Hydropathicity-based prediction of pain-causing NaV1.7 variants.

BACKGROUND: Mutation-induced variations in the functional architecture of the NaV1.7 channel protein are causally related to a broad spectrum of human pain disorders. Predicting in silico the phenotype of NaV1.7 variant is of major clinical importance; it can aid in reducing costs of in vitro pathophysiological characterization of NaV1.7 variants, as well as, in the design of drug agents for counteracting pain-disease symptoms. RESULTS: In this work, we utilize spatial complexity of hydropathic effects toward predicting which NaV1.7 variants cause pain (and which are neutral) based on the location of corresponding mutation sites within the NaV1.7 structure. For that, we analyze topological and scaling hydropathic characteristics of the atomic environment around NaV1.7's pore and probe their spatial correlation with mutation sites. We show that pain-related mutation sites occupy structural locations in proximity to a hydrophobic patch lining the pore while clustering at a critical hydropathic-interactions distance from the selectivity filter (SF). Taken together, these observations can differentiate pain-related NaV1.7 variants from neutral ones, i.e., NaV1.7 variants not causing pain disease, with 80.5[Formula: see text] sensitivity and 93.7[Formula: see text] specificity [area under the receiver operating characteristics curve = 0.872]. CONCLUSIONS: Our findings suggest that maintaining hydrophobic NaV1.7 interior intact, as well as, a finely-tuned (dictated by hydropathic interactions) distance from the SF might be necessary molecular conditions for physiological NaV1.7 functioning. The main advantage for using the presented predictive scheme is its negligible computational cost, as well as, hydropathicity-based biophysical rationalization.

Non-extensitivity and criticality of atomic hydropathicity around a voltage-gated sodium channel's pore: a modeling study.

Voltage-gated sodium channels (NavChs) are pore-forming membrane proteins that regulate the transport of sodium ions through the cell membrane. Understanding the structure and function of NavChs is of major biophysical, as well as clinical, importance given their key role in cellular pathophysiology. In this work, we provide a computational framework for modeling system-size-dependent, i.e., cumulative, atomic properties around a NavCh's pore. We illustrate our methodologies on the bacterial NavAb channel captured in a closed-pore state where we demonstrate that the atomic environment around its pore exhibits a bi-phasic spatial organization dictated by the structural separation of the pore domains (PDs) from the voltage-sensing domains (VSDs). Accordingly, a mathematical model describing packing of atoms around NavAb's pore is constructed that allows-under certain conservation conditions-for a power-law approximation of the cumulative hydropathic dipole field effect acting along NavAb's pore. This verified the non-extensitivity hypothesis for the closed-pore NavAb channel and revealed a long-range hydropathic interactions law regulating atom-packing around the NavAb's selectivity filter. Our model predicts a PDs-VSDs coupling energy of [Formula: see text] kcal/mol corresponding to a global maximum of the atom-packing energy profile. Crucially, we demonstrate for the first time how critical phenomena can emerge in a single-channel structure as a consequence of the non-extensive character of its atomic porous environment.

Cumulative hydropathic topology of a voltage-gated sodium channel at atomic resolution.

Voltage-gated sodium channels (NavChs) are biological pores that control the flow of sodium ions through the cell membrane. In humans, mutations in genes encoding NavChs can disrupt physiological cellular activity thus leading to a wide spectrum of diseases. Here, we present a topological connection between the functional architecture of a NavAb bacterial channel and accumulation of atomic hydropathicity around its pore. This connection is established via a scaling analysis methodology that elucidates how intrachannel hydropathic density variations translate into hydropathic dipole field configurations along the pore. Our findings suggest the existence of a nonrandom cumulative hydropathic topology that is organized parallel to the membrane surface so that pore's stability, as well as, gating behavior are guaranteed. Given the biophysical significance of the hydropathic effect, our study seeks to provide a computational framework for studying cumulative hydropathic topological properties of NavChs and pore-forming proteins in general.

Determinants of beat-to-beat variability of repolarization duration in the canine ventricular myocyte: a computational analysis.

