Past Semesters

October 28

Speaker: Hyukpyo Hong (University of Wisconsin — Madison)

Title: Ubiquitous Asymptotic Robustness in Biochemical Systems

Abstract: Living systems maintain stable internal states despite environmental fluctuations. Absolute concentration robustness (ACR) is a striking homeostatic phenomenon in which the steady-state concentration of a species remains invariant despite changes in total supply. In this talk, we introduce a previously underappreciated phenomenon, namely asymptotic ACR (aACR): approximate robustness can emerge solely from the network structure, without requiring exact ACR motifs or negligible parameters. We find that aACR is more pervasive than classical ACR and prove that this ubiquity stems solely from network structure. This notion of aACR would provide a rigorous and practical tool to analyze robust responses in broad biochemical systems.

November 4:

Speaker: Ruby Kim (University of Michigan)

Title: Mechanistic Modeling of Dopamine Rhythms

Abstract: The circadian clock shapes nearly 24-hour periodic rhythms throughout the body, from the activity of individual cells to our daily sleep/wake cycles. These rhythms can be self-sustained (for example, people still show circadian patterns even in total darkness), but they are also strongly influenced by the environment, especially light. Mathematical models of circadian rhythms can provide insight into many intriguing phenomena, including jet lag, mid-afternoon fatigue, and how animals sense the changing seasons. In this talk, I will present recent work using mathematical models to investigate the daily regulation of dopamine, a neurotransmitter involved in motivation, attention, and mood. Our models reveal how circadian control of dopamine metabolism leads to time-of-day effects of dopamine reuptake inhibitors commonly used to treat fatigue, ADHD, and depression. Furthermore, by modeling the collective activity of dopaminergic neurons, we identify intrinsic ~4-hour ultradian oscillations that arise independently of circadian input. These limit cycle oscillations exhibit flexible periods that can be modulated by pharmacological intervention. Overall, this talk will highlight the utility of mechanistic models for generating testable hypotheses about neuromodulatory systems.

November 11: Swati Patel (Oregon State University)

Title: Persistence and Elimination of Structured Populations Under Pulsed Control

Abstract: The efficacy of control interventions of harmful biological populations, such as chemotherapy against cancer cells, antibiotics against bacteria, and insecticide sprays against agricultural pests, are exacerbated in many cases by population structure. That is, when the population is heterogenous, such as through phenotypic plasticity, life stages, or spatially and the efficacy of control varies, then populations can harbor in states less vulnerable (or entirely resistant) to the control agent. In this talk, we develop results on the persistence (or elimination) of broad classes of structured population models with pulsed control interventions. With the goal of generalizing principles, we aim to establish when control will be effective and when will there be an optimal strategy for structured populations. We demonstrate the implications of our results in two empirical examples.

November 18: Cody FitzGerald (Northwestern University)

Title: Data-driven modeling of complex biological systems

Abstract: Finding simple data-driven and interpretable models of complex biological systems requires engaging with experimental and real-world data, which often come with a range of challenges. Typical biological data sets often feature sources of extrinsic and intrinsic noise, infrequent temporal sampling of the dynamics, and, usually, not all relevant states of the system can be experimentally measured. Additionally, for many biological systems, the true dimensionality is unknown. In this talk, I walk through a series of recent modeling projects using experimental and real-world data, each featuring a different data-related challenge. In particular, I will discuss using wolves as an ecological control strategy to limit the spread of Chronic Wasting Disease in deer populations, an inference problem in which we fit 13,824 separate gene regulatory network models to an RNA-seq data set in an attempt to learn what can honestly be said about the underlying regulatory mechanism, and using model selection for partially observed systems to infer a physiological model of the thermoregulatory system for Arctic hibernators. Finally, I will describe recent ongoing work using a super high-dimensional spatio-temporal data set from the City of Chicago, in which we attempt to understand the city as a cellular organism and infer its "organelles" directly from data.

