Using Stochastic Differential Equations to Model Gap-Junction Gating Dynamics in Cardiac Myocytes

The cell-to-cell propagation of the cardiac action potential allows for the electro-mechanical coupling of cells, which promotes the coordinated contraction of cardiac tissue, often referred to as the heartbeat. The main structures that promote electrical coupling between adjacent cardiac cells are pore-like proteins called gap junctions that line the membranes of such cells, allowing a channel for electrically charged ions to travel between cells. It is known that the conformational, and hence conducting, properties of gap-junction channels change as a function of local gap-junctional voltage and local ionic concentrations and are stochastic in nature. Many previous models of gap junctions have made a constant-resistance approximation or used an ODE model relating gating state to a local voltage. In this thesis, we extend a previous ODE model of gap-junction gating state by Henriquez et al. and formulate it as a system of stochastic differential equations (SDEs) by deriving the expected change vector and covariance matrix of the model and integrating the covariance with respect to a stochastic process, the Wiener Process. In doing so, we construct the first SDE-based model of gap-junction gating dynamics. This SDE description of the electrical coupling between cardiac cells is integrated into a 1D cable model where intracellular current dynamics are described using the Luo-Rudy 1 formulation. Monte Carlo simulations are performed on the resulting model in order to gather data used to construct distributions of several model responses of interest, including conduction block, conduction velocity, gap-junction current and gap-junction conductance. We find a smoothing effect occurs as the number of gap junctions considered increases, but at small numbers of gap junctions, such as those observed in many diseased states, stochastic effects can be pronounced. In such decoupled regimes, stochastic effects are found to have a large effect on the occurrence of conduction block, the cessation of action potential propagation at some tissue location, and are found to increase the variance in conduction velocity from cell to cell. The waiting time between when two consecutive gap junctions reach their maximum current was found to conform to a gamma distribution, with shape and scale parameters a function of the number of gap junctions. As the number of gap junctions increases, the spread of the waiting time distributions decreases. Gap-junctional conductance was modeled as a time-dependent Gaussian distribution, with a temporal variance decreasing as a function of the elapsed time after depolarization. In the case of conduction block, we show that an emulator function can be constructed to estimate the probability of occurrence, thereby reducing the need for a large number of computationally intensive Monte Carlo simulations. Along with probabilistically describing the stochastic gap- junction model, these distributions can be leveraged in larger-scale tissue-level simulations to incorporate stochastic gap-junction gating at a reduced computational cost

Multiscale Modeling of the Ventricles: From Cellular Electrophysiology to Body Surface Electrocardiograms

This work is focused on different aspects within the loop of multiscale modeling: On the cellular level, effects of adrenergic regulation and the Long-QT syndrome have been investigated. On the organ level, a model for the excitation conduction system was developed and the role of electrophysiological heterogeneities was analyzed. On the torso level a dynamic model of a deforming heart was created and the effects of tissue conductivities on the solution of the forward problem were evaluated

ATP-sensitive Potassium Channels and Cardiac Arrhythmia

PhDATP-sensitive potassium channels (KATP) open in response to metabolic challenge. They form of pore subunits (Kir6.1 or Kir6.2) and modulatory subunits (SUR1, SUR2A or SUR2B) and are ubiquitously expressed. Differential subunit composition between cardiac chambers was investigated, as were atrial anti-arrhythmic effects of KATP modulation. Selective pharmacology of KATP openers and inhibitors was confirmed in a heterologous expression system through whole-cell patch clamp. Isolated HL-1 cells (a murine atrial cardiomyocyte model) and murine atrial cardiomyocytes showed identical KATP pharmacological responses representing Kir6.2/SUR1 channels. Relative quantification of murine whole atrial RNA concurred, and was distinct from the ventricles (Kir6.2/SUR2). Human whole heart RNA from normal hearts exhibited a different pattern with no obvious chamber specificity. Kir6.1-/- and Kir6.2-/- mice demonstrated that both pore types contribute to electrophysiological parameters in isolated atrial cardiomyocytes, but Kir6.2 appears more important. In atrial tissue (Langendorff hearts), Kir6.2-/- more than Kir6.1-/- mice demonstrated increased effective refractory periods and reduced conduction velocity at baseline, and during hypoxia, compared to wildtype. A trend to reduced arrhythmogenicity was observed during programmed electrical stimulation in the Kir6.2-/- mouse. In syncytia of spontaneously beating HL-1 cells, KATP activation with diazoxide was met with rotational to uniform wavefront organisation and silencing of electrical activity in a dose-dependent manner, reversed with channel blockade. In Langendorff mouse hearts KATP inhibition reversed hypoxia induced slowing of spontaneous sinus node activation, but pharmacological activation alone did not, suggesting different mechanisms with hypoxic channel activation. Thus, both pore subunits contribute to the cardiac electrophysiology of murine atria, but Kir6.2 appears more important. HL-1 cells exhibit identical KATP pharmacology to murine atrial myocytes, which have a differential subunit composition compared to the ventricle. Any human cardiac KATP differential subunit expression needs further exploration. KATP activation and inhibition have anti-arrhythmic effects and this might be explored further clinically.Medical Research Council MR/L016230/1

