September 2
Speaker: Tin Phan (Los Alamos National Laboratories)
Title: Mathematical modeling reveals that latently infected cells reactivated by AZD5582 differ substantially from productively infected cells
Abstract: AZD5582 (AZD) is a promising latency reversing agent to enable the “shock-and-kill” strategy in HIV-1 cure research, due to its potent ability to reactivate latently infected cells while maintaining high specificity by targeting the non-canonical NF-κB pathway. Previous studies in rhesus macaques have demonstrated that AZD can promote the reactivation of latently infected cells, which can lead to a viral load increase of 2-3 logs. However, the resulting reduction of the latent reservoir is less robust. Quantitative analysis of this phenomenon is difficult due to limited and fluctuating low amplitude longitudinal viral load data. To overcome this obstacle, we developed an ensemble of mechanistic models and fit it to a data set obtained from 23 macaques treated with AZD in combination with other therapies. The model ensemble recapitulates the reactivation patterns observed in SIV RNA, the change in SIV CA-DNA, and provides robust estimates of key parameters related to the reactivated cells. We find that the reactivated cells produce fewer viruses, are less susceptible to viral cytotoxicity, and do not interact strongly with the immune response compared to productively infected cells. Reactivated cells likely enter a temporary state that is refractory to drug effects, prior to their return to latency. This refractory phase causes a diminishing return effect on the effectiveness of AZD. Thus, introducing a waiting time in between treatment periods to bypass this refractory phase may enhance the overall effect of AZD. Altogether, our results suggest the difference between AZD-reactivated cells and productively infected cells as the underlying mechanism responsible for the lack of reservoir reduction.
September 9
Speaker: Maliha Ahmed (Massachusetts Institute of Technology)
Title: Multiscale Modelling of Neurosteroid-mediated Seizure Trajectories in Childhood Absence Epilepsy
Abstract: Childhood absence epilepsy (CAE) is a pediatric generalized epilepsy disorder characterized by brief episodes of impaired consciousness and distinctive 2.5–5 Hz spike-wave discharges (SWDs) on electroencephalography. With a well-established genetic aetiology, this condition tends to resolve spontaneously during adolescence in most cases. While several mechanisms have been proposed for remission, understanding remains insufficient to guide early intervention practices. In this work, we first utilize a conductance-based thalamocortical network model that exhibits characteristic SWDs, to demonstrate that allopregnanolone, a progesterone metabolite known to enhance GABAa receptor-mediated inhibition, has an ameliorating effect on SWDs. To investigate the divergence between this finding and clinical observations, we developed an enhanced thalamocortical model that incorporates a layered cortical structure to explore regional cortical heterogeneity and frontocortical connectivity as potential resistance factors to ALLO-mediated recovery. Our results suggest that non-resolving CAE may be due not only to increased frontocortical connectivity but also to the composition of cell types within the network. We extended our investigation to examine whether these findings apply to CAE caused by different genetic mechanisms, particularly mutations in sodium channel genes by modelling their effects at the individual neuron level. Furthermore, we examined the degree to which these alterations lead to network-level pathological activity, as well as the influence of ALLO on these genetically distinct networks. Our results demonstrate that ALLO facilitates recovery from SWDs regardless of the underlying mutation type. However, enhanced frontocortical connectivity prevents recovery in some mutation types, particularly when mutation effects are severe. Altogether, our multi-scale computational framework demonstrates that CAE remission is determined by complex interactions between hormonal influences, genetic factors, and network connectivity patterns. These approaches not only advance our understanding of CAE specifically, but offer generalizable insights into the mathematical modelling of neurological conditions characterized by spontaneous shifts in brain dynamics.
September 16
Speaker: Peter Thomas (Case Western Reserve University)
Title: Stochastic Oscillators
Abstract: Phase reduction and isostable (or amplitude) reduction are important tools for studying synchronization, entrainment, and control of nonlinear limit cycle oscillators that arise throughout mathematical biology. Phase and amplitude coordinates were introduced classically for deterministic oscillators. The definitions of asymptotic phase, isochron, and isostable break down when oscillators are subject to stochastic forcing (noise). At the same time, there are models for biological oscillations in which the oscillations cease in the absence of noise. (Examples include excitable systems, quasicycle systems, and noisy heteroclinic cycles). In this talk I will review an approach to defining the asymptotic phase of a stochastic oscillator, as well as its isostable coordinates, by diagonalizing the stochastic Koopman operator. The talk will include a brief tutorial introduction to a stochastic oscillator toolbox developed with Max Kreider, who completed his PhD under my supervision last spring (https://github.com/MaxKreider/Stochastic_Oscillator_Workshop). The talk will also set the stage for Max Kreider's talk on synchronization and Arnold tongues for coupled stochastic oscillators scheduled for the Midwest Mathematical Biology Seminar for September 23, 2025.