Beat-to-beat variability of repolarization duration (BVR) is an intrinsic characteristic of cardiac function and a better marker of proarrhythmia than repolarization prolongation alone. The ionic mechanisms underlying baseline BVR in physiological conditions, its rate dependence, and the factors contributing to increased BVR in pathologies remain incompletely understood. Here, we employed computer modeling to provide novel insights into the subcellular mechanisms of BVR under physiological conditions and during simulated drug-induced repolarization prolongation, mimicking long-QT syndromes type 1, 2, and 3. We developed stochastic implementations of 13 major ionic currents and fluxes in a model of canine ventricular-myocyte electrophysiology. Combined stochastic gating of these components resulted in short- and long-term variability, consistent with experimental data from isolated canine ventricular myocytes. The model indicated that the magnitude of stochastic fluctuations is rate dependent due to the rate dependence of action-potential (AP) duration (APD). This process (the "active" component) and the intrinsic nonlinear relationship between membrane current and APD ("intrinsic component") contribute to the rate dependence of BVR. We identified a major role in physiological BVR for stochastic gating of the persistent Na(+) current (INa) and rapidly activating delayed-rectifier K(+) current (IKr). Inhibition of IKr or augmentation of INa significantly increased BVR, whereas subsequent ß-adrenergic receptor stimulation reduced it, similar to experimental findings in isolated myocytes. In contrast, ß-adrenergic stimulation increased BVR in simulated long-QT syndrome type 1. In addition to stochastic channel gating, AP morphology, APD, and beat-to-beat variations in Ca(2+) were found to modulate single-cell BVR. Cell-to-cell coupling decreased BVR and this was more pronounced when a model cell with increased BVR was coupled to a model cell with normal BVR. In conclusion, our results provide new insights into the ionic mechanisms underlying BVR and suggest that BVR reflects multiple potentially proarrhythmic parameters, including increased ion-channel stochasticity, prolonged APD, and abnormal Ca(2+) handling.

Local control of ß-adrenergic stimulation: Effects on ventricular myocyte electrophysiology and Ca(2+)-transient.

Local signaling domains and numerous interacting molecular pathways and substrates contribute to the whole-cell response of myocytes during ß-adrenergic stimulation (ßARS). We aimed to elucidate the quantitative contribution of substrates and their local signaling environments during ßARS to the canine epicardial ventricular myocyte electrophysiology and calcium transient (CaT). We present a computational compartmental model of ßARS and its electrophysiological effects. Novel aspects of the model include localized signaling domains, incorporation of ß1 and ß2 receptor isoforms, a detailed population-based approach to integrate the ßAR and Ca(2+)/Calmodulin kinase (CaMKII) signaling pathways and their effects on a wide range of substrates that affect whole-cell electrophysiology and CaT. The model identifies major roles for phosphodiesterases, adenylyl cyclases, PKA and restricted diffusion in the control of local cAMP levels and shows that activation of specific cAMP domains by different receptor isoforms allows for specific control of action potential and CaT properties. In addition, the model predicts increased CaMKII activity during ßARS due to rate-dependent accumulation and increased Ca(2+) cycling. CaMKII inhibition, reduced compartmentation, and selective blockade of ß1AR is predicted to reduce the occurrence of delayed afterdepolarizations during ßARS. Finally, the relative contribution of each PKA substrate to whole-cell electrophysiology is quantified by comparing simulations with and without phosphorylation of each target. In conclusion, this model enhances our understanding of localized ßAR signaling and its whole-cell effects in ventricular myocytes by incorporating receptor isoforms, multiple pathways and a detailed representation of multiple-target phosphorylation; it provides a basis for further studies of ßARS under pathological conditions.

Resonance-driven ion transport and selectivity in prokaryotic ion channels.

