T-World 3: Problem 1 - Rudy to Bers/Grandi or Bers/Grandi to Rudy?

 

Looking over the field, I clearly saw the pattern of different families of computer models being used for different tasks, being good for different things. The two families that would come up the most would be the “Rudy family” from the group of Yoram Rudy (e.g. Luo-Rudy, Hund-Rudy, O’Hara-Rudy, Heijman-Rudy) and the “Bers/Grandi family” (Shannon-Bers, Grandi-Bers, Morotti-Grandi). Our prior model ToR-ORd that we developed in the Rodriguez group would belong to the Rudy family with regards to its philosophy. (Please don’t read too much into the naming of the families – I needed a short and memorable naming, and I used PI’s names as they’re the closest unifying factors to the models; it is definitely not intended to take credit from other authors).

Both families of models are used for a range of tasks, but in general, one would see Rudy models used more for studies on electrophysiology, response to drugs, and early-afterdepolarization-driven arrhythmia, whereas the Bers/Grandi models would be often used for studies heavily involving calcium handling and ionic homeostasis. Perhaps the central difference between the two philosophies is how L-type calcium current and RyR calcium release are coupled. In the Rudy models, the coupling is direct (RyR release depends directly on L-type calcium current) – this is less realistic, but convenient for certain aspects. In Bers/Grandi models, the coupling is mediated by dyadic calcium concentration, more in line with reality.

We wanted to achieve a general model, which would have strong and realistic (as far as possible) calcium handling, but which would maintain the strengths of e.g. ToR-ORd for electrophysiological studies and drug simulations. The question naturally was – do we take ToR-ORd and we try to make calcium handling more realistic, or do we take one of the Bers/Grandi models and we work on electrophysiology? Being more familiar at the time with ToR-ORd, I thought it would be a better starting point. Unfortunately, it did not seem to work that well when I incorporated calcium-sensitive calcium release to replace the I_CaL-based one, no matter which formulation of RyR I tried. We could get somewhat reasonable behaviours in a single setting, but e.g. a model working reasonably at 1 Hz would be too prone to spontaneous calcium releases at fast pacing, or there would be other problems. In general, the models produced did not feel particularly stable and robust, even if they could be fine-tuned for particular applications. This just was not good enough, especially in a project hoping to deliver a generally robust and maximally general virtual cardiomyocyte.

At the time, I did not have a particularly great understanding of why it was so hard to get a good calcium-sensitive-calcium release, which I grasped only some time later when I worked more with Bers/Grandi models. The reason why I think models like ToR-ORd will struggle with calcium-sensitive calcium release is that they have very large junctional dyad compartment (the space where I_CaL channels and RyR meet) – around 2% of cell volume. Just for context, the whole subsarcolemmal compartment in Bers/Grandi models is 2%! The junctional volume in those models (based on reasonable estimates of dyad volumes and counts) is ca. 0.05%. Why does this make so much difference?

With a bit of oversimplification, you can imagine the I_CaL-RyR communication as a bucket (~ junctional dyad), where water trickles in from the left (calcium coming through I_CaL). Once the surface gets high enough, it touches and activates a second tube, which then injects a large amount of additional water (RyR release following sufficient calcium elevation in the dyad). This is a very basic model of calcium-induced calcium release. There, the dyad volume corresponds to the volume of the bucket. If you have a reasonably small bucket, this system can work more or less as expected, with reasonable kinetics (how long-lasting influx through I_CaL can trigger RyR release). Prior Grandi/Bers models fall into this category. However, if you make the bucket really large (like the models with 2% dyad volume) and maintain constant influx through I_CaL (which is known from experiments, not something to vary wildly), it suddenly takes ages to fill enough to trigger RyRs. Worse still, in reality, the bucket is leaky, due to NCX efflux and diffusion from dyads to the rest of the cell. Your RyRs never get stimulated enough. To fix this and get RyR to fire, you need to do what we did ages ago – make the release mechanism far more sensitive to calcium (i.e., you have a big bucket, but the RyR tube is very low). With a low-enough RyR threshold for activation, this can give release of decent kinetics when tweaked for a given condition. However, it makes the model too sensitive unfortunately. E.g. when there is a buildup of diastolic calcium at rapid pacing, that can already stimulate the RyR and lead to a spontaneous release. Any change slightly elevating dyadic calcium can provoke spontaneous release too easily. One could try to patch that through imposing various forms of additional refractoriness in some way, but I’m pretty sure it would cause other issued down the line – it is just too far from how the system works in reality. Of course, none of this dyad volume stuff matters as much when the I_CaL and RyR are coupled directly, as in ORd/ToR-ORd. That’s why these models work fine for many intents and purposes – it’s only when you try to make the calcium handling more realistic that problems arise.

In retrospect, this feels trivial, but that’s the funny thing about insights – they’re trivial when you have them.

In the end, even before I got the “bucket size insight”, I decided to start working with the Bers/Grandi models, trying to see how far I can get using them as a starting point. I expected I would try to mainly port a number of ionic currents from ToR-ORd - if nothing else, Bers/Grandi models have different concentrations and dynamics of their changes, due to different structure of compartments, so channel models are mostly not plug and play between different models.

However, as I played with the models (mainly Shannon, which is the simplest, and seemed comparably-behaving for key features of calcium handling), I also noticed some aspects of calcium handling that I was not too fond of:

1.      First, the calcium transient in the junctional dyad compartment seemed to have a very slow time to peak (30-40 ms versus 10-15ish estimated by most experiments). This has several implications:

a.      Slow early rise of calcium transient (which is relatively biphasic in the family of models, with an early slow rise followed by a very rapid one).

b.      I_CaL calcium-dependent inactivation either takes time too late, or has to be parametrized to respond to very low local levels of calcium, that are present around 10 ms after the stimulus.

c.      The late release deforms the early AP plateau, as the late elevation is picked up by calcium-sensitive currents (e.g. I_Cl(Ca)), yielding somewhat late depolarising current during early plateau.

2.      No alternans in the baseline models. To me, this is probably the most reliably evoke-able arrhythmogenic behaviour in the heart, obtained by simple rapid pacing. Missing that was a major issue to me. (besides, I love alternans, it’s such a funky behaviour with multiple possible contributing mechanisms – I think we’re far from having a complete understanding of it)

3.      Unexpected response to SERCA pump changes. Increasing SERCA would, as expected, shorten calcium transient duration, but it would also slightly reduce the amplitude – whereas it should increase it markedly! Conversely, reducing SERCA led to only a marginal reduction in calcium transient amplitude. This felt like a fairly major issue when it comes to representing beta-AR stimulation (where SERCA is increased) or diseases with SERCA downregulation.

In the end, just working on addressing those points via understanding how to adjust parameters of calcium handling took a lot of time before we even got to including other ionic channels. Segway-ing into the next section…