Does the small conductance Ca2+-activated K+ current (ISK) flow under physiological conditions in rabbit and human atrial isolated cardiomyocytes?

Background: Small conductance Ca2+-activated K+ current (ISK) may change cardiac atrial action potentials (AP) in response to altered [Ca2+]i; a potential therapeutic target for treating atrial fibrillation (AF). However, the contribution of ISK to atrial APs under physiological conditions is unclear. Furthermore, ISK may be enhanced in ventricles by heart failure, but whether by [Ca2+]i elevation in the non-failing ventricle is unknown. Aims: To test whether ISK flows under normal or increased global Ca2+]i, or with sub-sarcolemmal [Ca2+]i increase from APs in human and rabbit atrial cells. Also, to test an ISK blocker, ICAGEN (ICA), on rabbit left ventricular (LV) ion currents under [Ca2+]i elevation from Na+/Ca2+-exchanger (INa/Ca) stimulation. Methods: Myocytes were isolated enzymatically from hearts removed from anaesthetised rabbits, and from atrial tissues from consenting patients undergoing cardiac surgery. Whole-cell patch clamp (37°C) was used to record ion currents and APs (at 1, 2 or 3Hz), with [Ca2+]i measured using Fura-2. Results: A positive control tested stability/timing of K+ current (IK1) block: Ba2+(0.5 mM) significantly and reversibly decreased inward IK1 (at-115 mV) in 94% of LV cells, from -38.9±5.9 to -12.9±4.5 pA/pF (by 67%), and in 92% of atrial cells, by 43% (P0.05) at any [Ca2+]i, in rabbit or human (5-26 cells, 7-11 rabbits, 3-4 patients). APs recorded at 1 Hz (rabbit) were prolonged by 4-AP (ITO blocker; positive control): action potential depolarization at 30% repolarization (APD30) by 72%, at 70% repolarization (APD70) by 31%. By contrast, ICA (1 µM) had no effect on APD30-90, maximum diastolic potential (MDP), or Vmax, in human or rabbit. ICA at 10 µM (non-specific) increased APD70-90 vs time-matched controls. At 2 or 3 Hz, 1 µM ICA again had no effect on APs. In rabbit LV cells, stimulating INa/Ca increased [Ca2+]i (up to 2.8 µM) and inward /outward currents. ICA (1 µM) had no effect on [Ca2+]i or currents, whereas subsequent NiCl2 (10 mM; INa/Ca blocker) decreased them. By contrast, ICA 10 µM decreased outward (by 35%) and inward (49%) current, and [Ca2+]i (77%), with no effect of subsequent NiCl2. Conclusions: In rabbit and human atrial isolated myocytes, ISK may not flow under physiological conditions, nor during short bursts of supra-physiological stimulation, so atrial ISK activation (and thus its potential pharmacological inhibition during AF) may require changes to cellular electrophysiology or cell signalling systems to develop a sensitivity to ISK iii block. Furthermore, in non-failing LV myocytes, 1 µM ICA-sensitive ISK may not be activated by [Ca2+]i-elevation, and high ICA conc. may inhibit INa/Ca

Remote refocusing light-sheet fluorescence microscopy for high-speed 2D and 3D imaging of calcium dynamics in cardiomyocytes