Ion channels exhibit a remarkably high accuracy in selecting uniquely its associated type of ion. The mechanisms behind ion selectivity are not well understood. Current explanations build mainly on molecular biology and bioinformatics. Here we propose a simple physical model for ion selectivity based on the driven damped harmonic oscillator (DDHO). The driving force for this oscillator is provided by self-organizing harmonic turbulent structures in the dehydrating ionic flow through the ion channel, namely, oscillating pressure waves in one dimension, and toroidal vortices in two and three dimensions. Density fluctuations caused by these turbulences efficiently transmit their energy to aqua ions that resonate with the driving frequency. Consequently, these release their hydration shell and exit the ion channel as free ions. Existing modeling frameworks do not express the required complex spatiotemporal dynamics, hence we introduce a macroscopic continuum model for ionic dehydration and transport, based on the hydrodynamics of a dissipative ionic flow through an ion channel, subject to electrostatic and amphiphilic interactions. This model combines three classical physical fields: Navier-Stokes equations from hydrodynamics, Gauss's law from Maxwell theory, and the convection-diffusion equation from continuum physics. Numerical experiments with mixtures of chemical species of ions in various degrees of hydration indeed reveal the emergence of strong oscillations in the ionic flow that are instrumental in the efficient dehydration and cause a strong ionic jet into the cell. As such, they provide a powerful engine for the DDHO mechanism. Theoretical predictions of the modeling framework match significantly with empirical patch-clamp data. The DDHO standard response curve defines a unique resonance frequency that depends on the mass and charge of the ion. In this way, the driving oscillations act as a selection mechanism that filters out one specific ion. Application of the DDHO model to real ion data shows that this mechanism indeed clearly distinguishes between chemical species and between aqua and bare ions with a large Mahalanobis distance and high oscillator quality. The DDHO framework helps to understand how SNP mutations can cause severe genetic pathologies as they destroy the geometry of the channel and so alter the resonance peaks of the required ion type.

Physiology-based regularization of the electrocardiographic inverse problem.

The inverse problem of electrocardiography aims at noninvasively reconstructing electrical activity of the heart from recorded body-surface electrocardiograms. A crucial step is regularization, which deals with ill-posedness of the problem by imposing constraints on the possible solutions. We developed a regularization method that includes electrophysiological input. Body-surface potentials are recorded and a computed tomography scan is performed to obtain the torso-heart geometry. Propagating waveforms originating from several positions at the heart are simulated and used to generate a set of basis vectors representing spatial distributions of potentials on the heart surface. The real heart-surface potentials are then reconstructed from the recorded body-surface potentials by finding a sparse representation in terms of this basis. This method, which we named 'physiology-based regularization' (PBR), was compared to traditional Tikhonov regularization and validated using in vivo recordings in dogs. PBR recovered details of heart-surface electrograms that were lost with traditional regularization, attained higher correlation coefficients and led to improved estimation of recovery times. The best results were obtained by including approximate knowledge about the beat origin in the PBR basis.

In Vivo Validation of Electrocardiographic Imaging.

OBJECTIVES: The purpose of this study was to evaluate the accuracy of noninvasive reconstructions of epicardial potentials, electrograms, activation and recovery isochrones, and beat origins by simultaneously performing electrocardiographic imaging (ECGI) and invasive epicardial electrography in intact animals. BACKGROUND: Noninvasive imaging of electrical potentials at the epicardium, known as ECGI, is increasingly applied in patients to assess normal and abnormal cardiac electrical activity. METHODS: Body-surface potentials and epicardial potentials were recorded in normal anesthetized dogs. Computed tomography scanning provided a torso-heart geometry that was used to reconstruct epicardial potentials from body-surface potentials. RESULTS: Electrogram reconstructions attained a moderate accuracy compared with epicardial recordings (median correlation coefficient: 0.71), but with considerable variation (interquartile range: 0.36 to 0.86). This variation could be explained by a spatial mismatch (overall resolution was <20 mm) that was most apparent in regions with electrographic transition. More accurate derivation of activation times (Pearson R: 0.82), recovery times (R: 0.73), and the origin of paced beats (median error: 10 mm; interquartile range: 7 to 17 mm) was achieved by a spatiotemporal approach that incorporates the characteristics of the respective electrogram and neighboring electrograms. Reconstruction of beats from repeated single-site pacing showed a stable localization of origin. Cardiac motion, currently ignored in ECGI, correlates negatively with reconstruction accuracy. CONCLUSIONS: ECGI shows a decent median accuracy, but variability in electrogram reconstruction can be sizable. At present, therefore, clinical interpretations of ECGI should not be made on the basis of single electrograms only. Incorporating local spatiotemporal characteristics allows for accurate reconstruction of epicardial activation and recovery patterns, and beat origin localization to a 10-mm precision. Even more reliable interpretations are expected when the influences of cardiac motion are accounted for in ECGI.

