Random walk analysis of restricted metabolite diffusion in skeletal myofibril systems

Crowding within synaptic junctions influences the degradation of nucleotides by CD39 and CD73 ectonucleotidases

Synapsed cells can communicate using exocytosed nucleotides like adenosine triphosphate (ATP). Ectonucleotidases localized to synaptic junctions degrade nucleotides into metabolites like adenosine monophosphate (AMP) or adenosine. Oftentimes nucleotide degradation occurs in a sequential manner, of which ATP degradation by CD39 and CD73 is a representative example. Here, CD39 first converts ATP and adenosine diphosphate (ADP) into AMP, after which AMP is dephosphorylated into adenosine by CD73. Hence, the concerted activity of CD39 and CD73 can help shape cellular responses to extracellular ATP. In a previous study, we demonstrated that coupled CD39 and CD73 activity within synapse-like junctions is strongly controlled by the enzymes' co-localization, their surface charge densities, and the electrostatic potential of the surrounding cell membranes. In this study, we demonstrate that crowders within synaptic junctions, which can include globular proteins like cytokines and membrane-bound proteins, impact coupled CD39 and CD73 ectonucleotidase activity and, in turn, the availability of intrasynapse ATP. Specifically, we developed a spatially explicit, reaction-diffusion model for the coupled conversion of ATP → AMP and AMP → adenosine in a model synaptic junction with crowders that is solved via the finite element method. Our modeling results suggest that the association rate for ATP to CD39 is strongly influenced by the density of intrasynaptic protein crowders, as increasing crowder density generally suppressed ATP association kinetics. Much of this suppression can be rationalized based on a loss of configurational entropy. The surface charges of crowders can further influence the association rate, with the surprising result that favorable crowder-nucleotide electrostatic interactions can yield CD39 association rates that are faster than crowder-free configurations. However, attractive crowder-nucleotide interactions decrease the rate and efficiency of adenosine production, which in turn increases the availability of ATP and AMP within the synapse relative to crowder-free configurations. These findings highlight how CD39 and CD73 ectonucleotidase activity, electrostatics, and crowding within synapses influence the availability of nucleotides for intercellular communication.

The Sliding Filament Theory Since Andrew Huxley: Multiscale and Multidisciplinary Muscle Research

Two groundbreaking papers published in 1954 laid out the theory of the mechanism of muscle contraction based on force-generating interactions between myofilaments in the sarcomere that cause filaments to slide past one another during muscle contraction. The succeeding decades of research in muscle physiology have revealed a unifying interest: to understand the multiscale processes-from atom to organ-that govern muscle function. Such an understanding would have profound consequences for a vast array of applications, from developing new biomimetic technologies to treating heart disease. However, connecting structural and functional properties that are relevant at one spatiotemporal scale to those that are relevant at other scales remains a great challenge. Through a lens of multiscale dynamics, we review in this article current and historical research in muscle physiology sparked by the sliding filament theory.

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.

Evaluation of Diffusional Characteristics and Microstructure in Unilateral Vocal Fold Paralysis Using Diffusion Tensor Imaging

OBJECTIVE

To investigate the value of diffusion tensor imaging (DTI) in the evaluation of vocal fold tissue microstructure after recurrent laryngeal nerve (RLN) injury.

METHODS

Six canines were divided into 2 groups: a unilateral vocal fold paralysis group (n = 4) and a control group (n = 2). The RLN was cut in the unilateral vocal fold paralysis group, and no intervention was applied in the control group. After 4 months, the canines' larynges were removed and placed in a small animal magnetic resonance imaging (MRI) system (9.4T BioSpec MRI; Bruker, Germany). After scanning, the vocal folds were isolated, sectioned, and stained. The slides were then analyzed for the cross-sectional area and muscle fiber density through feature extraction technology. Pearson correlation analysis was performed on the DTI scan and histological section extraction results.

RESULTS

In the vocal fold muscle layer, the fractional anisotropy (FA) of the unilateral RLN injury group was higher than that of the control group, and the Tensor Trace was lower than that of the control group. This difference was statistically significant, P < .05. In the lamina propria, the FA of the unilateral RLN injury group was lower than that of the control group, P > .05, and the Tensor Trace was lower than that of the control group, P < .05. The muscle fiber cross-sectional area of the RLN injury group was significantly smaller than the control group with statistical significance, P < .05, and the density of muscle fibers was lower, P < .05. The correlation coefficient between FA and the cross-sectional area was -0.838, P = .002, and .726; P = .017 between Tensor Trace and the cross-sectional area.

CONCLUSION

Diffusion tensor imaging is an effective method to assess the changes in the microstructure of atrophic vocal fold muscle tissue after RLN injury.

Relationships between tissue microstructure and the diffusion tensor in simulated skeletal muscle

PURPOSE

To establish a series of relationships defining how muscle microstructure and diffusion tensor imaging (DTI) are related.

