Quantitative analysis of cellular metabolic dissipative, self-organized structures

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.

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 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.

In silico Determination of Some Conditions Leading to Glycolytic Oscillations and Their Interference With Some Other Processes in E. coli Cells

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).

Information Theory in Computational Biology: Where We Stand Today

"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.

Under Diffusion Control: from Structuring Matter to Directional Motion

Self-organization in synthetic chemical systems is quickly developing into a powerful strategy for designing new functional materials. As self-organization requires the system to exist far from thermodynamic equilibrium, chemists have begun to go beyond the classical equilibrium self-assembly that is often applied in bottom-up supramolecular synthesis, and to learn about the surprising and unpredicted emergent properties of chemical systems that are characterized by a higher level of complexity and extended reactivity networks. The present review focuses on self-organization in reaction-diffusion systems. Selected examples show how the emergence of complex morphogenesis is feasible in synthetic systems leading to hierarchically and nanostructured matter. Starting from well-investigated oscillating reactions, recent developments extend diffusion-limited reactivity to supramolecular systems. The concept of dynamic instability is introduced and illustrated as an additional tool for the design of smart materials and actuators, with emphasis on the realization of motion even at the macroscopic scale. The formation of spatio-temporal patterns along diffusive chemical gradients is exploited as the main channel to realize symmetry breaking and therefore anisotropic and directional mechanical transformations. Finally, the interaction between external perturbations and chemical gradients is explored to give mechanistic insights in the design of materials responsive to external stimuli.

Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach

In this paper, the problem of robust stability of nonlinear genetic regulatory networks (GRNs) is investigated. The developed method is an integral sliding mode control based redesign for a class of perturbed dissipative switched GRNs with time delays. The control law is redesigned by modifying the dissipativity-based control law that was designed for the unperturbed GRNs with time delays. The switched GRNs are switched from one mode to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law and the transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The redesigned control law forces the GRN to always remain on the sliding surface and the dissipativity is maintained from the initial time in the presence of the norm-bounded perturbations. The global stability of the perturbed GRNs is maintained if the unperturbed model is globally dissipative. The designed control law for the perturbed GRNs guarantees robust exponential or asymptotic stability of the closed-loop network depending on the type of stability of the unperturbed model. The results are applied to a nonlinear switched GRN, and its convergence to the origin is verified by simulation.

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.

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.

Compartmentalization and metabolic channeling for multienzymatic biosynthesis: practical strategies and modeling approaches

: The construction of efficient enzyme complexes for multienzymatic biosynthesis is of increasing interest in order to achieve maximum yield and to minimize the interference due to shortcomings that are typical for straightforward one-pot multienzyme catalysis. These include product or intermediate feedback inhibition, degeneration, and diffusive losses of reaction intermediates, consumption of co-factors, and others. The main mechanisms in nature to tackle these effects in transient or stable protein associations are the formation of metabolic channeling and microcompartments, processes that are desirable also for multienzymatic biosynthesis in vitro. This chapter provides an overview over two main aspects. First, numerous recent strategies for establishing compartmentalized multienzyme associations and constructed synthetic enzyme complexes are reviewed. Second, the computational methods at hand to investigate and optimize such associations systematically, especially with focus on large multienzyme complexes and metabolic channeling, are discussed. Perspectives on future studies of multienzymatic biosynthesis concerning compartmentalization and metabolic channeling are presented.

Regulation of respiration in muscle cells in vivo by VDAC through interaction with the cytoskeleton and MtCK within Mitochondrial Interactosome

