Using mathematics to study Alzheimer’s disease

Shantia Yarahmadian, an associate professor in Mississippi State University’s Department of Mathematics and Statistics, studies how metals such as copper and zinc affect amyloid beta, a protein that can aggregate and form the plaques associated with Alzheimer’s disease.

Published in Bulletin of Mathematical Biology, the research builds on Yarahmadian’s ongoing efforts to use mathematical modeling to better understand the complex biological processes involved in Alzheimer’s disease.

Mathematical modeling allows scientists to represent complex biological interactions through equations and simulations. Researchers can use these models to test how different factors affect biological processes and predict what may happen when conditions change.

“All biological phenomena occur in the physical world, in space and time, and involve changes in shape, quantity, and matter,” said Yarahmadian, a faculty member in MSU’s Department of Mathematics and Statistics. “Thanks to its abstract power, mathematics allows us to discover patterns, test hypotheses, and make predictions that are not possible through observation alone. Mathematics does not replace laboratory or clinical research; it complements it by helping us understand larger systems, identify the most influential mechanisms, and guide future experiments.”

This approach may be especially valuable for Alzheimer’s disease, which involves many interacting biological processes that are difficult to study individually.

How copper and zinc affect amyloid beta aggregation

To investigate how Alzheimer’s-related plaques develop, Yarahmadian created a mathematical framework that simulates the chemical reactions that occur when metals such as copper and zinc interact with amyloid beta.

Amyloid beta proteins can stick together in a process called aggregation. Over time, these clusters can contribute to plaque formation, one of the hallmarks of Alzheimer’s disease.

The model examines how metal ions, which are charged forms of metals, affect the accumulation of amyloid beta. Researchers can also use it to explore two potential therapeutic approaches designed to interfere with protein aggregation.

Instead of relying solely on laboratory experiments, scientists can use simulations to examine how changes in these interactions affect plaque formation and identify promising directions for additional research.

Mathematical predictions align with laboratory results

Mathematical models are most useful when their predictions reflect what happens in real experiments. To evaluate the framework, Yarahmadian and his collaborators compared its results with laboratory measurements obtained using atomic force microscopy.

This imaging technique uses extremely thin probes to examine structures at a microscopic scale, allowing researchers to study small clusters of proteins and other substances.

The mathematical model successfully reproduced patterns observed in the experiments. This agreement suggests that the framework captures important aspects of how amyloid beta proteins aggregate under the conditions studied.

The findings provide evidence that mathematical simulations can help researchers investigate the mechanisms behind protein aggregation and explore ways to influence the process. However, the research does not establish an effective treatment for Alzheimer’s disease. Instead, it offers a potential tool for guiding future laboratory and clinical research.

For Yarahmadian, the motivation behind the work extends beyond a mathematical challenge. A deeper understanding of Alzheimer’s disease biology could ultimately help scientists develop more effective strategies against the disease.

“What attracted me to researching Alzheimer’s disease is its combination of profound human impact and extraordinary biological complexity,” he says. “My goal is to use mathematical modeling to identify important mechanisms and generate insights that will guide future experimental and therapeutic studies.”