Schedule for: 23w5142 - Mathematical Methods for Exploring and Analyzing Morphological Shapes across Biological Scales

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

BIRS Lounge (PDC 2nd floor)

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Animal cells from different tissues look quite different from each other, but even the same type of cell adopts a variety of different morphologies when cultured in identical conditions. We argue that these different morphologies are not completely random and are related to internal cell states. Here I will describe some of our work exploring this hypothesis. We have imaged thousands of cells in different experimental conditions and use many morphological parameters to measure cell shape and cytoskeletal morphology. Using this data, along with machine learning methods, we show that quantifiers of cell shape and cytoskeletal texture can be used to discriminate between different cell states. Projections of the data to lower-dimensional shape space can be used to distinguish between similar and dissimilar changes in shape. Pharmacological drugs that perturb the cytoskeletal can also be identified by morphological changes. We show that we can distinguish between cancer cells that differ by a single inserted gene mutation. Analysis of images using an interpretable convolutional neural network method showed that CNNs are sensitive to local features of actin structure. Our results show that cellular images are indeed information-rich and can be used as a single cell assay of cell state.

Form is function. Just as the beaks of Darwin’s finches are adapted to suit their specific ecological niche, so too do cells exhibit morphologies that associate with their function. Neurons stereotypically have long axons and dendrites to facilitate connection to other neurons and for long-range information transmission. Indeed, the distortion of normal cellular morphology is often the first clinical indicator of disease. Metaplasia, for example is a key tissue marker of progression to cancer. Yet, beyond universal extraction of morphological measurements as a readout of a cell’s functional response, little is known of the mechanisms by which morphology could regulate cell signalling, function and fate and their contribution to pathogenesis. From a molecular viewpoint, cell morphology, more specifically the cell membrane is indispensable for extra- and intra- cellular signalling. Not only does the membrane contain the receptors that allow sensing and trigger signal transduction, with channels for protein transport but crucially the interface for cell-to-cell contact and serves as a catalyst for biochemical reactions. How do signalling molecules spatially distribute relative to subcellular morphological structure like blebs, lamellipodia or filopodia? How does this distribution change over time or in response to microenvironmental changes? Could the morphological structures even be the gatekeeper for a molecular signal to affect a bona fide functional cell response? To begin to systematically study and answer such questions quantitatively from observational data requires the ability to perform computation on 3D cell surfaces across space and time. Here, I will present a generalized surface-computing framework we have developed, u-Unwrap3D for analyzing arbitrary cell morphologies and both external and internal surface-proximal signals including surface contacts, structures, and molecular intensity. u-Unwrap3D brings together and generalizes the idea of surface unwrapping prevalent in map-making, 3D computer graphics design, human brain atlases and embryo development in a manner applicable to cells. Specifically, u-Unwrap3D develops distortion-minimizing and topology-preserving bidirectional mappings that enables the 3D cell surface at every video timepoint to be projected into shared lower dimensional topographic and 2D image coordinate spaces. This enables us to perform computations using the most suited surface coordinate representation including the decomposition of local surface structures from their underlying global geometry and their tracking over time. I will demonstrate this on timelapse videos of 3D cell blebbing and ruffling.

Mycobacterial pathogens represent some of the most virulent microbes causing millions of deaths worldwide annually. Central to our incapacity to deal with these infections is the ability for genetically sensitive bacilli to phenotypically resist killing by both cidal antibiotics and host immunity. We developed Long-Term Time-Lapse Atomic Force Microscopy (LTTL-AFM) as an advanced imaging modality driving discovery-based, hypothesis-generating research focused on redefining the fundamental principles for how mycobacteria live and die. The molecular mechanisms for many fundamental cell processes in mycobacteria are unknown in part because homologs from evolutionarily disparate microbes are not encoded. Using LTTL-AFM, we have established new foundations in knowledge driving fundamental cell processes, such as 1) division site selection, 2) division mechanics, 3) bi-pole elongation dynamics, 4) cell mechanical morphotype switching, or even 5) death (for which we still have no understanding in microbiology). My talk will focus on showcasing how I have used LTTL-AFM to investigate microbial life within a biophysical world, beyond the dogmas established by biochemistry research over the past century.

