis to be applicable. These hypotheses were examined for patterns that are well-characterized for solidification and wear processes. We tested the governing equations for bifurcations (the onset of new patterns) and for reorganization (the fine tuning of existing patterns) with published experimental data, across the range of solidification morphologies and nonequilibrium phases, for metallic glass and featureless crystalline solids. The self-assembling features of surface-texture patterns for friction and wear conditions were also modeled with the entropy generation (MEPR) principle, including defect production (wear debris). We found that surface texture and entropy generation in the control volume could be predictive for self-organization. The main results of this study provide support to the hypothesis that self-organized patterns are a consequence of the maximum entropy production rate per volume principle. Patterns at any scale optimize a certain outcome and have utility. We discuss some similarities between the self-organization behavior of both inanimate and living systems, with ideas regarding the optimizing features of self-organized pattern features that impact functionality, beauty, and consciousness.

Self-Organization and Information Processing: From Basic Enzymatic Activities to Complex Adaptive Cellular Behavior

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.

Is the cell really a machine?

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes.

Spatial Organization of Metabolic Enzyme Complexes in Cells

The organization of metabolic multienzyme complexes has been hypothesized to benefit metabolic processes and provide a coordinated way for the cell to regulate metabolism. Historically, their existence has been supported by various in vitro techniques. However, it is only recently that the existence of metabolic complexes inside living cells has come to light to corroborate this long-standing hypothesis. Indeed, subcellular compartmentalization of metabolic enzymes appears to be widespread and highly regulated. On the other hand, it is still challenging to demonstrate the functional significance of these enzyme complexes in the context of the cellular milieu. In this review, we discuss the current understanding of metabolic enzyme complexes by primarily focusing on central carbon metabolism and closely associated metabolic pathways in a variety of organisms, as well as their regulation and functional contributions to cells.

A Generalized Spatial Measure for Resilience of Microbial Systems

The emergent property of resilience is the ability of a system to return to an original state after a disturbance. Resilience may be used as an early warning system for significant or irreversible community transition; that is, a community with diminishing or low resilience may be close to catastrophic shift in function or an irreversible collapse. Typically, resilience is quantified using recovery time, which may be difficult or impossible to directly measure in microbial systems. A recent study in the literature showed that under certain conditions, a set of spatial-based metrics termed recovery length, can be correlated to recovery time, and thus may be a reasonable alternative measure of resilience. However, this spatial metric of resilience is limited to use for step-change perturbations. Building upon the concept of recovery length, we propose a more general form of the spatial metric of resilience that can be applied to any shape of perturbation profiles (for example, either sharp or smooth gradients). We termed this new spatial measure “perturbation-adjusted spatial metric of resilience” (PASMORE). We demonstrate the applicability of the proposed metric using a mathematical model of a microbial mat.

System-wide assembly of pathways and modules hierarchically reveal metabolic mechanism of cerebral ischemia

The relationship between cerebral ischemia and metabolic disorders is poorly understood, which is partly due to the lack of comparative fusing data for larger complete systems and to the complexity of metabolic cascade reactions. Based on the fusing maps of comprehensive serum metabolome, fatty acid and amino acid profiling, we identified 35 potential metabolic biomarkers for ischemic stroke. Our analyses revealed 8 significantly altered pathways by MetPA (Metabolomics Pathway Analysis, impact score >0.10) and 15 significantly rewired modules in a complex ischemic network using the Markov clustering (MCL) method; all of these pathways became more homologous as the number of overlapping nodes was increased. We then detected 24 extensive pathways based on the total modular nodes from the network analysis, 12 of which were new discovery pathways. We provided a new perspective from the viewpoint of abnormal metabolites for the overall study of ischemic stroke as well as a new method to simplify the network analysis by selecting the more closely connected edges and nodes to build a module map of stroke.

