Arrhythmogenic effects of ultra-long and bistable cardiac action potentials

Contemporary accounts of the initiation of cardiac arrhythmias typically rely on after-depolarizations as the trigger for reentrant activity. The after-depolarizations are usually triggered by calcium entry or spontaneous release within the cells of the myocardium or the conduction system. Here we propose an alternative mechanism whereby arrhythmias are triggered autonomously by cardiac cells that fail to repolarize after a normal heartbeat. We investigated the proposal by representing the heart as an excitable medium of FitzHugh-Nagumo cells where a proportion of cells were capable of remaining depolarized indefinitely. As such, those cells exhibit bistable membrane dynamics. We found that heterogeneous media can tolerate a surprisingly large number of bistable cells and still support normal rhythmic activity. Yet there is a critical limit beyond which the medium is persistently arrhythmogenic. Numerical analysis revealed that the critical threshold for arrhythmogenesis depends on both the strength of the coupling between cells and the extent to which the abnormal cells resist repolarization. Moreover, arrhythmogenesis was found to emerge preferentially at tissue boundaries where cells naturally have fewer neighbors to influence their behavior. These findings may explain why atrial fibrillation typically originates from tissue boundaries such as the cuff of the pulmonary vein.     

Mesoscopic biochemical basis of isogenetic inheritance and canalization: stochasticity, nonlinearity, and emergent landscape

Biochemical reaction systems in mesoscopic volume, under sustained environmental chemical gradient(s), can have multiple stochastic attractors. Two distinct mechanisms are known for their origins: (a) Stochastic single-molecule events, such as gene expression, with slow gene on-off dynamics; and (b) nonlinear networks with feedbacks. These two mechanisms yield different volume dependence for the sojourn time of an attractor. As in the classic Arrhenius theory for temperature dependent transition rates, a landscape perspective provides a natural framework for the system's behavior. However, due to the nonequilibrium nature of the open chemical systems, the landscape, and the attractors it represents, are all themselves emergent properties of complex, mesoscopic dynamics. In terms of the landscape, we show a generalization of Kramers' approach is possible to provide a rate theory. The emergence of attractors is a form of self-organization in the mesoscopic system; stochastic attractors in biochemical systems such as gene regulation and cellular signaling are naturally inheritable via cell division. Delbrück-Gillespie's mesoscopic reaction system theory, therefore, provides a biochemical basis for spontaneous isogenetic switching and canalization.     

Multiscale feature analysis of salivary gland branching morphogenesis

Pattern formation in developing tissues involves dynamic spatio-temporal changes in cellular organization and subsequent evolution of functional adult structures. Branching morphogenesis is a developmental mechanism by which patterns are generated in many developing organs, which is controlled by underlying molecular pathways. Understanding the relationship between molecular signaling, cellular behavior and resulting morphological change requires quantification and categorization of the cellular behavior. In this study, tissue-level and cellular changes in developing salivary gland in response to disruption of ROCK-mediated signaling by are modeled by building cell-graphs to compute mathematical features capturing structural properties at multiple scales. These features were used to generate multiscale cell-graph signatures of untreated and ROCK signaling disrupted salivary gland organ explants. From confocal images of mouse submandibular salivary gland organ explants in which epithelial and mesenchymal nuclei were marked, a multiscale feature set capturing global structural properties, local structural properties, spectral, and morphological properties of the tissues was derived. Six feature selection algorithms and multiway modeling of the data was performed to identify distinct subsets of cell graph features that can uniquely classify and differentiate between different cell populations. Multiscale cell-graph analysis was most effective in classification of the tissue state. Cellular and tissue organization, as defined by a multiscale subset of cell-graph features, are both quantitatively distinct in epithelial and mesenchymal cell types both in the presence and absence of ROCK inhibitors. Whereas tensor analysis demonstrate that epithelial tissue was affected the most by inhibition of ROCK signaling, significant multiscale changes in mesenchymal tissue organization were identified with this analysis that were not identified in previous biological studies. We here show how to define and calculate a multiscale feature set as an effective computational approach to identify and quantify changes at multiple biological scales and to distinguish between different states in developing tissues.     