In this talk, I will present a suit of models for single cell migration based on geometric surface PDEs as well as bulk reaction-diffusion systems coupled with viscoelastic continuum mechanics for the cytoskeleton. These models fall under the general concept of geometric bulk-surface PDEs. These models allow us to describe more faithfully, experimental observations both for single and collective cell migration. As a by-product of these models, I will showcase both directed and random cell migration as well as imaged-based cell migration that naturally allows us to quantify automaticaly proliferation rates associated with cell division.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

The reaction and transport of various chemical species in cells such as calcium or ATP are well described by systems of differential equations. However, capturing the full spatiotemporal details of these signaling networks, particularly within the complicated geometries exhibited by real cells, presents a unique computational challenge. Not only are the resulting systems of partial differential equations (PDEs) often highly nonlinear, but they are mixed-dimensional, involving reactions that occur across multiple surfaces (e.g. the plasma membrane and organelle membranes) and volumes (e.g. the cytosol and the interior of organelles). Recently, we developed a software package, Spatial Modeling Algorithms for Reaction and Transport (SMART), tailored to assembling and solving systems of mixed-dimensional PDEs within realistic cell geometries. SMART is an open-source Python-based package and uses the finite element library FEniCS to solve these systems. Here, we present applications of this software to model signaling dynamics in cellular or subcellular geometries acquired from electron microscopy. In particular, we consider neuron calcium dynamics within individual dendritic spines and at the whole-cell level, including various fluxes occurring between the cytosol and the endoplasmic reticulum. We find a key role for surface area to volume ratios in regulating the local amplification of reactions. Furthermore, we demonstrate that the localization of receptors is a strong determinant of calcium transient timing and magnitude.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Motivated by continuous heterogeneity in cryo-EM, I will discuss mathematical methods to discover low-dimensionality in datasets consisting of 3D volumes (e.g., molecules). The basic mechanism is the by-now classic method of diffusion maps, which computes the leading eigenvectors of an affinity matrix. In the talk I will focus on two innovations to the diffusion maps framework for situations when the data points are shapes: 1) the use of optimal transport-based affinities; and 2) infinite data augmentation to account for rotational ambiguities. To illustrate the results, numerical experiments will be included.

Cryogenic electron microscopy (cryo-EM) has transformed structural biology by allowing to reconstruct 3D biomolecular structures up to near-atomic resolution. However, the 3D reconstruction process remains challenging, as the 3D structures may exhibit substantial shape variations, while the 2D image acquisition suffers from a low signal-to-noise ratio, requiring to acquire very large datasets that are time-consuming to process. Current reconstruction methods are precise but computationally expensive, or faster but lack a physically-plausible model of large molecular shape variations. To fill this gap, we propose CryoChains that encodes large deformations of biomolecules via rigid body transformation of their chains, while representing their finer shape variations with the normal mode analysis framework of biophysics. Our synthetic data experiments on the human GABA\_B and heat shock protein show that CryoChains gives a biophysically-grounded quantification of the heterogeneous conformations of biomolecules, while reconstructing their 3D molecular structures at an improved resolution compared to the current fastest, interpretable deep learning method.

We review and introduce some Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short discussion of various approaches at building Riemannian metrics on shape spaces (with a special focus on the foundations of the large deformation diffeomorphic metric mapping algorithm), we introduce elastic metrics and growth models that can be derived from them. In the latter context, a new class of metrics, involving an infinitesimal growth tensor, is considered and some of its properties are studied. This is joint work with Nicolas Charon.

