Organizers:

• Marty Golubitsky - 📧

• Jiaxin Jin - 📧

Upcoming Talks:

TBA (click here to connect the zoom)

Previous Talks:

Fall 2021

September 9, 2021

Speaker: David Terman, Ohio State University

Title: Modeling the effect of cerebral capillary blood flow on neuronal firing.

Abstract: Adequate cerebral blood flow has long been recognized as essential for the maintenance of neuronal function while interruption of cerebral blood flow for durations as short as minutes can result in permanent brain damage. A primary goal of this work is to determine how a neuron’s ability to respond to synaptic input depends on parameters that control cerebral blood flow. A complex mathematical model is constructed that integrates detailed biophysical models of neuronal action potentials, mitochondrial ATP production and cerebral capillary blood flow. Both dynamical systems analysis and numerical simulations are used to determine how the maximum frequency at which the neurons can respond to synaptic input depends on capillary blow flow, as well as the ability of astrocytes to buffer extracellular potassium. Results are presented for both the cases of homogenous and heterogeneous capillary networks. These results demonstrate that heterogeneity of the capillary flow results in a decrease in the ability of neurons to respond to synaptic stimulation and that intact glial function provides a further protective role for the neurons.

September 16, 2021

No seminar.

September 23, 2021

Speaker: Avner Friedman, Ohio State University

Title: Mathematical models of cancer drug resistance.

Abstract: Drug resistance is a primary obstacle in cancer treatment. In many patients who first respond well to treatment, relapse occurs within months. The question how to overcome drug resistance is currently explored in many clinical trials, by using combination of drugs, or by changing protocols of treatment. Mathematical model can be useful in explaining how resistance to cancer drug develops, and then suggesting how to overcome it within this talk I will give several such examples. The mathematical models are represented by dynamical systems of PDEs for variables which are cells densities, concentrations of proteins (cytokines) and drugs, within a tumor; the tumor boundary is evolving in time, it is a free boundary, unknown in advance. The model is validated by comparison the simulations of the model with mice data. The drugs we shall consider are mostly immunotherapy, PD-1 and CTLA-4 inhibitors; these drugs, which were developed a few years ago, revolutionized the treatment of melanoma, lung cancer and other cancers, but have been associated with resistance.

September 30, 2021

Speaker: Adriana Dawes, Ohio State University

Title: Multiscale modeling of cell fate specification.

Abstract: During development, cells take on specific fates to properly build tissues and organs. These cell fates are regulated by short and long range signaling mechanisms, as well as feedback on gene expression and protein activity. However, how these short and long range signals work to control patterning during development, and how the same network can lead to species specific responses to perturbations, is not yet understood. Exploiting the high conservation of developmental pathways, we theoretically and experimentally explore mechanisms of cell fate patterning during development of the egg laying structure (vulva) in nematode worms. We developed differential equation models of the main signaling networks (EGF/Ras, Notch and Wnt) responsible for vulval cell fate specification, and validated them using experimental data. A complex, biologically based model identified key network components for wild type patterning, and demonstrated that higher correlations between parameters render a network more sensitive to perturbations. Analysis of a simplified model indicated that short and long range signaling play complementary roles in developmental patterning. The rich data sets produced by these models form the basis for further analysis and increase our understanding of cell fate regulation in development.

October 7, 2021

Speaker: Hao Wang, University of Alberta

Title: Stoichiometric phytoplankton dynamics and niche differentiation in the light spectrum.

Abstract: Algal blooms are becoming a global concern due to the increasing prevalence of eutrophication. Often, algae and bacteria interact, within the well-mixed epilimnion, in a loose commensalistic way. Here we analyze stoichiometric models for algal dynamics and for bacteria-algae dynamics. The algae-only dynamics exhibit rich transient behavior, and the driving biological mechanisms are studied and understood via a multiple time-scale analysis. We further perform global qualitative analysis of both models. There are three dynamical scenarios determined by the basic reproductive numbers of algae and bacteria. We use these models to make specific predictions about how the relative balance of algae and bacteria should change in response to varied nutrient and light availability. The bacteria-algae model successfully reproduces empirical respiration data. In the second part of my talk, I will present our recent work on light wavelength spectra as to when coexistence of many phytoplankton species is expected based on the degree of niche differentiation and overall turbidity of the water.