September 23
Speaker: Maxwell Kreider (Pennsylvania State University)
Title: Synchronization of Stochastic Oscillators: Arnold Tongues and Koopman Eigenfunctions
Abstract: Phase reduction is an effective theoretical and numerical tool for studying synchronization of coupled deterministic oscillators. Stochastic oscillators require new definitions of asymptotic phase. The Q-function, i.e., the slowest decaying complex mode of the stochastic Koopman operator (SKO), was proposed as a means of phase reduction for stochastic oscillators. In this talk, we show that the Q-function approach also leads to a novel definition of "synchronization" for coupled stochastic oscillators. A system of coupled oscillators in the synchronous regime may be viewed as a single (higher-dimensional) oscillator. Therefore, we investigate the relation between the Q-functions of the uncoupled oscillators and the higher-dimensional Q-function for the coupled system. We propose a definition of synchronization between coupled stochastic oscillators in terms of the eigenvalue spectrum of Kolmogorov's backward operator (the generator of the Markov process, or the SKO) of the higher dimensional coupled system. We observe a novel type of bifurcation reflecting (i) the relationship between the leading eigenvalues of the SKO for the coupled system and (ii) qualitative changes in the cross-spectral density of the coupled oscillators. Using our proposed definition, we observe synchronization domains for symmetrically-coupled stochastic oscillators that are analogous to Arnold tongues for coupled deterministic oscillators. Finding a Q-phase reduction for a system of coupled stochastic oscillators requires solving a high-dimensional PDE, which is numerically challenging. If time permits, we will discuss a data-driven machine learning approach to compute Q-functions for high-dimensional (n>3) systems of coupled stochastic oscillators. The talk will also build on material from Peter Thomas's talk on phase reduction for stochastic oscillators scheduled for the Midwest Mathematical Biology Seminar for September 16, 2025.
September 30
Speaker: Po-Chun Kuo (Purdue University)
Title: Dynamics of immersed interface problems in Stokes flow
Abstract: Immersed interface problems in Stokes flow are a fluid structure interaction problem. One of the simplest of such problems is the 2D Peskin problem, in which a 1D closed elastic structure is immersed in a 2D Stokes fluid. This has been studied computationally and analytically. We extend the 2D Peskin problem into two different cases:
(1) 2D inextensible interface problem.
(2) 3D Peskin problem.
In the 2D inextensible interface problem, we assume that the interface is inextensible. Through the boundary integral method, we reformulate the problem into two contour equations, an evolution equation and a tension determination equation. We first study the well-posedness and the regularity of the generalized tension determination problem in Hölder spaces. Next, we use a suitable time-weighted Hölder space to study the well-posedness and the regularity of the dynamic problem.
We also study the Peskin problem in the 3D case. With the boundary integral method, the 3D Peskin may be reformulated to an evolution equation on a unit sphere 𝕊2 for the elastic interface. We use more than one local chart to prove that the problem is well-posed in low-regularity Hölder spaces. Moreover, we prove that the elastic membrane becomes smooth instantly in time.
October 7
Speaker: Naghmeh Akhavan (University of Michigan)
Title: Mathematical Modeling of Collective Cell Migration in Drosophila Egg Development
Abstract: Collective cell migration is a fundamental process in development, homeostasis, and disease, yet its regulatory mechanisms remain incompletely understood. While single-cell motility has been extensively studied, the coordinated movement of cell clusters in crowded, heterogeneous environments is less well-characterized. Here, we combine mechanistic modeling and phase-field simulations to investigate the migration of the border cell cluster within the Drosophila melanogaster egg chamber. Our framework integrates mechanical and chemical interactions between the cluster, surrounding nurse cells, and the oocyte, incorporating a novel Tangential Interface Migration (TIM) force to capture contact-mediated propulsion. The phase-field formulation enables the simulation of complex topological changes, volume constraints, and the influence of extracellular geometry. By coupling this representation with chemoattractant diffusion and receptor-mediated signaling, we demonstrate that extracellular space geometry and chemoattractant distribution jointly determine migration trajectories, speed, and cohesion.
October 14
Speaker: Hwai-Ray Tung (University of Utah)
Title: Strolling through space - missed antibiotic doses and extreme first passage times
Abstract: In the first half of the talk, we consider the effects of different patient responses after missing an antibiotic dose using a mathematical model that links antibiotic concentration with bacteria dynamics. We show using simulations that, in some circumstances, (a) missing just a few doses can cause treatment failure, and (b) this failure can be remedied by simply taking a double dose after a missed dose. We then develop an approximate random walk model that is analytically tractable and use it to understand when it might be advisable to take a double dose after a missed dose. In the second half, we ask how long it takes for a searcher to find a target when searchers are being added over time. This quantity is of interest in a variety of biological scenarios, including cell signaling, ant foraging, and finding mates with pheromones. Our rigorous theory applies to many models of stochastic motion, including random walks on discrete networks and diffusion on continuous state spaces, and our results constitute a rare instance in which extreme value statistics can be determined exactly for strongly correlated random variables.