Functional Imaging of Mitochondria in Saponin-permeabilized Mice Muscle Fibers

Confocal laser-scanning and digital fluorescence imaging microscopy were used to quantify the mitochondrial autofluorescence changes of NAD(P)H and flavoproteins in unfixed saponin-permeabilized myofibers from mice quadriceps muscle tissue. Addition of mitochondrial substrates, ADP, or cyanide led to redox state changes of the mitochondrial NAD system. These changes were detected by ratio imaging of the autofluorescence intensities of fluorescent flavoproteins and NAD(P)H, showing inverse fluorescence behavior. The flavoprotein signal was colocalized with the potentiometric mitochondria-specific dye dimethylaminostyryl pyridyl methyl iodide (DASPMI), or with MitoTracker™ Green FM, a constitutive marker for mitochondria. Within individual myofibers we detected topological mitochondrial subsets with distinct flavoprotein autofluorescence levels, equally responding to induced rate changes of the oxidative phosphorylation. The flavoprotein autofluorescence levels of these subsets differed by a factor of four. This heterogeneity was substantiated by flow-cytometric analysis of flavoprotein and DASPMI fluorescence changes of individual mitochondria isolated from mice skeletal muscle. Our data provide direct evidence that mitochondria in single myofibers are distinct subsets at the level of an intrinsic fluorescent marker of the mitochondrial NAD–redox system. Under the present experimental conditions these subsets show similar functional responses.     

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.     

Diffusion Coefficients of Endogenous Cytosolic Proteins from Rabbit Skinned Muscle Fibers

Efflux time courses of endogenous cytosolic proteins were obtained from rabbit psoas muscle fibers skinned in oil and transferred to physiological salt solution. Proteins were separated by gel electrophoresis and compared to load-matched standards for quantitative analysis. A radial diffusion model incorporating the dissociation and dissipation of supramolecular complexes accounts for an initial lag and subsequent efflux of glycolytic and glycogenolytic enzymes. The model includes terms representing protein crowding, myofilament lattice hindrance, and binding to the cytomatrix. Optimization algorithms returned estimates of the apparent diffusion coefficients, D(r,t), that were very low at the onset of diffusion (∼10⁻¹⁰ cm² s⁻¹) but increased with time as cytosolic protein density, which was initially high, decreased. D(r,t) at later times ranged from 2.11 × 10⁻⁷ cm² s⁻¹ (parvalbumin) to 0.20 × 10⁻⁷ cm² s⁻¹ (phosphofructose kinase), values that are 3.6- to 12.3-fold lower than those predicted in bulk water. The low initial values are consistent with the presence of complexes in situ; the higher later values are consistent with molecular sieving and transient binding of dissociated proteins. Channeling of metabolic intermediates via enzyme complexes may enhance production of adenosine triphosphate at rates beyond that possible with randomly and/or sparsely distributed enzymes, thereby matching supply with demand.     

Diffusion Coefficients of Endogenous Cytosolic Proteins from Rabbit Skinned Muscle Fibers

Efflux time courses of endogenous cytosolic proteins were obtained from rabbit psoas muscle fibers skinned in oil and transferred to physiological salt solution. Proteins were separated by gel electrophoresis and compared to load-matched standards for quantitative analysis. A radial diffusion model incorporating the dissociation and dissipation of supramolecular complexes accounts for an initial lag and subsequent efflux of glycolytic and glycogenolytic enzymes. The model includes terms representing protein crowding, myofilament lattice hindrance, and binding to the cytomatrix. Optimization algorithms returned estimates of the apparent diffusion coefficients, D(r,t), that were very low at the onset of diffusion (∼10⁻¹⁰ cm² s⁻¹) but increased with time as cytosolic protein density, which was initially high, decreased. D(r,t) at later times ranged from 2.11 × 10⁻⁷ cm² s⁻¹ (parvalbumin) to 0.20 × 10⁻⁷ cm² s⁻¹ (phosphofructose kinase), values that are 3.6- to 12.3-fold lower than those predicted in bulk water. The low initial values are consistent with the presence of complexes in situ; the higher later values are consistent with molecular sieving and transient binding of dissociated proteins. Channeling of metabolic intermediates via enzyme complexes may enhance production of adenosine triphosphate at rates beyond that possible with randomly and/or sparsely distributed enzymes, thereby matching supply with demand.     