October 14, 2021

No seminar.

October 21, 2021

Speaker: Grzegorz A. Rempala, Ohio State University

Title: Modeling a new pandemic with an old equation. 2020-21 Ohio statewide SIR models for COVID-19.

Abstract: The COVID-19 pandemic has inspired much work on mathematical models of epidemics over the past 18 months. In particular, the classical ODE model of susceptible-infected-recovered (SIR) and its modifications have been frequently used for various predictions and statistical analysis of the epidemic dynamics. In this talk, I will describe the specific SIR-type model developed by OSU in March 2020 to help the Ohio Governor’s office with planning for pandemic response. In particular, I will explain model's probabilistic interpretation and its connection with the popular Sellkie algorithm for constructing trajectories of non-Markovian epidemics.

October 28, 2021

Speaker: Daniel B. Larremore, University of Colorado Boulder

Title: Mathematical Models for Disease Mitigation via Testing.

Abstract: Prior to the approval of COVID-19 vaccines, transmission mitigation via repeated testing was shown to be an effective approach to break chains of transmission and decrease the burden of COVID-19. Why do these approaches work just as well with highly sensitive PCR tests and less sensitive rapid antigen tests? Will they continue to work with the delta variant? And, in an era of vaccination, what if only the unvaccinated population is tested? Answering these questions requires us to link mathematical models of within-host viral kinetics to the broader epidemiology of transmission. To do so, we will introduce a simple model for viral dynamics, symptom screening, and testing at the scale of the individual infection. We'll then show how to link these results with more typical models of infectious disease dynamics at the scale of a community. In so doing, we'll develop a more general theory of disease mitigation via testing, and explore the role of testing in partially vaccinated communities, with and without patterns of social homophily by vaccination status.

November 4, 2021

Speaker: Wasiur Rahman Khuda Bukhsh, University of Nottingham

Title: A functional central limit theorem for epidemic processes on configuration model random graphs.

Abstract: We consider a stochastic compartmental epidemic process on configuration model (CM) random graphs with a given degree distribution. The vertices are compartmentalized according to different immunological statues (susceptible, infected). We describe the disease dynamics in terms of the counts of vertices with different immunological statuses as well as the counts of different types of edges connecting those vertices. Our goal in this talk is to approximate the epidemic process in the non-equilibrium (transient or non-stationary) regime. To this end, we will discuss a functional central limit theorem for appropriately scaled counts of different types of vertices and edges in the limit of a large graph, i.e., as the number of vertices increases to infinity. (This is a joint work with Casper Woroszylo, Heinz Koeppl and Grzegorz Rempała. Preprint is available: https://arxiv.org/pdf/1703.06328.pdf)

November 11, 2021

No seminar.

November 18, 2021

Speaker: Chad Topaz, Williams College

Title: A Topological View of Collective Behavior.

Abstract: From nanoparticle assembly to synchronized neurons to locust swarms, collective behaviors abound anywhere in nature that objects or agents interact. Investigators modeling collective behavior face a variety of challenges involving data from simulation and/or experiment. These challenges include exploring large, complex data sets to understand and characterize the system, inferring the model parameters that most accurately reflect a given data set, and assessing the goodness-of-fit between experimental data sets and proposed models. Topological data analysis provides a lens through which these challenges may be addressed. In this talk, I will introduce the core ideas of topological data analysis for newcomers to the field. Then, I will highlight how these topological techniques can be applied to models arising from the study of groups displaying collective motion, such as bird flocks, fish schools, and insect swarms. The key approach is to characterize a system's dynamics via the time-evolution of topological invariants called Betti numbers, accounting for persistence of topological features across multiple scales. One can then use the topological characterisation in concert with exploratory data analysis, statistics, and machine learning.

November 25, 2021

No seminar.

December 2, 2021

No seminar.

Spring 2022

January 20, 2022

Speaker: Peter Hinow, University of Wisconsin - Milwaukee

Title: Automated Feature Extraction from Large Cardiac Electrophysiological Data Sets.

