Arrhythmia Mechanisms and Calcium Handling

The intracellular Ca2+ handling system is responsible for linking the electrical and mechanical systems of the heart. However, there are potential consequences of the complexities of the system required to maintain this function which can promote arrhythmia - conditions where the normal rhythm of the heart is interrupted and cardiac output (the amount of blood pumped by the heart) is reduced. The links between the Ca2+ handling and electrical systems underlies this potentially dangerous behaviour, but the precise mechanisms of the emergence of pro-arrhythmic dynamics in the coupling of these systems is poorly understood. My research uses computational models to study these mechanisms from the sub-cellular to the whole heart scale.

Pro-arrhythmic Ca2+ dynamics

Excitation-contraction coupling in cardiac cells relies on complex spatio-temporal dynamics, dependent on both protein function and cellular structure. This system will be briefly described here. We must first cover the concept of the Action Potential and its relation to the intracellular Ca2+ handling cycle. We will then look at two types of abnormal behaviour which have been linked to arrhythmia: spontaneous Ca2+ waves and Ca2+ transient alternans.


Concept: The Action Potential

Cardiac cells are encased by a cell membrane. Differences in the concentration of charged particles (called ions) inside and outside the cell result in a membrane potential - a difference in electric potential across the membrane. The Action Potential refers to the change in this membrane potential during excitation, illustrated below.

Animation: The Action Potential. Left panel shows a schematic of a cell with different types of ion and the channels which allow them to pass (coloured circles and channels), and the right panel shows the membrane potential at different stages of the Action Potential.

Ions can cross the cell membrane through specialised proteins (called ion channels), which can open or close to allow or prevent the passage of ions.

As ions flow through these ion channels, the movement of charge creates ionic currents which can change the membrane potential. Because the opening and closing of ion channels can also be controlled by the membrane potential, the currents can be coordinated to create the shape of the Action Potential.

There are multiple types of ion channel, each associated with specific ions (sodium, potassium, calcium and others).

"Inward" currents are those where positive charge enters the cell (yellow and red in the animation) - they make the membrane potential more positive, which we call “depolarisation”: Larger inward currents generally mean greater excitability and longer durations of the Action Potential.

"Outward" currents are those where positive charge leaves the cell (blue in the animation) – they make the membrane potential more negative, which we call "repolarisation": Larger outward currents generally mean lower excitability and shorter duration.

The balance of multiple different currents, controlled by the expression (amount of) each type of ion channel, can therefore control Action Potentials with different shapes and properties to match the varying requirements of cardiac function in different animals and under different conditions (e.g. rest versus exercise).



Concept: The intracellular Ca2+ handling cycle

The intracellular Ca2+ handling cycle is what couples the electrical and mechanical functions of a cell. Associated with each given cellular excitation (the Action Potential) is the intracellular Ca2+ transient (orange trace in the animation below), where the mechanical force follows this profile (with a delay). In order to maintain reproducible Ca2+ transients on every beat, cardiac cells require a sophisticated and regulated system to control the dynamics of the intracellular Ca2+ concentration. In broad terms, the system is determined by a process referred to as "calcium-induced-calcium-release" (described and illustrated below).

Animation: The intracellular Ca2+ handling cycle. Left panel shows a schematic of the cellular components involved in Ca2+ handling: the surface membrane and T-tubules (TT); the intracellular Ca2+ store called the Sarcoplasmic Reticulum (SR; blue-green); the contractile proteins (myofilaments); the Ca2+ carrying flux channels responsible for the initial influx (red), intracellular Ca2+ release (blue), SR refilling (yellow) and Ca2+ extrusion (green). Arrows indicate the timing and direction of fluxes. Green areas indicate high Ca2+ concentration. The right panel shows the Action Potential (blue) and whole-cell Ca2+ transient (orange) at each phase.

The Intracellular Ca2+ handling cycle:

  1. Influx: Ca2+ ions enter the cell during the AP, through openings of channels in the cell membrane which are primarily selectively permeable to Ca2+ ions (these are represented by the red channel in the illustration above and AP illustration previous).
  2. Release: Local elevation of Ca2+ concentration promotes binding with Ca2+-release channels (blue channels in the animation) on the surface of the intracellular Ca2+ store, the "SR"; these channels open, releasing a larger amount of Ca2+ from the store into the bulk intracellular space.
  3. Diffusion: This Ca2+ then propagates throughout the cell, filling the volume of the intracellular space.
  4. Contraction: This global elevation of Ca2+ concentration promotes binding with contractile proteins, called myofilaments, which hinge together to cause cellular contraction.
  5. Relaxation: During relaxation, Ca2+ is released from its binding sites with the myofilaments.
  6. And the resting levels of Ca2+ are restored through energy dependent ion-pumps which refill the intracellular Ca2+ store (yellow channels) and remove Ca2+ into the extracellular space (green channels).
All of these various fluxes must balance in order to maintain homeostasis; imbalance in these fluxes as well as degradation of the various protein function can result in failed coupling between the electrical and mechanical function and/or pro-arrhythmic behaviour (abnormal cellular dynamics which promote a loss of the regular rhythm of the heart).



