Ultrastructure and cardiac impulse scaling up from microscopic to macroscopic conduction

Authors: Zhilin Qu, Peter Hanna, Olujimi A. Ajijola, Alan Garfinkel, Kalyanam Shivkumar

Abstract

The standard conception of cardiac conduction is based on the cable theory of nerve conduction, which treats cardiac tissue as a continuous syncytium described by the Hodgkin–Huxley equations. However, cardiac tissue is composed of discretized cells with microscopic and macroscopic heterogeneities and discontinuities, such as subcellular localizations of sodium channels and connexins. In addition to this, there are heterogeneities in the distribution of sympathetic and parasympathetic nerves, which powerfully regulate impulse propagation. In the continuous models, the ultrastructural details, i.e. the microscopic heterogeneities and discontinuities, are ignored by ‘coarse graining’ or ‘smoothing’. However, these ultrastructural components may play crucial roles in cardiac conduction and arrhythmogenesis, particularly in disease states. We discuss the current progress of modelling the effects of ultrastructural components on electrical conduction, the issues and challenges faced by the cardiac modelling community, and how to scale up conduction properties at the subcellular (microscopic) scale to the tissue and whole‐heart (macroscopic) scale in future modelling and experimental studies, i.e. how to link the ultrastructure at different scales to impulse conduction and arrhythmogenesis in the heart.

Introduction

Cardiac contraction is originated by electrical impulses generated from the sinoatrial node, which conduct to the atria, atrioventricular node, the His‐Purkinje system and, finally, the ventricles. Current theories of cardiac conduction are based mainly on the continuous cable model of nerve conduction developed by Hodgkin and Huxley (1952). The Hodgkin–Huxley equations were modified or extended to describe ionic currents and action potential dynamics in single cardiac cells, impulse conduction in a one‐dimensional (1D) cable, two‐dimensional (2D) and three‐dimensional (3D) tissue, as well as anatomically based whole‐heart models (Qu et al., 2014). Mechanistic insights and theories derived from the continuous models have been used to explain experimental and clinical observations, which have greatly improved our understanding of cardiac conduction in general.

However, cardiac tissue is composed of discretized cells that are coupled electrically, and the continuous models may not describe the conduction dynamics properly, particularly under disease conditions. In the continuous cable theory, cardiac tissue is treated as a syncytium, ignoring the subcellular localizations of ion channels and ultrastructures at the cellular and tissue scales. Computational models incorporating detailed discretized structural information have been developed to investigate their effects on cardiac conduction. In this article, we discuss current progress and the issues or challenges faced by the cardiac modelling community to scale up the conduction properties at the subcellular (microscopic) scale to the tissue and whole‐heart (macroscopic) scale, i.e. how to link the emerging data on ultrastructure at different scales to impulse conduction and arrhythmogenesis in the heart.

Ultrastructure in the heart

Cardiac myocytes are elongated cells with irregularly varying shapes and sizes (Fig. 1A ). Myocytes in cardiac muscle form an irregular myocyte network in which a myocyte is connected to a number of others. For example, in normal canine ventricular tissue, one myocyte is connected on average to 11 other myocytes (Hoyt et al., 1989; Peters & Wit, 1998). Myocytes are electrically and mechanically coupled via connections at the intercalated discs (IDs) (Leo‐Macías et al., 2015; Nielsen et al., 2023). The IDs are located at the cell ends, which contain three types of adherens, desmosomes and gap junctions (Fig. 1B ). Adherens and desmosomes provide strong myocyte adhesion to resist shearing force during contraction and mechanical coupling for mechanical energy transmission. Gap junctions facilitate electrical coupling for electrical impulse conduction. Gap junctions are hemichannels composed of connexin (Cx) proteins (Desplantez et al., 2007). The known connexins expressed in the heart are Cx43, Cx40 and Cx45. Ventricular tissue mainly expresses Cx43; atrial tissue expresses both Cx43 and Cx40. Cx45 can be detected in both the ventricular and atrial myocardium at very low levels. In normal adult hearts, gap junctions mainly localize in the IDs at the cell ends with a small portion laterally (Fig. 1C ). Under disease conditions, such as in heart failure and ischaemia, or in young and aged hearts, lateral Cx43 is more abundant, a phenomenon referred to as Cx43 lateralization (Hesketh et al., 2010; Martins‐Marques et al., 2020; Saffitz et al., 2007; Severs et al., 2008; Vreeker et al., 2014). Besides its role in forming gap junctions, Cx43 also exhibits non‐gap junction functions (Leo‐Macias, Agullo‐Pascual, Delmar, 2016; Rhett et al., 2011), such as regulating ionic currents. For example, the sodium (Na^+^) current I Na becomes smaller in Cx43‐deficient myocytes (Jansen et al., 2012).

