MS06 - MFBM-08

Mathematical methods for biological shape data analysis (Part 1)

Thursday, July 17 at 10:20am

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Note: this minisymposia has multiple sessions. The other session is: and Part-2.

Wenjun Zhao (UBC/Wake Forest University), Khanh Dao Duc (UBC)

Description:

Advances in imaging have for the past few years revolutionized our understanding of biological processes, illustrated by the recent mapping of trillions of human cells, or the explosive rate at which thousands of new protein 3D structures are now determined every year. This unprecedented surge of new biological data yields various mathematical problems and challenges at multiple spatial and time scales for interpreting and analyzing morphological shapes and shape dynamics, which finds close connections to machine learning, statistics, and physics. In this context, our proposed mini-symposium focuses on the mathematical, physical, and statistical aspects of shapes that describe the morphologies of biological structures—from molecules and intracellular organelles to cells, tissues, and organs—and how new modeling tools in this field can help elucidate fundamental biological questions. Intended for a diverse audience of mathematicians, physicists, and computational and experimental biologists, the symposium will feature complementary talks covering multiple aspects of imaging data analysis, ranging from the interplay between cell shapes and fate to new discoveries in protein dynamics through Riemannian geometry. To foster collaboration, share insights, and educate junior scientists, we have invited a diverse panel of participants and speakers from various institutes and career stages, including graduate students, postdocs, and faculty members.

Ben Cardoen

University of Birmingham

"Shape discovery of functional interaction between proteins and organelles in the presence of weak oracle distances in superresolution microscopy"

Novel superresolution microscopy (SRM) allows mesoscale (5-150 nm) discovery in situ, in both live and fixed cells. Unlike EM based approaches, it is less costly, less invasive, and enables tagging of individual targets with fluorescence, at a cost of lower precision. Multichannel SRM enables the study of interacting organelles and protein complexes with use cases such as : ER-Mitochondria contacts, HIV ingress, HIV coat forming, protein complex formation dynamics, chromatic dynamics, and neurotransmitter patterns. Interaction at mesoscale is defined as distance mediated state change. Where EM based analysis is ideally placed to reconstruct stable structure, SRM can describe equilibria and diversity. However, SRM is characterized by complex non-additive noise, and localizes objects with an uncertainty and precision that can be as high as the size of or distance between objects. In other words, SRM interaction analysis works with weak distance oracles. Second, the physics at the mesoscale are decidedly non-linear, calling for algorithms that leverage these factors. Finally, a number of underappreciated SRM specific confounding factors can disrupt downstream analysis. In this talk I will give an overview of those challenges, and review how current methods elucidate interaction patterns from SRM data. Using a new computational paradigm to formalize interaction mathematically, I will review underappreciated confounding factors that can comprise SRM interaction analysis. Finally, using in silico data I will illustrate the potential and limitations of current computational techniques to recover distance mediated state change from SRM data. We will measure if we can detect pentagonal versus hexagonal protein conformations, typical in membrane coat function to form spherical structures, or in the capsid coat of the HIV1 virus.

Ashok Prasad

Colorado State University

"Static Shapes and Dynamic Networks: Morphological Analysis of Cellular Identity"

Cell morphology offers a powerful and underutilized lens for understanding cellular identity, behavior, and state. While transcriptomic and proteomic profiling have revolutionized our capacity to characterize cells, quantitative morphological features can provide complementary insights into cell state and function. In this talk, I will present our recent work demonstrating that cells can be robustly classified using a range of morphological metrics derived from microscopy images. I will also discuss our ongoing efforts to develop morphological features that are sensitive to the dynamics of intracellular structures, such as the actin cytoskeleton and other dynamic polymer networks. We simulate the actin cytoskeleton, incorporating the action of molecular motors and cross-linkers, and look for features that are sensitive to different initial conditions and differences in temporal dynamics. Ultimately, we seek to build a framework in which cellular morphology is treated as a high-dimensional, information-rich signature of cell state. This work contributes to a broader vision of morphology-based phenotyping as a bridge between structure and function in living systems.

Felix Zhou

UT Southwestern

"Methods to identify causal links between morphology and cell signaling"

Form is function. Just as Darwin’s finches have beaks adapted to their ecological niche, so too do cell morphology associate with its function. Indeed, cell shape changes are widely used as a first clinical indicator of disease. Conventionally, we have thought of shape as downstream of a cell’s molecular processes. However, recently we have found that the shape of protrusions on cell surfaces might also directly drive signaling whereby changes to their properties, such as curvature and thickness dynamically in time, modify signaling cascades and ultimately affect fate. For example, we found a previously undescribed role of blebbing - dynamic hemispherical protrusions in melanoma cells to activate prosurvival signals and avoid the normal checkpoint program of programmed cell death – a prerequisite step for cancer metastasis. Causal investigation of shape and signaling is notoriously difficult due to the intricate feedback between the two. Notably, shape changes are a product of molecular signals. Consequently, we have been developing statistical causal inference techniques to systematically test for causal links between 3D cell shapes segmented from microscopy videos with jointly measured molecular signal intensities from fluorescent biosensors. Here, I will talk about 3 general computational frameworks we have developed to enable this: u-Segment3D to segment the 3D surface, leveraging pretrained generalist 2D segmentation models; u-Unwrap3D to bidirectionally map the segmented 3D surface to a 2D image; and u-InfoTrace to adapt 1D causal measures and test spatiotemporal causality in the 2D unwrapped images. I will demonstrate example application to diverse videos of 3D cell blebbing, cancer-immune cell interaction, and organoids.

Joe Kileel

UT Austin

"Method of moments for determining macromolecular shapes in cryo-EM"

In this talk, I will present method of moments based approaches for 3D reconstruction of molecular conformations from datasets of noisy 2D images in cryo-electron microscopy. I will present progress both theoretically and computationally for these methods, in particular leveraging prior and side information to improve the cryo-EM reconstruction. Method of moments based solvers also provide a more general methodology, and may be applicable to other inverse problems involving shape data.

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Annual Meeting for the Society for Mathematical Biology, 2025.