The high prevalence and poor prognosis of heart failure are two key drivers for research into cardiac electrophysiology and regeneration. Dyssynchrony in calcium release and loss of structural organization within individual cardiomyocytes (CM) has been linked to reduced contractile strength and arrhythmia. Correlating calcium dynamics and cell microstructure requires multidimensional imaging with high spatiotemporal resolution. In light-sheet fluorescence microscopy (LSFM), selective plane illumination enables fast optically sectioned imaging with lower phototoxicity, making it suitable for imaging subcellular dynamics. In this work, a custom remote refocusing LSFM system is applied to studying calcium dynamics in isolated CM, cardiac cell cultures and tissue slices. The spatial resolution of the LSFM system was modelled and experimentally characterized. Simulation of the illumination path in Zemax was used to estimate the light-sheet beam waist and confocal parameter. Automated MATLAB-based image analysis was used to quantify the optical sectioning and the 3D point spread function using Gaussian fitting of bead image intensity distributions. The results demonstrated improved and more uniform axial resolution and optical sectioning with the tighter focused beam used for axially swept light-sheet microscopy. High-speed dual-channel LSFM was used for 2D imaging of calcium dynamics in correlation with the t-tubule structure in left and right ventricle cardiomyocytes at 395 fps. The high spatio-temporal resolution enabled the characterization of calcium sparks. The use of para-nitro-blebbistatin (NBleb), a non-phototoxic, low fluorescence contraction uncoupler, allowed 2D-mapping of the spatial dyssynchrony of calcium transient development across the cell. Finally, aberration-free remote refocusing was used for high-speed volumetric imaging of calcium dynamics in human induced pluripotent stem-cell derived cardiomyocytes (hiPSC-CM) and their co-culture with adult-CM. 3D-imaging at up to 8 Hz demonstrated the synchronization of calcium transients in co-culture, with increased coupling with longer co-culture duration, uninhibited by motion uncoupling with NBleb.Open Acces

Analysis and applications of models of single-cell cardiac electrical excitation

For over a century, cardiac electrophysiology modelling has been widely used for studying various problems of normal or abnormal heart rhythm, which is essential for understanding the disease mechanisms, provide accurate diagnoses and develop a new treatment. This thesis focuses on several analysis and applications of models in single-cell cardiac electrical excitation. In particular, I aim to study some typical challenges present in cardiac electrophysiology modelling, which is, variability in action potentials (AP) and their effects on cardiac anti-arrhythmic drugs, mechanisms of cardiac alternans and efficient numerical solver. To address the problems, I use various action potential models initially a range of biophysically detailed models, then focusing on a single simplified model. This thesis consists of two main parts, excluding the part for background and introductory materials. The first and most important part, in terms of effort and time spent, is devoted to the investigation of action potential variability in a population of rabbit ventricular myocytes and their effects on cardiac anti-arrhythmic drugs. To determine the distributions of ion channel conductance values that capture the electrophysiological heterogeneity measured in large populations of cells, I apply the experimentally-calibrated population of models introduced by Britton et al. (2013), constructing from randomly varied ion conductances combinations. The model population is further used to quantitatively predict the range of response to the application of hERG and L-type calcium channel blocks. I implement the methodologies on three different AP models to study the capability of the cell models in predicting the drug effects. The models are a rabbit AP model by Shannon et al. (2004) and two human AP models by Ten Tusscher et al. (2004) and O’Hara et al. (2011). The AP responses following channel blocks are compared and analysed. The second part of the thesis covers the analysis and application of a simplified ionic cardiac model. The model used is a modified version of caricature Noble model by Biktashev et al. (2008). Our first task is to propose the model as a generic model of cardiac electrophysiology by using a parameter estimation method. The model’s parameters are adjusted so that it can reproduce AP morphologies of various cell types. In particular, the model is fitted to three different AP models which are Purkinje model by Noble (1962), ventricular model by Luo and Rudy (1991) and atrial model by Courtemanche et al. (1998). The action potential duration restitution curve of targeted models are also reproduced. The similar model template now can be used for various regions of the heart by changing the parameter values. Furthermore, the modified caricature Noble model is fitted to experimental measurements of healthy and failing myocytes by McIntosh et al. (2000). I analyse the difference between parameter values from fitting works intending to find the physiological meaning for AP differences shown in experimental recordings. Parameter fitting of modified caricature Noble model demonstrates that it can replace other more complicated models, and it can also be used as a prototype to look for cardiac alternans and to construct an efficient numerical method. The modified caricature Noble model is further used to develop an efficient numerical method for simulation of cardiac action potential model by taking into account the asymptotic solutions of the system. In order to achieve this, I implement the heterogenous multiscale method proposed by Weinan and Engquist (2003). The proposed method exhibits better stability and efficiency compared to other numerical solvers. The drawbacks of the method are also explained. Finally, the application of the model is extended by utilising it to study the mechanisms of cardiac alternans. The objective is to determine parameters and variables in the model that are responsible for generating action potential duration alternans. Using the slow-slow-time system of the model, an explicit discrete restitution map is derived and their equilibrium branches and bifurcations are studied. The bifurcations of equilibria of these maps are studied to identify regions in the parameter space of the model where normal response and alternans exhibit. Also, using the full system of the model, a framework formulated in terms of a boundary value problem is developed, which can be used to construct various branches of the action potential duration restitution map. At the end of the work, I perform some numerical simulations by fitting the caricature Noble model to models of normal response and alternans. The differences in parameter values are analysed and used to understand the onset of alternans. Importantly, the result shows that the magnitude of time-dependent potassium current can induce or suppress alternans

