October 5, 2023

Oscillations in Prion Protein Concentration: A Neuron-Centered Spatiotemporal Model of The Unfolded Protein Response

Neurodegenerative disorders are severe illnesses that affect the brain and central nervous system. Several neurodegenerative diseases are characterized by the slow, spatial spread of toxic proteins in the brain. Among the rare types, prion diseases stand out. In prion diseases, a recruitment mechanism occurs, whereby previously normal proteins can transform into toxic forms due to interactions with other toxic proteins. These proteins can induce stress in neurons, leading to the activation of the Unfolded Protein Response (UPR). The UPR slows down or halts the production of proteins, indirectly reducing the burden of harmful proteins. However, the UPR can also trigger processes that lead to cell death, and its involvement has been observed in the progression of several neurodegenerative diseases. In this presentation, we will introduce a spatiotemporal mathematical model to describe how the UPR mechanism functions in prion diseases. Our model centers around a single neuron and involves two representative types of protein: P (healthy) and S (toxic). This model is formulated as a coupled system of nonlinear reaction-diffusion equations, featuring a delayed and nonlinear flux for protein P. The inclusion of a delay time is necessary because during periods of stress, the cessation of P-production is not instantaneous; instead, it involves a sequence of signal transmissions to gradually reduce P production. By introducing a delay at the boundary, we observe oscillations in the levels of proteins P and S under certain parameter regimes. Additionally, we find that these oscillations become more pronounced when the clearance rate of protein S and its diffusion capacity are small relative to those of protein P. Furthermore, the oscillations become more ubiquitous as delays in initiating the UPR increase. In our model, we observe that decreasing the production of protein P, enhancing the clearance of protein S, and reducing the recruitment rate are the most effective mechanisms for reducing the overall intensity of the UPR.

About the speaker

Omar Sharif is a dedicated graduate student currently pursuing his Ph.D. in Computational Mathematics with a specialization in network modeling in neurodegenerative diseases (Alzheimer and Parkinsons disease) at the University of Texas Rio Grande Valley.  

Prior to his doctoral studies, Omar held a prominent position as a Lecturer (Senior Scale) in the Mathematics and Statistics Department at Universal College Bangladesh, where he contributed significantly to the Monash University pathway program. He also served as a Lecturer (Senior Scale) within the General Educational Development department at Daffodil International University (DIU).  

Omar's academic journey began with his Bachelor of Science (Hons) degree in Mathematics, followed by a Master of Science in Applied Mathematics, both of which he successfully completed at the University of Dhaka, Bangladesh. He further expanded his horizons by pursuing a Master of Science (Research) in Financial Statistics at Universiti Tunku Abdul Rahman in Malaysia. During this time, his research efforts were concentrated on the fields of Data Science, Artificial Intelligence, mathematical modeling in health science, and the Malaysian stock market.  

His research career has been marked by a deep commitment to computational mathematics, data analysis and mathematical modeling. He has made notable contributions to the understanding of the Malaysian stock market, focusing on data analysis and assessing market efficiency in developing countries. Furthermore, Omar has actively collaborated with researchers from diverse disciplines within the field of Data Science. 

In his multidisciplinary research endeavors, Omar Sharif has dedicated himself to the exploration of adaptive mathematical models, bridging the gap between mathematics and real-world applications. His work continues to be instrumental in advancing our understanding of complex systems and their practical implications.