Besides Cx43 subcellular localization, ion channels are also distributed heterogeneously within a myocyte. For example, the cardiac isoform of the Na^+^ channel (Nav1.5) is more densely expressed in the IDs than in the lateral sarcolemmal (SL) membrane (Lin et al., 2011; Vreeker et al., 2014). This is consistent with the observation that Nav1.5 colocalizes with Cx43 (Fig. 1D ) and adherens (Leo‐Macias, Agullo‐Pascual, Sanchez‐Alonso, et al., 2016; Maier et al., 2004; Raisch et al., 2018). Furthermore, the kinetics of Na^+^ channels in the IDs are different from those in the lateral SL membrane, the steady‐state activation curve shifts to more negative voltages, and the steady‐state inactivation curve shifts to more positive voltage (Lin et al., 2011; Weinberg, 2023). In addition to the heterogeneous distribution within the SL, Nav1.5 and other ion channels also distribute differently between the SL and T‐tubular membranes. T‐tubules are subcellular structures in atrial and ventricular myocytes, invaginations of the sarcolemma membrane that form a T‐tubular network inside the cell (Brandenburg et al., 2016; Soeller & Cannell, 1999; Song et al., 2006, 2018). In normal ventricular myocytes, there is a well‐organized T‐tubular network (Fig. 2A ), whose membrane accounts for 21–64% of the total membrane of the myocyte, based on different studies (Hong & Shaw, 2017). Under disease conditions, such as heart failure (Guo et al., 2013; Lyon et al., 2009; Sachse et al., 2012; Song et al., 2006), the T‐tubular system is disrupted, resulting in a less dense and more irregular T‐tubular network (Fig. 2B ). Remodelling of the T‐tubular system alters not only excitation–contraction (E–C) coupling dynamics (Nivala et al., 2015) but also the excitation itself (Fig. 2C ) (Sacconi et al., 2012). In atrial myocytes, the T‐tubular networks are usually much less dense and very heterogeneous between regions in the same heart (Arora et al., 2017; Frisk et al., 2014; Glukhov et al., 2015; Kirk et al., 2003) and between species (Richards et al., 2011). Purkinje fibre cells are largely free of T‐tubules (Boyden et al., 1989; di Maio et al., 2007; Legato, 1973). T‐tubules are also largely absent in myocytes in early development, in cultured myocytes and in stem‐cell derived cardiac myocytes (Brette & Orchard, 2003; Chen et al., 1995; Lieu et al., 2009; Lipp et al., 1996; Liu et al., 2009). Brette & Orchard (2007, 2006) performed quantitative analyses of ion channel distribution between the SL and the T‐tubular membrane in rat ventricular myocytes. They estimated that the T‐tubular membrane accounts for only 30% of the total membrane of a rat ventricular myocyte, but contains 80% of the calcium (Ca^2+^) and 63% of the Na^+^–Ca^2+^ exchange currents. Nav1.5 is slightly denser in the SL than in the T‐tubular membrane. Besides the cardiac isoform (Nav1.5), ventricular myocytes also contain three neural isoforms of the Na^+^ channel (Nav1.1, Nav1.3 and Nav1.6) (Brette & Orchard, 2006; Kaufmann et al., 2013; Maier et al., 2004, 2002), which are predominantly found in the T‐tubules. The neural isoforms account for roughly a quarter of the Na^+^ channels in the T‐tubules and 10% of the Na^+^ channels of the whole cell. The subcellular Nav1.5 channel distribution also changes under disease conditions (Petitprez et al., 2011; Rivaud et al., 2017).

Cardiac myocytes are coupled mechanically through the IDs that are mainly located at the cell ends, and thus they align in certain ways (Fig. 1A ) to form myocyte fibres that optimize contractile function. The fibre directions rotate in the heart transmurally and from apex to base (Nielsen et al., 1991; Scollan et al., 2000; Streeter et al., 1969). In many tissue or whole‐heart simulations incorporating fibre structures (Liu et al., 2019; Trayanova, 2011; Xie et al., 2004), continuous tissue models are used. However, the myocyte fibres form sheets and bundles with discontinuous or laminar structures (Fig. 2A ), which cause discontinuous conduction in the heart and can also impact defibrillation (Hooks et al., 2002, 2007).