TBA

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

This talk will discuss some of our recent works in leveraging Riemannian metric settings on shape spaces to perform various shape analysis and processing tasks on surface mesh data. We will specifically consider the framework of (elastic) second-order Sobolev invariant Riemannian metrics on the space of 3D surfaces and introduce a convenient relaxed formulation of the geodesic distance estimation problem, which allows to numerically deal with triangulated surfaces of potentially inconsistent mesh structure and partial correspondences. We will also show how this numerical approach can be extended to other central tasks such as the extrapolation and parallel transport of surface trajectories, or the estimation of the mean and principal components in a population of surface shapes. In the last part of the talk, we shall present a constrained variation of this model in which deformations are restricted via the use of data-driven deformation bases, and show applications of this idea to the problem of analyzing pose and shape variability in datasets of human body sequences.

The Allen Institute for Cell Science aims to understand the principles by which human induced pluripotent stem cells (hiPSCs) establish and maintain robust dynamic localization of cellular structures, and how they transition between states during differentiation and disease. To do this, we take advantage of 3D microscopy images of the Allen Cell Collection (www.allencell.org), a collection of endogenous fluorescently tagged hiPSC lines, each representing a particular cellular organelle or structure. A major challenge in cell biology is being able to fully describe the morphological variability of intracellular structures using a small set of numbers that are generative and interpretable. To overcome this challenge, we design appropriate image data representations depending on the complexity of the intracellular structure of interest. We use spherical harmonics expansion to represent cell and nuclear shapes of hiPS cells together with an analysis framework that permits comparison between populations of cells. We show how this framework can be used to reveal the polarization of intracellular structures in cells located at the edge of hiPS colonies. We use point clouds and signed distance functions as inputs to a rotation equivariant variational autoencoder (VAE) to explicitly represent more complex intracellular structures. We applied this framework to DNA replication foci (via PCNA) and nucleoli (via nucleophosmin) and found that we can get compact representations and high-fidelity reconstructions. We show that signed distance functions are more appropriate data representation for irregular shapes with variable numbers of pieces like nucleoli. For both PCNA and nucleoli, the learned latent representations capture known aspects of variability seen by eye (e.g., changes in total volume and number of pieces) and can be used as good predictors of cell cycle in the case of PCNA. Future work will extend these analyses beyond the nucleus, to intracellular structures with other characteristic geometries and interactions.

Morphogenesis is a dynamic process in which developmental systems transform into specialized complex structures. In insects, imaginal disc are sacs of epithelial cells that develop into the adult appendages. During the third larval instar of the fruit fly, Drosophila melanogaster, the wing disc transforms from a flat arrangement of cells into a highly-folded epithelium. The locations of these folds are precisely positioned to separate different populations of cells and are required to drive key morphogenetic events during metamorphosis. While the morphogenetic signals and mechanical forces that drive the formation of these folds have been investigated in previous studies, little is known about the contribution of patterning and cell proliferation to the formation of these folds. For example, are folds driven by proliferation of a few cells that leave the epithelial plane or cells from the flat part of the disc are pulled into the folds? Are there patterning cues that limit the extent of this process? Are cell proliferation enhanced by lowered tension driven by fold formation? In this talk, we will show quantitatively that fold formation is coupled to cell proliferation. Furthermore, when the wing selector gene, vestigial, is inhibited cells, are driven into the folds suggesting that the processes of morphogenesis, growth, and cell differentiation are tightly regulated in this system.

Recent advances in single-cell techniques catalyze an emerging field of studying how cells convert from one phenotype to another, in a step-by-step process. Two grand technical challenges, however, impede further development of the field. Fixed cell–based approaches can provide snapshots of high-dimensional expression profiles but have fundamental limits on revealing temporal information, and fluorescence-based live-cell imaging approaches provide temporal information but are technically challenging for multiplex long-term imaging. I will discuss our efforts on reconstructing the dynamics of cellular state transitions using live cell imaging and deep-learning facilitated image analyses.

