Scroll Waves and Filaments in Excitable Media of Higher Spatial Dimension.

Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic or electrical scroll waves in the heart. Here we show that such phenomena can be extended to a space of four or more dimensions and propose that connections of excitable elements in a network setting can be regarded as additional spatial dimensions. Numerical simulations are performed in four dimensions using the FitzHugh-Nagumo model, showing that the vortices rotate around a two-dimensional surface which we define as the superfilament. Evolution equations are derived for general superfilaments of codimension two in an N-dimensional space, and their equilibrium configurations are proven to be minimal surfaces. We suggest that biological excitable systems, such as the heart or brain which have nonlocal connections can be regarded, at least partially, as multidimensional excitable media and discuss further possible studies in this direction.

Amyloidogenic Peptides: New Class of Antimicrobial Peptides with the Novel Mechanism of Activity.

Antibiotic-resistant bacteria are recognized as one of the leading causes of death in the world. We proposed and successfully tested peptides with a new mechanism of antimicrobial action "protein silencing" based on directed co-aggregation. The amyloidogenic antimicrobial peptide (AAMP) interacts with the target protein of model or pathogenic bacteria and forms aggregates, thereby knocking out the protein from its working condition. In this review, we consider antimicrobial effects of the designed peptides on two model organisms, E. coli and T. thermophilus, and two pathogenic organisms, P. aeruginosa and S. aureus. We compare the amino acid composition of proteomes and especially S1 ribosomal proteins. Since this protein is inherent only in bacterial cells, it is a good target for studying the process of co-aggregation. This review presents a bioinformatics analysis of these proteins. We sum up all the peptides predicted as amyloidogenic by several programs and synthesized by us. For the four organisms we studied, we show how amyloidogenicity correlates with antibacterial properties. Let us especially dwell on peptides that have demonstrated themselves as AMPs for two pathogenic organisms that cause dangerous hospital infections, and in which the minimal inhibitory concentration (MIC) turned out to be comparable to the MIC of gentamicin sulfate. All this makes our study encouraging for the further development of AAMP. The hybrid peptides may thus provide a starting point for the antibacterial application of amyloidogenic peptides.

Multiple Antimicrobial Effects of Hybrid Peptides Synthesized Based on the Sequence of Ribosomal S1 Protein from Staphylococcus aureus.

The need to develop new antimicrobial peptides is due to the high resistance of pathogenic bacteria to traditional antibiotics now and in the future. The creation of synthetic peptide constructs is a common and successful approach to the development of new antimicrobial peptides. In this work, we use a simple, flexible, and scalable technique to create hybrid antimicrobial peptides containing amyloidogenic regions of the ribosomal S1 protein from Staphylococcus aureus. While the cell-penetrating peptide allows the peptide to enter the bacterial cell, the amyloidogenic site provides an antimicrobial effect by coaggregating with functional bacterial proteins. We have demonstrated the antimicrobial effects of the R23F, R23DI, and R23EI hybrid peptides against Staphylococcus aureus, methicillin-resistant S. aureus (MRSA), Pseudomonas aeruginosa, Escherichia coli, and Bacillus cereus. R23F, R23DI, and R23EI can be used as antimicrobial peptides against Gram-positive and Gram-negative bacteria resistant to traditional antibiotics.

Minimal Functional Clusters Predict the Probability of Reentry in Cardiac Fibrotic Tissue.

Cardiac fibrosis is a well-known arrhythmogenic condition which can lead to sudden cardiac death. Physically, fibrosis can be viewed as a large number of small obstacles in an excitable medium, which may create nonlinear wave turbulence or reentry. The relation between the specific texture of fibrosis and the onset of reentry is of great theoretical and practical importance. Here, we present a conceptual framework which combines functional aspects of propagation manifested as conduction blocks, with reentry wavelength and geometrical clusters of fibrosis. We formulate them into the single concept of minimal functional cluster and through extensive simulations show that it characterizes the path of reexcitation accurately, and importantly its size distribution quantitatively predicts the reentry probability for different fibrosis densities and tissue excitabilities.

Self-organization of conducting pathways explains electrical wave propagation in cardiac tissues with high fraction of non-conducting cells.

