Modeling of spatial metabolite distributions in the cardiac sarcomere

Co-localization and confinement of ecto-nucleotidases modulate extracellular adenosine nucleotide distributions

Nucleotides comprise small molecules that perform critical signaling roles in biological systems. Adenosine-based nucleotides, including adenosine tri-, di-, and mono-phosphate, are controlled through their rapid degradation by diphosphohydrolases and ecto-nucleotidases (NDAs). The interplay between nucleotide signaling and degradation is especially important in synapses formed between cells, which create signaling 'nanodomains'. Within these 'nanodomains', charged nucleotides interact with densely-packed membranes and biomolecules. While the contributions of electrostatic and steric interactions within such nanodomains are known to shape diffusion-limited reaction rates, less is understood about how these factors control the kinetics of nucleotidase activity. To quantify these factors, we utilized reaction-diffusion numerical simulations of 1) adenosine triphosphate (ATP) hydrolysis into adenosine monophosphate (AMP) and 2) AMP into adenosine (Ado) via two representative nucleotidases, CD39 and CD73. We evaluate these sequentially-coupled reactions in nanodomain geometries representative of extracellular synapses, within which we localize the nucleotidases. With this model, we find that 1) nucleotidase confinement reduces reaction rates relative to an open (bulk) system, 2) the rates of AMP and ADO formation are accelerated by restricting the diffusion of substrates away from the enzymes, and 3) nucleotidase co-localization and the presence of complementary (positive) charges to ATP enhance reaction rates, though the impact of these contributions on nucleotide pools depends on the degree to which the membrane competes for substrates. As a result, these contributions integratively control the relative concentrations and distributions of ATP and its metabolites within the junctional space. Altogether, our studies suggest that CD39 and CD73 nucleotidase activity within junctional spaces can exploit their confinement and favorable electrostatic interactions to finely control nucleotide signaling.

Enzyme Fusion Removes Competition for Geranylgeranyl Diphosphate in Carotenogenesis

Geranylgeranyl diphosphate (GGPP), a prenyl diphosphate synthesized by GGPP synthase (GGPS), represents a metabolic hub for the synthesis of key isoprenoids, such as chlorophylls, tocopherols, phylloquinone, gibberellins, and carotenoids. Protein-protein interactions and the amphipathic nature of GGPP suggest metabolite channeling and/or competition for GGPP among enzymes that function in independent branches of the isoprenoid pathway. To investigate substrate conversion efficiency between the plastid-localized GGPS isoform GGPS11 and phytoene synthase (PSY), the first enzyme of the carotenoid pathway, we used recombinant enzymes and determined their in vitro properties. Efficient phytoene biosynthesis via PSY strictly depended on simultaneous GGPP supply via GGPS11. In contrast, PSY could not access freely diffusible GGPP or time-displaced GGPP supply via GGPS11, presumably due to liposomal sequestration. To optimize phytoene biosynthesis, we applied a synthetic biology approach and constructed a chimeric GGPS11-PSY metabolon (PYGG). PYGG converted GGPP to phytoene almost quantitatively in vitro and did not show the GGPP leakage typical of the individual enzymes. PYGG expression in Arabidopsis resulted in orange-colored cotyledons, which are not observed if PSY or GGPS11 are overexpressed individually. This suggests insufficient GGPP substrate availability for chlorophyll biosynthesis achieved through GGPP flux redirection to carotenogenesis. Similarly, carotenoid levels in PYGG-expressing callus exceeded that in PSY- or GGPS11-overexpression lines. The PYGG chimeric protein may assist in provitamin A biofortification of edible plant parts. Moreover, other GGPS fusions may be used to redirect metabolic flux into the synthesis of other isoprenoids of nutritional and industrial interest.