The principal function of the nucleus is to facilitate storage, retrieval, and maintenance of the genetic information. A unique feature of nucleoplasm—the fluid of the nucleus—is that it contains chromatin (DNA) and RNA. In contrast to other important biological polymer hydrogels, such as mucus and extracellular matrix, the nucleic acid polymers have a sequence that encodes both genetic information and strongly influences spatial organization. How does crowding in a sequence specific hydrogel influence spatial organization of the dynamic molecular components responsible for nuclear function? We are becoming increasingly aware of the role of liquid-liquid phase separation (LLPS) in cellular processes in the nucleus and the cytoplasm. Complex molecular interactions over a wide range of timescales can cause large biopolymers (RNA, protein, etc) to phase separate from the surrounding nucleoplasm or cytoplasm into distinct biocondensates (spherical droplets in the simplest cases). I will discuss recent work modelling the role of nuclear biocondensates in neurodegenerative disease and several ongoing projects modelling molecular organization in the nucleus.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Since the resolution revolution in cryo-EM the method has become a dominant technique for high resolution structure determination of biological macromolecules. However, it is often still treated as a method for obtaining individual high resolution structures, as had been the necessity for decades with X-ray crystallography, despite the potential access it gives to the conformational ensemble of any given molecule. Here we delve into existing techniques for the analysis of conformational heterogeneity of single particle cryo-EM datasets, discussing the caveats of different methodologies, difficulties that arise when analyzing certain types of real datasets (e.g. membrane proteins), and the importance of realistic protocols for fake cryo-EM data generation for the production of ground truth conformational ensembles to benchmark these methods.

Cryo-electron microscopy (cryo-EM) is a technique for reconstructing the 3-dimensional (3D) structures of biomolecules from electron microscopy images. A key step in cryo-EM is to infer atomic coordinates as well as chemical identities from experimentally resolved cryo-EM maps (molecular shapes). Recently, shape-recognition-based de novo building methods have shown the potential to streamline this process. However, they cannot build complete structures due to insufficient cryo-EM map resolution. In the related field of protein folding, AlphaFold2 has made a breakthrough in predicting protein structures from sequences alone, but with certain limitations. A notable limitation is AlphaFold2's inability to predict structures for proteins with multiple stable conformations. To overcome these issues, we developed a new method named "Fragment-guided Flexible Fitting" (FFF) that bridges protein structure prediction and molecular shape recognition with flexible fitting. In this talk, I will present the algorithm behind FFF and its application to real-world cryo-EM experimental data.

In this research, we would like to identify the morphological features of the cells in the H$\&$E images that can be used as a biomarker of senescent cells. This will allow identification of senescent cells in histology data lacking other forms of data, like (single-cell or spot-level) gene expression. For example, this would allow us to correlate levels of senescence with outcome in clinically annotated H$\&$E samples. We will first calculate senescence score using spot level gene expression in spatial transcriptomics data. Then we will compute morphological features in H$\&$E data for the same cells. Then, we will correlate the two and find a pattern between morphological features and senescence score. We use Endometrium of patients with endometriosis (a tissue type expected to have senescent cells). We calculate the senescence score per spot based on gene expression profile of SenMayo marker gene set using spatial transcriptomics data. We also calculate the stromal scores using the expression profile of the marker genes for stroma for endometrium tissue and as expected we observed that spots with high senescence score have high stromal score. To quantify morphological features of the cells we use high resolution image of the tissue stained with hematoxylin and eosin. We developed a workflow in python which uses Stardist package to segment the nuclei images and extract their boundary. Then we developed a pipeline using cell profiler software to extract morphology features of the cells. Some of the features are calculated based on nuclei mask like area, perimeter, etc. Some other features are calculated based on pixel intensities within each nucleus. For this purpose, the H$\&$E image is first split into hematoxylin and eosin channels and then features like mean intensity and standard deviation of intensity of the pixels per nuclei are calculated separately for hematoxylin and eosin stains. In addition, we measure some neighboring features such as number of the cells that are touching each cell or percent of the cell boundary in contact with other cells. Then we calculate the mean and standard deviation of the features for cells that fall inside each spot. We have total of 400 morphology features per spot so far. We found that the features calculated based on intensity of the images have higher correlation with senescence score than features that are calculated based on nuclei mask. Using correlation analysis between senescence score and morphology features we found that there is high correlation between some of the features and senescence score(up to 0.4). We will further explore linear and non-linear models using morphology features to predict senescence score. We will also cluster the spots based on morphology and check to see if the cells with similar senescence score cluster together.