Membrane Currents in Mammalian Ventricular Heart Muscle Fibers Using a Voltage-Clamp Technique

Bundles of sheep ventricular fibers were voltage-clamped utilizing a modified sucrose gap technique and intracellular voltage control. An action potential was fired off in the usual way, and the clamp circuit was switched on at preselected times during activity. Clamping the membrane back to its resting potential during the early part of an action potential resulted in a surge of inward current. The initial amplitude of this current surge decreased as the clamp was switched on progressively later during the action potential. Inward current decreasing as a function of time was also recorded if the membrane potential was clamped beyond the presumed K equilibrium potential (to -130 mv). Clamping the membrane to the inside positive range (+40 mv to +60 mv) at different times of an action potential resulted in a step of outward current which was not time-dependent. The results suggest that normal repolarization of sheep ventricle depends on a time-dependent decrease of inward current (Na, Ca) rather than on a time-dependent increase of outward current (K).     

Ultrastructure of Type 2A Extrafusal Muscle Fibers and Muscle Spindle Intrafusal Fibers of Adult Rats after Prolonged Swimming

We compared the ultrastructure of type 2A extrafusal muscle fibers, the nuclear chain, and other intrafusal fibers of muscle spindle (muscle stretch mechanoreceptor) in adult rats after prolonged swimming (5–10 h/day, 10 days). The Golgi apparatus was expressed moderately in type 2A extrafusal fibers and hypertrophied in the motor B zone of nuclear chain intrafusal fibers. Intense development of the Golgi apparatus in the nuclear chain intrafusal fiber appears to be related to glycogenolysis in the autophagous vacuoles, involvement in the lysosome activity, and plasma membrane renewal. Recapitulation of the mechanism of glycogen autophagy, which is observed in newborn rats during mobilization of glycogen from the liver and muscle, was demonstrated in adult rats under the influence of physical load in the nuclear chain and nuclear bag₂ intrafusal fibers and in type 2A extrafusal fibers. This is accounted for by a weak differentiation of the intrafusal muscle fibers: structurally, they are similar to myotubes and have specific features of blood supply and innervation. Individual features of experimental adult rats may also play a certain role.     

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of “smoothing” the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.     

Autocatalytic Loop,Amplification and Diffusion: A Mathematical and Computational Model of Cell Polarization in Neural Chemotaxis

The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.     

A Theoretical Analysis of the Capacitance of Muscle Fibers Using a Distributed Model of the Tubular System

A model is developed to predict the changes in total capacitance (i.e. total charge stored divided by surface membrane potential) of the tubular system of muscle fibers. The tubular system is represented as a punctated disc and the area of membrane across which current flows is represented as a punctated annulus, the capacitance of the muscle fiber being proportional to this area. The area can be determined from a distributed model of the tubular system, in which the only resistance to radial current flow is presumed to be in the lumen of the tubules. Calculations are made of the variation of capacitance expected as the conductivity of the bathing solution is varied. These calculations include the effects of fixed charge in the tubular lumen and the effects of changes in the shape and volume of the tubular system in solutions of low conductivity. The calculated results fail to fit comparable experimental data, although they do qualitatively account for the known variation of the radial spread of contraction with conductivity of the bathing medium. It is pointed out that the existence of a significant "access resistance" at the mouth of the tubules might explain the discrepancy between theory and experiment.     

Muscle Fiber Types in Crabs: Studies on Single Identified Muscle Fibers

SYNOPSIS. Based on electrophysiological and histochemical data,four types of muscle fibers (types I, II, III and IV) can beidentified in the closer of the crab Eriphia. Although characteristicsused for typing vary among the fibers of a particular type,the combination of several parameters permits an assignment.Of particular significance for typing is the myosin ATPase activityand its stability after preincubation at different pH levels.The fiber types defined for the closer muscle can also be foundin the other leg muscles of riphia. Single, electrophysiologically identified fibers of each typewere quantitatively analyzed for several key enzymes of oxidativeand glycolytic energy metabolism (GAPDH, LDH, CS, IDH, HAD).Despite the variations found, different metabolic types canbe defined. The typing derived from biochemical studies correlateswell with that obtained electrophysiologically and histochemically.The variability of the biochemical properties, however, seemsto be considerably larger. The type I fibers can be regarded as slow oxidative, the typeII and III fibers as fast oxidative glycolytic, and the typeIV fibers as fast glycolytic.     

Action Potential-Evoked Calcium Release Is Impaired in Single Skeletal Muscle Fibers from Heart Failure Patients

Background

Exercise intolerance in chronic heart failure (HF) has been attributed to abnormalities of the skeletal muscles. Muscle function depends on intact excitation-contraction coupling (ECC), but ECC studies in HF models have been inconclusive, due to deficiencies in the animal models and tools used to measure calcium (Ca²⁺) release, mandating investigations in skeletal muscle from HF patients. The purpose of this study was to test the hypothesis that Ca²⁺ release is significantly impaired in the skeletal muscle of HF patients in whom exercise capacity is severely diminished compared to age-matched healthy volunteers.

