September 1
Speaker: Calina Copos (Northeastern University)
Title: Emergence of biased behavior in small cell clusters
Abstract: Left/right asymmetry is a hallmark of living systems, where local interactions among energy-consuming components generate organized large-scale organization. To isolate the minimal ingredients underlying this process, we study cell doublets as the smallest nontrivial collective unit.
Combining experiments and mechanobiochemical modeling, we show how mechanical coupling between cells can generate (and modulate) a directionality bias in collective migration. The first example focuses on a mechanochemical model of cell pairs migrating on flat substrates, where we have identified two motility modes: the individual contributor (IC) mode, in which each cell generates its own traction force dipole, and the supracellular (S) mode, characterized by a single dipole spanning the pair. These motility modes are observed in experimental systems, but with different biases depending on the cell type — amoeboid cells predominantly adopt the IC mode, while mesenchymal cells favor the S mode. We show that the model can capture the emergence of both motility modes and that importantly, not cell-cell interactions, but the extent of protrusions modulate which motility mode is preferred. Lastly, we will discuss a macroscopic, agent-based model for bias in the rotational movement of cell pairs. Together, these models illustrate how symmetry breaking, local interactions, and environmental geometry combine to produce directed behavior in cellular systems.
September 8
Speaker: Yuta Hozumi (Georgia Tech)
Title: Topological Insight into Viral Evolution
Abstract: Biological sequences are often represented using the frequencies of short subsequences, or k-mers. While these representations are computationally convenient, they provide limited information about how k-mers are organized and related within a sequence. In this talk, I will present a topological framework for characterizing the multiscale organization of k-mers in genomic sequences. By combining persistent homology with spectral information from the persistent Laplacian, the resulting representation captures both topological and geometric features that are not reflected by k-mer frequencies alone. I will demonstrate how these descriptors can be used to compare and classify viral genomic sequences and to construct quantitative measures of genetic similarity. I will conclude by discussing how this framework can be extended to develop more general structure-aware representations for biological sequence data.
September 15
Speaker: Pei Liu (Pennsylvania State University)
Title: From Liquid Crystals to Knots: Mathematical Modeling of Bacteriophage DNA
Abstract: Bacteriophages densely pack their long dsDNA genome inside a protein capsid, where the confined DNA exhibits hexagonal chromonic liquid-crystalline ordering with knotted structure that depends sensitively on the surrounding conditions. Understanding how this organization emerges, and how it affects the resulting genome delivery, presents an interesting mathematical modeling problem at the interface of material science and mathematical biology.
In this talk, I will present a continuum modeling framework for bacteriophage DNA based on liquid-crystal theory and variational principles. We model the packed DNA as a confined chromonic liquid crystal and develop thermodynamically consistent models incorporating elastic, electrostatic, and entropic effects. Bifurcation analysis and numerical simulations reveal how the competition between bending and twisting elasticity can drive structural transitions and the formation of helical DNA configurations inside the capsid. I will then discuss how the resulting DNA configurations are connected to topology. By combining deterministic continuum models with stochastic dynamics, we investigate the distribution of DNA knot types and compare the model predictions with experimental and structural observations. Experimental measurements of DNA layer positions and knot probability distributions are used to calibrate key model parameters.
September 22
Speaker: Zhisheng Shuai (University of Central Florida)
Title: Quantifying Population Heterogeneity Using Generalized Inverses: Implications for Spatial Ecology and Epidemiology
Abstract: Understanding how spatial and temporal heterogeneity influences population and disease dynamics is one of the key challenges in ecology and epidemiology. In this talk, we explore the application of generalized inverses to quantify and analyze variability in population persistence, growth rates, and disease invasibility. By leveraging this mathematical framework, we examine how habitat heterogeneity, resource distribution, and migration patterns influence population stability and resilience. Our approach provides novel insights into the role of environmental variability in shaping long-term population outcomes, with implications for conservation strategies, ecological management, and infectious disease prevention.
September 29
Speaker: Olivia Clifton (University of Illinois Urbana-Champaign)
Title: Pattern Formation Through Nonlocal Competition and Facilitation
Abstract: We investigate population dynamics in a single species with spatially nonlocal competition and facilitation, with local diffusion. One particular motivation is dryland vegetation patterns. Although these have been largely studied in the mathematical literature using reaction-diffusion models for water and biomass, a large number of math-bio models instead consider a single-component model for biomass, incorporating spatial competition for water or resources directly using nonlocal kernels. These models often choose the specific kernels arbitrarily, and we are interested in determining the role of kernel choice in pattern formation.
We investigate pattern formation when varying two main parameters: the death rate (encoding environmental harshness), and the relative spatial scales of competition vs. facilitation. We find supercritical pattern-forming bifurcations from a uniform spatial state to a periodic state, with significant dependence of the onset and wavelength of patterns on the shape of the nonlocal kernels. Past onset, numerical continuation reveals a typical ‘Turing before tipping’ motif where patterned states survive in conditions where a uniform state is no longer stable. Here, qualitative behavior seems to differ between kernels. We particularly compare two classes of kernels: those whose Fourier transforms are nonnegative, and those whose Fourier transforms do take on negative values, highlighting subtleties in the latter case.