Marching to the Beat of Calcium

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Calcium is one of the most important minerals found in our bodies and comprises approximately 1.5 to 2% of our body weight (1). Single-atom calcium ions are of the most versatile biological messengers known. Rapid, transient changes in calcium concentration directly control muscle contraction, cell locomotion, and neural transmission, among other things. Sustained, elevation of calcium signals is pivotal for numerous biological processes ranging from gene expression, to fertilization, to apoptosis or programmed cell death (2). Did you know that there is a functional linkage between intracellular calcium levels and cardiac arrhythmias? A better understanding of this relationship can very well lead to therapeutic prevention of life-threatening arrhythmias.

Dr. Saleet Jafri, a bioinformatics professor at George Mason University and a member of the Krasnow Institute of Advanced Study, has worked closely with faculty at GMU as well as at other universities. Their research efforts have culminated in the construction of a three-dimensional model simulation of the rat ventricular myocyte. The use of this stochastic model would allow them to make a connection between aberration in normal calcium homeostasis and how this can result in cardiac arrhythmias (3). In order to efficiently use this model, a numerical method was to be developed. Dr. Jafri and his team went on to develop the Ultrafast Monte Carlo Method, which was used to calculate the open probability of ryanodine receptors and the occurrence of a calcium leak. This GPU-enabled method is less expensive and more computationally efficient than other methods previously used for stochastic stimulations. The Ultrafast Monte Carlo Method employs the use of the Euler method, which is important for solving differential equations. By building this model, Dr. Jafri and his team attempt to answer fundamental questions regarding the mechanisms underlying arrhythmias that could not be answered with previous modeling efforts (2).

Process of excitation-contraction coupling in the cardiomyocte.
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Dr. Jafri clearly stressed the importance of understanding calcium dynamics and the mechanisms underlying it prior to understanding arrhythmias. Calcium acts as a signaling molecule in the excitation-contraction coupling of cardiac muscle. This physiological process relies predominantly on a mechanism known as calcium-induced calcium release (CICR). Central to this process are the calcium release units (CRUs). CRUs, consisting of t-tubules of cardiac muscle and the sarcoplasmic reticulum (SR) contain ryanodine receptors (RyRs) that, after detecting an influx of calcium, activate and result in the release of calcium from the SR to the cytoplasm (4). The release of calcium from the SR by activation of RyRs is triggered by the opening of L-type calcium channels or by the stochastic opening of a single RyR. These synchronized stochastic openings are referred to as calcium sparks (4).

Calcium sparks are the elementary release events that sum to produce a calcium transient, which is a term used to describe the increase in cytosolic calcium. Calcium sparks are visualized using confocal microscopy techniques. With regards to the termination of calcium release, many different elements come into play. According to Dr. Jafri, calcium sparks terminate because of the influence of three specific factors on RyRs gating: a large number of RyRs, coupled gating of RyRs, and finally, calcium concentration in the SR lumenal (2). Calcium sparks are important in maintaining calcium homeostasis via a mechanism known as 'calcium leak'. This calcium leak balances the SR calcium-ATPase flux. Increases in SR calcium means an increase in calcium leak (3). This results in calcium overload which causes membrane depolarization and leads to an arrhythmia. There is also an 'invisible leak', a certain amount of leak that has not been measured or accounted for. Dr. Jafri and his team address this issue using the 'sticky cluster model' (2).

Peaks of a calcium transient, action potential , and cardiac muscle contraction.
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Calcium sparks can be seen in this image as yellow and red spots. This cell was loaded with Fluo-3, a fluorescent  calcium indicator.
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Dr. Jafri and the team have implemented their three-dimensional stochastic model of calcium dynamics to better understand the primary mechanism underlying calcium wave generation. They examined the resting and individual calcium spark behavior using their 3D model and the Ultrafast Monte Carlo Method. They also simulated a SR calcium leak experiment in which caffeine was used. In addition, they examined the effects of phosphorylation on calcium spark generation. They have come to learn that the activation of a single RyR of the calcium release units would result in neighboring RyRs to become active as well, generating a synchronized influx of calcium from the SR to the cytoplasm (2). Once 6 or more RyRs open, the remaining channels open as well, resulting in a calcium spark. As for calcium release termination, it occurs by reduced calcium concentration in the SR which then results in stochastic closure, coupled gating, and reduced opening of RyRs (5).

The research that has been conducted by Dr. Jafri and others is pivotal in better understanding calcium entrained cardiac arrhythmias. Their work is invaluable in that it lays the groundwork on which future research can be built upon. Perhaps by using this model, in the future, researchers would be able to understand abnormalities in ryanodine receptors for example, or mutations associated with these receptors. New pharmacological or genetic strategies can be developed to treat disorders associated with the heart. There are certain rate and rhythm control medications that have been developed to help treat arrhythmias. Calcium channel blockers have been used as anti-arrhythmiac agents, but are associated with dangerous side effects and even death. Would it be possible to employ the Ultrafast Monte Carlo Method to simulate the effectiveness of medications to treat different heart conditions? Can the basic idea of stochastic stimulations be used in the treatment of other disorders?

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References:

1. http://www.crcnetbase.com/doi/abs/10.1201/9780203912393.ch6
2. Jafri, Dr. Saleet. "Understanding the Molecular Basis of Calcium-Entrained Cardiac Arrhythmia by GPU-Enabled Monte Carlo Simulation", Department of Molecular Neuroscience, Krasnow Institute For Advanced Study. 4 October 2012. Seminar.
3. Hoang-Trong, M. T., G. S. B. Williams, A. C. Chikando, E. A. Sobie, W. J. Lederer, and M. S. Jafri. 2011. Stochastic Simulation of Cardiac Calcium Dynamics and Waves.Conf Proc IEEE Eng Med Biol Soc. 2011: 4677-4680.
4. Williams, G. S. B., A. C. Chikando, T. M. Hoang-Trong, E. A. Sobie, W. J. Lederer, and M. S. Jafri. 2011. Dynamics of Calcium Sparks and Calcium Leak in Heart. Biophys. J.101:1287-1296.
5. Sobie, E. A., K. W. Dilly, J. d. S. Cruz, W. J. Lederer, and M. S. Jafri. 2002.Termination of cardiac of Ca²⁺ sparks: an investigative mathematical model of calcium-induced calcium release. Biophys. J. 83:59-78