Intracellular Energy-Transfer Networks and High-Resolution Respirometry: A Convenient Approach for Studying Their Function

Compartmentalization of high-energy phosphate carriers between intracellular micro-compartments is a phenomenon that ensures efficient energy use. To connect these sites, creatine kinase (CK) and adenylate kinase (AK) energy-transfer networks, which are functionally coupled to oxidative phosphorylation (OXPHOS), could serve as important regulators of cellular energy fluxes. Here, we introduce how selective permeabilization of cellular outer membrane and high-resolution respirometry can be used to study functional coupling between CK or AK pathways and OXPHOS in different cells and tissues. Using the protocols presented here the ability of creatine or adenosine monophosphate to stimulate OXPHOS through CK and AK reactions, respectively, is easily observable and quantifiable. Additionally, functional coupling between hexokinase and mitochondria can be investigated by monitoring the effect of glucose on respiration. Taken together, high-resolution respirometry in combination with permeabilization is a convenient approach for investigating energy-transfer networks in small quantities of cells and tissues in health and in pathology.

Bioenergetics of the aging heart and skeletal muscles: Modern concepts and controversies

Age-related alterations in the bioenergetics of the heart and oxidative skeletal muscle tissues are of crucial influence on their performance. Until now the prevailing concept of aging was the mitochondrial theory, the increased production of reactive oxygen species, mediated by deficiency in the activity of respiratory chain complexes. However, studies with mitochondria in situ have presented results which, to some extent, disagree with previous ones, indicating that the mitochondrial theory of aging may be overestimated. The studies reporting age-related decline in mitochondrial function were performed using mainly isolated mitochondria. Measurements on this level are not able to take into account the system level properties. The relevant information can be obtained only from appropriate studies using cells or tissue fibers. The functional interactions between the components of Intracellular Energetic Unit (ICEU) regulate the energy production and consumption in oxidative muscle cells. The alterations of these interactions in ICEU should be studied in order to find a more effective protocol to decelerate the age-related changes taking place in the energy metabolism. In this article, an overview is given of the present theories and controversies of causes of age-related alterations in bioenergetics. Also, branches of study, which need more emphasis, are indicated.

Restrictions in ATP diffusion within sarcomeres can provoke ATP-depleted zones impairing exercise capacity in chronic obstructive pulmonary disease

BACKGROUND

Chronic obstructive pulmonary disease (COPD) is characterized by the inability of patients to sustain a high level of ventilation resulting in perceived exertional discomfort and limited exercise capacity of leg muscles at average intracellular ATP levels sufficient to support contractility.

METHODS

Myosin ATPase activity in biopsy samples from healthy and COPD individuals was implemented as a local nucleotide sensor to determine ATP diffusion coefficients within myofibrils. Ergometric parameters clinically measured during maximal exercise tests in both groups were used to define the rates of myosin ATPase reaction and aerobic ATP re-synthesis. The obtained parameters in combination with AK- and CK-catalyzed reactions were implemented to compute the kinetic and steady-state spatial ATP distributions within control and COPD sarcomeres.

RESULTS

The developed reaction-diffusion model of two-dimensional sarcomeric space identified similar, yet extremely low nucleotide diffusion in normal and COPD myofibrils. The corresponding spatio-temporal ATP distributions, constructed during imposed exercise, predicted in COPD sarcomeres a depletion of ATP in the zones of overlap between actin and myosin filaments along the center axis at average cytosolic ATP levels similar to healthy muscles.

CONCLUSIONS

ATP-depleted zones can induce rigor tension foci impairing muscle contraction and increase a risk for sarcomere damages. Thus, intra-sarcomeric diffusion restrictions at limited aerobic ATP re-synthesis can be an additional risk factor contributing to the muscle contractile deficiency experienced by COPD patients.

GENERAL SIGNIFICANCE

This study demonstrates how restricted substrate mobility within a cellular organelle can provoke an energy imbalance state paradoxically occurring at abounding average metabolic resources.

Molecular and subcellular-scale modeling of nucleotide diffusion in the cardiac myofilament lattice

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.

