Seminars and Colloquia by Series

Evolutionary de Rham-Hodge method and its applications in SARS-CoV-2 studying

Series
Mathematical Biology Seminar
Time
Friday, December 2, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jiahui ChenMichigan State University -- Department of Mathematics

Please Note: The classroom version of this event will be held in Skiles 005. Everyone on campus at Georgia Tech is highly encouraged to attend this version. The virtual version will be administered through Zoom (https://gatech.zoom.us/j/99514218896).

This talk will discuss an evolutionary de Rham-Hodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds constructed from filtration, which induces a family of evolutionary de Rham complexes. While the present method can be easily applied to close manifolds, the emphasis is given to more challenging compact manifolds with 2-manifold boundaries, which require appropriate analysis and treatment of boundary conditions on differential forms to maintain proper topological properties. Three sets of Hodge Laplacians are proposed to generate three sets of topology-preserving singular spectra, for which the multiplicities of zero eigenvalues correspond to exact topological invariants. To demonstrate the utility of the proposed method, the application is considered for the predictions of binding free energy (BFE) changes of protein-protein interactions (PPIs) induced by mutations with machine learning modeling. It has a great application in studying the SARS-CoV-2 virus' infectivity, antibody resistance, and vaccine breakthrough, which will be presented in this talk.

Identifiability and inference of phylogenetic birth-death models

Series
Mathematical Biology Seminar
Time
Friday, October 28, 2022 - 15:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Jonathan TerhorstUniversity of Michigan - Department of Statistics

The phylogenetic birth-death process is a probabilistic model of evolution that
is widely used to analyze genetic data. In a striking result, Louca & Pennell
(Nature, 2020) recently showed that this model is statistically unidentifiable,
meaning that an arbitrary number of different evolutionary hypotheses are
consistent with any given data set. This grave finding has called into question
the conclusions of a large number of evolutionary studies which relied on this
model.

In this talk, I will give an introduction to the phylogenetic birth-death
process, and explain Louca and Pennell's unidentifiability result. Then, I will
describe recent positive results that we have obtained, which establish that, by
restricting the evolutionary hypothesis space in certain biologically plausible
ways, statistical identifiability is restored. Finally, I will discuss some
complementary hardness-of-estimation results which show that, even in identifiable
model classes, obtaining reliable inferences from finite amounts of data may be
extremely challenging.

No background in this area is assumed, and the talk will be accessible to a
mathematically mature audience. This is joint work with Brandon Legried.

Zoom link:  https://gatech.zoom.us/j/99936668317

Reconstructing ancestral sequences in large trees

Series
Mathematical Biology Seminar
Time
Thursday, April 28, 2022 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 006 and ONLINE
Speaker
Brandon LegriedSoutheast Center for Mathematics and Biology

Please Note: Meeting link: https://bluejeans.com/865908583/9834

Statistical consistency in phylogenetics has traditionally referred to the accuracy of estimating mutation rates and phylogenies for a fixed number of species as we increase the amount of data within their signatures, such as DNA and protein sequences. Analyzing sequences undergoing indel mutations (insertions and deletions of sites) has provided a venue for understanding what power can be provided by a lot of data. In this talk, we discuss some of the failings of this approach. For instance, it will be shown that phylogeny estimation is impossible for infinitely long sequences, even with infinite data. This motivates a dual type of statistical consistency, where the number of species is taken to infinity rather than the size of each signature. Here, we give polynomial-time algorithms for ancestral sequence estimation and sequence alignment for reference phylogenies with so many species that they are sufficiently dense. Based on joint work with Louis Fan and Sebastien Roch.

