Welcome to the fourth lecture in the course, Integrated Analysis in Systems Biology. Today, we will cover the second research article titled Human Atrial Action Potential and Calcium Model. One of the reasons we chose this research article is that we think it's a good example of a dynamical model developed based on experimental data that produced experimental predictions with mechanistic insight. This particular model provides a framework to understand the pathophysiology of human chronic atrial fibrillation. This type of model is extremely useful given the limited access of, to human tissue for experimental studies. So today, we're going to cover the biological background and motivation. We'll cover some heart physiology. We'll define what's atrial fibrillation, and the goal of the study. We will then use this study to illustrate the steps in developing a dynamical model. Such as developing the model from an existing model, validating the model against experimental data, simulating the biology, and generating novel predictions. And then the summary and conclusions. So let's start with some heart physiology. During a normal heartbeat, electrical activity starts with the pacemaker cells of the sinus node, found right here. This electrical activity then propagates to the ventricles via the AV node or the atrial ventricle node, resulting in contraction of the ventricles. And the coordinated contraction actually is what pumps the blood out of the heart. All of this electrical activity underlying heart contractions is driven by action potentials in specific cells of the heart. The shape of the action potential is highly variable, and it depends on whether the cell is located in one of the nodes of the heart, such as the, the sinus node, or the AV node, or in the atria, or the ventricle. The action potential shape is the result of the activity of voltage-gated ion channels giving rise to different currents. Cell-type irritability in the shape of the action potential is due to the different combinations of ion channels that are expressed in these cells. As we mentioned, in a normal heartbeat, the sinus note gives rise to the sinus rhythm. And that gives rise to electrical activity that spreads throughout the atria. But during atrial fibrillation, there's an aberrant electrical activity throughout the atria. Atrial fibrillation causes a very rapid and irregular firing of the atrial cells. It's one of the most common sustained types of arrhythmias. Arrhythmias are abnormal heart rhythm. And they are common in elderly population. They are serious cause of concern as they are thought to be the main cause of embolic stroke, and it, they can be fatal. It has been observed that rapid atrial pacing can sometimes give rise to isolated atrial fibrillation events. And these episodes tend to become more persistent over time as observed in this figure. So an initial episode can be short lived, but after several hours, it can become much longer. And after many days, or weeks, it can become persistent or sustained. But what exactly maintains this persistent or chronic atrial fibrillation episodes is not completely clear. What it is known is that there is significant cardiac remodeling that may contribute to chronic atrial fibrillation. And by cardiac remodeling, I mean that there's electrical and structural and contractile properties of the heart that change. And these changes seem to promote or perpetuate atrial fibrillation. And the identity of these changes are not completely known, but we know some of them. For example, under electrical remodeling we know that there are changes that basically lead to less contractility of the atria, and also a decrease in the duration of the action potential of the atria. We also know that some of the reasons why there are these changes in atrial contractility, and changes to the action potential shape is that there is a decrease in L-type calcium channel expression. And there's also a reduction in the amplitude of calcium transients in the atria. So in this study they develop a computational model of human atrial myocytes. And what was different about this model than other models is that it had a very detailed calcium component that could recapitulate these calcium transients. They also use the model to understand how these calcium transients are affected during atrial fibrillation. This model was based on an existing model ventricular myocytes. And this is a common theme when you're doing dynamical models. For example, if you recall from Eric Sobie's lecture on dynamical models, he went through the Tyson model cell cycle the original model in 1991, and also the 1993 model in which there was a lot more mechanistic detail. And the difference between these two models is that the 1993 model had a lot more of the biological process, and was, this models is similar, and that is built based on a previous model. The model that it was based on, it was the 2010 ventricular model. And from this model, they developed the atrial model that they're presenting in this study. And the way that they obtain the atrial model is that they made some changes to recapitulate the geometry of atrial myocytes. They tend to be smaller so they change the surface to volume ratio. They also change the current, and this is representing the differences in the expression of channels and pumps that exist between atrial versus ventricular cells. In this study, they also have developed a different type of model where they took the atrial model, which should represent what a normal atrial cell would behave like to one that, what you would find in a chronic atrial fibrillation situation. And again, they change the current to reflect some of the remodeling events that are thought to underlie some of these sustained or chronic atrial fibrillation episodes. And they also did some changes to the calcium handling so that the transients would be effected. And finally, they also looked at how adrenergic stress, so modulation of the adrenergic system could also affect chronic atrial fibrillation. And they did this by representing the regulation of cyclic AMP dependent protein kinase A on the conductances of channels and pumps. And for this lecture, we're not going to cover any of the data related to the adrenergic model, but we will concentrate mostly on the atrial model, and the chronic atrial fibrillation model. So in the first step of this study, it was showing us how they built the model. The first figure they show us with the ventricular myocyte model looks like, and you see that the action potential shape is very different to what the action potential shape of the atrial myocyte model is. Figure 1 basically gives us how all the currents that make up the action potential are different in the two models. If you want to see a detailed description of all the different currents and changes that they used to differentiate the ventricular myocyte model from the atrial model, they're all listed in table 1. And I'm not going to go over every single current that they describe, I'm just going to highlight some of the current. The first current I want to