Mathematical Biology Seminar - Spring 2024

For questions about the seminar schedule, please contact Kristina Wicke.

January 24

Fatemeh Ahmadpoor, NJIT

Extreme mechanics of flexible biological and crystalline nanostructures

Flexible nanostructures are ubiquitous. Biological membranes--- lipid bilayers--- are considered Nature's flexible nanostructures due to their very small thickness, which governs cell's viability and functionality through mechanical deformations. In the realm of man-made flexible nanostructures, molybdenum disulfide, phosphorene, boron nitride, and MXenes---to name a few--- are fascinating for numerous reasons. Both biological and crystalline membranes are modeled as elastic sheets and are extremely flexible. Their bending stiffness is quite small and comparable with the thermal energy kBT, that at room temperature they fluctuate noticeably. These thermal fluctuations appear to impact the overall mechanics and physics of crystalline and biological membranes. The study of statistical mechanics of thermal fluctuations of flexible nanostructures is rendered rather complicated due to the necessity of accounting for constitutive and geometric nonlinearities and various boundary conditions. Existing treatments draw heavily on analogies in the high-energy physics literature and are hard to extend or modify in the typical contexts that permeate mechanics, materials, and cell mechanics literature. In this talk, I will review some of our recent efforts in developing mechanics-based methodologies to implement concepts of advanced statistical mechanics in continuum mechanics modeling of flexible nanostructures. Our framework provides a novel and unique route to extract mechanical properties of materials from thermal fluctuations spectra, addresses the unexpected stiffening of fluctuating surfaces with size, and provides insights into the fundamental mechanisms of interactions of nanostructures with biological systems.

February 07

Mengjia Xu, NJIT

Hyperbolic graph embedding for MEG brain network analysis

An expansive area of research focuses on discerning patterns of alterations in functional brain networks from the early stages of Alzheimer’s disease, even at the subjective cognitive decline (SCD) stage. Here, we developed a novel hyperbolic MEG brain network embedding framework for transforming high-dimensional complex MEG brain networks into lower-dimensional hyperbolic representations. Using this model, we computed hyperbolic embeddings of the MEG brain networks of two distinct participant groups: individuals with SCD and healthy controls. We demonstrated that these embeddings preserve both local and global geometric information, presenting reduced distortion compared to rival models, even when brain networks are mapped into low-dimensional spaces. In addition, our findings showed that the hyperbolic embeddings encompass unique SCD-related information that improves the discriminatory power above and beyond that of connectivity features alone. Notably, we introduced a unique metric—the radius of the node embeddings—which effectively proxies the hierarchical organization of the brain. Using this metric, we identified subtle hierarchy organizational differences between the two participant groups, suggesting reduced hierarchy in the dorsal attention, frontoparietal, and ventral attention subnetworks among the SCD group. Last, we assessed the correlation between these hierarchical variations and cognitive assessment scores, revealing associations with diminished performance across multiple cognitive evaluations in the SCD group. Overall, this study presents the first evaluation of hyperbolic embeddings of MEG brain networks, offering novel insights into brain organization, cognitive decline, and potential diagnostic avenues of Alzheimer’s disease. 

February 14

Sarah Strikwerda, University of Pennsylvania

Well-posedness of PDE-ODE coupling with applications to tissue perfusion

In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. The local and global features can be accounted for through a PDE-ODE coupling. I will discuss the well-posedness results for the PDE and our fixed-point strategy to show well-posedness of the PDE-ODE coupled system.

February 21

Yuchi Qiu, University of California, Irvine

Multiscale modeling and topological data analysis in artificial intelligence-driven biology

Artificial intelligence (AI) has emerged as a pivotal tool in biology, revolutionizing data analysis at both large-scale and single-cell levels. However, the lack of interpretability in AI poses challenges in extracting intricate functions and dynamics from high-dimensional, complex heterogeneous, and noisy biological data. In this talk, we aim to address these challenges by investigating dynamics and topology of data via multiscale modeling and topological data analysis. First, we wilmathl discuss our approaches for deciphering cellular spatio-temporal dynamics, focusing on the interplay between gene regulation, spatial signals, and intercellular mechanical interactions. Our approaches include stochastic simulations, the subcellular element method, and reaction diffusion equations. Building upon this foundation, we have developed a deep learning-based dynamical model using unbalanced dynamic optimal transport to connect time-course single-cell transcriptomic snapshots and interrogate underlying gene regulatory networks. Lastly, we will discuss AI models designed to expedite protein design that incorporate a persistent spectral Laplacian method, large language models, and a hierarchical clustering-based Bayesian optimization approach.