Stability analysis of one-dimensional dynamical systems applied to an isolated beating heart

In this paper we propose a new model of an isolated beating heart. The model is described by a one-dimensional non-linear discrete dynamical system which depends on several parameters. Applying stability analysis we investigate the dynamic properties of the non-linear system. We find those domains in the parameter space in which the equilibrium point of the system (the fixed point) and the periodic orbits are attractors and in which they are unstable. These domains correspond to a normal and abnormal beating heart, i.e. when the end diastolic volumes are stable time invariant and time variant, respectively. On transition between these domains there is a bifurcation which gives rise to a pair of attracting points of period 2. This case corresponds to the simplest type of period doubling behavior of an abnormal beating heart, called mechanical alternans. Our results provide qualitative and quantitative predictions which can be used for comprehensive experimental design.     

An Inverse Finite Element Method for Determining the Tissue Compressibility of Human Left Ventricular Wall during the Cardiac Cycle

The determination of the myocardium’s tissue properties is important in constructing functional finite element (FE) models of the human heart. To obtain accurate properties especially for functional modeling of a heart, tissue properties have to be determined in vivo. At present, there are only few in vivo methods that can be applied to characterize the internal myocardium tissue mechanics. This work introduced and evaluated an FE inverse method to determine the myocardial tissue compressibility. Specifically, it combined an inverse FE method with the experimentally-measured left ventricular (LV) internal cavity pressure and volume versus time curves. Results indicated that the FE inverse method showed good correlation between LV repolarization and the variations in the myocardium tissue bulk modulus K (K = 1/compressibility), as well as provided an ability to describe in vivo human myocardium material behavior. The myocardium bulk modulus can be effectively used as a diagnostic tool of the heart ejection fraction. The model developed is proved to be robust and efficient. It offers a new perspective and means to the study of living-myocardium tissue properties, as it shows the variation of the bulk modulus throughout the cardiac cycle.     

Engineered heart tissue grafts improve systolic and diastolic function in infarcted rat hearts

The concept of regenerating diseased myocardium by implantation of tissue-engineered heart muscle is intriguing, but convincing evidence is lacking that heart tissues can be generated at a size and with contractile properties that would lend considerable support to failing hearts. Here we created large (thickness/diameter, 1-4 mm/15 mm), force-generating engineered heart tissue from neonatal rat heart cells. Engineered heart tissue formed thick cardiac muscle layers when implanted on myocardial infarcts in immune-suppressed rats. When evaluated 28 d later, engineered heart tissue showed undelayed electrical coupling to the native myocardium without evidence of arrhythmia induction. Moreover, engineered heart tissue prevented further dilation, induced systolic wall thickening of infarcted myocardial segments and improved fractional area shortening of infarcted hearts compared to controls (sham operation and noncontractile constructs). Thus, our study provides evidence that large contractile cardiac tissue grafts can be constructed in vitro, can survive after implantation and can support contractile function of infarcted hearts.     

Distinct enhancers regulate skeletal and cardiac muscle-specific expression programs of the cardiac alpha-actin gene in Xenopus embryos

During vertebrate embryonic development, cardiac and skeletal muscle originates from distinct precursor populations. Despite the profound structural and functional differences in the striated muscle tissue they eventually form, such progenitors share many features such as components of contractile apparatus. In vertebrate embryos, the alpha-cardiac actin gene encodes a major component of the myofibril in both skeletal and cardiac muscle. Here, we show that expression of Xenopus cardiac alpha-actin in the myotomes and developing heart tube of the tadpole requires distinct enhancers within its proximal promoter. Using transgenic embryos, we find that mutations in the promoter-proximal CArG box and 5 bp downstream of it specifically eliminate expression of a GFP transgene within the developing heart, while high levels of expression in somitic muscle are maintained. This sequence is insufficient on its own to limit expression solely to the myocardium, such restriction requiring multiple elements within the proximal promoter. Two additional enhancers are active in skeletal muscle of the embryo, either one of which has to interact with the proximal CArG box for correct expression to be established. Transgenic reporters containing multimerised copies of CArG box 1 faithfully detect most sites of SRF expression in the developing embryo as do equivalent reporters containing the SRF binding site from the c-fos promoter. Significantly, while these motifs possess a different A/T core within the CC(A/T)(6)GG consensus and show no similarity in flanking sequence, each can interact with a myotome-specific distal enhancer of cardiac alpha-actin promoter, to confer appropriate cardiac alpha-actin-specific regulation of transgene expression. Together, these results suggest that the role of CArG box 1 in the cardiac alpha-actin gene promoter is to act solely as a high-affinity SRF binding site.     