Non-negative CP tensor decomposition to identify response signatures in omics time-course experiments

Series
Mathematical Biology Seminar
Time
Wednesday, April 27, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Anna KonstorumYale University

Please Note: Meeting Link: https://gatech.zoom.us/j/94882290086 (Meeting ID: 948 8229 0086, Passcode: 264830)

A central goal of biological experiments that generate omics time-course data is the discovery of patterns, or signatures, of response. A natural representation of such data is in the form of a third-order tensor. For example, if the dataset is from a bulk RNASeq experiment, which measures tissue-level gene expression collected at multiple time points, the data can be structured into a gene-by-subject-by-time tensor. We consider the use of a non-negative CANDECOMP/PARAFAC (CP) decomposition (NCPD) on the tensor to derive rank-one components that correspond to biologically meaningful signatures.  To assess whether over-factoring has occurred in a model, we develop the maximum internal n-similarity score (mINS) score. We use the mINS as well as other metrics to choose a model rank for downstream analysis. We show that on time-course data profiling vaccination responses against the Influenza and Bordetella Pertussis pathogens, our NCPD pipeline yields novel and informative signatures of response. We finish with outstanding research challenges in the application of tensor decomposition to modern biological datasets.

The Spatio-Temporal Dynamics of Synthetic Microbial Consortia

Series
Mathematical Biology Seminar
Time
Wednesday, April 20, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Krešimir JosićUniversity of Houston

Please Note: Meeting Link: https://gatech.zoom.us/j/94882290086 (Meeting ID: 948 8229 0086, Passcode: 264830)

Modeling is essential in the design of genetic circuits with desired properties. I will review several examples where mathematical models have been central to the development and understanding of the dynamic of synthetic organisms. I will start with a discussion of synthetic bacterial consortia that exhibit emergent oscillatory behavior - when co-cultured, the interaction between two bacterial strains results in population-level transcriptional oscillations. The spatio-temporal dynamics of such consortia, including synchrony between distant parts of the population, depend sensitively on the architecture of the underlying genetic circuits. I will then describe how oscillations, and other spatiotemporal patterns can arise in consortia of cells that individually exhibit bistable dynamics. I will show how simplified mathematical models can help us understand how order emerges in these system, how robust oscillations and other patterns can arise, and how they are maintained. 

Formal grammar modeling three-stranded DNA:RNA braids

Series
Mathematical Biology Seminar
Time
Wednesday, April 13, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Margherita Maria FerrariUniversity of South Florida

Meeting Link: https://gatech.zoom.us/j/94882290086 (Meeting ID: 948 8229 0086, Passcode: 264830)

Abstract: R-loops are three-stranded structures formed by a DNA:RNA hybrid and a single strand of DNA, often appearing during transcription. Although R-loops can threaten genome integrity, recent studies have shown that they also play regulatory roles in physiological processes. However, little is known about their structure and formation. In this talk, we introduce a model for R-loops based on formal grammars, that are systems to generate words widely applied in molecular biology. In this framework, R-loops are described as strings of symbols representing the braiding of the strands in the structure, where each symbol corresponds to a different state of the braided structure. We discuss approaches to develop a stochastic grammar for R-loop prediction using experimental data, as well as refinements of the model by incorporating the effect of DNA topology on R-loop formation.

 

Competition, Phenotypic Adaptation, and the Evolution of a Species' Range

Series
Mathematical Biology Seminar
Time
Wednesday, March 30, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Farshad ShiraniSchool of Mathematics, Georgia Institute of Technology

Please Note: Please Note: Meeting Link: https://bluejeans.com/426529046/8775

Why is a species’ geographic range where it is? Immediate thoughts such as penguins cannot climb steep cliffs or colonize deserts are often not the answer. In fact, identifying causes of species’ range limits is a fundamental problem in evolutionary ecology that has crucial implications in conservation biology and understanding mechanisms of speciation.

In this talk, I will briefly introduce some of the biotic, genetic, and environmental processes that can determine a species’ range. I will then focus on two of such processes, competition and (mal)adaptation to heterogeneous environments, that are commonly thought to halt  species’ range expansion and stabilize their range boundary. I will present a model of species range dynamics that incorporates these eco-evolutionary processes in a community of biologically related species. I will discuss biologically plausible ranges of values for the parameters of this model, and will demonstrate its dynamic behavior in a number of different evolutionary regimes.