The conduction of electrical impulses from the atrioventricular node to the ventricles is via the His‐Purkinje fibre network (Fig. 2B ), a complex structure (Atkinson et al., 2011; Liu & Cherry, 2015) that facilitates synchronous excitation and contraction of the ventricles. A key issue is the coupling of Purkinje fibre cells with ventricular they need to be coupled in a way that maintains the fast conduction in the Purkinje fibre network but overcomes the source–sink effect to activate the ventricles. While ventricular myocytes and the Purkinje network constitute the necessary components for the working ventricles, there are other types of cells that play non‐trivial roles in cardiac E–C coupling and arrhythmogenesis, such as neural cells (Fukuda et al., 2015; Kawano et al., 2003). The neural cells or nerve fibres exhibit a dense distribution, intermingled with myocytes in the heart (Fig. 2C ) (Zhu et al., 2022). Moreover, nerve fibres may send processes through the myocyte, i.e. a nerve fibre may penetrate the cell membrane to locate inside the cell (Fig. 2D ). Under disease conditions, neural remodelling results in more heterogeneous nerve fibre distributions (Ajijola et al., 2013; Cao et al., 2000; Chang et al., 2001; Dajani et al., 2023). Fibroblasts are another type of cell that can exhibit non‐trivial electrophysiological effects in the heart (Camelliti et al., 2005; Wang et al., 2023; Xie et al., 2009), which can become more prominent in cardiac diseases, such as ischaemia.

Subcellular action potential conduction

In the continuous cable theory models, the subcellular and cellular ultrastructural details are ignored by ‘coarse graining’ or ‘smoothing’. In computer simulations, the continuous models are discretized into coupled ‘computational cells’, either uniformly or in the form of brick walls (Hubbard et al., 2007; Xie et al., 2009). The membrane potential in a ‘computational cell’ is uniform without subcellular heterogeneities. However, the structural heterogeneities at the subcellular scale can still be important for conduction at the tissue scale. For example, due to the heterogeneities in the T‐tubular network, depolarizations of the T‐tubular membrane and SL membrane may not be synchronous, as shown in optical mapping experiments (Fig. 3C ). Therefore, the T‐tubular network affects not only E–C coupling but also electrical conduction at the subcellular scale, which eventually affects conduction at the tissue and organ scales. Besides T‐tubules, there are other intracellular structural heterogeneities that may impact E–C coupling and action potential conduction. However, even without the subcellular heterogeneities, heterogeneous localization of Cx43 can result in complex subcellular action potential conduction (Fig. 4), as demonstrated in computer models by Spach & Heidlage (1995) and Spach et al. (2000).

The perinexus, ephaptic coupling and beyond

The ID is the specialized structure coupling cardiac myocytes mechanically and electrically, and is a highly complex structure (Hoyt et al., 1989; Leo‐Macías et al., 2015; Leo‐Macias, Agullo‐Pascual, Sanchez‐Alonso, et al., 2016; Pinali et al., 2015; Vanslembrouck et al., 2020; Zhang et al., 1996). Namely, the ID exhibits a tortuous and plicate structure (Fig. 5A ) which contains gap junctions, adherens and desmosomes (Fig. 5B ). In the gap junction regions (Figs 1B and 5B ), the cell membranes are closely positioned (∼2 nm) to allow formation of the gap junctions. Close to the gap junction region, the adjacent cell membranes have larger separations, ranging from 2 to 100 nm, where adherens and desmosomes are located. The region in close proximity to the gap junction region is called the perinexus (Fig. 5C ), a term coined by Rhett and colleagues (Gourdie, 2019; Rhett and Gourdie, 2012; Rhett et al., 2013). High‐resolution imaging showed that Nav1.5 in this region is colocalizing with other proteins, such as Cx43 and adhesion proteins (Leo‐Macias, Agullo‐Pascual, Sanchez‐Alonso, et al., 2016; Rhett et al., 2012; Veeraraghavan et al., 2015).

While gap junction coupling for myocyte‐to‐myocyte conduction has been the mainstream theory for cardiac conduction, an alternative theory, called ephaptic coupling, has been in existence for decades, first proposed by Sperelakis and Mann in 1977 (Sperelakis, 2002; Sperelakis & Mann, 1977). In this theory, a direct current flow from one myocyte to another, as in the case of gap junction coupling, is not required, but rather, conduction occurs via the change of the electrical field between the cells during depolarization. That is, the depolarization of one myocyte alters the electrical field or potential in the cleft, which then changes the transmembrane potential of the adjacent myocyte, causing it to depolarize (Fig. 4A ). Specifically, opening of the Na^+^ channel during depolarization of one myocyte (Cell 1) causes Na^+^ ions to enter the myocyte from the cleft space, lowering the potential of the cleft space (from ϕc=0 to ϕc<0). A lower potential of the cleft space then causes an increase in transmembrane potential (Vm2=ϕi2−ϕc) of the other cell (Cell 2). Once Vm2 reaches the Na^+^ channel activation threshold, the Na^+^ channels in Cell 2 open to depolarize the cell, resulting in conduction from Cell 1 to Cell 2. According to computer modelling studies (Kucera et al., 2002; Lin & Keener, 2010), for ephaptic coupling to occur, it requires sufficiently many Na^+^ channels in the cleft membrane and a proper volume of the cleft space (or distance between the two cells). The perinexus is the physical entity that can satisfy the volume requirement and the presence of enough Na^+^ channels.