Network topology of NaV1.7 mutations in sodium channel-related painful disorders.

BACKGROUND: Gain-of-function mutations in SCN9A gene that encodes the voltage-gated sodium channel NaV1.7 have been associated with a wide spectrum of painful syndromes in humans including inherited erythromelalgia, paroxysmal extreme pain disorder and small fibre neuropathy. These mutations change the biophysical properties of NaV1.7 channels leading to hyperexcitability of dorsal root ganglion nociceptors and pain symptoms. There is a need for better understanding of how gain-of-function mutations alter the atomic structure of Nav1.7. RESULTS: We used homology modeling to build an atomic model of NaV1.7 and a network-based theoretical approach, which can predict interatomic interactions and connectivity arrangements, to investigate how pain-related NaV1.7 mutations may alter specific interatomic bonds and cause connectivity rearrangement, compared to benign variants and polymorphisms. For each amino acid substitution, we calculated the topological parameters betweenness centrality (B ct ), degree (D), clustering coefficient (CC ct ), closeness (C ct ), and eccentricity (E ct ), and calculated their variation (Δ value = mutant value -WT value ). Pathogenic NaV1.7 mutations showed significantly higher variation of |ΔB ct | compared to benign variants and polymorphisms. Using the cut-off value ±0.26 calculated by receiver operating curve analysis, we found that ΔB ct correctly differentiated pathogenic NaV1.7 mutations from variants not causing biophysical abnormalities (nABN) and homologous SNPs (hSNPs) with 76% sensitivity and 83% specificity. CONCLUSIONS: Our in-silico analyses predict that pain-related pathogenic NaV1.7 mutations may affect the network topological properties of the protein and suggest |ΔB ct | value as a potential in-silico marker.

Wavelet-sparsity based regularization over time in the inverse problem of electrocardiography.

Noninvasive, detailed assessment of electrical cardiac activity at the level of the heart surface has the potential to revolutionize diagnostics and therapy of cardiac pathologies. Due to the requirement of noninvasiveness, body-surface potentials are measured and have to be projected back to the heart surface, yielding an ill-posed inverse problem. Ill-posedness ensures that there are non-unique solutions to this problem, resulting in a problem of choice. In the current paper, it is proposed to restrict this choice by requiring that the time series of reconstructed heart-surface potentials is sparse in the wavelet domain. A local search technique is introduced that pursues a sparse solution, using an orthogonal wavelet transform. Epicardial potentials reconstructed from this method are compared to those from existing methods, and validated with actual intracardiac recordings. The new technique improves the reconstructions in terms of smoothness and recovers physiologically meaningful details. Additionally, reconstruction of activation timing seems to be improved when pursuing sparsity of the reconstructed signals in the wavelet domain.

Realistic training data improve noninvasive reconstruction of heart-surface potentials.

The inverse problem of electrocardiography is to noninvasively reconstruct electrical heart activity from body-surface electrocardiograms. Solving this problem is beneficial to clinical practice. However, reconstructions cannot be obtained straightforwardly due to the ill-posed nature of this problem. Therefore, regularization schemes are necessary to arrive at realistic solutions. To date, no electrophysiological data have been used in reconstruction methods and regularization schemes. In this study, we used a training set of simulated heart-surface potentials to create a realistic basis for reconstructions of electrical cardiac activity. We tested this method in computer simulations and in one patient. The quality of reconstruction improved significantly after projection of the results of traditional regularization methods on this new basis, both in silico (p<0.01) and in vivo (p<0.05). Thus, we demonstrate that the novel concept of applying electrophysiological data might be useful to improve noninvasive reconstruction of electrical heart activity.