March 06 (Virtual Only)

Puneeth Deraje, University of Toronto

Spatial Inference from Ancestral Recombination Graphs using Brownian Motion

Ancestral Recombination Graphs (ARGs) are a way of visualizing the genealogies of large regions of the genome, possibly the whole genome, which might have undergone recombination in the past. It is a generalization of coalescent tree to networks that can account for recombination. Recombination allows branches to split due to recombination as well as coalesce, leading to loops in the graph. While they encode the complete genealogical information of the samples, ARGs are complex objects and extracting relevant information is difficult. One of the many secrets that it holds is the spatial history of the samples. In this talk, I will discuss a method we developed that uses Brownian Models on networks to estimate dispersal rate and the location of genetic ancestors from the ARG. I will outline the mathematical structure and the biological interpretations of an ARG. Then I will talk about the problems posed in using Brownian Motion on networks and the solution we developed.

March 20

Caterina Stamoulis, Harvard Medical School

Human brain development from the lens of topological and dynamic optimization

Human brain development is relatively long (occurs over almost two decades of life) and biologically heterogeneous process. It is characterized by sensitive periods, during which the brain undergoes profound topological and neurodynamic changes in order to support increasingly complex cognitive skills. These changes occur non-uniformly across the brain. Regions that support functions critical to survival develop rapidly in early life, whereas brain areas supporting high-level cognitive processes, such as decision-making and executive control, continue to maturate throughout adolescence and into young adulthood. Neural maturation involves dynamic and topological changes across scales of spatial organization, from neural connection pruning and synapse elimination at the microscale, to macroscale topological changes in large human brain networks. In this talk I will discuss our recent work that integrates big data (multimodal neuroimaging from ~5,000 youth) with tools from control theory and network science in order to characterize topological and dynamic brain changes in adolescence, a sensitive period of heightened neural maturation and profound reorganization of brain circuits. This reorganization is examined as a topological optimization process that is necessary for the brain to acquire its final (adult) configuration, and efficiently support complex cognitive processing.

March 27

Sean Lawley, University of Utah

Stochastics in Medicine: Delaying Menopause and Missing Drug Doses

Stochastic modeling and analysis can help answer pressing medical questions. In this talk, I will attempt to justify this claim by describing recent work on two problems in medicine. The first problem concerns ovarian tissue cryopreservation, which is a proven tool to preserve ovarian follicles prior to gonadotoxic treatments. Can this procedure be applied to healthy women to delay or eliminate menopause? How can it be optimized? The second problem concerns medication nonadherence. What should you do if you miss a dose of medication? How can physicians design dosing regimens that are robust to missed/late doses? I will describe (a) how stochastics theory offers insights into these questions and (b) the mathematical questions that emerge from this investigation. The first problem is based on joint work with Joshua Johnson (University of Colorado School of Medicine), John Emerson (Yale University), and Kutluk Oktay (Yale School of Medicine).

April 03 (Virtual Only)

Majid Bani-Yaghoub, University of Missouri-Kansas City

Understanding the Behaviors of Biological Waves Using Mathematical Models with Nonlocality

Nonlocal models incorporate the influence of distant locations on local dynamics, which can lead to better explanations of biological waves. In the present work, I introduce a nonlocal delay model to understand the behaviors of invasive species possibly influenced by extreme weather events.  This includes long-range propagations of invasive insects, such as emerald ash borer, characterized by the speed, direction, and amplitude of monotonic and oscillatory wave solutions of the nonlocal model. In the second part of this talk, I will focus on nonlocal models that are extensions of the classical susceptible-infected-recovered model. These models exhibit fair amounts of agreement with various COVID-19 datasets, showcasing their potential as promising tools to measure the severity of epidemic waves.

April 17

Takuya Ito, IBM Research

Multitask and compositional representations in human brains and neural networks

Humans can perform a variety of tasks that require diverse cognitive functions. What are the computational principles that enable these abilities? In this talk, I will cover work that characterizes the properties of multitask and compositional representations in the human brain, and address how we can use these insights to build better artificial neural network models. I will end with a discussion of recent work at IBM that works towards building a cognitive science for artificial neural network systems, and how these insights may inform how to embed more robust cognitive functions in these systems.

Last Updated: February 22, 2024