Elements of the cellular metabolic structure

A large number of studies have demonstrated the existence of metabolic covalent modifications in different molecular structures, which are able to store biochemical information that is not encoded by DNA. Some of these covalent mark patterns can be transmitted across generations (epigenetic changes). Recently, the emergence of Hopfield-like attractor dynamics has been observed in self-organized enzymatic networks, which have the capacity to store functional catalytic patterns that can be correctly recovered by specific input stimuli. Hopfield-like metabolic dynamics are stable and can be maintained as a long-term biochemical memory. In addition, specific molecular information can be transferred from the functional dynamics of the metabolic networks to the enzymatic activity involved in covalent post-translational modulation, so that determined functional memory can be embedded in multiple stable molecular marks. The metabolic dynamics governed by Hopfield-type attractors (functional processes), as well as the enzymatic covalent modifications of specific molecules (structural dynamic processes) seem to represent the two stages of the dynamical memory of cellular metabolism (metabolic memory). Epigenetic processes appear to be the structural manifestation of this cellular metabolic memory. Here, a new framework for molecular information storage in the cell is presented, which is characterized by two functionally and molecularly interrelated systems: a dynamic, flexible and adaptive system (metabolic memory) and an essentially conservative system (genetic memory). The molecular information of both systems seems to coordinate the physiological development of the whole cell.

On the dynamics of the adenylate energy system: homeorhesis vs homeostasis

Biochemical energy is the fundamental element that maintains both the adequate turnover of the biomolecular structures and the functional metabolic viability of unicellular organisms. The levels of ATP, ADP and AMP reflect roughly the energetic status of the cell, and a precise ratio relating them was proposed by Atkinson as the adenylate energy charge (AEC). Under growth-phase conditions, cells maintain the AEC within narrow physiological values, despite extremely large fluctuations in the adenine nucleotides concentration. Intensive experimental studies have shown that these AEC values are preserved in a wide variety of organisms, both eukaryotes and prokaryotes. Here, to understand some of the functional elements involved in the cellular energy status, we present a computational model conformed by some key essential parts of the adenylate energy system. Specifically, we have considered (I) the main synthesis process of ATP from ADP, (II) the main catalyzed phosphotransfer reaction for interconversion of ATP, ADP and AMP, (III) the enzymatic hydrolysis of ATP yielding ADP, and (IV) the enzymatic hydrolysis of ATP providing AMP. This leads to a dynamic metabolic model (with the form of a delayed differential system) in which the enzymatic rate equations and all the physiological kinetic parameters have been explicitly considered and experimentally tested in vitro. Our central hypothesis is that cells are characterized by changing energy dynamics (homeorhesis). The results show that the AEC presents stable transitions between steady states and periodic oscillations and, in agreement with experimental data these oscillations range within the narrow AEC window. Furthermore, the model shows sustained oscillations in the Gibbs free energy and in the total nucleotide pool. The present study provides a step forward towards the understanding of the fundamental principles and quantitative laws governing the adenylate energy system, which is a fundamental element for unveiling the dynamics of cellular life.

Attractor metabolic networks

BACKGROUND

The experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a Systemic Metabolic Structure in the cell, characterized by a set of different enzymatic reactions always locked into active states (metabolic core) while the rest of the catalytic processes are only intermittently active. This global metabolic structure was verified for Escherichia coli, Helicobacter pylori and Saccharomyces cerevisiae, and it seems to be a common key feature to all cellular organisms. In concordance with these observations, the cell can be considered a complex metabolic network which mainly integrates a large ensemble of self-organized multienzymatic complexes interconnected by substrate fluxes and regulatory signals, where multiple autonomous oscillatory and quasi-stationary catalytic patterns simultaneously emerge. The network adjusts the internal metabolic activities to the external change by means of flux plasticity and structural plasticity.

METHODOLOGY/PRINCIPAL FINDINGS

In order to research the systemic mechanisms involved in the regulation of the cellular enzymatic activity we have studied different catalytic activities of a dissipative metabolic network under different external stimuli. The emergent biochemical data have been analysed using statistical mechanic tools, studying some macroscopic properties such as the global information and the energy of the system. We have also obtained an equivalent Hopfield network using a Boltzmann machine. Our main result shows that the dissipative metabolic network can behave as an attractor metabolic network.

