Analysis of noisy transient signals based on Gaussian process regression.

Dynamic systems such as cells or tissues generate, either spontaneously or in response to stimuli, transient signals that carry information about the system. Characterization of recorded transients is often hampered by a low signal-to-noise ratio (SNR). Reduction of the noise by filtering has limited use due to partial signal distortion. Occasionally, transients can be approximated by a mathematical function, but such a function may not hold correctly if recording conditions change. We introduce here the model-independent approximation method for general noisy transient signals based on the Gaussian process regression. The method was implemented in the software TransientAnalyzer, which detects transients in a record, finds their best approximation by the Gaussian process, constructs a surrogate spline function, and estimates specified signal parameters. The method and software were tested on a cellular model of the calcium concentration transient corrupted by various SNR levels and recorded at a low sampling frequency. Statistical analysis of the model data sets provided the error of estimation <7.5% and the coefficient of variation of estimates <17% for peak SNR = 5. The performance of Gaussian process regression on signals of diverse experimental origin was even better than fitting by a function. The software and its description are available on GitHub.

SARS-CoV-2 Exploits Non-Canonical Autophagic Processes to Replicate, Mature, and Egress the Infected Vero E6 Cells.

The coronavirus transforms the cytoplasm of susceptible cells to support virus replication. It also activates autophagy-like processes, the role of which is not well understood. Here, we studied SARS-CoV-2-infected Vero E6 cells using transmission electron microscopy and autophagy PCR array. After 6-24 h post-infection (hpi), the cytoplasm of infected cells only contained double-membrane vesicles, phagophores, and phagosomes engulfing virus particles and cytoplasmic debris, including damaged mitochondria. The phagosomes interacted with the viral nucleoprotein complex, virus particles, mitochondria, and lipid droplets. The phagosomes transformed into egress vacuoles, which broke through the plasmalemma and discharged the virus particles. The Vero E6 cells exhibited pronounced virus replication at 6 hpi, which stabilized at 18-24 hpi at a high level. The autophagy PCR array tests revealed a significant upregulation of 10 and downregulation of 8 autophagic gene markers out of 84. Altogether, these results underline the importance of autophagy-like processes for SARS-CoV-2 maturation and egress, and point to deviations from a canonical autophagy response.

In silico simulations reveal that RYR distribution affects the dynamics of calcium release in cardiac myocytes.

The dyads of cardiac myocytes contain ryanodine receptors (RYRs) that generate calcium sparks upon activation. To test how geometric factors of RYR distribution contribute to the formation of calcium sparks, which cannot be addressed experimentally, we performed in silico simulations on a large set of models of calcium release sites (CRSs). Our models covered the observed range of RYR number, density, and spatial arrangement. The calcium release function of CRSs was modeled by RYR openings, with an open probability dependent on concentrations of free Ca2+ and Mg2+ ions, in a rapidly buffered system, with a constant open RYR calcium current. We found that simulations of spontaneous sparks by repeatedly opening one of the RYRs in a CRS produced three different types of calcium release events (CREs) in any of the models. Transformation of simulated CREs into fluorescence signals yielded calcium sparks with characteristics close to the observed ones. CRE occurrence varied broadly with the spatial distribution of RYRs in the CRS but did not consistently correlate with RYR number, surface density, or calcium current. However, it correlated with RYR coupling strength, defined as the weighted product of RYR vicinity and calcium current, so that CRE characteristics of all models followed the same state-response function. This finding revealed the synergy between structure and function of CRSs in shaping dyad function. Lastly, rearrangements of RYRs simulating hypothetical experiments on splitting and compaction of a dyad revealed an increased propensity to generate spontaneous sparks and an overall increase in calcium release in smaller and more compact dyads, thus underlying the importance and physiological role of RYR arrangement in cardiac myocytes.

Magnesium Ions Moderate Calcium-Induced Calcium Release in Cardiac Calcium Release Sites by Binding to Ryanodine Receptor Activation and Inhibition Sites.