highlight is the L-type calcium current. This was an inward current consisting of calcium coming into the myocyte, and it's present in both atrial cells and ventricular cells. The other two currents I would like to point to you, ultra-rapid delay rectified potassium current called KUR, that is present only in atrial cells, not in ventricular cells. And then I want to point to you, the inward rectifier potassium current that is present in both the atrial and ventricular cells, but with different levels. And both of these currents they're potassium currents so they're outward currents, meaning, the potassium leaves the cell. Next, they decided to calibrate their model against experimental data that they obtain from human atrial cells that were from normal individuals, or they were obtained from individuals that had suffered from chronic atrial fibrillation. What they did is that they voltage-clamped these cells and they did a certain protocol of voltage clamping. The reason for that is that they wanted to create conditions to inactivate the sodium current so the, only the calcium current will be there, so potassium current was also blocked. And what they found is that in normal, or cells that had been exposed only to sinus rhythm, there was a significant component to the calcium L-type current. And that this same current was decrease in human atrial cells that had undergone chronic atrial fibrillation. And this experimental data was used to calibrate the, the model, and as you can, as you can see they match. Next, they wanted to calibrate the calcium transient. So the calcium handling component of the model. And what they did is, again, they measure using a dye, a calcium dye, the ability of the atrial cells to have calcium transients. And as you can see, the normal cells had a substantial calcium transient. Atrial cells that had undergone chronic atrial fibrillation up here to have a, a smaller calcium transient. And this was recapitulated in their model, and this decrease in calcium transient could be due to a decrease in the L-type channel current. And next the authors wanted to look at the rate dependent changes to action potentials, and calcium transients. And it is known that when you change your, the heart rate, there's a physiological change. And experimentally, one can examine the relationship between rate or pacing and calcium transients and contractility in isolated myocytes. There's an established relationship in healthy myocytes, that the faster the pacing, the larger the calcium transient, and the stronger the cellular contraction. And this is observed as a change in the cellular length. But what about the, how does rate affect action potentials? Well, for action potentials, faster pacing results in decrease in the action potential duration. And part of this is due to the partial inactivation of L-type calcium currents that are inactivated by intracellular calcium, and also by larger activation of the delay rectifier potassium current. As part of their model validation the authors examined the simulated action potential changes as a function of pacing rate. There was experimental data that shown that if you increase pacing rate from 0.5 hertz to 2 hertz, you see that there is a decrease in the action potential duration in control atrial cells. And in, in cells in the chronic atrial fibrillation conditions this adaptation to an increase in pacing appears to be lost, suggesting that these cell, the action potential of these cells is not sensitive to changes in pacing rate. What is interesting is that there was experimental data that had shown that control cells, normal atrial cells, could also lose this adaptation to changes in pacing rate by blocking the L-type channel with Nifedipine. And all these features could be nicely recapitulated in the simulations, where you see, where you show that an increase in pacing rate results in a decrease in the action potential duration. That in the atrial fibrillation cells, this decrease is not as evident, and that the blockade of the L-typed costume channel in the control cells has a similar effect where you lose, you lose the, the adaptation of the action potential to changes in pacing rate. One of the, the model predictions is that the, this change in pacing could have a significant effect in the calcium transients in normal cells. And that the, so and as you can see here, that as you increase the pacing rate, you see that there's also a significant increase in the magnitude of the calcium transients. Conditions that mimic atrial fibrillation or in a normal cell that lacks the L-type channel current you see that the ability, the magnitude of the calcium transient change is not as pronounced as in the control cells. Another model prediction involves the ultra rapid delay of rectified potassium current that is present mostly in atrial cells, and not at ventricles. There had been some experimental data that had shown that the blockade of this current could improve atrial contractility by increasing the plateau of the action potential. And the blockade of this current has very little effect on the action potential duration in both the control cells and the atrial fibrillation cells. And the model doesn't capture exactly that there does seem to be a small change. There seems to be a small effect on action potential duration, both in normal or in, in the chronic atrial fibrillation. But what the model does is that it predicts that this blockade will have a large effect in the calcium transients, and the magnitude of the calcium transients. And that could be used to actually, to counteract a decrease in the atrial contractility that is observed in chronic atrial fibrillation. And there was some data to support this. As in, as a dose-dependein increase in contractility, let's observe when this channel was blocked. So to summarize the findings of this research article, this model that the authors developed may actually be very helpful in the targeting of atrial specific currents. It was the first atrial model to include a detailed description of calcium transients along with the electrophysiology. And the model does a fairly, a fairly good job recapitulating the modulation of action potential duration by pacing rate changes. And it does validate that the L-type current is key to modulation. And finally, they predict that targeting ultra rapid delay rectifier potassium current could enhance atrial contractility by increasing the magnitude of these calcium transient. And in terms of the lecture, we want to summarize some key points that I think we, we want to stress, which are that dynamical models are usually built from existing models. And they're based, the good dynamical models, like this one that we just presented, are based on extensive multilevel experimental data. And they go through a lot of effort to validate the model with comparisons to the ex, to other experimental data. And finally, these models are incredibly useful because they can produce experimental predictions that can be testable, and lead to novel insight. So with that, I will end today's lecture, and thank you.