CONCLUSIONS/SIGNIFICANCE

We have found that the systemic enzymatic activities are governed by attractors with capacity to store functional metabolic patterns which can be correctly recovered from specific input stimuli. The network attractors regulate the catalytic patterns, modify the efficiency in the connection between the multienzymatic complexes, and stably retain these modifications. Here for the first time, we have introduced the general concept of attractor metabolic network, in which this dynamic behavior is observed.

Quantitative analysis of the effective functional structure in yeast glycolysis

The understanding of the effective functionality that governs the enzymatic self-organized processes in cellular conditions is a crucial topic in the post-genomic era. In recent studies, Transfer Entropy has been proposed as a rigorous, robust and self-consistent method for the causal quantification of the functional information flow among nonlinear processes. Here, in order to quantify the functional connectivity for the glycolytic enzymes in dissipative conditions we have analyzed different catalytic patterns using the technique of Transfer Entropy. The data were obtained by means of a yeast glycolytic model formed by three delay differential equations where the enzymatic rate equations of the irreversible stages have been explicitly considered. These enzymatic activity functions were previously modeled and tested experimentally by other different groups. The results show the emergence of a new kind of dynamical functional structure, characterized by changing connectivity flows and a metabolic invariant that constrains the activity of the irreversible enzymes. In addition to the classical topological structure characterized by the specific location of enzymes, substrates, products and feedback-regulatory metabolites, an effective functional structure emerges in the modeled glycolytic system, which is dynamical and characterized by notable variations of the functional interactions. The dynamical structure also exhibits a metabolic invariant which constrains the functional attributes of the enzymes. Finally, in accordance with the classical biochemical studies, our numerical analysis reveals in a quantitative manner that the enzyme phosphofructokinase is the key-core of the metabolic system, behaving for all conditions as the main source of the effective causal flows in yeast glycolysis.

Molecular system bioenergics of the heart: experimental studies of metabolic compartmentation and energy fluxes versus computer modeling

In this review we analyze the recent important and remarkable advancements in studies of compartmentation of adenine nucleotides in muscle cells due to their binding to macromolecular complexes and cellular structures, which results in non-equilibrium steady state of the creatine kinase reaction. We discuss the problems of measuring the energy fluxes between different cellular compartments and their simulation by using different computer models. Energy flux determinations by ¹⁸O transfer method have shown that in heart about 80% of energy is carried out of mitochondrial intermembrane space into cytoplasm by phosphocreatine fluxes generated by mitochondrial creatine kinase from adenosine triphosphate (ATP), produced by ATP Synthasome. We have applied the mathematical model of compartmentalized energy transfer for analysis of experimental data on the dependence of oxygen consumption rate on heart workload in isolated working heart reported by Williamson et al. The analysis of these data show that even at the maximal workloads and respiration rates, equal to 174 μmol O₂ per min per g dry weight, phosphocreatine flux, and not ATP, carries about 80–85% percent of energy needed out of mitochondria into the cytosol. We analyze also the reasons of failures of several computer models published in the literature to correctly describe the experimental data.

The metabolic core and catalytic switches are fundamental elements in the self-regulation of the systemic metabolic structure of cells

BACKGROUND

Experimental observations and numerical studies with dissipative metabolic networks have shown that cellular enzymatic activity self-organizes spontaneously leading to the emergence of a metabolic core formed by a set of enzymatic reactions which are always active under all environmental conditions, while the rest of catalytic processes are only intermittently active. The reactions of the metabolic core are essential for biomass formation and to assure optimal metabolic performance. The on-off catalytic reactions and the metabolic core are essential elements of a Systemic Metabolic Structure which seems to be a key feature common to all cellular organisms.

METHODOLOGY/PRINCIPAL FINDINGS

In order to investigate the functional importance of the metabolic core we have studied different catalytic patterns of a dissipative metabolic network under different external conditions. The emerging biochemical data have been analysed using information-based dynamic tools, such as Pearson's correlation and Transfer Entropy (which measures effective functionality). Our results show that a functional structure of effective connectivity emerges which is dynamical and characterized by significant variations of bio-molecular information flows.