METHODS

The relationship among key microstructural features of skeletal muscle (fiber size, fibrosis, edema, and permeability) and the diffusion tensor were systematically simulated over physiologically relevant dimensions individually, and in combination, using a numerical simulation application. Stepwise multiple regression was used to identify which microstructural features of muscle significantly predict the diffusion tensor using single-echo and multi-echo DTI pulse sequences. Simulations were also performed in models with histology-informed geometry to investigate the relationship between fiber size and the diffusion tensor in models with real muscle geometry.

RESULTS

Fiber size is the strongest predictor of λ2, λ3, mean diffusivity, and fractional anisotropy in skeletal muscle, accounting for approximately 40% of the variance in the diffusion model when calculated with single-echo DTI. This increased to approximately 70% when diffusion measures were calculated from the short T2 component of the multi-echo DTI sequence. This nonlinear relationship begins to plateau in fibers with greater than 60-μm diameter.

CONCLUSIONS

As the normal fiber size of a human muscle fiber is 40 to 60 μm, this suggests that DTI is a sensitive tool to monitor muscle atrophy, but may be limited in measurements of muscle with larger fibers. Magn Reson Med 80:317-329, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

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.

Computer modeling of electron and proton transport in chloroplasts

Photosynthesis is one of the most important biological processes in biosphere, which provides production of organic substances from atmospheric CO2 and water at expense of solar energy. In this review, we contemplate computer models of oxygenic photosynthesis in the context of feedback regulation of photosynthetic electron transport in chloroplasts, the energy-transducing organelles of the plant cell. We start with a brief overview of electron and proton transport processes in chloroplasts coupled to ATP synthesis and consider basic regulatory mechanisms of oxygenic photosynthesis. General approaches to computer simulation of photosynthetic processes are considered, including the random walk models of plastoquinone diffusion in thylakoid membranes and deterministic approach to modeling electron transport in chloroplasts based on the mass action law. Then we focus on a kinetic model of oxygenic photosynthesis that includes key stages of the linear electron transport, alternative pathways of electron transfer around photosystem I (PSI), transmembrane proton transport and ATP synthesis in chloroplasts. This model includes different regulatory processes: pH-dependent control of the intersystem electron transport, down-regulation of photosystem II (PSII) activity (non-photochemical quenching), the light-induced activation of the Bassham-Benson-Calvin (BBC) cycle. The model correctly describes pH-dependent feedback control of electron transport in chloroplasts and adequately reproduces a variety of experimental data on induction events observed under different experimental conditions in intact chloroplasts (variations of CO2 and O2 concentrations in atmosphere), including a complex kinetics of P700 (primary electron donor in PSI) photooxidation, CO2 consumption in the BBC cycle, and photorespiration. Finally, we describe diffusion-controlled photosynthetic processes in chloroplasts within the framework of the model that takes into account complex architecture of chloroplasts and lateral heterogeneity of lamellar system of thylakoids. The lateral profiles of pH in the thylakoid lumen and in the narrow gap between grana thylakoids have been calculated under different metabolic conditions. Analyzing topological aspects of diffusion-controlled stages of electron and proton transport in chloroplasts, we conclude that along with the NPQ mechanism of attenuation of PSII activity and deceleration of PQH2 oxidation by the cytochrome b6f complex caused by the lumen acidification, the intersystem electron transport may be down-regulated due to the light-induced alkalization of the narrow partition between adjacent thylakoids of grana. The computer models of electron and proton transport described in this article may be integrated as appropriate modules into a comprehensive model of oxygenic photosynthesis.

Diffusion-Tensor MRI Based Skeletal Muscle Fiber Tracking

A skeletal muscle's function is strongly influenced by the internal organization and geometric properties of its fibers, a property known as muscle architecture. Diffusion-tensor magnetic resonance imaging-based fiber tracking provides a powerful tool for non-invasive muscle architecture studies, has three-dimensional sensitivity, and uses a fixed frame of reference. Significant advances have been made in muscle fiber tracking technology, including defining seed points for fiber tracking, quantitatively characterizing muscle architecture, implementing denoising procedures, and testing validity and repeatability. Some examples exist of how these data can be integrated with those from other advanced MRI and computational methods to provide novel insights into muscle function. Perspectives are offered regarding future directions in muscle diffusion-tensor imaging, including needs to develop an improved understanding for the microstructural basis for reduced and anisotropic diffusion, establish the best practices for data acquisition and analysis, and integrate fiber tracking with other physiological data.

Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle

Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction-diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction-diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle.

Functional and topological aspects of pH-dependent regulation of electron and proton transport in chloroplasts in silico

In this work, we summarize results of computer simulation of electron and proton transport processes coupled to ATP synthesis in chloroplasts performed within the frames of a mathematical model developed as a system of differential equations for concentrations of electron carriers and hydrogen ion inside and outside the granal and stromal thylakoids. The model takes into account topological peculiarities and lateral heterogeneity of the chloroplast lamellar system. This allowed us to analyze the influence of restricted diffusion of protons inside small compartments of a chloroplast (e.g., in the narrow inter-thylakoid gap) on electron transport processes. The model adequately describes two modes of pH-dependent feedback control of electron transport associated with: (i) the acidification of the thylakoid lumen, which causes the slowing down of plastoquinol oxidation and stimulates an increase in dissipation of excess energy in PS2, and (ii) the alkalization of stroma, inducing the activation of the BBC (Bassham-Benson-Calvin) cycle and intensified consumption of ATP and NADPH. The influence of ATP on electron transport is mediated by modulation of the thylakoid membrane conductivity to protons through the ATP synthase complexes. We also analyze the contribution of alternative electron transport pathways to the maintenance of optimal balance between the energy donating and energy consuming stages of the light-induced photosynthetic processes.

