Application of regularized Richardson-Lucy algorithm for deconvolution of confocal microscopy images.

Although confocal microscopes have considerably smaller contribution of out-of-focus light than widefield microscopes, the confocal images can still be enhanced mathematically if the optical and data acquisition effects are accounted for. For that, several deconvolution algorithms have been proposed. As a practical solution, maximum-likelihood algorithms with regularization have been used. However, the choice of regularization parameters is often unknown although it has considerable effect on the result of deconvolution process. The aims of this work were: to find good estimates of deconvolution parameters; and to develop an open source software package that would allow testing different deconvolution algorithms and that would be easy to use in practice. Here, Richardson-Lucy algorithm has been implemented together with the total variation regularization in an open source software package IOCBio Microscope. The influence of total variation regularization on deconvolution process is determined by one parameter. We derived a formula to estimate this regularization parameter automatically from the images as the algorithm progresses. To assess the effectiveness of this algorithm, synthetic images were composed on the basis of confocal images of rat cardiomyocytes. From the analysis of deconvolved results, we have determined under which conditions our estimation of total variation regularization parameter gives good results. The estimated total variation regularization parameter can be monitored during deconvolution process and used as a stopping criterion. An inverse relation between the optimal regularization parameter and the peak signal-to-noise ratio of an image is shown. Finally, we demonstrate the use of the developed software by deconvolving images of rat cardiomyocytes with stained mitochondria and sarcolemma obtained by confocal and widefield microscopes.

Functional coupling as a basic mechanism of feedback regulation of cardiac energy metabolism.

In this review we analyze the concepts and the experimental data on the mechanisms of the regulation of energy metabolism in muscle cells. Muscular energetics is based on the force-length relationship, which in the whole heart is expressed as a Frank-Starling law, by which the alterations of left ventricle diastolic volume change linearly both the cardiac work and oxygen consumption. The second basic characteristics of the heart is the metabolic stability--almost constant levels of high energy phosphates, ATP and phosphocreatine, which are practically independent of the workload and the rate of oxygen consumption, in contrast to the fast-twitch skeletal muscle with no metabolic stability and rapid fatigue. Analysis of the literature shows that an increase in the rate of oxygen consumption by order of magnitude, due to Frank-Starling law, is observed without any significant changes in the intracellular calcium transients. Therefore, parallel activation of contraction and mitochondrial respiration by calcium ions may play only a minor role in regulation of respiration in the cells. The effective regulation of the respiration under the effect of Frank-Starling law and metabolic stability of the heart are explained by the mechanisms of functional coupling within supramolecular complexes in mitochondria, and at the subcellular level within the intracellular energetic units. Such a complex structural and functional organisation of heart energy metabolism can be described quantitatively by mathematical models.

Metabolic consequences of functional complexes of mitochondria, myofibrils and sarcoplasmic reticulum in muscle cells.

Regulation of mitochondrial respiration both by endogenous and exogenous ADP in the cells in situ was studied in isolated and permeabilized cardiomyocytes, permeabilized cardiac fibers and 'ghost' fibers (all with a diameter of 10-20 micro m) at different (0-3 micro moll(-1)) free Ca(2+) concentrations in the medium. In all these preparations, the apparent K(m) of mitochondrial respiration for exogenous ADP at free Ca(2+) concentrations of 0-0.1 micro moll(-1) was very high, in the range of 250-350 micro moll(-1), in contrast to isolated mitochondria in vitro (apparent K(m) for ADP is approximately 20 micro moll(-1)). An increase in the free Ca(2+) concentration (up to 3 micro moll(-1), which is within physiological range), resulted in a very significant decrease of the apparent K(m) value to 20-30 micro moll(-1), a decrease of V(max) of respiration in permeabilized intact fibers and a strong contraction of sarcomeres. In ghost cardiac fibers, from which myosin was extracted but mitochondria were intact, neither the high apparent K(m) for ADP (300-350 micro moll(-1)) nor V(max) of respiration changed in the range of free Ca(2+) concentration studied, and no sarcomere contraction was observed. The exogenous-ADP-trapping system (pyruvate kinase + phosphoenolpyruvate) inhibited endogenous-ADP-supported respiration in permeabilized cells by no more than 40%, and this inhibition was reversed by creatine due to activation of mitochondrial creatine kinase. These results are taken to show strong structural associations (functional complexes) among mitochondria, sarcomeres and sarcoplasmic reticulum. Inside these complexes, mitochondrial functional state is controlled by channeling of ADP, mostly via energy- and phosphoryl-transfer networks, and apparently depends on the state of sarcomere structures.