Ryanodine receptor channels at calcium release sites of cardiac myocytes operate on the principle of calcium-induced calcium release. In vitro experiments revealed competition of Ca2+ and Mg2+ in the activation of ryanodine receptors (RyRs) as well as inhibition of RyRs by Mg2+. The impact of RyR modulation by Mg2+ on calcium release is not well understood due to the technical limitations of in situ experiments. We turned instead to an in silico model of a calcium release site (CRS), based on a homotetrameric model of RyR gating with kinetic parameters determined from in vitro measurements. We inspected changes in the activity of the CRS model in response to a random opening of one of 20 realistically distributed RyRs, arising from Ca2+/Mg2+ interactions at RyR channels. Calcium release events (CREs) were simulated at a range of Mg2+-binding parameters at near-physiological Mg2+ and ATP concentrations. Facilitation of Mg2+ binding to the RyR activation site inhibited the formation of sparks and slowed down their activation. Impeding Mg-binding to the RyR activation site enhanced spark formation and speeded up their activation. Varying Mg2+ binding to the RyR inhibition site also dramatically affected calcium release events. Facilitation of Mg2+ binding to the RyR inhibition site reduced the amplitude, relative occurrence, and the time-to-end of sparks, and vice versa. The characteristics of CREs correlated dose-dependently with the effective coupling strength between RyRs, defined as a function of RyR vicinity, single-channel calcium current, and Mg-binding parameters of the RyR channels. These findings postulate the role of Mg2+ in calcium release as a negative modulator of the coupling strength among RyRs in a CRS, translating to damping of the positive feedback of the calcium-induced calcium-release mechanism.

Structural variability of dyads relates to calcium release in rat ventricular myocytes.

Cardiac excitation-contraction coupling relies on dyads, the intracellular calcium synapses of cardiac myocytes, where the plasma membrane contacts sarcoplasmic reticulum and where electrical excitation triggers calcium release. The morphology of dyads and dynamics of local calcium release vary substantially. To better understand the correspondence between the structure and the functionality of dyads, we estimated incidences of structurally different dyads and of kinetically different calcium release sites and tested their responsiveness to experimental myocardial injury in left ventricular myocytes of rats. According to the structure of dyads estimated in random electron microscopic images of myocardial tissue, the dyads were sorted into 'compact' or 'loose' types. The calcium release fluxes, triggered at local calcium release sites in patch-clamped ventricular myocytes and recorded by laser scanning confocal fluorescence microscopy, were decomposed into 'early' and 'late' components. ANOVA tests revealed very high correlation between the relative amplitudes of early and late calcium release flux components and the relative occurrences of compact and loose dyads in the control and in the injured myocardium. This finding ascertained the relationship between the structure of dyads and the functionality of calcium release sites and the responsiveness of calcium release sites to physical load in cardiac myocytes.

The problem of accuracy in single-channel open probability measurements.

The function of ion channels to mediate the flux of ions through membranes of living cells depends on their number, conductance, and open probability. The open probability, PO, characterizes gating of channels that is sensitive to experimental conditions and that can be determined in single-channel experiments. Individual experimental records and even whole series of single-channel activity measurements represent random samples of the stochastic gating continuous in time. The aim of this study was to understand the relationship between the accuracy (trueness and precision) of PO determination and the method of single-channel activity data collection. We used simulated single-channel experiments with variable settings of data collection for a range of open probability values. We found that at low PO, the trueness of PO determination depends on the average number of channel openings per record, while the precision of PO determination depends on the total number of channel openings in the whole dataset and on the distribution of open and closed times. We derived relationships that allow planning of single-channel experiments for the required accuracy of PO determination over a large span of open probabilities.

Calcium Signaling and Contractility in Cardiac Myocyte of Wolframin Deficient Rats.