Concept: Spontaneous Ca2+ waves

Individual ion channels are described by “stochastic dynamics”, that is, they are governed by probabilistic random state transitions (referring to the channel changing its form, for example, to allow or prevent the passage of ions). At the whole-cell scale, the thousands of channels present in the cell average out to give predictable and well-maintained deterministic behaviour. However, at the individual channel scale, no such averaging exists.

The Ca2+ system of cardiac cells contains a feedback mechanism which can amplify the effect of these probabilistic channel transitions: recall from the above description of the intracellular Ca2+ handling system that the release channels (red) are sensitive to Ca2+ while also releasing Ca2+ into the same volume to which they are sensitive. This has potentially disastrous consequences: random openings of single channels can elevate the local Ca2+ concentration sufficiently to trigger the opening of more channels and further release. This is what we call a Ca2+ “spark”.

Animation: Spontaneous calcium waves. The top panel shows an expanded schematic of the cellular Ca2+ handling system (as described previously). The bottom panel shows a simulation of a Ca2+ wave in the 3D volume of a cell. The right panels show the corresponding whole-cell averages for Ca2+ concentration (top; yellow), NCX current (middle; green) and membrane potential (bottom; red) at each stage of behaviour. What is shown are two non-propagating spontaneous Ca2+ sparks, followed by one which develops into a full-cell wave.

If the spark is sufficiently large, or appropriately timed relative to surrounding spontaneous sparks, then it can propagate throughout the cell as a wave. While this wave is propagating, the channels responsible for Ca2+ removal (green – “NCX”) are activated. These channels remove Ca2+ and result in a net inward current. Recall that inward currents act to increase the membrane potential. If the current is sufficiently large, this increase in membrane potential can trigger a full Action Potential, just as if the cell were stimulated. Spontaneous Action Potentials mean ones which are not activated by neighbouring excitation under normal conditions - they no longer are dependent on normal pacemaking for excitation. They can potentially lead to spontaneous excitations in tissue – the exact type of excitation which can trigger an arrhythmia event. Shown in the illustration is a spontaneous release which does not have sufficient amplitude to trigger a full Action Potential (which is more common than ones which do).


Concept: Ca2+ transient alternans

Ca2+ transient alternans refers to a dynamic behaviour in which the magnitude of the Ca2+ transient alternates on a beat-to-beat basis. This means that the contractile force developed by the cell also alternates on a beat-to-beat basis, between large and small contractions. This can interrupt the cardiac pumping function required by the body. Moreover, they can underlie Action Potential alternans – when the morphology and duration of the Action Potential alternates. If this is not synchronised between different regions of tissue, it can cause electrical conduction abnormalities which can lead to arrhythmia.

Whereas Ca2+ transient alternans are defined at the whole-cell scale (it is the magnitude of the whole-cell average which we are interested in), the behaviour is determined by spatial dynamics within the cell – each local cellular region either undergoes full or incomplete release (as a simplification), and it is the number of regions which undergo full release which determines the overall magnitude. Thus, Ca2+ transient alternans are characterised by spatial non-uniformity of the local concentration.

Figure: Example of Ca2+ transient alternans. The top panel shows the whole-cell average, whereas the bottom panel shows the underlying concentrations along the length of the cell.

Researching Pro-arrhythmic Calcium Dynamics

Multi-scale modelling of the intracellular Ca2+ handling system

Because the intracellular Ca2+ handling system depends on both channel dynamics and intracellular structure, sophisticated and accurate computational models of the system require consideration of both of these factors - "spatio-temporal" Ca2+ handling models. At these microscopic scales, random transitions of the channel proteins are a critical property of successful calcium-induced-calcium-release, and so the models must employ non-deterministic components (deterministic referring to equations which give the exact same answer with the same inputs) to reproduce these stochastic dynamics (referring to behaviour which depends on randomness, so the exact same answer is not given for repeated solutions using the same inputs).