Cardiac fibrosis occurs in many forms of heart disease and is considered to be one of the main arrhythmogenic factors. Regions with a high density of fibroblasts are likely to cause blocks of wave propagation that give rise to dangerous cardiac arrhythmias. Therefore, studies of the wave propagation through these regions are very important, yet the precise mechanisms leading to arrhythmia formation in fibrotic cardiac tissue remain poorly understood. Particularly, it is not clear how wave propagation is organized at the cellular level, as experiments show that the regions with a high percentage of fibroblasts (65-75%) are still conducting electrical signals, whereas geometric analysis of randomly distributed conducting and non-conducting cells predicts connectivity loss at 40% at the most (percolation threshold). To address this question, we used a joint in vitro-in silico approach, which combined experiments in neonatal rat cardiac monolayers with morphological and electrophysiological computer simulations. We have shown that the main reason for sustainable wave propagation in highly fibrotic samples is the formation of a branching network of cardiomyocytes. We have successfully reproduced the morphology of conductive pathways in computer modelling, assuming that cardiomyocytes align their cytoskeletons to fuse into cardiac syncytium. The electrophysiological properties of the monolayers, such as conduction velocity, conduction blocks and wave fractionation, were reproduced as well. In a virtual cardiac tissue, we have also examined the wave propagation at the subcellular level, detected wavebreaks formation and its relation to the structure of fibrosis and, thus, analysed the processes leading to the onset of arrhythmias.

An audit of uncertainty in multi-scale cardiac electrophysiology models.

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Considering discrepancy when calibrating a mechanistic electrophysiology model.

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Gap19, a Cx43 Hemichannel Inhibitor, Acts as a Gating Modifier That Decreases Main State Opening While Increasing Substate Gating.

Cx43 hemichannels (HCs) are electrically and chemically gated transmembrane pores with low open probability and multiple conductance states, which makes kinetic studies of channel gating in large datasets challenging. Here, we developed open access software, named HemiGUI, to analyze HC gating transitions and investigated voltage-induced HC opening based on up to ≈4000 events recorded in HeLa-Cx43-overexpressing cells. We performed a detailed characterization of Cx43 HC gating profiles and specifically focused on the role of the C-terminal tail (CT) domain by recording the impact of adding an EGFP tag to the Cx43 CT end (Cx43-EGFP) or by supplying the Cx43 HC-inhibiting peptide Gap19 that interferes with CT interaction with the cytoplasmic loop (CL). We found that Gap19 not only decreased HC opening activity to the open state (≈217 pS) but also increased the propensity of subconductance (≈80 pS) transitions that additionally became slower as compared to the control. The work demonstrates that large sample transition analysis allows detailed investigations on Cx43 HC gating and shows that Gap19 acts as a HC gating modifier by interacting with the CT that forms a crucial gating element.

Antimicrobial and Amyloidogenic Activity of Peptides. Can Antimicrobial Peptides Be Used against SARS-CoV-2?

At present, much attention is paid to the use of antimicrobial peptides (AMPs) of natural and artificial origin to combat pathogens. AMPs have several points that determine their biological activity. We analyzed the structural properties of AMPs, as well as described their mechanism of action and impact on pathogenic bacteria and viruses. Recently published data on the development of new AMP drugs based on a combination of molecular design and genetic engineering approaches are presented. In this article, we have focused on information on the amyloidogenic properties of AMP. This review examines AMP development strategies from the perspective of the current high prevalence of antibiotic-resistant bacteria, and the potential prospects and challenges of using AMPs against infection caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).

Dynamical anchoring of distant arrhythmia sources by fibrotic regions via restructuring of the activation pattern.

Rotors are functional reentry sources identified in clinically relevant cardiac arrhythmias, such as ventricular and atrial fibrillation. Ablation targeting rotor sites has resulted in arrhythmia termination. Recent clinical, experimental and modelling studies demonstrate that rotors are often anchored around fibrotic scars or regions with increased fibrosis. However, the mechanisms leading to abundance of rotors at these locations are not clear. The current study explores the hypothesis whether fibrotic scars just serve as anchoring sites for the rotors or whether there are other active processes which drive the rotors to these fibrotic regions. Rotors were induced at different distances from fibrotic scars of various sizes and degree of fibrosis. Simulations were performed in a 2D model of human ventricular tissue and in a patient-specific model of the left ventricle of a patient with remote myocardial infarction. In both the 2D and the patient-specific model we found that without fibrotic scars, the rotors were stable at the site of their initiation. However, in the presence of a scar, rotors were eventually dynamically anchored from large distances by the fibrotic scar via a process of dynamical reorganization of the excitation pattern. This process coalesces with a change from polymorphic to monomorphic ventricular tachycardia.

A Mathematical Model of Neonatal Rat Atrial Monolayers with Constitutively Active Acetylcholine-Mediated K+ Current.