Ephaptic coupling has been demonstrated in many modelling studies (Greer‐Short et al., 2017; Hichri et al., 2018; Ivanovic & Kucera, 2021, 2002, 2022; Lin & Keener, 2010; Ly & Weinberg, 2022; Moise et al., 2021; Mori et al., 2008; Wang et al., 2023; Wei & Tolkacheva, 2020; Weinberg, 2023). Although a direct experimental demonstration is still not available, indirect experimental evidence has been shown under different conditions, mainly by Poelzing and colleagues (Adams et al., 2023; Blair et al., 2024; George et al., 2016; Raisch et al., 2018; Veeraraghavan et al., 2015, 2016). In these experimental studies, the main experimental approach is to alter the volume of the perinexus using chemical agents to observe their effects on conduction velocities.

Besides its roles in ephaptic coupling, the perinexus may also play important roles in repolarization under gap junction coupling. For example, the depletion of Na^+^ in the cleft affects the driving force of I Na, which can affect the late component of I Na and thus the late I Na‐related repolarization properties (Greer‐Short et al., 2017; Nowak et al., 2020, 2021; Wu et al., 2021).

Scaling up microscopic conduction to macroscopic problems and challenges

Numerical methods using either finite differences or finite element methods are used in computer simulations of continuous tissue models. In the finite difference methods, cells are discretized into coupled ‘computational cells’, either uniformly or in the form of rectangular brick walls (Hubbard et al., 2007; Xie et al., 2004, 2009). In the finite element methods, they are discretized into ‘elements’ with irregular geometries and sizes based on the shape and boundary of the tissue (Nielsen et al., 1991; Rogers & McCulloch, 1994; Sack et al., 2018; Vigmond et al., 2002). In these approaches, the discretized tissue does not resemble how the cells are arranged in actual tissue (Fig. 1A ), and to facilitate large‐scale simulations, the computational cells or elements are usually much larger than the actual myocytes. While the advantage of the continuous models is to allow large‐scale computer simulations and facilitate theory development, ignoring the ultrastructural details may impact the prediction power of the models or even give rise to incorrect predictions, particularly in disease conditions where ultrastructural remodelling may become non‐trivial for cardiac conduction and arrhythmogenesis.

On the other hand, discretized tissue models consisting of myocytes with realistic geometries and sizes have been developed (Hubbard & Henriquez, 2012; Hubbard et al., 2007; Spach & Heidlage, 1995; Spach et al., 2000). While one can implement the microscopic/ultrastructural details into this type of model [for example, Jæger et al. (2023) used very high spatial (0.5 nm) and temporal (0.02 ns) resolutions with ultrastructural details to simulate a two‐cell system], this also causes problems and challenges in modelling and simulations for large‐tissue or whole‐organ simulations that are needed for investigating cardiac conduction and arrhythmogenesis. In other words, it is computationally challenging to scale up the conduction behaviours at the microscopic (subcellular and small tissue size) to macroscopic (large tissue and whole‐heart) levels. Here we briefly discuss the problems and challenges, and what needs to be done in the future.

