Here we recount the evolution of the project in a series of email exchanges.
How did the idea of the project come about?
NRG: My fascination with complex systems started during my PhD years. Back then, I remember reading about the Daisyworld model of temperature control in planets, which predicts the counter-intuitive behavior of temperature rise/drop in response to a decrease/increase in heat influx. That work encouraged me to search for the general conditions underlying the existence of such systems, potentially in biological systems. I presented the first results of that project as a poster in a Mathematical Biology conference held in Dundee, Scotland, in 2003. Afterward, the project came to a long pause until I finished my PhD and postdoctoral research on amyloid aggregation and its NMR-based structural biology. After I got my first independent principal investigator position in UMG Göttingen, I decided to revive and further develop the project, which led to a publication in J Theor Biol (1) together with Davood Bakhtiari (then a postdoc in Göttingen) and Armin Rashidi (a former Mathematical Biologist, then a faculty member of Hemato-oncology department in Univ. Minnesota). In that paper, we introduced the concept of “reverse allostasis”, determined the minimal conditions for its existence, and showed how relatively easily those conditions could be fulfilled in coupled biochemical and biological systems. In the next step, considering the known coupling between amyloid aggregation and inflammation in Alzheimer’s disease, I was curious to see how rich and complex the dynamics of that coupled system could be. Indeed, my initial simulations had shown the propensity of coupled aggregation-inflammation systems for oscillatory dynamics. To further explore this idea, I teamed up with Kalyan Chakrabarti, a former colleague in Göttingen who had just started his position at Krea University, India, and also asked Davood to rejoin the project. That led to a wonderful cross-continent collaboration through numerous online meetings during Covid time and afterward, that finally led to our joint paper in NPJ Systems Biology and Applications.
Why are oscillations important in Alzheimer’s Disease?
KSC: I have been interested in the oscillations in biochemical systems. Previously, Abuthahir Abdulrahuman (Dept of Computer Science, Krea University), Gaurav Raina (Electrical Engineering, IIT Madras), and I analyzed the local stability, convergence, and bifurcation properties of a reduced Boissonade-De Kepper (BD) model, in the presence of time-delayed feedback. We investigated the model undergoing a Hopf bifurcation when the conditions for local stability were violated. The paper discussed the conditions under which the model can show sub-critical or super-critical Hopf bifurcation (2).
When we started the discussion about the progression of Alzheimer’s Disease with Nasrollah and Davood, we realized that the aggregation model might show oscillatory behavior. The oscillatory behavior might explain some of the puzzling features of the onset of Alzheimer’s disease. A comparison of our results with the literature provides a strong hint that oscillations are bad for the immune system and can cause the onset of Alzheimer’s disease. In our model, the oscillations have periods of about 30 minutes to several hours. Our results suggest that a new strategy for monitoring the biomarkers is needed to predict the risk of onset of the disease. Several undergraduate students learned modeling ODEs, programming, and system biology concepts from this project as part of their capstone thesis.
What was the motivation for studying Alzheimer’s Disease?
DB: Since my undergraduate years I have always been interested in mathematical simulation of molecular and biological systems. At the end of 2015 and 2016 after my PostDoc at the Max Planck Institute in Göttingen I got involved with a project about reverse allostasis and its minimal conditions conceived by Nasrollah Rezaei-Ghaleh, published in 2017 (1). As a pharmacist, I was always in the intersection of multiple disciplines of natural science. The area of systems biology has an intersection with mathematics, which has always been my favorite. In 2022, I rejoined the project with my former colleagues Nasrollah and Kalyan as an international, long-distance collaboration.
[1] Rezaei-Ghaleh, N., Bakhtiari, D. & Rashidi, A. Reverse allostasis in biological systems: minimal conditions and implications. J. Theor. Biol. 426, 134–139 (2017).
[2] Abdulrahuman, A. Chakrabarti, K. S. & Raina, G. Stability, convergence and bifurcation of a reduced Boissonade-De Kepper model with delayed feedback, IFAC-PapersOnLine, 54, 76-83, (2021)
Oscillatory dynamics of Alzheimer’s progression