Atrial fibrillation (AF) is the most frequent form of arrhythmia occurring in the industrialized world. Because of its complex nature, each identified form of AF requires specialized treatment. Thus, an in-depth understanding of the bases of these arrhythmias is essential for therapeutic development. A variety of experimental studies aimed at understanding the mechanisms of AF are performed using primary cultures of neonatal rat atrial cardiomyocytes (NRAMs). Previously, we have shown that the distinct advantage of NRAM cultures is that they allow standardized, systematic, robust re-entry induction in the presence of a constitutively-active acetylcholine-mediated K+ current (IKACh-c). Experimental studies dedicated to mechanistic explorations of AF, using these cultures, often use computer models for detailed electrophysiological investigations. However, currently, no mathematical model for NRAMs is available. Therefore, in the present study we propose the first model for the action potential (AP) of a NRAM with constitutively-active acetylcholine-mediated K+ current (IKACh-c). The descriptions of the ionic currents were based on patch-clamp data obtained from neonatal rats. Our monolayer model closely mimics the action potential duration (APD) restitution and conduction velocity (CV) restitution curves presented in our previous in vitro studies. In addition, the model reproduces the experimentally observed dynamics of spiral wave rotation, in the absence and in the presence of drug interventions, and in the presence of localized myofibroblast heterogeneities.

Measurement and structure of spiral wave response functions.

The rotating spiral waves that emerge in diverse natural and man-made systems typically exhibit a particle-like behaviour since their adjoint critical eigenmodes (response functions) are often seen to be localised around the spiral core. We present a simple method to numerically compute response functions for circular-core and meandering spirals by recording their drift response to many elementary perturbations. Although our method is computationally more expensive than solving the adjoint system, our technique is fully parallellisable, does not suffer from memory limitations and can be applied to experiments. For a cardiac tissue model with the linear spiral core, we find that the response functions are localised near the turning points of the trajectory.

Perpetuation of torsade de pointes in heterogeneous hearts: competing foci or re-entry?

KEY POINTS: The underlying mechanism of torsade de pointes (TdP) remains of debate: perpetuation may be due to (1) focal activity or (2) re-entrant activity. The onset of TdP correlates with action potential heterogeneities in different regions of the heart. We studied the mechanism of perpetuation of TdP in silico using a 2D model of human cardiac tissue and an anatomically accurate model of the ventricles of the human heart. We found that the mechanism of perpetuation TdP depends on the degree of heterogeneity. If the degree of heterogeneity is large, focal activity alone can sustain a TdP, otherwise re-entrant activity emerges. This result can help to understand the relationship between the mechanisms of TdP and tissue properties and may help in developing new drugs against it. ABSTRACT: Torsade de pointes (TdP) can be the consequence of cardiac remodelling, drug effects or a combination of both. The mechanism underlying TdP is unclear, and may involve triggered focal activity or re-entry. Recent work by our group has indicated that both cases may exist, i.e. TdPs induced in the chronic atrioventricular block (CAVB) dog model may have a focal origin or are due to re-entry. Also it was found that heterogeneities might play an important role. In the current study we have used computational modelling to further investigate the mechanisms involved in TdP initiation and perpetuation, especially in the CAVB dog model, by the addition of heterogeneities with reduced repolarization reserve in comparison with the surrounding tissue. For this, the TNNP computer model was used for computations. We demonstrated in 2D and 3D simulations that ECGs with the typical TdP morphology can be caused by both multiple competing foci and re-entry circuits as a result of introduction of heterogeneities, depending on whether the heterogeneities have a large or a smaller reduced repolarization reserve in comparison with the surrounding tissue. Large heterogeneities can produce ectopic TdP, while smaller heterogeneities will produce re-entry-type TdP.

Effect of global cardiac ischemia on human ventricular fibrillation: insights from a multi-scale mechanistic model of the human heart.

Acute regional ischemia in the heart can lead to cardiac arrhythmias such as ventricular fibrillation (VF), which in turn compromise cardiac output and result in secondary global cardiac ischemia. The secondary ischemia may influence the underlying arrhythmia mechanism. A recent clinical study documents the effect of global cardiac ischaemia on the mechanisms of VF. During 150 seconds of global ischemia the dominant frequency of activation decreased, while after reperfusion it increased rapidly. At the same time the complexity of epicardial excitation, measured as the number of epicardical phase singularity points, remained approximately constant during ischemia. Here we perform numerical studies based on these clinical data and propose explanations for the observed dynamics of the period and complexity of activation patterns. In particular, we study the effects on ischemia in pseudo-1D and 2D cardiac tissue models as well as in an anatomically accurate model of human heart ventricles. We demonstrate that the fall of dominant frequency in VF during secondary ischemia can be explained by an increase in extracellular potassium, while the increase during reperfusion is consistent with washout of potassium and continued activation of the ATP-dependent potassium channels. We also suggest that memory effects are responsible for the observed complexity dynamics. In addition, we present unpublished clinical results of individual patient recordings and propose a way of estimating extracellular potassium and activation of ATP-dependent potassium channels from these measurements.