Lung tissue mechanics as an emergent phenomenon

The mechanical properties of lung parenchymal tissue are both elastic and dissipative, as well as being highly nonlinear. These properties cannot be fully understood, however, in terms of the individual constituents of the tissue. Rather, the mechanical behavior of lung tissue emerges as a macroscopic phenomenon from the interactions of its microscopic components in a way that is neither intuitive nor easily understood. In this review, we first consider the quasi-static mechanical behavior of lung tissue and discuss computational models that show how smooth nonlinear stress-strain behavior can arise through a percolation-like process in which the sequential recruitment of collagen fibers with increasing strain causes them to progressively take over the load-bearing role from elastin. We also show how the concept of percolation can be used to link the pathologic progression of parenchymal disease at the micro scale to physiological symptoms at the macro scale. We then examine the dynamic mechanical behavior of lung tissue, which invokes the notion of tissue resistance. Although usually modeled phenomenologically in terms of collections of springs and dashpots, lung tissue viscoelasticity again can be seen to reflect various types of complex dynamic interactions at the molecular level. Finally, we discuss the inevitability of why lung tissue mechanics need to be complex.     

Multiple mixed-type attractors in a competition model

We show that a discrete-time, two-species competition model with Ricker (exponential) nonlinearities can exhibit multiple mixed-type attractors. By this is meant dynamic scenarios in which there are simultaneously present both coexistence attractors (in which both species are present) and exclusion attractors (in which one species is absent). Recent studies have investigated the inclusion of life-cycle stages in competition models as a casual mechanism for the existence of these kinds of multiple attractors. In this paper we investigate the role of nonlinearities in competition models without life-cycle stages.     

From Genes to Flower Patterns and Evolution: Dynamic Models of Gene Regulatory Networks

Genes and proteins form complex dynamical systems or gene regulatory networks (GRN) that can reach several steady states (attractors). These may be associated with distinct cell types. In plants, the ABC combinatorial model establishes the necessary gene combinations for floral organ cell specification. We have developed dynamic gene regulatory network (GRN) models to understand how the combinatorial selection of gene activity is established during floral organ primordia specification as a result of the concerted action of ABC and non-ABC genes. Our analyses have shown that the floral organ specification GRN reaches six attractors with gene configurations observed in primordial cell types during early stages of flower development and four that correspond to regions of the inflorescence meristem. This suggests that it is the overall GRN dynamics rather than precise signals that underlie the ABC model. Furthermore, our analyses suggest that the steady states of the GRN are robust to random alterations of the logical functions that define the gene interactions. Here we have updated the GRN model and have systematically altered the outputs of all the logical functions and addressed in which cases the original attractors are recovered. We then reduced the original three-state GRN to a two-state (Boolean) GRN and performed the same systematic perturbation analysis. Interestingly, the Boolean GRN reaches the same number and type of attractors as reached by the three-state GRN, and it responds to perturbations in a qualitatively identical manner as the original GRN. These results suggest that a Boolean model is sufficient to capture the dynamical features of the floral network and provide additional support for the robustness of the floral GRN. These findings further support that the GRN model provides a dynamical explanation for the ABC model and that the floral GRN robustness could be behind the widespread conservation of the floral plan among eudicotyledoneous plants. Other aspects of evolution of flower organ arrangement and ABC gene expression patterns are discussed in the context of the approach proposed here. álvaro Chaos, Max Aldana and Elena Alvarez-Buylla contributed equally to this work.     

The Problem of Colliding Networks and its Relation to Cell Fusion and?Cancer

Cell fusion, a process that merges two or more cells into one, is required for normal development and has been explored as a tool for stem cell therapy. It has also been proposed that cell fusion causes cancer and contributes to its progression. These functions rely on a poorly understood ability of cell fusion to create new cell types. We suggest that this ability can be understood by considering cells as attractor networks whose basic property is to adopt a set of distinct, stable, self-maintaining states called attractors. According to this view, fusion of two cell types is a collision of two networks that have adopted distinct attractors. To learn how these networks reach a consensus, we model cell fusion computationally. To do so, we simulate patterns of gene activities using a formalism developed to simulate patterns of memory in neural networks. We find that the hybrid networks can assume attractors that are unrelated to parental attractors, implying that cell fusion can create new cell types by nearly instantaneously moving cells between attractors. We also show that hybrid networks are prone to assume spurious attractors, which are emergent and sporadic network states. This finding means that cell fusion can produce abnormal cell types, including cancerous types, by placing cells into normally inaccessible spurious states. Finally, we suggest that the problem of colliding networks has general significance in many processes represented by attractor networks, including biological, social, and political phenomena.     