Mechanisms of altered Ca²⁺ handling in heart failure

Ca²⁺ plays a crucial role in connecting membrane excitability with contraction in myocardium. The hallmark features of heart failure are mechanical dysfunction and arrhythmias; defective intracellular Ca²⁺ homeostasis is a central cause of contractile dysfunction and arrhythmias in failing myocardium. Defective Ca²⁺ homeostasis in heart failure can result from pathological alteration in the expression and activity of an increasingly understood collection of Ca²⁺ homeostatic and structural proteins, ion channels, and enzymes. This review focuses on the molecular mechanisms of defective Ca²⁺ cycling in heart failure and considers how fundamental understanding of these pathways may translate into novel and innovative therapies.

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.

ATP binding and cross-bridge detachment steps during full Ca²⁺ activation: comparison of myofibril and muscle fibre mechanics by sinusoidal analysis

Single myofibrils 50–60 μm length and 2–3 μm diameter were isolated from rabbit psoas muscle fibres, and cross-bridge kinetics were studied by small perturbations of the length (∼0.2%) over a range of 15 frequencies (1–250 Hz). The experiments were performed at 15◦C in the presence of 0.05–10 mM MgATP, 8mM phosphate (Pi), 200 mM ionic strength with KAc (acetate), pCa 4.35–4.65, and pH 7.0. Two exponential processes, B and C, were resolved in tension transients. Their apparent rate constants (2πb and 2πc) increased as the [MgATP] was raised from 0.05 mM to 1mM, and then reached saturation at [MgATP] ≥ 1. Given that these rate constants were similar (c/b ∼1.7) at [Pi] ≥ 4 mM, they were combined to achieve an accurate estimate of the kinetic constants: their sum and product were analysed as functions of [MgATP]. These analyses yielded K1 =2.91 ± 0.31 mM −1, k2 =288 ± 36 s−1, and k−2 =10 ± 21 s−1 (±95% confidence limit, n =13 preparations), based on the cross-bridge model: AM+ATP ↔ (step 1) AM.ATP ↔ (step 2) A+M.ATP, where K1 is the ATP association constant (step 1), k2 is the rate constant of the cross-bridge detachment (step 2), and k−2 is the rate constant of its reversal step. These kinetic constants are respectively comparable to those observed in single fibres from rabbit psoas (K1 =2.35 ± 0.31 mM −1, k2 =243 ± 22 s−1, and k−2 =6 ± 14 s−1; n =8 preparations) when analysed by the same methods and under the same experimental conditions. These values are respectively not significantly different from those obtained in myofibrils, indicating that the same kinetic constants can be deduced from myofibril and muscle fibre studies, in terms of ATP binding and cross-bridge detachments steps. The fact that K1 in myofibrils is 1.2 times that in fibres (P≈0.05) may be explained by a small concentration gradient of ATP, ADP and/or Pi in single fibres.

A three-dimensional simulation model of cardiomyocyte integrating excitation-contraction coupling and metabolism

Recent studies have revealed that Ca(2+) not only regulates the contraction of cardiomyocytes, but can also function as a signaling agent to stimulate ATP production by the mitochondria. However, the spatiotemporal resolution of current experimental techniques limits our investigative capacity to understand this phenomenon. Here, we created a detailed three-dimensional (3D) cardiomyocyte model to study the subcellular regulatory mechanisms of myocardial energetics. The 3D cardiomyocyte model was based on the finite-element method, with detailed subcellular structures reproduced, and it included all elementary processes involved in cardiomyocyte electrophysiology, contraction, and ATP metabolism localized to specific loci. The simulation results were found to be reproducible and consistent with experimental data regarding the spatiotemporal pattern of cytosolic, intrasarcoplasmic-reticulum, and mitochondrial changes in Ca(2+); as well as changes in metabolite levels. Detailed analysis suggested that although the observed large cytosolic Ca(2+) gradient facilitated uptake by the mitochondrial Ca(2+) uniporter to produce cyclic changes in mitochondrial Ca(2+) near the Z-line region, the average mitochondrial Ca(2+) changes slowly. We also confirmed the importance of the creatine phosphate shuttle in cardiac energy regulation. In summary, our 3D model provides a powerful tool for the study of cardiac function by overcoming some of the spatiotemporal limitations of current experimental approaches.