Single-Particle Electron Cryomicroscopy (cryo-EM) will soon become the leading technique for determining 3-D molecular structures at high resolution. In cryo-EM, the 3-D structure needs to be determined from many 2-D noisy tomographic projection images of the molecule taken at unknown viewing directions. Existing computational methods in cryo-EM are based on (weighted) Euclidean distances for both 2-D image analysis and 3-D volume analysis. In this talk we will give three vignettes of the cryo-EM computational pipeline for which non-Euclidean metrics are an appealing alternative: 2-D image classification, 3-D volume alignment, and 3-D heterogeneity analysis.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

In this talk, three different mathematical techniques that may be considered "multi-scale" will be surveyed with some examples of applications. One technique comes from harmonic analysis: the use of multiscale a.k.a. multiresolution analysis in transforms like wavelet and shearlet, as well as their use within morphological component analysis, which was originally developed to separate different types of astrophysical data. Another technique comes from topological data analysis, namely persistence homology, which tracks features like holes and texture. An application to classification of cloud types will be given. Finally, a technique to find subspaces of increasing dimension to best represent a data set, called the flag median, will be presented with applications from computer vision.

Quasi-conformal geometry has recently emerged as a useful tool in imaging science. In this talk, we will discuss how quasi-conformal theory can be applied for quantifying biological shape variation. More specifically, quasi-conformal mappings can be used for establishing a 1-1 correspondence between two biological shapes with prescribed feature landmarks exactly matched. Moreover, the quasi-conformal distortion encodes important information about the local geometric difference between two shapes. Examples across biological scales are presented to demonstrate the effectiveness of the method.

Methods for performing hypothesis testing on anatomical surfaces, such as multivariate T-tests on corresponding vertices, tend to produce non-meaningful results when the collection of surfaces vary over multiple species, as is often the case in evolutionary anthropology; it is difficult to determine which areas on which surfaces differ in a statistically significant sense. Furthermore, anthropological settings often suffer from low sample sizes, calling the reliability of parametric methods into question. Motivated by these problems, we propose to a novel nonparametric statistical test based on apply manifold moving least-squares (MMLS), a technique for computing approximating manifolds for high-dimensional point clouds, to spaces of corresponding patches on a given collection of surfaces of interest. Specifically, we use the Riemannian metric of the learned manifold to define a notion of distance between any two patches, for which we have theoretical guarantees of approximation accuracy under mild assumptions, and propose a test based on bootstrapped distributions of distances on the manifold. As an application, we use this test in combination with standard statistical rank tests to quantitatively compare a molar found in the Nakwai region of Kenya with those of four different primate genera, the results of which may shed light on evolutionary timelines of primates. If time permits, we will briefly go over the detail of SAMS, the manifold learning-based registration process used in the course of this study. Joint work with Doug Boyer, Ingrid Daubechies, and Barak Sober.