Atrium-specific Kir3.x determines inducibility, dynamics, and termination of fibrillation by regulating restitution-driven alternans.

BACKGROUND: Atrial fibrillation is the most common cardiac arrhythmia. Ventricular proarrhythmia hinders pharmacological atrial fibrillation treatment. Modulation of atrium-specific Kir3.x channels, which generate a constitutively active current (I(K,ACh-c)) after atrial remodeling, might circumvent this problem. However, it is unknown whether and how I(K,ACh-c) contributes to atrial fibrillation induction, dynamics, and termination. Therefore, we investigated the effects of I(K,ACh-c) blockade and Kir3.x downregulation on atrial fibrillation. METHODS AND RESULTS: Neonatal rat atrial cardiomyocyte cultures and intact atria were burst paced to induce reentry. To study the effects of Kir3.x on action potential characteristics and propagation patterns, cultures were treated with tertiapin or transduced with lentiviral vectors encoding Kcnj3- or Kcnj5-specific shRNAs. Kir3.1 and Kir3.4 were expressed in atrial but not in ventricular cardiomyocyte cultures. Tertiapin prolonged action potential duration (APD; 54.7±24.0 to 128.8±16.9 milliseconds; P<0.0001) in atrial cultures during reentry, indicating the presence of I(K,ACh-c). Furthermore, tertiapin decreased rotor frequency (14.4±7.4 to 6.6±2.0 Hz; P<0.05) and complexity (6.6±7.7 to 0.6±0.8 phase singularities; P<0.0001). Knockdown of Kcnj3 or Kcnj5 gave similar results. Blockade of I(K,ACh-c) prevented/terminated reentry by prolonging APD and changing APD and conduction velocity restitution slopes, thereby altering the probability of APD alternans and rotor destabilization. Whole-heart mapping experiments confirmed key findings (e.g., >50% reduction in atrial fibrillation inducibility after I(K,ACh-c) blockade). CONCLUSIONS: Atrium-specific Kir3.x controls the induction, dynamics, and termination of fibrillation by modulating APD and APD/conduction velocity restitution slopes in atrial tissue with I(K,ACh-c). This study provides new molecular and mechanistic insights into atrial tachyarrhythmias and identifies Kir3.x as a promising atrium-specific target for antiarrhythmic strategies.

Small size ionic heterogeneities in the human heart can attract rotors.

Rotors occurring in the heart underlie the mechanisms of cardiac arrhythmias. Answering the question whether or not the location of rotors is related to local properties of cardiac tissue has important practical applications. This is because ablation of rotors has been shown to be an effective way to fight cardiac arrhythmias. In this study, we investigate, in silico, the dynamics of rotors in two-dimensional and in an anatomical model of human ventricles using a Ten Tusscher-Noble-Noble-Panfilov (TNNP) model for ventricular cells. We study the effect of small size ionic heterogeneities, similar to those measured experimentally. It is shown that such heterogeneities cannot only anchor, but can also attract, rotors rotating at a substantial distance from the heterogeneity. This attraction distance depends on the extent of the heterogeneities and can be as large as 5-6 cm in realistic conditions. We conclude that small size ionic heterogeneities can be preferred localization points for rotors and discuss their possible mechanism and value for applications.

Chiral selection and frequency response of spiral waves in reaction-diffusion systems under a chiral electric field.

Chirality is one of the most fundamental properties of many physical, chemical, and biological systems. However, the mechanisms underlying the onset and control of chiral symmetry are largely understudied. We investigate possibility of chirality control in a chemical excitable system (the Belousov-Zhabotinsky reaction) by application of a chiral (rotating) electric field using the Oregonator model. We find that unlike previous findings, we can achieve the chirality control not only in the field rotation direction, but also opposite to it, depending on the field rotation frequency. To unravel the mechanism, we further develop a comprehensive theory of frequency synchronization based on the response function approach. We find that this problem can be described by the Adler equation and show phase-locking phenomena, known as the Arnold tongue. Our theoretical predictions are in good quantitative agreement with the numerical simulations and provide a solid basis for chirality control in excitable media.

Computer based method for identification of fibrotic scars from electrograms and local activation times on the epi- and endocardial surfaces of the ventricles.