November 25: Farshad Shirani (Emory University)

Title: Infinite-Dimensional Dynamics, Spatiotemporal Gamma Oscillations, and Balance of Excitation and Inhibition in Cortical Networks

Abstract: In this talk, I first present some analytical and computational results on the global dynamics of a mean field model of EEG activity in the neocortex. The model is a degenerate system of coupled ODEs and PDEs, with subtle solution irregularities. I show that the model possesses a global attracting set, which is non-compact for some biologically reasonable parameter values. This further implies that the model can present infinite-dimensional dynamics, a property that sounds crucial for the functionality of the neocortex. I also present computational results on generation and spatial propagation of gamma oscillations in the solutions of the model. The results identify challenges in interpreting and modelling temporal patterns of EEG recordings, originating mainly from the low spatial resolution of EEG electrodes. I then switch to a biologically more detailed but local mean-field model and present some results on how variations in key structural and physiological parameters of cortical networks may affect balance of excitation and inhibition in the networks. When a critical level of imbalance is created, the results predict a transition of cortical activity to a high amplitude slow oscillatory (1-4 Hz) regime. Such oscillatory activities are known to be strongly correlated with states of diminished consciousness.

December 2: Ted Loch-Temzelides (Rice University)

Title: Symbiosis emergence and abandonment in nature: a coordination game approach

Abstract: We employ an n-player coordination game to model mutualism emergence and abandonment. We illustrate our findings in the context of the host--host interactions among plants in plant-mycorrhizal fungi (MF) mutualisms. The coordination game payoff structure captures the insight that mutualistic strategies lead to robust advantages only after such "biological markets" reach a certain scale. The game gives rise to three types of Nash equilibria, which correspond to the states derived in studies of the ancestral reconstruction of the mycorrhizal symbiosis in seed plants. We show that all types of Nash equilibria correspond to steady states of a dynamical system describing the underlying evolutionary process. We then employ methods from large deviation theory on discrete-time Markov processes to study stochastic evolutionary dynamics. We provide a sharp analytical characterization of the stochastic steady states and of the transition dynamics across Nash equilibria and employ simulations to illustrate these results in special cases. We find that the mutualism is abandoned and re-established several times through evolutionary time, but the mutualism may persist the majority of time. Changes that reduce the benefit-to-cost ratio associated with the symbiosis increase the likelihood of its abandonment. While the mutualism establishment and abandonment could result from direct transitions across the mutualistic and non-mutualistic states, it is far more likely for such transitions to occur indirectly through intermediate partially mutualistic states. The MF-plant mutualism might be (partially or fully) abandoned by plants even if it provides overall superior fitness.

December 9: Binan Gu (Worcester Polytechnic Institute)

Title: Modeling Cell Transport in Deformable Microenvironments: From Engineered Scaffolds to the Blood–Brain Barrier

Abstract:

Transport in deformable tubular microenvironments is fundamental to both engineered and physiological systems. I will present two mathematical models that, while motivated by distinct biological questions, share a unifying structure: coupling between fluid flow, biochemical transport, and mechanical deformation within dynamically changing geometries.

The first model concerns cell proliferation in tissue-engineering scaffolds, where nutrient transport and pore-scale connectivity regulate growth. We represent the scaffold as a metric graph, solving advection–diffusion–reaction PDEs on edges with conservation laws at vertices to capture global geometric effects. Large-ensemble simulations across randomly generated architectures identify structural features that enhance proliferation. The experimentally measurable outcome is time-dependent total cell volume gain, providing a bridge between scaffold design and functional performance.

The second model addresses neutrophil extravasation across the blood–brain barrier, formulated as migration through a viscoelastic intercellular cleft whose radius evolves via a Kelvin–Voigt wall law coupled to pipe flow, chemokine transport, and chemically modulated wall elasticity. This first-principles formulation reveals how wall deformation changes hydraulic resistance and influences chemokine transport, thereby regulating cellular motion. The biologically relevant output is passage time and conditions for successful transmigration.

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