Given a collection of surfaces with common key features, that have a rough correspondence, commonly the shape variation in the geometric configuration is considered. However, collating the geometric information of the triangular meshes is sometimes challenging due to the subtle variation of these shapes. A common practice is to model the collection of low-dimensional manifolds as a (nonlinear) fibre bundle with a connection. Even though the connection is known only approximately, its presence can be used to study the base manifold geometry using fibre bundle diffusion. In this talk, we propose a new method for efficiently registering such collections given initial correspondences with varying degrees of accuracy. This method leads to an improvement of the correspondence maps, which can then be exploited to study the base manifold geometry with greater accuracy. We demonstrate our methodology on a toy model, as well as on a collection of anatomical surfaces, and aim to shed light on questions in evolutionary anthropology.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Protein sequence — encoding the unique folded structure and consequently function — plays a profound role in biological information processing. This central dogma, however, appears to be challenged by Intrinsically Disordered Proteins (IDP) that lack unique folded structure, requiring an ensemble-centric view point. Despite the high degree of disorder, IDPs have specific ensemble average conformational features and function that depend on the sequence, not just the composition of the amino acids. How do we unravel the hidden code relating sequence, conformational ensemble and function ? Borrowing principles and tools of theoretical polymer physics we are discovering elegant mathematical relations as a function of sequence (respecting exact placement of the amnio acids) giving rise to high ·dimensional matrices that serve as molecular blueprints of IDPs. These information rich matrices have dual role. First, they map sequence features to a map of three dimensional conformational features and provide insights on how to alter conformations (e.g collapse or expansion) using biological regulators (mutation, phosphorylation). Second, these matrices combined with data science tools hold promise to detect functionally similar IDPs, an unmet challenge in IDPs due to failure of traditional tools of sequence/structure alignment developed for folded proteins.

The evolution of circulating viruses is shaped by their need to evade antibody response, which mainly targets the glycoprotein (spike). However, this diversity explores the antigenic space unequally, allowing pathogens such as the influenza virus to impose complex immunodominance hierarchies that distract antibody responses away from crucial sites of virus vulnerability. We developed a computational model of affinity maturation to map the patterns of immunodominance that evolve upon immunization with natural and engineered displays (nano-particles) of hemagglutinin, the influenza vaccine antigen. In this talk, I will show how antibody responses can be focused upon functionally conserved, but immunologically recessive sites on the influenza spike that are the target of human broadly neutralizing antibodies -- a step toward a universal flu vaccine. I will further show that geometry plays an integral part in shaping the evolution of the seasonal flu H1N1 and coronavirus spikes. Taking advantage of 3D models of the virus, we find that antibody pressure, through the geometrical organization of spikes on the viral surface, governs their spike mutability. Studying the mutability patterns of SARS-CoV-2, we find that over time, it acquired, at low frequency, several mutations at antibody-accessible positions, which could indicate possible escape as defined by our model. Hence, we offer a geometry-based approach to assess whether a pandemic virus is changing its mutational pattern to that indicative of a circulating virus.

Inferring biomolecular heterogeneity with cryogenic sample electron microscopy (cryo-EM) is an ambiguous problem that benefits from distinctions and formalization. Depending on the way of representing the latent space, the underlying source distributions can become entangled in the observed distribution through the image formation model. Here I examine source distribution estimation in a minimal toy synthetic setting involving simple forms of heterogeneity, projection, and measurement noise. I show source distribution estimation in amortized variational inference with an evidence lower bound (ELBO) objective. I jointly infer parameters for an amortized posterior distribution of pose and heterogeneity on each measurement, and simultaneously update a running estimate of the source distribution. Although during the measurement process we may lose information about heterogeneity, we can still uniquely identify the underlying source distribution that best explains the data by making a commitment to a parametric forward model, and a distribution family for the latent heterogeneity.

Morphologies of complex spatial structures like the cellular cytoskeleton are the product of a network of molecular interactions between proteins and other biomolecules. Learning about these molecular interactions by studying the evolution of the morphology with time is a difficult inverse problem. Simulations provide a controlled way of learning the role of different model parameters by selectively tuning their relative strengths and observing the resulting behavior. I used the Cytosim simulation package to explore the effect of motor proteins and cross linkers on cytoskeleton dynamics. While this forward approach of running simulation to generate data provided insights into changes in model dynamics with model parameters, it has also provided synthetic data for the inverse approach. In this second approach, we aim to distinguish between models from only the simulation output. For this purpose, I developed a tool that can qualitatively capture information from changes to a cell’s complex cytoskeleton. My tool is reasonably successful at distinguishing models by analyzing simulation data generated with different input parameters. This study systematically investigates the scope of this tool as a classification task, and indicates its potential use in analyzing experimental data.