Cardiac mechanoenergetics replicated by cross-bridge model.

The aim of this work is to reproduce the experimentally measured linear dependence of cardiac muscle oxygen consumption on stress-strain area using a model, composed of a three-state Huxley-type model for cross-bridge interaction and a phenomenological model of Ca2+-induced activation. By selecting particular cross-bridge cycling rate constants and modifying the cross-bridge activation model, we replicated the linear dependence between oxygen consumption and stress-strain area together with other important mechanical properties of cardiac muscle such as developed stress dependence on the sarcomere length and force-velocity relationship. The model predicts that (1) the amount of the "passenger" cross bridges, i.e., cross bridges that detach without hydrolyzing ATP molecule, is relatively small and (2) ATP consumption rate profile within a beat and the amount of the passenger cross bridges depend on the contraction protocol.

Role of the creatine/phosphocreatine system in the regulation of mitochondrial respiration.

The mechanism of metabolic regulation of mitochondrial respiration in cardiac muscle cells was studied experimentally in the permeabilized heart fibres of mice and by computer modelling in silico. The experiments showed that the rate of mitochondrial respiration could be controlled by local production of ADP by mitochondrial creatine kinase in the intermembrane space of mitochondria. The spatially inhomogenous reaction-diffusion model of compartmentalized energy transfer was used to analyse which metabolite level in cytoplasm may be important for regulation of respiration. At low and moderate workloads, up to VO2 equal to 70 micromol min-1 g-1 dry weight, the only factor to which respiration responded was inorganic phosphate. At the values of VO2 higher than 70 micromol min-1 g-1 dry weight, the respiration rate responded mostly to changes in creatine, phosphocreatine and then time-averaged (over the contractile cycle) ADP concentrations in the cytoplasm. These results are taken to show that under conditions of moderate workloads, creatine kinase activity at given physiological creatine and phosphocreatine concentrations (apparent maximal activity achievable under these conditions) is in excess to oxidative phosphorylation rate, which is controlled by Pi concentration changes starting from very low values of the latter. At higher workloads mi-CK should be upregulated by increasing creatine and decreasing phosphocreatine concentrations, and only at very high workloads the ADP diffusion flux should be increased to upregulate oxidative phosphorylation. Thus, on the basis of the study in silico of compartmentalized energy transfer by phophocreatine/creatine system, the authors conclude that there exist multiple parallel regulatory factors controlling the rate of oxygen consumption in dependence of the workload. If creatine kinase is inhibited (and there is no myokinase activity), respiration requires high diffusive flux of ADP back into mitochondria, which is the sole regulator of respiration. This needs, however, increased ADP concentrations in the cytoplasm, which in turn result in inhibition of contraction.

Regulation of mitochondrial respiration in heart cells analyzed by reaction-diffusion model of energy transfer.

The purpose of this study is to investigate theoretically which intracellular factors may be important for regulation of mitochondrial respiration in working heart cells in vivo. We have developed a model that describes quantitatively the published experimental data on dependence of the rate of oxygen consumption and metabolic state of working isolated perfused rat heart on workload over its physiological range (Williamson JR, Ford G, Illingworth J, Safer B. Circ Res 38, Suppl I, I39-I51, 1976). Analysis of this model shows that for phosphocreatine, creatine, and ATP the equilibrium assumption is an acceptable approximation with respect to their diffusion in the intracellular bulk water phase. However, the ADP concentration changes in the contraction cycle in a nonequilibrium workload-dependent manner, showing the existence of the intracellular concentration gradients. The model shows that workload-dependent alteration of ADP concentration in the compartmentalized creatine kinase system may be taken, together with the changes in P(i) concentration, to be among the major components of the metabolic feedback signal for regulation of respiration in muscle cells.