Wolframin (Wfs1) is a membrane protein of the sarco/endoplasmic reticulum. Wfs1 mutations are responsible for the Wolfram syndrome, characterized by diabetic and neurological symptoms. Although Wfs1 is expressed in cardiac muscle, its role in this tissue is not clear. We have characterized the effect of invalidation of Wfs1 on calcium signaling-related processes in isolated ventricular myocytes of exon5-Wfs1 deficient rats (Wfs1-e5/-e5) before the onset of overt disease. Calcium transients and contraction were measured in field-stimulated isolated myocytes using confocal microscopy with calcium indicator fluo-3 AM and sarcomere length detection. Calcium currents and their calcium release-dependent inactivation were characterized in whole-cell patch-clamp experiments. At 4 months, Wfs1-e5/-e5 animals were euglycemic, and echocardiographic examination revealed fully compensated cardiac function. In field-stimulated isolated ventricular myocytes, both the amplitude and the duration of contraction of Wfs1-e5/-e5 animals were elevated relative to control Wfs1+/+ littermates. Increased contractility of myocytes resulted largely from prolonged cytosolic calcium transients. Neither the amplitude of calcium currents nor their voltage dependence of activation differed between the two groups. Calcium currents in Wfs1-e5/-e5 myocytes showed a larger extent of inactivation by short voltage prepulses applied to selectively induce calcium release-dependent inactivation of calcium current. Neither the calcium content of the sarcoplasmic reticulum, measured by application of 20 mmol/l caffeine, nor the expression of SERCA2, determined from Western blots, differed significantly in myocytes of Wfs1-e5/-e5 animals compared to control ones. These experiments point to increased duration of calcium release in ventricular myocytes of Wfs1-e5/-e5 animals. We speculate that the lack of functional wolframin might cause changes leading to upregulation of RyR2 channels resulting in prolongation of channel openings and/or a delay in termination of calcium release.

Endoplasmic reticulum stress induces cardiac dysfunction through architectural modifications and alteration of mitochondrial function in cardiomyocytes.

Aims: Endoplasmic reticulum (ER) stress has recently emerged as an important mechanism involved in the pathogenesis of cardiovascular diseases. However, the molecular mechanisms by which ER stress leads to cardiac dysfunction remain poorly understood. Methods and results: In this study, we evaluated the early cardiac effects of ER stress induced by tunicamycin (TN) in mice. Echocardiographic analysis indicated that TN-induced ER stress led to a significant impairment of the cardiac function. Electron microscopic observations revealed that ultrastructural changes of cardiomyocytes in response to ER stress manifested extensively at the level of the reticular membrane system. Smooth tubules of sarcoplasmic reticulum in connection with short sections of rough ER were observed. The presence of rough instead of smooth reticulum was increased at the interfibrillar space, at the level of dyads, and in the vicinity of mitochondria. At the transcriptional level, ER stress resulted in a substantial decrease in the expression of the major regulator of mitochondrial biogenesis PGC-1α and of its targets NRF1, Tfam, CS, and COXIV. At the functional level, ER stress also induced an impairment of mitochondrial Ca2+ uptake, an alteration of mitochondrial oxidative phosphorylation, and a metabolic remodelling characterized by a shift from fatty acid to glycolytic substrate consumption. Conclusions: Our findings show that ER stress induces cytoarchitectural and metabolic alterations in cardiomyocytes and provide evidences that ER stress could represent a primary mechanism that contributes to the impairment of energy metabolism reported in most cardiac diseases.

Reconstruction of membrane current by deconvolution and its application to membrane capacitance measurements in cardiac myocytes.

Correct detection of membrane currents under whole-cell patch-clamp conditions is limited by the transfer function of a recording system. The low-pass output filter of a recording amplifier alters the time course of membrane current and causes errors in relevant descriptors. To solve these problems, we developed a practical procedure for reconstruction of the time course of membrane currents based on deconvolution of recorded currents in frequency domain. The procedure was tested on membrane capacitance estimates from current responses to step voltage pulses. The reconstructed current responses, in contrast to original current records, could be described exactly by an adequate impedance model of a recorded cell. The reconstruction allowed to increase the accuracy and reliability of membrane capacitance measurements in wide range of cell sizes and to suppress the cross-talk errors well below the noise. Moreover, it allowed resolving the instabilities in recording conditions arising from parasitic capacitance and seal resistance variation. Complex tests on hardware models, on simulated data sets, and on living cells confirmed robustness and reliability of the deconvolution procedure. The aptitude of the method was demonstrated in isolated rat cardiac myocytes by recording of spontaneous vesicular events, by discerning the formation of a fusion pore, and by revealing artefacts due to unstable seal resistance.

