Global self-regulation of the cellular metabolic structure

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.

Information theory in systems biology. Part I: Gene regulatory and metabolic networks

"A Mathematical Theory of Communication", was published in 1948 by Claude Shannon to establish a framework that is now known as information theory. In recent decades, information theory has gained much attention in the area of systems biology. The aim of this paper is to provide a systematic review of those contributions that have applied information theory in inferring or understanding of biological systems. Based on the type of system components and the interactions between them, we classify the biological systems into 4 main classes: gene regulatory, metabolic, protein-protein interaction and signaling networks. In the first part of this review, we attempt to introduce most of the existing studies on two types of biological networks, including gene regulatory and metabolic networks, which are founded on the concepts of information theory.

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.

Modular organization of cardiac energy metabolism: energy conversion, transfer and feedback regulation

To meet high cellular demands, the energy metabolism of cardiac muscles is organized by precise and coordinated functioning of intracellular energetic units (ICEUs). ICEUs represent structural and functional modules integrating multiple fluxes at sites of ATP generation in mitochondria and ATP utilization by myofibrillar, sarcoplasmic reticulum and sarcolemma ion-pump ATPases. The role of ICEUs is to enhance the efficiency of vectorial intracellular energy transfer and fine tuning of oxidative ATP synthesis maintaining stable metabolite levels to adjust to intracellular energy needs through the dynamic system of compartmentalized phosphoryl transfer networks. One of the key elements in regulation of energy flux distribution and feedback communication is the selective permeability of mitochondrial outer membrane (MOM) which represents a bottleneck in adenine nucleotide and other energy metabolite transfer and microcompartmentalization. Based on the experimental and theoretical (mathematical modelling) arguments, we describe regulation of mitochondrial ATP synthesis within ICEUs allowing heart workload to be linearly correlated with oxygen consumption ensuring conditions of metabolic stability, signal communication and synchronization. Particular attention was paid to the structure-function relationship in the development of ICEU, and the role of mitochondria interaction with cytoskeletal proteins, like tubulin, in the regulation of MOM permeability in response to energy metabolic signals providing regulation of mitochondrial respiration. Emphasis was given to the importance of creatine metabolism for the cardiac energy homoeostasis.

Affinity purification-mass spectrometry and network analysis to understand protein-protein interactions

By determining protein-protein interactions in normal, diseased and infected cells, we can improve our understanding of cellular systems and their reaction to various perturbations. In this protocol, we discuss how to use data obtained in affinity purification-mass spectrometry (AP-MS) experiments to generate meaningful interaction networks and effective figures. We begin with an overview of common epitope tagging, expression and AP practices, followed by liquid chromatography-MS (LC-MS) data collection. We then provide a detailed procedure covering a pipeline approach to (i) pre-processing the data by filtering against contaminant lists such as the Contaminant Repository for Affinity Purification (CRAPome) and normalization using the spectral index (SIN) or normalized spectral abundance factor (NSAF); (ii) scoring via methods such as MiST, SAInt and CompPASS; and (iii) testing the resulting scores. Data formats familiar to MS practitioners are then transformed to those most useful for network-based analyses. The protocol also explores methods available in Cytoscape to visualize and analyze these types of interaction data. The scoring pipeline can take anywhere from 1 d to 1 week, depending on one's familiarity with the tools and data peculiarities. Similarly, the network analysis and visualization protocol in Cytoscape takes 2-4 h to complete with the provided sample data, but we recommend taking days or even weeks to explore one's data and find the right questions.

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.

The control of brain mitochondrial energization by cytosolic calcium: the mitochondrial gas pedal

This review focuses on problems of the intracellular regulation of mitochondrial function in the brain via the (i) supply of mitochondria with ADP by means of ADP shuttles and channels and (ii) the Ca(2+) control of mitochondrial substrate supply. The permeability of the mitochondrial outer membrane for adenine nucleotides is low. Therefore rate dependent concentration gradients exist between the mitochondrial intermembrane space and the cytosol. The existence of dynamic ADP gradients is an important precondition for the functioning of ADP shuttles, for example CrP-shuttle. Cr at mM concentrations instead of ADP diffuses from the cytosol through the porin pores into the intermembrane space. The CrP-shuttle isoenzymes work in different directions which requires different metabolite concentrations mainly caused by dynamic ADP compartmentation. The ADP shuttle mechanisms alone cannot explain the load dependent changes in mitochondrial energization, and a complete model of mitochondrial regulation have to account the Ca(2+) -dependent substrate supply too. According to the old paradigmatic view, Ca(2+) (cyt) taken up by the mitochondrial Ca(2+) uniporter activates dehydrogenases within the matrix. However, recently it was found that Ca(2+) (cyt) at low nM concentrations exclusively activates the state 3 respiration via aralar, the mitochondrial glutamate/aspartate carrier. At higher Ca(2+) (cyt) (> 500 nM), brain mitochondria take up Ca(2+) for activation of substrate oxidation rates. Since brain mitochondrial pyruvate oxidation is only slightly influenced by Ca(2+) (cyt) , it was proposed that the cytosolic formation of pyruvate from its precursors is tightly controlled by the Ca(2+) dependent malate/aspartate shuttle. At low (50-100 nM) Ca(2+) (cyt) the pyruvate formation is suppressed, providing a substrate limitation control in neurons. This so called "gas pedal" mechanism explains why the energy metabolism of neurons in the nucleus suprachiasmaticus could be down-regulated at night but activated at day as a basis for the circadian changes in Ca(2+) (cyt) . It also could explain the energetic disadvantages caused by altered Ca(2+) (cyt) at mitochondrial diseases and neurodegeneration.

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.

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.