MS09 - MFBM-18 Part 2 of 2

Geometrical and Topological Methods for Data-Driven Modeling (Part 2)

Friday, July 18 at 4:00pm

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Note: this minisymposia has multiple sessions. The other session is: and Part-1.

Dhananjay Bhaskar (Yale University), Bernadette Stolz-Pretzer

Description:

The increasing complexity of modern biomedical datasets necessitates advanced mathematical frameworks that reveal intrinsic structures beyond traditional statistical approaches. Geometrical and topological methods provide powerful tools to extract robust and interpretable patterns from high-dimensional, noisy, and multimodal data, enabling more effective data-driven modeling. This minisymposium will explore recent advances at the intersection of geometry, topology, and mathematical modeling, highlighting techniques such as persistent homology, sheaf theory, optimal transport, manifold learning, and geometric deep learning. Speakers will present applications to diverse fields ranging from oncology, liver disease to neuroscience, demonstrating how these methods enhance our understanding of complex biological systems, disease progression, and cellular organization. By fostering interdisciplinary dialogue, this session aims to showcase novel approaches that push the boundaries of data-driven discovery and advance mathematical techniques for biomedical research.

Eunbi Park

Georgia Institute of Technology

"Topological data analysis of pattern formation of human induced pluripotent stem cell colonies"

Understanding the multicellular organization of stem cells is vital for determining the mechanisms that coordinate cell fate decision-making during differentiation; these mechanisms range from neighbor-to-neighbor communication to tissue-level biochemical gradients. Current methods for quantifying multicellular patterning tend to capture the spatial properties of cell colonies at a fixed scale and typically rely on human annotation. We present a computational pipeline that utilizes topological data analysis to generate quantitative, multiscale descriptors which capture the shape of data extracted from 2D multichannel microscopy images. By applying our pipeline to certain stem cell colonies, we detected subtle differences in patterning that reflect distinct spatial organization associated with loss of pluripotency. These results yield insight into putative directed cellular organization and morphogen-mediated, neighbor-to-neighbor signaling. Because of its broad applicability to immunofluorescence microscopy images, our pipeline is well-positioned to serve as a general-purpose tool for the quantitative study of multicellular pattern formation.

Jian Tang

Mila - Quebec AI Institute

"Geometric Deep Learning for Protein Design"

Proteins are workhorses of living cells. Understanding the functions of proteins is critical to many applications such as biomedicine and synthetic biology. Thanks to recent biotechnology breakthroughs such as gene sequencing and Cryo-EM, a large amount of protein data (such as protein sequences and structures) are generated, providing a huge opportunity for AI. As the functions of proteins are determined by their structures, in this talk, I will introduce our recent work on protein understanding based on protein 3D structures with geometric deep learning. I will introduce three different topics including protein representation learning, generative models for protein structure prediction, and generative models for protein design, and also how these techniques are used for real-world applications in protein design.

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Annual Meeting for the Society for Mathematical Biology, 2025.