Excitable dynamics of flares and relapses in autoimmune diseases 2023 Lebel et al

https://www.sciencedirect.com/science/article/pii/S2589004223021612

Summary:
Many autoimmune disorders exhibit flares in which symptoms erupt and then decline, as exemplified by multiple sclerosis (MS) in its relapsing-remitting form. Existing mathematical models of autoimmune flares often assume regular oscillations, failing to capture the stochastic and non-periodic nature of flare-ups. We suggest that autoimmune flares are driven by excitable dynamics triggered by stochastic events auch as stress, infection and other factors. Our minimal model, involving autoreactive and regulatory T-cells, demonstrates this concept. Autoimmune response initiates antigen-induced expansion through positive feedback, while regulatory cells counter the autoreactive cells through negative feedback. The model explains the decrease in MS relapses during pregnancy and the subsequent surge postpartum, based on lymphocyte dynamics. Additionally, it identifies potential therapeutic targets, predicting significant reduction in relapse rate from mild adjustments of regulatory T cell activity or production. These findings indicate that excitable dynamics may underlie flare-ups across various autoimmune disorders, potentially informing treatment strategies.

Graphical abstract:

 

I struggle to see how such a model bares any relevance to reality.

The modelling of the noise, which is the essence of the model, is completely arbitrary. They want to see some basic dynamics, so they just use an SDE with constant diffusion. My guess is that the authors were very motivated by mathematical neuroscience and Integrate-and-fire models with diffusive noise. The massive difference to mathematical neuroscience or other fields of mathematical modelling is however that there’s always explicit reasoning for things to be this way rather than an arbitrary choice, i.e. the noise can explicitly be derived from some biophysical phenomena (in mathematical neurosciences the noise term can be explicitly be derived, for example by an diffusion approximation of ion channel noise, synaptic input in Stein’s model, etc). In mathematical neuroscience (where I'm still very sceptical that the majority of the work is somehow connected to reality) a lot of progress was made via animals models that are sufficiently easy to understand which meant one was able to go from Hodgkin-Huxley to the models of today. I'm unsure whether a similar approach would be fruitful in autoimmunity, since from what I can tell, there is a massive gap between supposed animals models of autoimmunity and what is witness in humans.

For a microscopic description to capture the dynamics of the mezoscopic or even macroscopic and the model to resemble reality, requires an intrinsic understanding of the microscopic, from what I can tell that unfortunately isn’t the case for autoimmunity.

It’s extremely easy to come up with a model with excitable dynamics by just writing down an SDE, using Hawkes processes or doing something similar. To me it seems like that was what they wanted to end up with, rather than possibly having an accurate model that accounts for the microscopic intricacies.

This is quite common in mathematical biology. Mathematicians don’t care whether their models depict reality because they just want to work on something interesting and contrary to physicists, biologists typically don’t have sufficiently many mathematical skills to work on such problems in depth. The oscillatory flare dynamic models are clearly incorrect, but I think the same will be said here in the future. However, biology and especially autoimmunity is still at the very beginning of it’s “mathematisation”, so one can hope that this is just a starting point and building block for future work.

 

They haven't even got the basic elements of causation right.
The seem not to have noticed that there are no auto reactive T cells in most autoimmune disease.
They also seem not to have noticed that generation of B cell clones is itself stochastic.
Worse still they describe environmental factors as stochastic instead.
Completely hopeless.

I am not sure neuroscience models are any better though!

 

@Jonathan Edwards do you think it would be fruitful to pick an autoimmune disease that is somewhat better understood and try to model things from there? Is there sufficient understanding at some scale or on a subset of something to have a meaningful model?

I don't think the goal could be for this to directly lead anywhere, but as the understanding grows in upcoming years/decades so could the models?

 

We have quite good models of autoimmune disease. Good enough to have found very effective treatments. The sad thing is that people do not read the literature and do not get an adequate background knowledge in the complex dynamics we do know about. So they end up not only re-inventing wheels but ones that don't roll.

 

If I remember the above study correctly the authors claim that most mathematical models are systems of ODEs and you state that some inherent properties of autoimmune diseases are stochastic and should be modelled as such. Unless I’m missing something that would mean there’s some sort of gap in the current mathematical models (of course there can be an abundance of ways to somewhat sufficiently model stochastic phenomena deterministically)?

It’s mainly a question of self-interest, asking if I was to ever regain cognitive health, whether this was a field I could work in, where somewhat useful contributions could still be made. My, possibly wrong impression, was that in the growing field of mathematical biology (where naturally almost all work is being done for fun, rather then with currently useful applications) there’s for example an abundance of mathematicians working in things such as neuroscience, but only very few working on autoimmunity.

 

Not really. We know that the generation of specific B cell clones and antibodies is entirely stochastic and that is part of the model. There isn't any need to do any mathematical modelling in detail because the implications are clear from a qualitative overview. And because you end up with billions of molecular species interacting there is no possibility of tracing the process in fine detail anyway so one has to work with general principles - like clearing out enough clones to allow feedback signals to collapse.