Abstract: A new multi-electrode array-based application for the long-term recording of action potentials from electrogenic cells makes possible exciting cardiac electrophysiology studies in health and disease. With hundreds of simultaneous electrode recordings being acquired over a period of days, the main challenge becomes achieving reliable signal identification and quantification. We set out to develop an algorithm capable of automatically extracting regions of high-quality action potentials from terabyte size experimental results and to map the trains of action potentials into a low-dimensional feature space for analysis. Our automatic segmentation algorithm finds regions of acceptable action potentials in large data sets of electrophysiological readings. We use spectral methods and support vector machines to classify our readings and to extract relevant features. We are able to show that action potentials from the same cell site can be recorded over days without detrimental effects to the cell membrane. The variability between measurements 24 h apart is comparable to the natural variability of the features at a single time point. Our work contributes towards a non-invasive approach for cardiomyocyte functional maturation, as well as developmental, pathological, and pharmacological studies. As the human-derived cardiac model tissue has the genetic makeup of its donor, a powerful tool for individual drug toxicity screening emerges.

January 27, 2022

No seminar.

February 3, 2022

Speaker: Jiaxin Jin, Ohio State University

Title: Existence and uniqueness on weakly reversible and deficiency zero realizations.

Abstract: Different networks can generate the same dynamical system under mass-action kinetics. Therefore, the problem of identifying the underlying network of a dynamical system is not well-posed, in general. Here we show that the problem of identifying an underlying weakly reversible deficiency zero network is well-posed, in the sense that the solution is unique whenever it exists. Moreover, the weakly reversible and deficiency zero systems are remarkably stable where they have a unique positive steady state within each invariant polyhedron, and cannot give rise to oscillations or chaotic dynamics. So we also design an efficient algorithm for the identification of these networks. A similar approach may be used for the identification of network representations of lowest deficiency, and allow for wider applicability of classical results for networks with positive deficiency, such as the Deficiency One Theorem.

February 10, 2022

Speaker: Casey Diekman, New Jersey Institute of Technology

Title: Data Assimilation and Dynamical Systems Analysis of Circadian Rhythmicity and Entrainment.

Abstract: Circadian rhythms are biological oscillations that align our physiology and behavior with the 24-hour environmental cycles conferred by the Earth’s rotation. In this talk, I will discuss two projects that focus on circadian clock cells in the brain and the entrainment of circadian rhythms to the light-dark cycle. Most of what we know about the electrical activity of circadian clock neurons comes from studies of nocturnal (night-active) rodents, hindering the translation of this knowledge to diurnal (day-active) humans. In the first part of the talk, we use data assimilation and patch-clamp recordings from the diurnal rodent Rhabdomys pumilio to build the first mathematical models of the electrophysiology of circadian neurons in a day-active species. We find that the electrical activity of circadian neurons is similar overall between nocturnal and diurnal rodents but that there are some interesting differences in their responses to inhibition. In the second part of the talk, we use tools from dynamical systems theory to study the reentrainment of a model of the human circadian pacemaker following perturbations that simulate jet lag. We show that the reentrainment dynamics are organized by invariant manifolds of fixed points of a 24-hour stroboscopic map and use these manifolds to explain a rapid reentrainment phenomenon that occurs under certain jet lag scenarios.

February 17, 2022

Speaker: Deena Schmidt, University of Nevada - Reno

Title: Contagion Dynamics on an Adaptive Network: Norovirus as a Case Study.

Abstract: Classical contagion models, such as SIR, and other infectious disease models typically assume a well-mixed contact process. This may be unrealistic for infectious disease spread where the contact structure changes due to individuals' responses to the infectious disease. For instance, individuals showing symptoms might isolate themselves, or individuals that are aware of an ongoing epidemic in the population might reduce or change their contacts. Here we investigate contagion dynamics in an adaptive network context, meaning that the contact network is changing over time due to individuals responding to an infectious disease in the population. We generate an age-structured contact network from human interaction data described in the well-known POLYMOD study. We consider norovirus as a specific example and investigate questions related to disease dynamics and applications to public health.

February 24, 2022

Speaker: Wenrui Hao, Pennsylvania State University

Title: Data-driven modeling on Alzheimer's disease.