As shown in many simulation studies, heterogeneous subcellular localizations of Cx43 and Nav1.5 play important roles in conduction in both gap junction and ephaptic coupling. Although T‐tubules have been phenomenologically modelled in many computer models, few modelling studies have been carried out to investigate how T‐tubular structure affects intracellular action potential depolarization and conduction (Vermij et al., 2019). It is well known that altered T‐tubular network structure affects intracellular Ca^2+^ release, yet how it affects action potential conduction is less known. Experimental evidence showed that the T‐tubular network may play an important role in action potential conduction (Fig. 3C ). In real cardiac tissue, myocytes are not arranged as bricks in a brick wall, but in a much more complex and irregular manner (Fig. 1A ). As shown in computer simulations, heterogeneous Cx43 localization alone combined with irregular arrangements of myocytes can result in complex intracellular conduction patterns (Fig. 4). Therefore, one can imagine the following conduction scenarios by considering the subcellular heterogeneities of Cx43, Na^+^ channel and T‐tubular network (Fig. 6): Under normal conditions (Fig. 6A ), Cx43 is mainly distributed at the cell ends and Nav1.5 density is higher at the cell ends. When one myocyte (the red one) depolarizes, it causes depolarization of the two adjacent cells (following the red arrows) through the end‐to‐end connection with either gap junction coupling or ephaptic coupling. These two cells then cause depolarization of the cell above the red cell, resulting in action potential conduction toward the cell centre from the two ends. This process continues, resulting in regenerative conduction in tissue. Although the cells are only coupled end‐to‐end (longitudinally), due to the manner of cell connection, an effective transverse conduction is realized. In this case, the anisotropic ratio is mainly determined by the geometry of the cell arrangement.Under diseased conditions (Fig. 6B ), such as heart failure, T‐tubule density is reduced and Cx43 localization is remodelled. As a consequence, the action potential may not be able to conduct throughout the cell (dashed arrows) but can still conduct from cell to cell (the solid red arrows). Failure of intracellular action potential conduction may attenuate Ca^2+^ release and thus contraction, but electrical conduction can still succeed in the tissue.

Under both scenarios, conduction is impacted by the volume of the cleft or perinexus. In the absence of gap junction coupling (i.e. ephaptic coupling only), conduction fails when this volume is either too small or too large. In the presence of gap junction coupling, conduction is affected by the cleft volume when it is small. This is because activation of the Na^+^ channel lowers the Na^+^ concentration in the cleft space, which lowers the driving force of I Na to weaken conduction. When the cleft volume is sufficiently large, the change of Na^+^ concentration becomes negligible and thus does not affect the gap junction‐mediated conduction. Besides Na^+^, change in K^+^ in the cleft may affect the driving force of K^+^ currents which may also impact depolarization and repolarization. Besides the volume of the cleft space, whether the extracellular volume of the T‐tubules has a role in depolarization or repolarization is unknown. Experiments have shown that the luminal diameter of T‐tubules ranges from 20 to 450 nm (Hong & Shaw, 2017). In general, it is not clear whether the ion concentrations in the extracellular space change during the action potential, particularly in fibrotic tissue, where the extracellular volume is reduced. Another largely ignored structural detail in cardiac tissue modelling is neuro‐myocyte interactions. Although the neural effects are modelled via β‐adrenergic, cholinergic and other signalling pathways, no computer modelling studies have been carried out to simulate the structural details of neuro‐myocyte interactions, such as neuromuscular junctions (Franzoso et al., 2022; Zaglia & Mongillo, 2017).

Cardiac conduction and arrhythmias are tissue‐scale phenomena, which cannot be fully understood using single cells or small tissue models of a few coupled cells. A reasonable tissue size and geometry are needed to reveal the tissue‐scale phenomena, such as re‐entry. It is computationally feasible to include the subcellular heterogeneities in a single cell or a small tissue model of coupled cells, but this may be computationally challenging, if not impossible, for large‐tissue or whole‐organ simulations. However, genetic changes or therapeutic targets are at the molecular scales, yet the molecular effects or readouts on medical consequences are at the organ and systems scales (such as ECG) or at the population scale (such as epidemiology of diseases) (Fig. 7). While continuous models are computationally more tractable, a molecular‐level change may result in changes in heterogeneities at the microscopic (cellular and subcellular) scales that cannot be ignored as in continuous models via coarse graining or smoothing. Multiscale modelling approaches need to be developed and employed for such complex medical problems (Qu et al., 2011, 2022). More importantly, different scales of experimental observations are needed to provide data and validations for multiscale modelling.

Synopsis

Cardiac conduction, E–C coupling and arrhythmias are tissue‐ and organ‐scale phenomena that may not be correctly or accurately described by the continuous models that have been used widely by the modelling community thus far. The continuous models have ignored the microscopic (subcellular and cellular) structural details via coarse graining or smoothing, and thus discretized models taking into account the microscopic details from recent experimental advances are now needed. However, this is not computationally tractable at the organ and systems levels and therefore novel computational approaches need to be developed. More importantly, different scales of experimental data and observations are needed to provide data and validations for multiscale modelling.

Additional information

Competing interests

None declared.

Author contributions

Z.Q. drafted the manuscript. All authors participated in the original design of the project and the writing and revision of the manuscript. All authors approved the final version of the manuscript and confirm that all persons designated as authors qualify for authorship, and all those who qualify for authorship are listed.

Funding

This work was supported by NIH grants P01 HL164311 and R01 HL175074 and the Leducq International Network of Excellence Program Award.

Supporting information