Methods and Findings

Using state-of-the-art electrophysiological and optical techniques in single muscle fibers from biopsies of the locomotive vastus lateralis muscle, we measured the action potential (AP)-evoked Ca²⁺ release in 4 HF patients and 4 age-matched healthy controls. The mean peak Ca²⁺ release flux in fibers obtained from HF patients (10±1.2 µM/ms) was markedly (2.6-fold) and significantly (p<0.05) smaller than in fibers from healthy volunteers (28±3.3 µM/ms). This impairment in AP-evoked Ca²⁺ release was ubiquitous and was not explained by differences in the excitability mechanisms since single APs were indistinguishable between HF patients and healthy volunteers.

Conclusions

These findings prove the feasibility of performing electrophysiological experiments in single fibers from human skeletal muscle, and offer a new approach for investigations of myopathies due to HF and other diseases. Importantly, we have demonstrated that one step in the ECC process, AP-evoked Ca²⁺ release, is impaired in single muscle fibers in HF patients.     

Optical Diffraction Studies of Muscle Fibers

A new technique to monitor light diffraction patterns electrically is applied to frog semitendinosus muscle fibers at various levels of stretch. The intensity of the diffraction lines, sarcomere length change, and the length-dispersion (line width) were calculated by fast analogue circuits and displayed in real time. A heliumneon laser (wavelength 6328 Å) was used as a light source. It was found that the intensity of the first-order diffraction line drops significantly (30-50%) at an optimal sarcomere length of 2.8 μm on isometric tetanic stimulation. Such stimulation produced contraction of half-sarcomeres by about 22 nm presumably by stretching inactive elements such as tendons. The dispersion of the sarcomere lengths is extremely small, and it is proportional to the sarcomere length (less than 4%). The dispersion increases on stimulation. These changes on isometric tetanic stimulation were dependent on sarcomere length. No vibration or oscillation in the averaged length of the sarcomeres was found during isometric tetanus within a resolution of 3 nm; however, our observation of increased length dispersion of the sarcomeres together with detection of the averaged shortening of the sarcomere lengths suggests the presence of asynchronous cyclic motions between thick and thin filaments. An alternative explanation is simply an increase of the length dispersion of sarcomeres without cyclic motions.     

Anastral Spindle Assembly: A Mathematical Model

Assembly of an anastral spindle was modeled as a two-stage process: first, the aggregation of microtubule foci or asters around the chromosomes, and second, the elongation of cross-linked microtubules and onset of bipolarity. Several possibilities involving diffusion and transport were investigated for the first stage, and the most feasible was found to be binding of the asters to cytoskeletal filaments and directed transport toward the chromosomes. For the second stage, a differential-equation model was formulated and solved numerically; it involves cross-linking of microtubules with those aligned with the spindle axis and between microtubules bound to different chromosomes, and sliding of microtubules along the spindle axis to elongate the spindle. Ncd was postulated to perform both functions. The model shows that spindle formation begins with rapid cross-linking of microtubules, followed by elongation, which continues until the population of microtubules aligned with the spindle axis is depleted and microtubules cross-linking different chromosomes dominate. It also shows that when sliding is inhibited, short bipolar spindles still form, and if clustering is enhanced, normal-length spindles can form, although requiring longer assembly time. These findings are consistent with spindle assembly in live wild-type and ncd mutant Drosophila oocytes.     

Growth Associated Protein 43 Is Expressed in Skeletal Muscle Fibers and Is Localized in Proximity of Mitochondria and Calcium Release Units

The neuronal Growth Associated Protein 43 (GAP43), also known as B-50 or neuromodulin, is involved in mechanisms controlling pathfinding and branching of neurons during development and regeneration. For many years this protein was classified as neuron-specific, but recent evidences suggest that a) GAP43 is expressed in the nervous system not only in neurons, but also in glial cells, and b) probably it is present also in other tissues. In particular, its expression was revealed in muscles from patients affected by various myopathies, indicating that GAP43 can no-longer considered only as a neuron-specific molecule. We have investigated the expression and subcellular localization of GAP43 in mouse satellite cells, myotubes, and adult muscle (extensor digitorum longus or EDL) using Western blotting, immuno-fluorescence combined to confocal microscopy and electron microscopy. Our in vitro results indicated that GAP43 is indeed expressed in both myoblasts and differentiating myotubes, and its cellular localization changes dramatically during maturation: in myoblasts the localization appeared to be mostly nuclear, whereas with differentiation the protein started to display a sarcomeric-like pattern. In adult fibers, GAP43 expression was evident with the protein labeling forming (in longitudinal views) a double cross striation reminiscent of the staining pattern of other organelles, such as calcium release units (CRUs) and mitochondria. Double immuno-staining and experiments done in EDL muscles fixed at different sarcomere lengths, allowed us to determine the localization, from the sarcomere Z-line, of GAP43 positive foci, falling between that of CRUs and of mitochondria. Staining of cross sections added a detail to the puzzle: GAP43 labeling formed a reticular pattern surrounding individual myofibrils, but excluding contractile elements. This work leads the way to further investigation about the possible physiological and structural role of GAP43 protein in adult fiber function and disease.     