CONCLUSIONS/SIGNIFICANCE

We have quantified essential aspects of the metabolic core functionality. The always active enzymatic reactions form a hub--with a high degree of effective connectivity--exhibiting a wide range of functional information values being able to act either as a source or as a sink of bio-molecular causal interactions. Likewise, we have found that the metabolic core is an essential part of an emergent functional structure characterized by catalytic modules and metabolic switches which allow critical transitions in enzymatic activity. Both, the metabolic core and the catalytic switches in which also intermittently-active enzymes are involved seem to be fundamental elements in the self-regulation of the Systemic Metabolic Structure.

Intracellular Energetic Units regulate metabolism in cardiac cells

This review describes developments in historical perspective as well as recent results of investigations of cellular mechanisms of regulation of energy fluxes and mitochondrial respiration by cardiac work - the metabolic aspect of the Frank-Starling law of the heart. A Systems Biology solution to this problem needs the integration of physiological and biochemical mechanisms that take into account intracellular interactions of mitochondria with other cellular systems, in particular with cytoskeleton components. Recent data show that different tubulin isotypes are involved in the regular arrangement exhibited by mitochondria and ATP-consuming systems into Intracellular Energetic Units (ICEUs). Beta II tubulin association with the mitochondrial outer membrane, when co-expressed with mitochondrial creatine kinase (MtCK) specifically limits the permeability of voltage-dependent anion channel for adenine nucleotides. In the MtCK reaction this interaction changes the regulatory kinetics of respiration through a decrease in the affinity for adenine nucleotides and an increase in the affinity for creatine. Metabolic Control Analysis of the coupled MtCK-ATP Synthasome in permeabilized cardiomyocytes showed a significant increase in flux control by steps involved in ADP recycling. Mathematical modeling of compartmentalized energy transfer represented by ICEUs shows that cyclic changes in local ADP, Pi, phosphocreatine and creatine concentrations during contraction cycle represent effective metabolic feedback signals when amplified in the coupled non-equilibrium MtCK-ATP Synthasome reactions in mitochondria. This mechanism explains the regulation of respiration on beat to beat basis during workload changes under conditions of metabolic stability. This article is part of a Special Issue entitled "Local Signaling in Myocytes."

Mitochondria-cytoskeleton interaction: distribution of β-tubulins in cardiomyocytes and HL-1 cells

Mitochondria-cytoskeleton interactions were analyzed in adult rat cardiomyocytes and in cancerous non-beating HL-1 cells of cardiac phenotype. We show that in adult cardiomyocytes βII-tubulin is associated with mitochondrial outer membrane (MOM). βI-tubulin demonstrates diffused intracellular distribution, βIII-tubulin is colocalized with Z-lines and βIV-tubulin forms microtubular network. HL-1 cells are characterized by the absence of βII-tubulin, by the presence of bundles of filamentous βIV-tubulin and diffusely distributed βI- and βIII-tubulins. Mitochondrial isoform of creatine kinase (MtCK), highly expressed in cardiomyocytes, is absent in HL-1 cells. Our results show that high apparent K(m) for exogenous ADP in regulation of respiration and high expression of MtCK both correlate with the expression of βII-tubulin. The absence of βII-tubulin isotype in isolated mitochondria and in HL-1 cells results in increased apparent affinity of oxidative phosphorylation for exogenous ADP. This observation is consistent with the assumption that the binding of βII-tubulin to mitochondria limits ADP/ATP diffusion through voltage-dependent anion channel of MOM and thus shifts energy transfer via the phosphocreatine pathway. On the other hand, absence of both βII-tubulin and MtCK in HL-1 cells can be associated with their more glycolysis-dependent energy metabolism which is typical for cancer cells (Warburg effect).

Quantitative analysis of cellular metabolic dissipative, self-organized structures

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.