Calcium release-dependent inactivation precedes formation of the tubular system in developing rat cardiac myocytes.

Developing cardiac myocytes undergo substantial structural and functional changes transforming the mechanism of excitation-contraction coupling from the embryonic form, based on calcium influx through sarcolemmal DHPR calcium channels, to the adult form, relying on local calcium release through RYR calcium channels of sarcoplasmic reticulum stimulated by calcium influx. We characterized day-by-day the postnatal development of the structure of sarcolemma, using techniques of confocal fluorescence microscopy, and the development of the calcium current, measured by the whole-cell patch-clamp in isolated rat ventricular myocytes. We characterized the appearance and expansion of the t-tubule system and compared it with the appearance and progress of the calcium current inactivation induced by the release of calcium ions from sarcoplasmic reticulum as structural and functional measures of direct DHPR-RYR interaction. The release-dependent inactivation of calcium current preceded the development of the t-tubular system by several days, indicating formation of the first DHPR-RYR couplons at the surface sarcolemma and their later spreading close to contractile myofibrils with the growing t-tubules. Large variability of both of the measured parameters among individual myocytes indicates uneven maturation of myocytes within the growing myocardium.

Ultrastructural remodelling of slow skeletal muscle fibres in creatine kinase deficient mice: a quantitative study.

Creatine kinase content, isoform distribution, and participation in energy transfer are muscle type specific. We analysed ultrastructural changes in slow muscle fibres of soleus due to invalidation of creatine kinase (CK) to reveal a difference in the remodelling strategy in comparison with fast muscle fibres of gastrocnemius published previously. We have employed the stereological method of vertical sections and electron microscopy of soleus muscles of wild type (WT) and CK-/- mice. The mitochondrial volume density was 1.4× higher but that of sarcoplasmic reticulum (SR) was almost 5× lower in slow CK-/- muscles fibres than in WT fibres. The volume density of terminal cisterns and of t-tubules was also lower in CK-/- than in WT fibres. The analysis of organelle environment revealed increased neighbourhood of mitochondria and A-bands that resulted from the decreased volume density of SR, from relocation of mitochondria along myofibrils, and from intrusion of mitochondria to myofibrils. These processes direct ATP supply closer to the contractile machinery. The decreased interaction between mitochondria and SR suggests reduced dependence of calcium uptake on oxidative ATP production. In conclusion, the architecture of skeletal muscle cells is under control of a cellular program that optimizes energy utilization specifically for a given muscle type.

Quantitative analysis of calcium spikes in noisy fluorescent background.

Intracellular calcium signals are studied by laser-scanning confocal fluorescence microscopy. The required spatio-temporal resolution makes description of calcium signals difficult because of the low signal-to-noise ratio. We designed a new procedure of calcium spike analysis based on their fitting with a model. The accuracy and precision of calcium spike description were tested on synthetic datasets generated either with randomly varied spike parameters and Gaussian noise of constant amplitude, or with constant spike parameters and Gaussian noise of various amplitudes. Statistical analysis was used to evaluate the performance of spike fitting algorithms. The procedure was optimized for reliable estimation of calcium spike parameters and for dismissal of false events. A new algorithm was introduced that corrects the acquisition time of pixels in line-scan images that is in error due to sequential acquisition of individual pixels along the space coordinate. New software was developed in Matlab and provided for general use. It allows interactive dissection of temporal profiles of calcium spikes from x-t images, their fitting with predefined function(s) and acceptance of results on statistical grounds, thus allowing efficient analysis and reliable description of calcium signaling in cardiac myocytes down to the in situ function of ryanodine receptors.

