MS02 - NEUR-02

Modeling of Neurodegenerative Diseases

Monday, July 14 at 3:50pm

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Laurent PUJO-MENJOUET and Suzanne SINDI (Claude Bernard Lyon 1 University (Lyon, FRANCE))

Description:

This mini-symposium focuses on the mathematical modeling of neurodegenerative diseases, including Alzheimer's, Creutzfeldt-Jakob, and Parkinson's, among others. The approaches discussed may span various scales, ranging from molecular (such as protein dynamics) to cellular (e.g., intercellular communication) and tissue-level phenomena (e.g., the spread of pathologies in specific brain regions or the formation of amyloid plaques). The mathematical tools explored during the symposium comprise a wide range, including ordinary and delayed differential equations, partial differential equations with diverse structures (e.g., size, spatial, or hybrid models), and advanced techniques such as neural networks for image analysis and data augmentation. By addressing all scales and employing a variety of methods, this mini-symposium aims to shed light on the complex mechanisms underlying these often fatal diseases, which continue to pose significant scientific challenges and unanswered questions.

Théo LOUREAUX

University of California, Merced

"Modeling the Prion Aggregation Process During Polymerization Experiments Using Delay Differential Equations"

Prion proteins are notorious for their ability to induce neurodegenerative diseases by forming long fibrillar aggregates that accumulate in the brain. While the aggregation of these proteins and their fragmentation by oligomeric species is central to disease progression, the underlying mechanisms remain poorly understood. To better interpret experimental data, mathematical models have been developed to translate the key chemical reactions governing this process. In this talk, I present a novel modeling approach based on delay differential equations (DDEs), designed to capture the time-dependent features of prion polymerization dynamics. I will demonstrate how this framework aligns with experimental observations from polymerization assays in which prion monomers are thermally induced to aggregate. The model not only fits the data well but also suggests an alternative perspective on the interplay between aggregation and fragmentation, offering a new theoretical lens on prion dynamics.

Ashish Raj

University of California San Francisco

"Biophysical modeling of pathology progression in dementia and its implementation using physics-informed neural networks"

This presentation will focus on developing mathematical and computational models that use the brain’s structural connectivity to predict the development of brain diseases, including Alzheimer’s, Parkinson’s, Huntington’s, ALS and other neurodegenerative diseases. I will first describe our original proposal that Alzheimer and other dementias are underpinned by misfolded pathologies that spread on the brain structural connectome. This process can be mathematically captured by the so-called 'Network Diffusion Model'. Several examples from AD, ALS, Huntington's, Parkinson's and other dementias will be demonstrated. I will then present new extensions of this model in many meaningful ways, incorporating protein aggregation, clearance, active axonal transport, and mediation by external genes, cells and neuroinflammation. Deep neural network implementations of these complex and computationally prohibitive models will be motivated, and preliminary work on physics-informed neural networks will be presented. I will also briefly describe recent work in modeling brain electrophysiology using similar graph spectral models. All above models centrally involve the brain’s complex network Laplacian eigen-spectrum and “graph harmonics.” Through this work, we have found significant differences in the model’s parameters that relate healthy brains to Alzheimer’s disease, sleep, epilepsy and infant brain maturation. The related papers will be briefly highlighted.

Human Rezaei

INRAE, Jouy-en-Josas FRANCE

"Intrinsic Dynamics and Deterministic Diversification Drive a New Model of Prion Replication and Dissemination"

Through experimental approaches combining nanoscale infrared spectroscopy and dynamic atomic force microscopy, we investigated the intrinsic dynamics of PrPSc assemblies outside the context of templated replication. These studies revealed that PrPSc assemblies exhibit an inherent capacity for structural diversification and material exchange, leading us to establish a new replication model. This model incorporates deterministic structural diversification and proposes that prion assemblies can undergo catalytic conformational transitions independently of replication events, challenging the notion that replication alone governs strain specificity. Building on these findings, we developed a stochastic reaction-diffusion framework that integrates nonlinear replication dynamics and tissue responses. Using the Gillespie algorithm, we modeled neuroinvasion as a complex and emergent process shaped by strain-specific PrPSc behavior and anatomical connectivity. This integrative approach offers new insights into how structural diversity is maintained within populations of prions and how it contributes to strain-dependent tropism and pathogenesis. By shifting the focus from purely replication-driven models to those considering intrinsic structural dynamics, this work proposes a revised conceptual framework for prion propagation, with broader implications for other protein misfolding diseases.

Laurent Pujo-Menjouet

University Claude Bernard Lyon 1 - Camille Jordan Institute

"Modeling the formation of perinuclear crowns made of agglutinated ATM proteins observed in fibroblasts from patients affected by Alzheimer’s disease"

Alzheimer’s disease is a progressive neurodegenerative disorder marked by the irreversible loss of brain cells. In response to oxidative stress, ATM proteins typically migrate to the nucleus to detect and repair double-strand DNA breaks. However, recent studies suggest that APOE proteins may accumulate at the nuclear envelope, blocking the entry of ATM proteins and resulting in the formation of a characteristic perinuclear crown. To better understand this phenomenon and evaluate potential therapeutic interventions, we propose two modeling approaches: a compartmental model and a reaction-diffusion system that capture the physical interactions between ATM and APOE proteins. Both models incorporate key biological processes, including protein transport, monomer aggregation, and the dissociation of dimers and complexes. We explore the effects of irradiation and antioxidant treatments on the disintegration of the perinuclear crown. Our simulations suggest that the combined use of these two strategies is the most effective in delaying crown reformation, highlighting a promising therapeutic avenue for Alzheimer’s disease.

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Annual Meeting for the Society for Mathematical Biology, 2025.