Modeling and topological data analysis of zebrafish-skin patterns

Series
Mathematical Biology Seminar
Time
Wednesday, March 16, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Alexandria VolkeningPurdue University

Please Note: Meeting Link: https://bluejeans.com/426529046/8775

Wild-type zebrafish are named for their dark and light stripes, but mutant zebrafish feature variable skin patterns, including spots and labyrinth curves. All of these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells in the skin. This leads to the question: how do cell interactions change to create mutant patterns? The longterm biological motivation for my work is to shed light on this question — I strive to help link genes, cell behavior, and visible animal characteristics. Toward this goal, I build agent-based models to describe cell behavior in growing fish body and fin-shaped domains. However, my models are stochastic and have many parameters, and comparing simulated patterns, alternative models, and fish images is often a qualitative process. This, in turn, drives my mathematical goal: I am interested in developing methods for quantifying variable cell-based patterns and linking computational and analytically tractable models. In this talk, I will overview our agent-based models for body and fin pattern formation, share how topological data analysis can be used to quantify cell-based patterns and models, and discuss ongoing work on relating agent-based and continuum models for zebrafish patterns.

Multiscale Modeling of Prion Aggregate Dynamics in Yeast

Series
Mathematical Biology Seminar
Time
Wednesday, March 9, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Mikahl Banwarth-KuhnUniversity of California, Merced

Please Note: Meeting Link: https://bluejeans.com/426529046/8775

Prion proteins are responsible for a variety of fatal neurodegenerative diseases in mammals but are harmless to Baker's yeast (S. cerevisiae)- making it an ideal system for investigating the protein dynamics associated with prion diseases. Most mathematical frameworks for modeling prion aggregate dynamics either focus on protein dynamics in isolation, absent from a changing cellular environment, or modeling prion aggregate dynamics in a population of cells by considering the "average" behavior. However, such models are unable to reproduce in vivo properties of different yeast prion strains.

In this talk, I will show some results from recent individual-based simulations where we study how the organization of a yeast population depends on the division and growth properties of the colonies. Each individual cell has their own configuration of prion aggregates, and we study how the population level phenotypes are a natural consequence of the interplay between the cell cycle, budding cell division and aggregate dynamics. We quantify how common experimentally observed outcomes depend on population heterogeneity.

Recording link: https://bluejeans.com/s/lbpACr_YZ0N

Modeling subcellular dynamics of T6SS and its impact on interbacterial competition

Series
Mathematical Biology Seminar
Time
Wednesday, March 2, 2022 - 10:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Yuexia Luna LinÉcole Polytechnique Fédérale de Lausanne

Please Note: Meeting Link: https://bluejeans.com/426529046/8775

The type VI secretion system (T6SS) is a bacterial subcellular structure that has been likened to a molecular syringe, capable of directly injecting toxins into neighboring cells. Bacteria use T6SS to kill competitor cells, gaining limited space and resources, such as a niche in a host. T6SS has been found in about 25% of Gram negative bacteria, including some human pathogens. Thus, understanding regulation, control, and function of T6SS, as well as the role of T6SS in interbacterial competition, has far-reaching ramifications. However, there are many open questions in this active research area, especially since bacteria have evolved diverse ways in producing and engaging this lethal weapon.

In a multidisciplinary collaboration, we combine experiments and applied mathematics to address a central question about T6SS’s role in interbacterial competition: what is the connection between the subcellular dynamics of T6SS and the competitive strength of the population as a whole? Based on detailed microscopy data, we develop a model on the scale of individual T6SS structures, which is then integrated with an agent-based model (ABM) to enable multi-scale simulations. In this talk, we present the experimental data, the subcellular T6SS model, and findings about T6SS-dependent competitions obtained by simulating the ABM.

Recording link: https://bluejeans.com/s/6fzcqvzTQ5m

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