Construction of calcium release sites in cardiac myocytes.

Local character of calcium release in cardiac myocytes, as defined by confocal recordings of calcium sparks, implies independent activation of individual calcium release sites based on ryanodine receptor (RyR) channel recruitment. We constructed virtual calcium release sites (vCRSs) composed of a variable number of RyR channels distributed in clusters in accordance with the experimentally observed cluster size distribution. The vCRSs consisted either of a single virtual calcium release unit (vCRU), in which all clusters shared a common dyadic space, or of multiple virtual calcium release units (CRUs) containing one cluster each and having separate dyadic spaces. We explored the stochastic behavior of vCRSs to understand the activation and recruitment of RyRs during calcium sparks. RyRs were represented by the published allosteric gating model that included regulation by cytosolic Ca(2+) and Mg(2+). The interaction of Mg(2+) with the RyR Ca(2+)-binding sites and the refractory period of vCRSs were optimized to accord with the experimentally observed calcium dependence of calcium spark frequency. The Mg(2+)-binding parameters of RyRs that provided the best description of spark frequency depended on the number of RyRs assembled in the vCRSs. Adequate inhibitory effect of Mg(2+) on the calcium dependence of RyR open probability was achieved if the vCRSs contained at least three clusters. For the distribution of the number of open RyRs in evoked calcium sparks to correspond to the experimentally observed distribution of spark calcium release fluxes, at least three clusters had to share a common virtual CRU, in which ∼3 RyRs open to form an average spark. These results reconcile the small cluster size and stochastic placement of RyRs in the release sites with the estimates of the amount of RyR protein, volume density of calcium release sites, and the size of calcium release sites in rat cardiac myocytes.

Calcium spike variability in cardiac myocytes results from activation of small cohorts of ryanodine receptor 2 channels.

In mammalian cardiac myocytes, the elementary calcium releases triggered by step voltage stimuli manifest either as solitary or as twin spikes that vary widely in kinetics and amplitude for unknown reasons. Here we examined the variability of calcium spikes measured using line-scanning confocal microscopy in patch-clamped rat ventricular myocytes. Amplitude distributions of the single and of the first of twin spikes were broader than those of the second spikes. All could be best approximated by a sum of a few elementary Gaussian probability distribution functions. The latency distributions of the single and the first spikes were identical, much shorter and less variable than those of the second spikes. The multimodal distribution of spike amplitudes and the probability of occurrence of twin spikes were stochastically congruent with activation of only a few of the many RyR2 channels present in the release site cluster. The occurrence of twin release events was rare due to refractoriness of release, induced with a probability proportional to the number of RyR2s activated in the primary release event. We conclude that the variability of the elementary calcium release events supports a calcium signalling mechanism that arises from stochastics of RyR2 gating and from inactivation of local origin.

Frequency and release flux of calcium sparks in rat cardiac myocytes: a relation to RYR gating.

Cytosolic calcium concentration in resting cardiac myocytes locally fluctuates as a result of spontaneous microscopic Ca(2+) releases or abruptly rises as a result of an external trigger. These processes, observed as calcium sparks, are fundamental for proper function of cardiac muscle. In this study, we analyze how the characteristics of spontaneous and triggered calcium sparks are related to cardiac ryanodine receptor (RYR) gating. We show that the frequency of spontaneous sparks and the probability distribution of calcium release flux quanta of triggered sparks correspond quantitatively to predictions of an allosteric homotetrameric model of RYR gating. This model includes competitive binding of Ca(2+) and Mg(2+) ions to the RYR activation sites and allosteric interaction between divalent ion binding and channel opening. It turns out that at rest, RYRs are almost fully occupied by Mg(2+). Therefore, spontaneous sparks are most frequently evoked by random openings of the highly populated but rarely opening Mg(4)RYR and CaMg(3)RYR forms, whereas triggered sparks are most frequently evoked by random openings of the less populated but much more readily opening Ca(2)Mg(2)RYR and Ca(3)MgRYR forms. In both the spontaneous and the triggered sparks, only a small fraction of RYRs in the calcium release unit manages to open during the spark because of the limited rate of Mg(2+) unbinding. This mechanism clarifies the unexpectedly low calcium release flux during elementary release events and unifies the theory of calcium signaling in resting and contracting cardiac myocytes.