Compartmentation of membrane processes and nucleotide dynamics in diffusion-restricted cardiac cell microenvironment

Orchestrated excitation-contraction coupling in heart muscle requires adequate spatial arrangement of systems responsible for ion movement and metabolite turnover. Co-localization of regulatory and transporting proteins into macromolecular complexes within an environment of microanatomical cell components raises intracellular diffusion barriers that hamper the mobility of metabolites and signaling molecules. Compared to substrate diffusion in the cytosol, diffusional restrictions underneath the sarcolemma are much larger and could impede ion and nucleotide movement by a factor of 10(3)-10(5). Diffusion barriers thus seclude metabolites within the submembrane space enabling rapid and vectorial effector targeting, yet hinder energy supply from the bulk cytosolic space implicating the necessity for a shunting transfer mechanism. Here, we address principles of membrane protein compartmentation, phosphotransfer enzyme-facilitated interdomain energy transfer, and nucleotide signal dynamics at the subsarcolemma-cytosol interface. This article is part of a Special Issue entitled "Local Signaling in Myocytes".

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.

Compartmentation of glycogen metabolism revealed from 13C isotopologue distributions

Background

Stable isotope tracers are used to assess metabolic flux profiles in living cells. The existing methods of measurement average out the isotopic isomer distribution in metabolites throughout the cell, whereas the knowledge of compartmental organization of analyzed pathways is crucial for the evaluation of true fluxes. That is why we accepted a challenge to create a software tool that allows deciphering the compartmentation of metabolites based on the analysis of average isotopic isomer distribution.

Results

The software Isodyn, which simulates the dynamics of isotopic isomer distribution in central metabolic pathways, was supplemented by algorithms facilitating the transition between various analyzed metabolic schemes, and by the tools for model discrimination. It simulated ¹³C isotope distributions in glucose, lactate, glutamate and glycogen, measured by mass spectrometry after incubation of hepatocytes in the presence of only labeled glucose or glucose and lactate together (with label either in glucose or lactate). The simulations assumed either a single intracellular hexose phosphate pool, or also channeling of hexose phosphates resulting in a different isotopic composition of glycogen. Model discrimination test was applied to check the consistency of both models with experimental data. Metabolic flux profiles, evaluated with the accepted model that assumes channeling, revealed the range of changes in metabolic fluxes in liver cells.

Conclusions

The analysis of compartmentation of metabolic networks based on the measured ¹³C distribution was included in Isodyn as a routine procedure. The advantage of this implementation is that, being a part of evaluation of metabolic fluxes, it does not require additional experiments to study metabolic compartmentation. The analysis of experimental data revealed that the distribution of measured ¹³C-labeled glucose metabolites is inconsistent with the idea of perfect mixing of hexose phosphates in cytosol. In contrast, the observed distribution indicates the presence of a separate pool of hexose phosphates that is channeled towards glycogen synthesis.

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.

Regulation of respiration controlled by mitochondrial creatine kinase in permeabilized cardiac cells in situ. Importance of system level properties

The main focus of this investigation is steady state kinetics of regulation of mitochondrial respiration in permeabilized cardiomyocytes in situ. Complete kinetic analysis of the regulation of respiration by mitochondrial creatine kinase was performed in the presence of pyruvate kinase and phosphoenolpyruvate to simulate interaction of mitochondria with glycolytic enzymes. Such a system analysis revealed striking differences in kinetic behaviour of the MtCK-activated mitochondrial respiration in situ and in vitro. Apparent dissociation constants of MgATP from its binary and ternary complexes with MtCK, Kia and Ka (1.94+/-0.86 mM and 2.04+/-0.14 mM, correspondingly) were increased by several orders of magnitude in situ in comparison with same constants in vitro (0.44+/-0.08 mM and 0.016+/-0.01 mM, respectively). Apparent dissociation constants of creatine, Kib and Kb (2.12+/-0.21 mM 2.17+/-0.40 Mm, correspondingly) were significantly decreased in situ in comparison with in vitro mitochondria (28+/-7 mM and 5+/-1.2 mM, respectively). Dissociation constant for phosphocreatine was not changed. These data may indicate selective restriction of metabolites' diffusion at the level of mitochondrial outer membrane. It is concluded that mechanisms of the regulation of respiration and energy fluxes in vivo are system level properties which depend on intracellular interactions of mitochondria with cytoskeleton, intracellular MgATPases and cytoplasmic glycolytic system.