Perception of odors by a nonlinear model of the olfactory bulb

The behavior of the olfactory bulb is modeled as a network of interconnected cells with nonlinear dynamics. External inputs from sensory neurons are introduced as perturbations to subsets of cells within the network. We describe the attractors of the system and show how they can be classified and ordered according to their varying degrees of symmetry. By studying networks of attractors in the system's phase space, it is shown how different perturbations may evoke specific switches between various patterns of behavior. This ensures that different odors, even if present at extremely low concentrations, are able to evoke a specific spatio-temporal behavior in the olfactory bulb, permitting their unique perception. The model incorporates many of the processes proposed to mediate perception, such as the topographic organisation of sensory systems, destabilization of cortex by sensory input and synchronisation between neurons. It is also consistent with the character of the olfactory electroencephalogram.     

In silico identification of potential calcium dynamics and sarcomere targets for recovering left ventricular function in rat heart failure with preserved ejection fraction

Heart failure with preserved ejection fraction (HFpEF) is a complex disease associated with multiple co-morbidities, where impaired cardiac mechanics are often the end effect. At the cellular level, cardiac mechanics can be pharmacologically manipulated by altering calcium signalling and the sarcomere. However, the link between cellular level modulations and whole organ pump function is incompletely understood. Our goal is to develop and use a multi-scale computational cardiac mechanics model of the obese ZSF1 HFpEF rat to identify important biomechanical mechanisms that underpin impaired cardiac function and to predict how whole-heart mechanical function can be recovered through altering cellular calcium dynamics and/or cellular contraction. The rat heart was modelled using a 3D biventricular biomechanics model. Biomechanics were described by 16 parameters, corresponding to intracellular calcium transient, sarcomere dynamics, cardiac tissue and hemodynamics properties. The model simulated left ventricular (LV) pressure-volume loops that were described by 14 scalar features. We trained a Gaussian process emulator to map the 16 input parameters to each of the 14 outputs. A global sensitivity analysis was performed, and identified calcium dynamics and thin and thick filament kinetics as key determinants of the organ scale pump function. We employed Bayesian history matching to build a model of the ZSF1 rat heart. Next, we recovered the LV function, described by ejection fraction, peak pressure, maximum rate of pressure rise and isovolumetric relaxation time constant. We found that by manipulating calcium, thin and thick filament properties we can recover 34%, 28% and 24% of the LV function in the ZSF1 rat heart, respectively, and 39% if we manipulate all of them together. We demonstrated how a combination of biophysically based models and their derived emulators can be used to identify potential pharmacological targets. We predicted that cardiac function can be best recovered in ZSF1 rats by desensitising the myofilament and reducing the affinity to intracellular calcium concentration and overall prolonging the sarcomere staying in the active force generating state.     

Cooperative differentiation through clustering in multicellular populations

The coordinated development of multicellular organisms is driven by intercellular communication. Differentiation into diverse cell types is usually associated with the existence of distinct attractors of gene regulatory networks, but how these attractors emerge from cell-cell coupling is still an open question. In order to understand and characterize the mechanisms through which coexisting attractors arise in multicellular systems, here we systematically investigate the dynamical behavior of a population of synthetic genetic oscillators coupled by chemical means. Using bifurcation analysis and numerical simulations, we identify various attractors and attempt to deduce from these findings a way to predict the organized collective behavior of growing populations. Our results show that dynamical clustering is a generic property of multicellular systems. We argue that such clustering might provide a basis for functional differentiation and variability in biological systems.     

Histamine H1-Receptor in Heart: Unique Electrophoretic Mobility and Autoradiographic Localization

Histamine H1-receptors, visualized in the guinea pig heart by autoradiography using [125I]iodobolpyramine as a specific probe, are abundant in the nodal tissue and cardiac vessels but also occur heterogeneously in the myocardium. Following photoaffinity labeling with [125I]iodoazidophenpyramine and electrophoresis, the ligand binding domain of the heart H1-receptor was shown to be present on a major 68-kDa and a less abundant 54- to 58-kDa protein. The 68-kDa protein displayed a molecular size higher in heart than in all other tissues (56 kDa). This indicates the existence of at least two isoforms of the H1-receptor; the cardiac isoform, however, was pharmacologically indistinguishable from the common isoform studied in cerebellar membranes using available ligands. Its distinct electrophoretic properties suggest that the cardiac isoform may have a unique function.     