Application of the principles of systems biology and Wiener's cybernetics for analysis of regulation of energy fluxes in muscle cells in vivo

The mechanisms of regulation of respiration and energy fluxes in the cells are analyzed based on the concepts of systems biology, non-equilibrium steady state kinetics and applications of Wiener’s cybernetic principles of feedback regulation. Under physiological conditions cardiac function is governed by the Frank-Starling law and the main metabolic characteristic of cardiac muscle cells is metabolic homeostasis, when both workload and respiration rate can be changed manifold at constant intracellular level of phosphocreatine and ATP in the cells. This is not observed in skeletal muscles. Controversies in theoretical explanations of these observations are analyzed. Experimental studies of permeabilized fibers from human skeletal muscle vastus lateralis and adult rat cardiomyocytes showed that the respiration rate is always an apparent hyperbolic but not a sigmoid function of ADP concentration. It is our conclusion that realistic explanations of regulation of energy fluxes in muscle cells require systemic approaches including application of the feedback theory of Wiener’s cybernetics in combination with detailed experimental research. Such an analysis reveals the importance of limited permeability of mitochondrial outer membrane for ADP due to interactions of mitochondria with cytoskeleton resulting in quasi-linear dependence of respiration rate on amplitude of cyclic changes in cytoplasmic ADP concentrations. The system of compartmentalized creatine kinase (CK) isoenzymes functionally coupled to ANT and ATPases, and mitochondrial-cytoskeletal interactions separate energy fluxes (mass and energy transfer) from signalling (information transfer) within dissipative metabolic structures – intracellular energetic units (ICEU). Due to the non-equilibrium state of CK reactions, intracellular ATP utilization and mitochondrial ATP regeneration are interconnected by the PCr flux from mitochondria. The feedback regulation of respiration occurring via cyclic fluctuations of cytosolic ADP, Pi and Cr/PCr ensures metabolic stability necessary for normal function of cardiac cells.

Global self-regulation of the cellular metabolic structure

BACKGROUND

Different studies have shown that cellular enzymatic activities are able to self-organize spontaneously, forming a metabolic core of reactive processes that remain active under different growth conditions while the rest of the molecular catalytic reactions exhibit structural plasticity. This global cellular metabolic structure appears to be an intrinsic characteristic common to all cellular organisms. Recent work performed with dissipative metabolic networks has shown that the fundamental element for the spontaneous emergence of this global self-organized enzymatic structure could be the number of catalytic elements in the metabolic networks.

METHODOLOGY/PRINCIPAL FINDINGS

In order to investigate the factors that may affect the catalytic dynamics under a global metabolic structure characterized by the presence of metabolic cores we have studied different transitions in catalytic patterns belonging to a dissipative metabolic network. The data were analyzed using non-linear dynamics tools: power spectra, reconstructed attractors, long-term correlations, maximum Lyapunov exponent and Approximate Entropy; and we have found the emergence of self-regulation phenomena during the transitions in the metabolic activities.

CONCLUSIONS/SIGNIFICANCE

The analysis has also shown that the chaotic numerical series analyzed correspond to the fractional Brownian motion and they exhibit long-term correlations and low Approximate Entropy indicating a high level of predictability and information during the self-regulation of the metabolic transitions. The results illustrate some aspects of the mechanisms behind the emergence of the metabolic self-regulation processes, which may constitute an important property of the global structure of the cellular metabolism.

Oscillatory growth in lily pollen tubes does not require aerobic energy metabolism

Oscillatory tip growth in pollen tubes depends on prodigious amounts of energy. We have tested the hypothesis that oscillations in the electron transport chain lead to growth oscillations in lily (Lilium formosanum). Using three respiratory inhibitors, oligomycin, antimycin A, and cyanide, we find that pollen tube growth is much less sensitive to respiratory inhibition than respiration is. All three block respiration at concentrations severalfold lower than necessary to inhibit growth. Mitochondrial NAD(P)H and potentiometric JC-1 fluorescence, employed as markers for electron transport chain activity, rise rapidly in response to oligomycin, as expected. Pollen tube growth stops for several minutes before resuming. Subsequent growth has a lower mean rate, but continues to oscillate, albeit with a longer period. NAD(P)H fluorescence no longer exhibits coherent oscillations, and mitochondria no longer congregate directly behind the apex: they distribute evenly throughout the cell. Postinhibition growth relies on aerobic fermentation for energy production as revealed by an increase in ethanol in the media. These data suggest that oscillatory growth depends not on a single oscillatory pacemaker but rather is an emergent property arising from a number of stable limit cycles.