This review describes the recent experimental data on the importance of the VDAC-cytoskeleton interactions in determining the mechanisms of energy and metabolite transfer between mitochondria and cytoplasm in cardiac cells. In the intermembrane space mitochondrial creatine kinase connects VDAC with adenine nucleotide translocase and ATP synthase complex, on the cytoplasmic side VDAC is linked to cytoskeletal proteins. Applying immunofluorescent imaging and Western blot analysis we have shown that β2-tubulin coexpressed with mitochondria is highly important for cardiac muscle cells mitochondrial metabolism. Since it has been shown by Rostovtseva et al. that αβ-heterodimer of tubulin binds to VDAC and decreases its permeability, we suppose that the β-tubulin subunit is bound on the cytoplasmic side and α-tubulin C-terminal tail is inserted into VDAC. Other cytoskeletal proteins, such as plectin and desmin may be involved in this process. The result of VDAC-cytoskeletal interactions is selective restriction of the channel permeability for adenine nucleotides but not for creatine or phosphocreatine that favors energy transfer via the phosphocreatine pathway. In some types of cancer cells these interactions are altered favoring the hexokinase binding and thus explaining the Warburg effect of increased glycolytic lactate production in these cells. This article is part of a Special Issue entitled: VDAC structure, function, and regulation of mitochondrial metabolism.

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.

High efficiency of energy flux controls within mitochondrial interactosome in cardiac intracellular energetic units

The aim of our study was to analyze a distribution of metabolic flux controls of all mitochondrial complexes of ATP-Synthasome and mitochondrial creatine kinase (MtCK) in situ in permeabilized cardiac cells. For this we used their specific inhibitors to measure flux control coefficients (C(vi)(JATP)) in two different systems: A) direct stimulation of respiration by ADP and B) activation of respiration by coupled MtCK reaction in the presence of MgATP and creatine. In isolated mitochondria the C(vi)(JATP) were for system A: Complex I - 0.19, Complex III - 0.06, Complex IV 0.18, adenine nucleotide translocase (ANT) - 0.11, ATP synthase - 0.01, Pi carrier - 0.20, and the sum of C(vi)(JATP) was 0.75. In the presence of 10mM creatine (system B) the C(vi)(JATP) were 0.38 for ANT and 0.80 for MtCK. In the permeabilized cardiomyocytes inhibitors had to be added in much higher final concentration, and the following values of C(vi)(JATP) were determined for condition A and B, respectively: Complex I - 0.20 and 0.64, Complex III - 0.41 and 0.40, Complex IV - 0.40 and 0.49, ANT - 0.20 and 0.92, ATP synthase - 0.065 and 0.38, Pi carrier - 0.06 and 0.06, MtCK 0.95. The sum of C(vi)(JATP) was 1.33 and 3.84, respectively. Thus, C(vi)(JATP) were specifically increased under conditions B only for steps involved in ADP turnover and for Complex I in permeabilized cardiomyocytes within Mitochondrial Interactosome, a supercomplex consisting of MtCK, ATP-Synthasome, voltage dependent anion channel associated with tubulin βII which restricts permeability of the mitochondrial outer membrane.

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."

Metabolic self-organization of bioluminescent Escherichia coli

A possible reason for the complexity of the signals produced by bioluminescent biosensors might be self-organization of the cells. In order to verify this possibility, bioluminescence images of cultures of lux gene reporter Escherichia coli were recorded for several hours after being placed into 8-10 mm diameter cylindrical containers. It was found that luminous cells distribute near the three-phase contact line, forming irregular azimuthal waves. As we show, space-time plots of quasi-one-dimensional bioluminescence measured along the contact line can be simulated by reaction-diffusion-chemotaxis equations, in which the reaction term for the cells is a logistic (autocatalytic) growth function. It was found that the growth rate of the luminous cells (~0.02 s(-1)) is >100 times higher than the growth rate of E. coli. We provide an explanation for this result by assuming that E. coli exhibits considerable respiratory flexibility (the ability of oxygen-induced switching from one metabolic pathway to another). According to the simple two-state model presented here, the number of oxic (luminous) cells grows at the expense of anoxic (dark) cells, whereas the total number of (oxic and anoxic) cells remains unchanged. It is conjectured that the corresponding reaction-diffusion-chemotaxis model for bioluminescence pattern formation can be considered as a model for the energy-taxis and metabolic self-organization in the population of the metabolically flexible bacteria under hypoxic conditions.

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).