We examine how a specific instance of the elastic metric, the Square Root Velocity (SRV) metric, can be used to study and compare cellular morphologies from the contours they form on planar surfaces. We process a dataset of images from osteocarcoma (bone cancer) cells that includes different treatments known to affect the cell morphology, and perform a comparative statistical analysis between the linear and SRV metrics. Our study indicates superior performance of the SRV at capturing the cell shape heterogeneity, with a better separation between different cell groups when comparing their distance to their mean shape, as well as a better low dimensional representation when comparing stress statistics. Therefore, our study suggests the use of a Riemannian metric, such as the SRV as a potential tool to enhance morphological discrimination for large datasets of cancer cell images

Recent advances in coupling the nanoscale spatial resolution from Atomic Force Microscopy with continuous, long-term time-lapse imaging (LTTL-AFM) have allowed to study cell morphology dynamics at an unprecedented resolution. For mycobacteria, it has been shown that fundamental cellular processes (e.g., growth, division, and cell death) can be linked to specific shape patterns and phenotypes. However, quantifying the dynamics and biophysical heterogeneity of large population over time is still challenging due to the lack of automated tools and methods to systematically analyze time-series from LTTL-AFM. In collaboration with HA Eskandarian (UCSF), we developed an end-to-end pipeline to quantify the biophysical heterogeneity of cells imaged by LTTL-AFM. This pipeline combines (1) machine learning-based methods for cell tracking and segmentation, (2) algorithms from computational geometry and image analysis for the detection of division events and lineage reconstruction, and (3) non-linear dimensionality reduction methods and metrics for statistical analysis. We applied our pipeline to LTTL-AFM imaging datasets of isogenic populations of M. smegmatis cells and evaluated various biophysical features such as elongation rate, relative pole-elongation rates, and surface morphology upon division-site selection. We characterized and identified, for large populations, key determinants of bacterial cell division, as well as the phenotypic impact of various stress conditions imposed by antibiotic treatment on the mycobacterial cell surface.

Illustrations found in textbooks showcasing cell structures consist of hand-drawn cartoons or single images that fail to encompass the diverse range of morphological variations present in these structures. In the realm of cell biology, a significant shift is occurring, transitioning from crude approximations of cell structure shapes and spatial arrangements to the development of precise and spatially faithful models of cellular components. This transformation is being driven by computational techniques that aim to produce automated, concise, and statistically sound generative models of cellular organization using extensive biological datasets. An example of this progress is CellOrganizer, an open-source system for using microscope images to learn statistical models of the structure of cell components and how those components are organized relative to each other. These models effectively encapsulate the statistical deviations in the arrangement of cellular and subcellular elements by concurrently representing the distributions of their quantities, shapes, and spatial placements. Such models can be juxtaposed, and tailored to different cell types or conditions, to highlight discrepancies in their spatial structures. As generative models, they possess the ability to synthesize novel instances of cells based on the knowledge assimilated by the model. This also furnishes cell geometry information essential for subsequent biochemical simulation studies.

TBA

We present Cell Geometry, an open-source web-based platform for large-scale morphological cell shape analysis. Specifically, we focus on automating 3D cell segmentation and shape analysis using geometric machine learning. The goal of this project is twofold. The first is to perform these tasks at scale, wherein users can upload several terabytes of data and have all the processing done on our platform. Once done, users can download all of the segmentations, outputs of shape analysis such as tangent PCA, and any graphs/visualizations. The second is to make these advanced techniques in deep learning and differential geometry more accessible to researchers with less of a software background, and those who do not have access to the hardware resources to accomplish terabyte-scale analysis. Our segmentation method, CellECT 2.0 from BisQue, employs a rotation equivariant 3D UNET for accurate 3D cell segmentation. The output from this analysis gives us the surface coordinates which is used for the 3D shape analysis. Here, we use geomstats, an open-source Python package for computations and statistics on manifolds, to perform either 2D or 3D shape analysis such as computing mean shape---an important metric to distinguish between different experimental conditions, i.e. Normal vs. Disease. Join us as we launch the platform into a Beta Production Release!

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.