A cell architecture modeling system based on quantitative ultrastructural characteristics.

The architecture of living cells is difficult to describe and communicate; therefore, realistic computer models may help their understanding. 3D models should correspond both to qualitative and quantitative experimental data and therefore should include specific authoring tools such as appropriate visualization and stereological measures. For this purpose we have developed a problem solving environment for stereology-based modeling (PSE-SBM), which is an automated system for quantitative modeling of cell architecture. The PSE-SBM meets the requirement to produce models that correspond in stereological and morphologic terms to real cells and their organelles. Instead of using standard interactive graphing tools, our approach relies on functional modeling. We have built a system of implicit functions and set operations, organized in a hierarchical tree structure, which describes individual cell organelles and their 3D relations. Natural variability of size, shape, and position of organelles is achieved by random variation of the specific parameters within given limits. The resulting model is materialized by evaluation of these functions and is adjusted for a given set of specific parameters defined by the user. These principles are explained in detail, and modeling of segments of a muscle cell is used as an example to demonstrate the potential of the PSE-SBM for communication of architectural concepts and testing of structural hypotheses.

Local calcium release activation by DHPR calcium channel openings in rat cardiac myocytes.

The principal role of calcium current in the triggering of calcium release in cardiac myocytes is well recognized. The mechanism of how calcium current (I(Ca)) controls the intensity of calcium release is not clear because of the stochastic nature of voltage-dependent gating of calcium channels (DHPRs) and of calcium-dependent gating of ryanodine receptors (RyRs). To disclose the relation between DHPR openings and the probability of calcium release, local calcium release activation by I(Ca) was investigated in rat ventricular myocytes using patch-clamp and confocal microscopy. Calcium spikes were activated by temporally synchronized DHPR calcium current triggers, generated by instantaneous 'tail' I(Ca) and modulated by prepulse duration, by tail potential, and by the DHPR agonist BayK 8644. The DHPR-RyR coupling fidelity was determined from the temporal distribution of calcium spike latencies using a model based on exponentially distributed DHPR open times. The analysis provided a DHPR mean open time of approximately 0.5 ms, RyR activation time constant of approximately 0.6 ms, and RyR activation kinetics of the 4th order. The coupling fidelity was low due to the inherent prevalence of very short DHPR openings but was increased when DHPR openings were prolonged by BayK 8644. The probability of calcium release activation was high, despite low coupling fidelity, due to the activation of many DHPRs at individual release sites. We conclude that the control of calcium release intensity by physiological stimuli can be achieved by modulating the number and duration of DHPR openings at low coupling fidelity, thus avoiding the danger of inadvertently triggering calcium release events.

Evaluation of changes in secretory granules of atrial myocytes: a morphometric approach.

OBJECTIVE: To evaluate the sensitivity and applicability of stereologic analysis for estimating changes in the secretory granule content of atrial myocytes. STUDY DESIGN: The content of secretory granules in the right atrial myocytes of Sprague-Dawley (SD) and Lewis (LW) rats was assessed using a stereologic analysis of electron microscopic images under control conditions and in response to forced wheel running. RESULTS: Volume density analysis revealed significant heterogeneity in the granule content of different strains of rats. The content of the dark secretory granules was significantly lower in control LW compared with control SD rats. The difference in pale granule content was opposite but less pronounced. Forced wheel running did not elicit statistically significant changes in the granule volume density. However, it changed significantly the number of dark granules in each rat strain, albeit in opposite directions, most likely due to changes in the number of small dark granules. No change was observed in the case of pale granules. This suggests higher sensitivity of dark granules to enhanced physical load. CONCLUSION: Both the volume and the number of secretory granules should be estimated in parallel to reveal responses of the atrial secretory system to different internal or external stimuli.