Adding insult to injury - Inflammation at the heart of cardiac fibrosis

The fibrotic response has evolutionary worked in tandem with the inflammatory response to facilitate healing following injury or tissue destruction as a result of pathogen clearance. However, excessive inflammation and fibrosis are key pathological drivers of organ tissue damage. Moreover, fibrosis can occur in several conditions associated with chronic inflammation that are not directly caused by overt tissue injury or infection. In the heart, in particular, fibrotic adverse cardiac remodeling is a key pathological driver of cardiac dysfunction in heart failure. Cardiac fibroblast activation and immune cell activation are two mechanistic domains necessary for fibrotic remodeling in the heart, and, independently, their contributions to cardiac fibrosis and cardiac inflammation have been studied and reviewed thoroughly. The interdependence of these two processes, and how their cellular components modulate each other's actions in response to different cardiac insults, is only recently emerging. Here, we review recent literature in cardiac fibrosis and inflammation and discuss the mechanisms involved in the fibrosis-inflammation axis in the context of specific cardiac stresses, such as myocardial ischemia, and in nonischemic heart conditions. We discuss how the search for anti-inflammatory and anti-fibrotic therapies, so far unsuccessful to date, needs to be based on our understanding of the interdependence of immune cell and fibroblast activities. We highlight that in addition to the extensively reviewed role of immune cells modulating fibroblast function, cardiac fibroblasts are central participants in inflammation that may acquire immune like cell functions. Lastly, we review the gut-heart axis as an example of a novel perspective that may contribute to our understanding of how immune and fibrotic modulation may be indirectly modulated as a potential area for therapeutic research.     

Sensitively recorded breathing signals of rats and their nonlinear dynamics

Nonlinear dynamical properties of sensitively recorded breathing signals (SRBS), which include cardiac induced air flow pulsations so-called pneumocardiogram (PNCG) signals, are investigated, in this methodological study. For this purpose, we assessed the SRBS of laboratory rat. The nonlinear behaviors of SRBS were investigated by the reconstructing phase space, using the autocorrelation function and the false nearest neighbor method. The chaotic SRBS attractors were discussed from the point of view of the cardiopulmonary system. This method can be used to assess the heart performance and respiratory mechanics, and might be useful to design for the physiological studies of cardiorespiratory system in small laboratory animals.     

Sensitively recorded breathing signals of rats and their nonlinear dynamics

Nonlinear dynamical properties of sensitively recorded breathing signals (SRBS), which include cardiac induced air flow pulsations so-called pneumocardiogram (PNCG) signals, are investigated, in this methodological study. For this purpose, we assessed the SRBS of laboratory rat. The nonlinear behaviors of SRBS were investigated by the reconstructing phase space, using the autocorrelation function and the false nearest neighbor method. The chaotic SRBS attractors were discussed from the point of view of the cardiopulmonary system. This method can be used to assess the heart performance and respiratory mechanics, and might be useful to design for the physiological studies of cardiorespiratory system in small laboratory animals.     

The role of neuregulin/ErbB2/ErbB4 signaling in the heart with special focus on effects on cardiomyocyte proliferation

The signaling complex consisting of the growth factor neuregulin-1 (NRG1) and its tyrosine kinase receptors ErbB2 and ErbB4 has a critical role in cardiac development and homeostasis of the structure and function of the adult heart. Recent research results suggest that targeting this signaling complex may provide a viable strategy for treating heart failure. Clinical trials are currently evaluating the effectiveness and safety of intravenous administration of recombinant NRG1 formulations in heart failure patients. Endogenous as well as administered NRG1 has multiple possible activities in the adult heart, but how these are related is unknown. It has recently been demonstrated that NRG1 administration can stimulate proliferation of cardiomyocytes, which may contribute to repair failing hearts. This review summarizes the current knowledge of how NRG1 and its receptors control cardiac physiology and biology, with special emphasis on its role in cardiomyocyte proliferation during myocardial growth and regeneration.