These models allow mechanistic evaluation of the role of intracellular Ca2+ handling in both normal function and the emergence of pro-arrhythmogenic behaviour – alternans and Ca2+ waves. Models of different complexity can be developed for different purposes – highly detailed models at the sub-micron (that’s a millionth of a metre) resolution allow investigation of realistic structure-function relationships; more idealised lower resolution models allow large-scale simulations in theoretical parameter space.


Modelling alternans and waves at the detailed scale

Animation: Ca2+ transient alternans in a model cell with realistic structure. Only a portion of the cell is shown for clarity. Left panels show the intracellular (upper) and sarcoplasmic reticulum (lower) whole-cell average concentrations; right panels show the local concentration in the volume and a slice. Video and data from Colman et al. 2017 PLOS Comp. Biol

Using the detailed model of cellular Ca2+ handling described in the excitation-contraction Coupling section, the dynamics of both alternans and Ca2+ waves, and their dependence on sub-cellular structure, were investigated in this study.

The behaviour of alternans (video above) was shown to be heavily dependent on the specific cellular structure, wherein this structure reduced the phase variation on each beat - i.e., the regions which are activated on the small beat were less random using realistic structure (below).

Figure: Alternan dynamics in the cell models. Upper panels show the magnitude of Ca2+ transient alternans under different conditions. Lower panels show a comparison between realistic and idealised structure models, highlighting the differences in phase maps on successive low-amplitude beats between the two cases. Image and data from Colman et al. 2017 PLOS Comp. Biol

The model was also used to investigate the emergence and behaviour of Ca2+ waves, highlighting the complex nature of the local spatial gradients which emerge (video below).

Animation: Spontaneous Ca2+ wave in the structurally detailed cell model. Upper panel shows the whole-cell Ca2+ concentration; middle panel shows the Ca2+ concentration in the volume of the cell, with the colours scaled to the magnitude of the whole-cell average; lower panel shows the same but with the colours scaled to visualise the local gradients. Video and data from Colman et al. 2017 PLOS Comp. Biol


Modelling waves at the organ scale

Illustration of the scales involved in the different phenomena for which spontaneous Ca2+ release can manifest as arrhythmia. Left panel illustrates the local behaviour at the single-channel level and cell-structure which allows Ca2+ sparks to propagate; middle panel shows the cellular behaviour leading to spontaneous Action Potentials (“TA”); right panel shows the interaction of spontaneous focal excitation and tissue properties which can give rise to re-entry. The length-scales are illustrated, from the nanometre (billionth of a metre; 10-9) to the centimetre (10-2).

Whereas modelling these dynamics at the cellular scale can provide significant insight into their underlying mechanisms, arrhythmia cannot exist in single cells: it is, by definition, the loss of rhythm in the whole-heart. In order to understand their role in arrhythmia – for example, the emergence of spontaneous Ca2+ waves as spontaneous excitations in tissue (Figure and drescribed here) – we need to be able to implement these models in simulations of large-scale tissue. This presents a major research challenge: the models typically used for tissue simulations treat the cells as a “point-source”, that is, they consider only the whole-cell average behaviour; the models used to study spontaneous Ca2+ release must treat the cell as a spatial structure, and contain a hundred-thousand times more equations. We cannot practically simulate the thousands or millions of cells in tissue using these models – the range of scales is too large (Figure).

In these papers, a method was developed to incorporate spontaneous calcium release in point-source models which matched the behaviour and statistics of spatial cellular models, and could be determined dynamically from the model environment (Figure below). The approach used simple waveforms which represented the ion channel activity during spontaneous Ca2+ waves, whose shape could be easily determined either by user choice or from environmental model variables.

Illustration of the approaches to model spontaneous Ca2+ release in computationally efficient cell models. Panel A shows the structure of detailed spatial cell model (left) and the point-source non-spatial cell model (which considers the cell as a single volume). Panel B illustrates the use of analysing the statistics of the spatial cell model to define waveform functions which can be implemented in the non-spatial cell model.

Using this approach, the synchronisation of independent cellular spontaneous release leading to spontaneous focal excitation could be investigated (video), as well as its interaction with pharmacology and long-term interactions with re-entry.