In situ three-dimensional reconstruction of mouse heart sympathetic innervation by two-photon excitation fluorescence imaging

Background Sympathetic nerve wiring in the mammalian heart has remained largely unexplored. Resolving the wiring diagram of the cardiac sympathetic network would help establish the structural underpinnings of neurocardiac coupling. New Method We used two-photon excitation fluorescence microscopy, combined with a computer-assisted 3-D tracking algorithm, to map the local sympathetic circuits in living hearts from adult transgenic mice expressing enhanced green fluorescent protein (EGFP) in peripheral adrenergic neurons. Results Quantitative co-localization analyses confirmed that the intramyocardial EGFP distribution recapitulated the anatomy of the sympathetic arbor. In the left ventricular subepicardium of the uninjured heart, the sympathetic network was composed of multiple subarbors, exhibiting variable branching and looping topology. Axonal branches did not overlap with each other within their respective parental subarbor nor with neurites of annexed subarbors. The sympathetic network in the border zone of a 2-week-old myocardial infarction was characterized by substantive rewiring, which included spatially heterogeneous loss and gain of sympathetic fibers and formation of multiple, predominately nested, axon loops of widely variable circumference and geometry. Comparison with Existing Methods In contrast to mechanical tissue sectioning methods that may involve deformation of tissue and uncertainty in registration across sections, our approach preserves continuity of structure, which allows tracing of neurites over distances, and thus enables derivation of the three-dimensional and topological morphology of cardiac sympathetic nerves. Conclusions Our assay should be of general utility to unravel the mechanisms governing sympathetic axon spacing during development and disease

Functional heterogeneity of CPVT-mutant human cardiac ryanodine receptors: evaluation of the influence of S2031 and S2808 phosphorylation sites

Human cardiac ryanodine receptors (hRyR2) are calcium (Ca2+) release channels central to excitation-contraction coupling. Mutations in hRyR2 are linked to catecholaminergic polymorphic ventricular tachycardia (CPVT), a genetic disorder characterized by arrhythmia, occurring under adrenergic drive. Recent studies suggest gain-of-function mutant channels may undergo different mechanisms of dysfunction, with some showing altered Ca2+ release under basal conditions and others requiring an additional trigger (possibly in the form of β-adrenergic phosphorylation). This study evaluated whether mutants from different domains of hRyR2 (S2246L and N4104K) were functionally heterogeneous in a cellular setting and whether this was related to phosphorylation status. Cells (human embryonic kidney 293) expressing N4104K-hRyR2 displayed smaller, faster Ca2+ release events than those expressing the wild type (WT), while those of cells expressing S2246L-hRyR2 were similar to WT. However, a lower proportion of S2246L cells showed any kind of Ca2+ release functionality compared to those expressing WT or N4104K, reinforcing that these mutations cause different types of dysfunction. Assessment of phosphorylation status using site-specific antibodies for protein kinase A (PKA) target sites S2808 and S2031 showed that mutant phosphorylation levels were different to each other and to that of the WT, indicating a possible role of phosphorylation in this. Activation of PKA-mediated phosphorylation in cells using a cyclic AMP analogue resulted in changes to the kinetics of spontaneous Ca2+ release via WT hRyR2, but did not significantly affect that of mutants. Genetic phosphorylation at either PKA site (S2808D and S2031D) altered the Ca2+ release of mutants as well as WT hRyR2, but this was found to be due to changes in expression of sarco-endoplasmic reticulum Ca2+-ATPase (SERCa) pump, which also contributes to Ca2+ homeostasis. These findings reinforce the concept that phosphorylation is linked to dysfunction and contributes to our understanding of hRyR2 mutation in arrhythmia, highlighting that ‘gain-of-function’ does not necessarily equate to dysfunction via the same mechanism