Data-driven modeling in biology and medicine (Part 1)

Weitao Chen

University of California, Riverside

"A Mechanochemical Coupled Model to Understand Budding Behavior in Aging Yeast"

Cell polarization, in which a uniform distribution of substances becomes asymmetric due to internal or external stimuli, is a fundamental process underlying cell mobility and cell division. Budding yeast provides a good system to study how biochemical signals and mechanical properties coordinate with each other to achieve stable cell polarization and give rise to certain morphological change in a single cell. Recent experimental data suggests yeast budding develops into two trajectories with different bud shapes as mother cells become old. We first developed a 2D model to simulate biochemical signals on a shape-changing cell and investigated strategies for robust yeast mating. Then we extended and coupled this biochemical signaling model with a 3D subcellular element model to take into account cell mechanics, which was applied to investigate how the interaction between biochemical signals and mechanical properties affects the cell polarization and budding initiation. This 3D mechanochemical model was also applied to predict mechanisms underlying different bud shape formation due to cellular aging.

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Wenrui Hao

Pennsylvania State University

"Data-Driven Modeling in Alzheimer's Disease"

Alzheimer’s disease (AD) presents complex, nonlinear progression patterns driven by heterogeneous biomarker dynamics, spatial brain changes, and individual variability. Capturing these intricate dynamics requires modeling tools that are both expressive and computationally efficient. In this work, we introduce a Laplacian Eigenfunctions Neural Operator (LENO) framework for data-driven modeling of Alzheimer’s disease. By projecting the underlying spatial-temporal dynamics onto a basis of Laplacian eigenfunctions, LENO exploits the geometric structure of the brain while learning the nonlinear operator governing disease progression. Trained on multi-modal longitudinal data—including neuroimaging, biomarker profiles, and cognitive assessments—our approach enables efficient approximation of disease trajectories and identification of multiple progression pathways. The model not only achieves high predictive accuracy but also reveals interpretable spatial patterns aligned with known AD pathology. LENO provides a powerful computational tool for building digital twins of AD patients, supporting personalized diagnosis, subtyping, and forecasting of disease evolution.

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Leili Shahriyari

University of Massachusetts Amherst

"Data Driven QSP Modeling of Cancer: A Step Toward Personalized Treatment"

Our work explores the possibility of creating personalized mathematical models for cancer to better understand the progression of an individual's cancer. By simulating the unique characteristics of each tumor and its response to treatments, we aim to offer insights into personalized cancer care. Our method combines elements of mechanistic modeling and machine learning techniques to create individualized predictions. A central aspect of our approach is the use of a mechanistic model based on quantitative systems pharmacology (QSP). QSP is a computational method used to analyze drug interactions and effects, and it plays a crucial role in our project. The model includes a large system of nonlinear equations modeling both bio-chemical and bio-mechanical integrations in the tumors. We acknowledge that a common challenge in QSP modeling is accurately determining parameters, especially since traditional models often assume a general uniformity across different patients' diseases. This assumption can lead to limitations when calibrating parameters using varied data sources. Our objective is to build a more personalized mathematical framework by concentrating on individual patient data for parameter estimation. We adjust the QSP model parameters for each patient based on their unique data. Through detailed sensitivity analysis and uncertainty quantification, we identify key interactions in the model and define the range of our predictions. By integrating this tailored QSP model with insights into cellular and molecular interactions, we hope to better predict how cancer evolves and responds to specific treatments. We are excited about the potential this has for advancing personalized cancer therapy, though we are aware of the challenges and complexities involved in this endeavor.

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Nourridine Siewe

Rochester Institute of Technology

"Osteoporosis Induced by Cellular Senescence: A Mathematical model"

Osteoporosis is a disease characterized by loss of bone mass, where bones become fragile and more likely to fracture. Bone density begins to decrease at age 50, and a state of osteoporosis is defined by loss of more than 25%. Cellular senescence is a permanent arrest of normal cell cycle, while maintaining cell viability. The number of senescent cells increase with age. Since osteoporosis is an aging disease, it is natural to consider the question to what extend senescent cells induce bone density loss and osteoporosis. In this paper we use a mathematical model to address this question. We determine the percent of bone loss for men and women during age 50 to 100 years, and the results depend on the rate η of proliferation of senescent cell, with η=1 being the average rate. In the case η=1, the model simulations are in agreement with empirical data. We also consider senolytic drugs, like fisetin and quercetin, that selectively eliminate senescent cells, and assess their efficacy in terms of reducing bone loss. For example, at η=1, with estrogen hormonal therapy and early treatment with fisetin, bone density loss for women by age 75 is 23.4% (below osteoporosis), while with no treatment with fisetin it is 25.8% (osteoporosis); without even a treatment with estrogen hormonal therapy, bone loss of 25.3% occurs already at age 65.

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