Anisotropic diffusion of fluorescently labeled ATP in rat cardiomyocytes determined by raster image correlation spectroscopy

A series of experimental data points to the existence of profound diffusion restrictions of ADP/ATP in rat cardiomyocytes. This assumption is required to explain the measurements of kinetics of respiration, sarcoplasmic reticulum loading with calcium, and kinetics of ATP-sensitive potassium channels. To be able to analyze and estimate the role of intracellular diffusion restrictions on bioenergetics, the intracellular diffusion coefficients of metabolites have to be determined. The aim of this work was to develop a practical method for determining diffusion coefficients in anisotropic medium and to estimate the overall diffusion coefficients of fluorescently labeled ATP in rat cardiomyocytes. For that, we have extended raster image correlation spectroscopy (RICS) protocols to be able to discriminate the anisotropy in the diffusion coefficient tensor. Using this extended protocol, we estimated diffusion coefficients of ATP labeled with the fluorescent conjugate Alexa Fluor 647 (Alexa-ATP). In the analysis, we assumed that the diffusion tensor can be described by two values: diffusion coefficient along the myofibril and that across it. The average diffusion coefficients found for Alexa-ATP were as follows: 83 ± 14 μm²/s in the longitudinal and 52 ± 16 μm²/s in the transverse directions (n = 8, mean ± SD). Those values are ∼2 (longitudinal) and ∼3.5 (transverse) times smaller than the diffusion coefficient value estimated for the surrounding solution. Such uneven reduction of average diffusion coefficient leads to anisotropic diffusion in rat cardiomyocytes. Although the source for such anisotropy is uncertain, we speculate that it may be induced by the ordered pattern of intracellular structures in rat cardiomyocytes.

Metabolic compartmentation - a system level property of muscle cells: real problems of diffusion in living cells

Problems of quantitative investigation of intracellular diffusion and compartmentation of metabolites are analyzed. Principal controversies in recently published analyses of these problems for the living cells are discussed. It is shown that the formal theoretical analysis of diffusion of metabolites based on Fick's equation and using fixed diffusion coefficients for diluted homogenous aqueous solutions, but applied for biological systems in vivo without any comparison with experimental results, may lead to misleading conclusions, which are contradictory to most biological observations. However, if the same theoretical methods are used for analysis of actual experimental data, the apparent diffusion constants obtained are orders of magnitude lower than those in diluted aqueous solutions. Thus, it can be concluded that local restrictions of diffusion of metabolites in a cell are a system-level properties caused by complex structural organization of the cells, macromolecular crowding, cytoskeletal networks and organization of metabolic pathways into multienzyme complexes and metabolons. This results in microcompartmentation of metabolites, their channeling between enzymes and in modular organization of cellular metabolic networks. The perspectives of further studies of these complex intracellular interactions in the framework of Systems Biology are discussed.

The changes in the energy metabolism of human muscle induced by training

The biochemical effects of training programmes have been studied with a kinetic model of central metabolism, using enzyme activities and metabolite concentrations measured at rest and after 30 s maximum-intensity exercise, collected before and after long and short periods of training, which differed only by the duration of the rest intervals. After short periods of training the glycolytic flux at rest was three times higher than it had been before training, whereas during exercise the flux and energy consumption remained the same as before training. Long periods of training had less effect on the glycolytic flux at rest, but increased it in response to exercise, increasing the contribution of oxidative phosphorylation.