Simulation of the emergence of focal excitation in tissue following spontaneous Ca2+ release in individual cells. Both panels show an idealised 2D sheet of cardiac muscle; the left shows the Ca2+ concentrations in individual cells, and right the membrane potential. The noise in the left panel is the independently timed spontaneous Ca2+ release, which coordinate through tissue coupling to lead to a focal excitation. Video and data from Colman 2019 PLOS Comp. Biol


Interaction with pharmacology

Pharmacological treatment of cardiac arrhythmias presents multiple challenges due to the complex interacting roles of multiple components: drugs which effectively inhibit some behaviour may have safety issues in promoting others. The interaction of pharmacology and spontaneous Ca2+ waves has been studied in sufficiently less detail than other Action Potential properties, and only through approaches like those developed here can we use simulations to study these impacts at both the cellular and tissue scales.

Figure: Cellular behaviour in control and long-QT conditions, with and without the application of a pharmacological agent (“MC-II-157c”). Shown is the probability of a spontaneous Ca2+ release resulting in a full triggered Action Potential, and the impact of the pharmacological agent. Image and data from Colman et al. 2017 Frontiers in Physiology.

This this study, we applied these approaches to study the simultaneous impact of a pharmacological agent on modulating both cellular and tissue dynamics associated with a class of conditions referred to as “long-QT syndromes” – situations where ventricular repolarisation is delayed and the QT interval of the ECG is prolonged (see here for description of the ECG).

We demonstrated that at the single cell scale, the prolonged repolarisation promoted spontaneous Ca2+ calcium release; the agent both shortened the Action Potential duration and inhibited the manifestation of full spontaneous Action Potentials following spontaneous Ca2+ release. In tissue, this manifested as the prevention of the emergence of focal excitation.

Figure: Emergence of a spontaneous focal excitation in the long QT syndrome condition, which is inhibited by the application of the pharmacological agent. Image and data from Colman et al. 2017 Frontiers in Physiology.


Coupling with re-entry

Whereas the coupling between focal excitation and re-entry has been well established in one direction – focal excitation can interact with tissue properties to degenerate into re-entry – the long-term interactions and potential feedback mechanisms are far less clear.

Animation: Re-entry followed by focal excitation in a 3D model of the human atria. Left panel shows the voltage, middle the intracellular Ca2+ and right the sarcoplasmic reticulum Ca2+ concentration. A few cycles of re-entry are shown, before the behaviour self-terminates; this is followed by multiple focal excitations, which are caused by the high sarcoplasmic reticulum Ca2+ load induced by the rapid re-entrant excitation. Video and data from Colman 2019 PLOS Comp. Biol

Using the novel approaches developed, it was demonstrated that a period of re-entrant excitation – which rapidly excites cardiac tissue – could promote changes in cellular environmental variables which can lead to the emergence of spontaneous Ca2+ events and focal excitations in tissue. These can continue to drive arrhythmia following successful termination of re-entry.

Moreover, the interacting mechanisms acted to localise the focal excitation to a specific property of re-entry – the core of the scroll wave. This could potentially lead to behaviour where rapid focal excitation could interact with the tail of the previous re-entry, and drive rapid arrhythmia through mechanisms which switch between the two. This may further enhance the difficulty of successful pharmacological modulation, as terminating arrhythmia under these two mechanisms has different requirements.

Figure: Co-localisation of re-entry and focal excitation. The top panels show the evolution of voltage and Ca2+ during the final re-entrant excitation and the first focal. Middle panel shows how these are localised dependant on the timing of the focal excitation. Bottom panel shows a simulation which involved mechanism switching between re-entrant and focal excitation. Image and data from Colman 2019 PLOS Comp. Biol

Related publications

[23] Colman MA "Arrhythmia Mechanisms and Spontaneous Calcium Release: Bi-directional Coupling Between Re-entrant and Focal Excitation" PLOS Comput Biol. 2019 Aug 8;15(8):e107260.

16] Colman MA , Perez Alday EA, Holden AV, Benson AP "Trigger vs. Substrate: Multi-Dimensional Modulation of QT-Prolongation Associated Arrhythmic Dynamics by a hERG Channel Activator" Front. Physiol. 2017

[15] Colman MA , Pinali C, Trafford AW, Zhang H, Kitmitto A. "A Computational Model of Spatio-Temporal Cardiac Intracellular Calcium Handling with Realistic Structure and Spatial Flux Distribution from Sarcoplasmic Reticulum and T-tubules Reconstructions" PLOS Comp. Bio. 13(8).e1005714, 2017

Colman MA, Parra-Rojas C, Perez Alday EA. “From Microscopic Calcium Sparks to the ECG: Model Reduction Approaches for Multi-Scale Cardiac Simulation” In Computing in Cardiology (CinC), 2015.