A mathematical analysis of obstructed diffusion within skeletal muscle

Molecules are transported through the myofilament lattice of skeletal muscle fibers during muscle activation. The myofilaments, along with the myosin heads, sarcoplasmic reticulum, t-tubules, and mitochondria, obstruct the diffusion of molecules through the muscle fiber. In this work, we studied the process of obstructed diffusion within the myofilament lattice using Monte Carlo simulation, level-set and homogenization theory. We found that these intracellular obstacles significantly reduce the diffusion of material through skeletal muscle and generate diffusion anisotropy that is consistent with experimentally observed slower diffusion in the radial than the longitudinal direction. Our model also predicts that protein size has a significant effect on the diffusion of material through muscle, which is consistent with experimental measurements. Protein diffusion on the myofilament lattice is also anomalous (i.e., it does not obey Brownian motion) for proteins that are close in size to the myofilament spacing. The obstructed transport of Ca2+ and ATP-bound Ca2+ through the myofilament lattice also generates smaller Ca2+ transients. In addition, we used homogenization theory to discover that the nonhomogeneous distribution in the troponin binding sites has no effect on the macroscopic Ca2+ dynamics. The nonuniform sarcoplasmic reticulum Ca2+-ATPase pump distribution also introduces small asymmetries in the myoplasmic Ca2+ transients.

Proteomic analysis of activity-dependent synaptic plasticity in hippocampal neurons

Following long-term treatment with bicuculline and tetrodotoxin (TTX) aimed at modifying synaptic activity in cultured neurons, we used a proteomic approach to identify the associated changes in protein expression. The neurons were left untreated, or treated with bicuculline or TTX, and fractionated by means of differential detergent extraction, after which the proteins in each fraction were separated by means of two-dimensional (2D) gel electrophoresis, and 57 proteins of interest were identified by mass spectrometry. The proteins that showed altered expression and/or post-translational modifications include proteins or enzymes involved in regulating cell and protein metabolism, the cytoskeleton, or mitochondrial activity. These results suggest that extensive alterations in neuronal protein expression take place as a result of increased or decreased synaptic activity.

Hypothermia affects translocation of numerous cytoplasmic proteins following global cerebral ischemia

Using a decapitation ischemia model, we studied translocation of proteins to and from the cytosol in normothermic (NT) and hypothermic (HT) rat brains. 2D gel analysis identified 74 proteins whose cytosolic level changed significantly after 15 min of ischemia. HT preserved the cytosolic levels of several glycolytic enzymes, as well as many plasticity related proteins, otherwise decreased following NT ischemia. The levels of redox-related proteins was lower in HT than in NT. Our results indicate that translocation of proteins to and from the cytosol is an important issue during ischemia.

Intracellular diffusion of adenosine phosphates is locally restricted in cardiac muscle

Recent studies have revealed the structural and functional interactions between mitochondria, myofibrils and sarcoplasmic reticulum in cardiac cells. Direct channeling of adenosine phosphates between organelles identified in the experiments indicates that diffusion of adenosine phosphates is limited in cardiac cells due to very specific intracellular structural organization. However, the mode of diffusion restrictions and nature of the intracellular structures in creating the diffusion barriers is still unclear, and, therefore, a subject of active research. The aim of this work is to analyze the possible role of two principally different modes of restriction distribution for adenosine phosphates (a) the uniform diffusion restriction and (b) the localized diffusion limitation in the vicinity of mitochondria, by fitting the experimental data with the mathematical model. The reaction-diffusion model of compartmentalized energy transfer was used to analyze the data obtained from the experiments with the skinned muscle fibers, which described the following processes: mitochondrial respiration rate dependency on exogenous ADP and ATP concentrations; inhibition of endogenous ADP-stimulated respiration by pyruvate kinase (PK) and phosphoenolpyruvate (PEP) system; kinetics of oxygen consumption stabilization after addition of 2 mM MgATP or MgADP; ATPase activity with inhibited mitochondrial respiration; and buildup of MgADP concentration in the medium after addition of MgATP. The analysis revealed that only the second mechanism considered--localization of diffusion restrictions--is able to account for the experimental data. In the case of uniform diffusion restrictions, the model solution was in agreement only with two measurements: the respiration rate as a function of ADP or ATP concentrations and inhibition of respiration by PK + PEP. It was concluded that intracellular diffusion restrictions for adenosine phosphates are not distributed uniformly, but rather are localized in certain compartments of the cardiac cells.