Structure-function relationships in feedback regulation of energy fluxes in vivo in health and disease: mitochondrial interactosome

The aim of this review is to analyze the results of experimental research of mechanisms of regulation of mitochondrial respiration in cardiac and skeletal muscle cells in vivo obtained by using the permeabilized cell technique. Such an analysis in the framework of Molecular Systems Bioenergetics shows that the mechanisms of regulation of energy fluxes depend on the structural organization of the cells and interaction of mitochondria with cytoskeletal elements. Two types of cells of cardiac phenotype with very different structures were analyzed: adult cardiomyocytes and continuously dividing cancerous HL-1 cells. In cardiomyocytes mitochondria are arranged very regularly, and show rapid configuration changes of inner membrane but no fusion or fission, diffusion of ADP and ATP is restricted mostly at the level of mitochondrial outer membrane due to an interaction of heterodimeric tubulin with voltage dependent anion channel, VDAC. VDAC with associated tubulin forms a supercomplex, Mitochondrial Interactosome, with mitochondrial creatine kinase, MtCK, which is structurally and functionally coupled to ATP synthasome. Due to selectively limited permeability of VDAC for adenine nucleotides, mitochondrial respiration rate depends almost linearly upon the changes of cytoplasmic ADP concentration in their physiological range. Functional coupling of MtCK with ATP synthasome amplifies this signal by recycling adenine nucleotides in mitochondria coupled to effective phosphocreatine synthesis. In cancerous HL-1 cells this complex is significantly modified: tubulin is replaced by hexokinase and MtCK is lacking, resulting in direct utilization of mitochondrial ATP for glycolytic lactate production and in this way contributing in the mechanism of the Warburg effect. Systemic analysis of changes in the integrated system of energy metabolism is also helpful for better understanding of pathogenesis of many other diseases.

Regulatory crosstalk of the metabolic network

The metabolic network has a modular architecture, is robust to perturbations, and responds to biological stimuli and environmental conditions. Through monitoring by metabolite responsive macromolecules, metabolic pathways interact with the transcriptome and proteome. Whereas pathway interconnecting cofactors and substrates report on the overall state of the network, specialised intermediates measure the activity of individual functional units. Transitions in the network affect many of these regulatory metabolites, facilitating the parallel regulation of the timing and control of diverse biological processes. The metabolic network controls its own balance, chromatin structure and the biosynthesis of molecular cofactors; moreover, metabolic shifts are crucial in the response to oxidative stress and play a regulatory role in cancer.

The number of catalytic elements is crucial for the emergence of metabolic cores

Background

Different studies show evidence that several unicellular organisms display a cellular metabolic structure characterized by a set of enzymes which are always in an active state (metabolic core), while the rest of the molecular catalytic reactions exhibit on-off changing states. This self-organized enzymatic configuration seems to be an intrinsic characteristic of metabolism, common to all living cellular organisms. In a recent analysis performed with dissipative metabolic networks (DMNs) we have shown that this global functional structure emerges in metabolic networks with a relatively high number of catalytic elements, under particular conditions of enzymatic covalent regulatory activity.

Methodology/Principal Findings

Here, to investigate the mechanism behind the emergence of this supramolecular organization of enzymes, we have performed extensive DMNs simulations (around 15,210,000 networks) taking into account the proportion of the allosterically regulated enzymes and covalent enzymes present in the networks, the variation in the number of substrate fluxes and regulatory signals per catalytic element, as well as the random selection of the catalytic elements that receive substrate fluxes from the exterior. The numerical approximations obtained show that the percentages of DMNs with metabolic cores grow with the number of catalytic elements, converging to 100% for all cases.

Conclusions/Significance

The results show evidence that the fundamental factor for the spontaneous emergence of this global self-organized enzymatic structure is the number of catalytic elements in the metabolic networks. Our analysis corroborates and expands on our previous studies illustrating a crucial property of the global structure of the cellular metabolism. These results also offer important insights into the mechanisms which ensure the robustness and stability of living cells.