Cardiac fibrosis stands as one of the most critical conditions leading to lethal cardiac arrhythmias. Identifying the precise location of cardiac fibrosis is crucial for planning clinical interventions in patients with various forms of ventricular and atrial arrhythmias. As fibrosis impedes and alters the path of electrical waves, detecting fibrosis in the heart can be achieved through analyzing electrical signals recorded from its surface. In current clinical practices, it has become feasible to record electrical activity from both the endocardial and epicardial surfaces of the heart. This paper presents a computational method for reconstructing 3D fibrosis using unipolar electrograms obtained from both surfaces of the ventricles. The proposed method calculates the percentage of fibrosis in various ventricular segments by analyzing the local activation times and peak-to-peak amplitudes of the electrograms. Initially, the method was tested using simulated data representing idealized fibrosis in a heart segment; subsequently, it was validated in the left ventricle with fibrosis obtained from a patient with nonischemic cardiomyopathy. The method successfully determined the location and extent of fibrosis in 204 segments of the left ventricle model with an average error of 0.0±4.3% (N = 204). Moreover, the method effectively detected fibrotic scars in the mid-myocardial region, a region known to present challenges in accurate detection using electrogram amplitude as the primary criterion.

'Trapped re-entry' as source of acute focal atrial arrhythmias.

AIMS: Diseased atria are characterized by functional and structural heterogeneities, adding to abnormal impulse generation and propagation. These heterogeneities are thought to lie at the origin of fractionated electrograms recorded during sinus rhythm (SR) in atrial fibrillation (AF) patients and are assumed to be involved in the onset and perpetuation (e.g. by re-entry) of this disorder. The underlying mechanisms, however, remain incompletely understood. Here, we tested whether regions of dense fibrosis could create an electrically isolated conduction pathway (EICP) in which re-entry could be established via ectopy and local block to become 'trapped'. We also investigated whether this could generate local fractionated electrograms and whether the re-entrant wave could 'escape' and cause a global tachyarrhythmia due to dynamic changes at a connecting isthmus. METHODS AND RESULTS: To precisely control and explore the geometrical properties of EICPs, we used light-gated depolarizing ion channels and patterned illumination for creating specific non-conducting regions in silico and in vitro. Insight from these studies was used for complementary investigations in virtual human atria with localized fibrosis. We demonstrated that a re-entrant tachyarrhythmia can exist locally within an EICP with SR prevailing in the surrounding tissue and identified conditions under which re-entry could escape from the EICP, thereby converting a local latent arrhythmic source into an active driver with global impact on the heart. In a realistic three-dimensional model of human atria, unipolar epicardial pseudo-electrograms showed fractionation at the site of 'trapped re-entry' in coexistence with regular SR electrograms elsewhere in the atria. Upon escape of the re-entrant wave, acute arrhythmia onset was observed. CONCLUSIONS: Trapped re-entry as a latent source of arrhythmogenesis can explain the sudden onset of focal arrhythmias, which are able to transgress into AF. Our study might help to improve the effectiveness of ablation of aberrant cardiac electrical signals in clinical practice.

Directed Graph Mapping exceeds Phase Mapping for the detection of simulated 2D meandering rotors in fibrotic tissue with added noise.

Cardiac arrhythmias such as atrial fibrillation (AF) are recognised to be associated with re-entry or rotors. A rotor is a wave of excitation in the cardiac tissue that wraps around its refractory tail, causing faster-than-normal periodic excitation. The detection of rotor centres is of crucial importance in guiding ablation strategies for the treatment of arrhythmia. The most popular technique for detecting rotor centres is Phase Mapping (PM), which detects phase singularities derived from the phase of a signal. This method has been proven to be prone to errors, especially in regimes of fibrotic tissue and temporal noise. Recently, a novel technique called Directed Graph Mapping (DGM) was developed to detect rotational activity such as rotors by creating a network of excitation. This research aims to compare the performance of advanced PM techniques versus DGM for the detection of rotors using 64 simulated 2D meandering rotors in the presence of various levels of fibrotic tissue and temporal noise. Four strategies were employed to compare the performances of PM and DGM. These included a visual analysis, a comparison of F2-scores and distance distributions, and calculating p-values using the mid-p McNemar test. Results indicate that in the case of low meandering, fibrosis and noise, PM and DGM yield excellent results and are comparable. However, in the case of high meandering, fibrosis and noise, PM is undeniably prone to errors, mainly in the form of an excess of false positives, resulting in low precision. In contrast, DGM is more robust against these factors as F2-scores remain high, yielding F2≥0.931 as opposed to the best PM F2≥0.635 across all 64 simulations.