Preparation of Highly Coupled Rat Heart Mitochondria

The function of mitochondria in generation of cellular ATP in the process of oxidative phosphorylation is widely recognised. During the past decades there have been significant advances in our understanding of the functions of mitochondria other than the generation of energy. These include their role in apoptosis, acting as signalling organelles, mammalian development and ageing as well as their contribution to the coordination between cell metabolism and cell proliferation. Our understanding of biological processes modulated by mitochondria is based on robust methods for isolation and handling of intact mitochondria from tissues of the laboratory animals. Mitochondria from rat heart is one of the most common preparations for past and current studies of cellular metabolism including studies on knock-out animals.Here we describe a detailed rapid method for isolation of intact mitochondria with a high degree of coupling. Such preparation of rat heart mitochondria is an excellent object for functional and structural research on cellular bioenergetics, transport of biomolecules, proteomic studies and analysis of mitochondrial DNA, proteins and lipids.     

Hybrid Mathematical Model of Cardiomyocyte Turnover in the Adult Human Heart

Rationale

The capacity for cardiomyocyte regeneration in the healthy adult human heart is fundamentally relevant for both myocardial homeostasis and cardiomyopathy therapeutics. However, estimates of cardiomyocyte turnover rates conflict greatly, with a study employing C14 pulse-chase methodology concluding 1% annual turnover in youth declining to 0.5% with aging and another using cell population dynamics indicating substantial, age-increasing turnover (4% increasing to 20%).

Objective

Create a hybrid mathematical model to critically examine rates of cardiomyocyte turnover derived from alternative methodologies.

Methods and Results

Examined in isolation, the cell population analysis exhibited severe sensitivity to a stem cell expansion exponent (20% variation causing 2-fold turnover change) and apoptosis rate. Similarly, the pulse-chase model was acutely sensitive to assumptions of instantaneous incorporation of atmospheric C14 into the body (4-fold impact on turnover in young subjects) while numerical restrictions precluded otherwise viable solutions. Incorporating considerations of primary variable sensitivity and controversial model assumptions, an unbiased numerical solver identified a scenario of significant, age-increasing turnover (4–6% increasing to 15–22% with age) that was compatible with data from both studies, provided that successive generations of cardiomyocytes experienced higher attrition rates than predecessors.

Conclusions

Assignment of histologically-observed stem/progenitor cells into discrete regenerative phenotypes in the cell population model strongly influenced turnover dynamics without being directly testable. Alternatively, C14 trafficking assumptions and restrictive models in the pulse-chase model artificially eliminated high-turnover solutions. Nevertheless, discrepancies among recent cell turnover estimates can be explained and reconciled. The hybrid mathematical model provided herein permits further examination of these and forthcoming datasets.     

Diffusion of Ions in Myelinated Nerve Fibers

The diffusion of ions towards or away from the inner side of the nodal membrane in preparations, the cut ends of which are placed in various media, was investigated. The ion concentration changes were calculated by numerical solution of the unidimensional electrodiffusion equation under a variety of media compositions, axoplasmic diffusion coefficients, and internal anionic compositions. The potassium and cesium ion diffusion along the axon towards the node was determined experimentally by two different electrophysiological methods. On the basis of comparison between the experimental data and the computational predictions the axoplasmic potassium ion diffusion coefficient was determined to be almost equal to that in free aqueous solution, while that of cesium ion was close to one half of that in aqueous solution. Utilizing the values of diffusion parameters thus determined, we solved the electrodiffusion equation for a number of common experimental procedures. We found that in short fibers, cut 0.1-0.2 cm at each side of the node, the concentration approached values close to the new steady-state values within 5-30 min. In long fibers (over 1 cm long) steady-state concentrations were obtained only after a few hours. Under some conditions the internal concentrations transiently overshot the steady-state values. The diffusion potentials generated in the system were also evaluated. The ion concentration changes and generation of diffusion potential cannot be prevented by using side pools with cation content identical to that of the axoplasm.