Abstract: Alzheimer's disease (AD) affects more than 5 million people in the US. Recently, personalized treatment of AD provides a new way to manage AD patients' treatment plans. Such treatment requires a new approach to analyze the growing electronic AD brain data. In this talk, we will introduce a mathematical modeling approach to describe the progression of AD clinical biomarkers and also incorporate patient data for personalized prediction and optimal treatment. More specifically, an AD personalized prediction is provided via validating the mathematical model on a multi-institutional dataset of AD biomarkers. Personalized therapeutic simulation studies for AD patients are performed via adding optimal controls to this model.

March 3, 2022

Speaker: Xueying Wang, Washington State University

Title: Impact of varying community networks on disease invasion.

Abstract: We consider the spread of an infectious disease in a heterogeneous environment modeled as a network of patches. We focus on the invasibility of the disease, as quantified by the corresponding value of an approximation to the network basic reproduction number, R0, and study how changes in the network structure affect the value of R0. We provide a detailed analysis for two model networks, a star, and a path, and discuss the changes to the corresponding network structure that yield the largest decrease in R0. We develop both combinatorial and matrix analytic techniques, and we illustrate our theoretical results by simulations with the exact R0.

March 10, 2022

Speaker: Punit Gandhi, Virginia Commonwealth University

Title: A stochastic pulsed precipitation model for banded vegetation patterns in dryland ecosystems.

Abstract: Strikingly regular, large-scale patterns of vegetation growth were first documented by aerial photography in the Horn of Africa circa 1950, and are now known to exist in drylands across the globe. The patterns often appear on very gently sloped terrain as bands of dense vegetation alternating with bare soil, and conceptual reaction-advection-diffusion models suggest that they may be a be a precursor to ecosystem collapse under increasing aridity. A particular challenge for modeling these patterns is appropriately resolving fast processes during hours-long rainstorms while still being able to capture slow ecological dynamics such as the uphill migration of the vegetation bands, which has been observed to occur on the scale of a band width per century. We propose an impulsive reaction-diffusion framework that captures the fast hydrology associated with overland flow and infiltration during storms within instantaneous kicks to the soil water as the pattern evolves on the slow timescale. This pulsed-precipitation model predicts that the characteristic distance surface water travels before infiltrating into the soil during a storm plays a key role in setting the spacing between vegetation bands. Investigation under stochastic rainfall suggests rainfall characteristics, such as increased variability in storm depth and shorter rainy seasons, can hasten ecosystem collapse at low mean annual precipitation levels.

March 17, 2022

No seminar.

March 24, 2022

Speaker: Fernando Antoneli, Escola Paulista de Medicina, Universidade Federal de São Paulo

Title: Homeostasis Classification in Input-Output Networks.

Abstract: Homeostasis occurs in a biological or biochemical system when some output variable remains approximately constant as some input parameters vary over some range. Recently, Golubitsky and Stewart [Homeostasis, Singularities and Networks. J. Math. Biol. 74 (2017) 387-407] introduced the notion of 'infinitesimal homeostasis' allowing the use of implicit differentiation and singularity theory to study homeostasis in systems of differential equations. Networks consisting of nodes and unidirectional arrows encode systems of differential equations. Nodes correspond to state variables and arrows indicate which nodes are coupled to which. What distinguishes a network system of differential equations from a large system of differential equations is the capability to keep track of the output from each node individually. Hence, infinitesimal homeostasis is related to occurrence of 'singularities' at individual nodes. In this talk we explain a new approach to the study of the combinatorial structure and classification of homeostasis in 'input-output networks', that is, networks where we keep track of the output from a fixed node, as well as the node(s) affected by external input parameter(s). We will discuss homeostasis classification, with examples, in three kinds of networks: one input node - one input parameter, multiple input nodes - one input parameter and multiple input nodes - multiple input parameters. Joint work with Martin Golubitsky (Ohio), Ian Stewart (Warwick), Zhengyuan Huang (Michigan), Yangyang Wang (Iowa) and João Luiz de Oliveira Madeira (Bath).

March 31, 2022

Speaker: Sebastian Schreiber, University of California - Davis

Title: Species coexistence in an autocorrelated world.

Abstract: All species experience temporal fluctuations in environmental conditions e.g. temperature or mortality risk. These fluctuations often are autocorrelated e.g. warmer years tending to be followed by warmer years. How these autocorrelations influence species coexistence is, largely, an open problem. Benaim and Schreiber (J. Math. Bio. (2019) 79:393) developed theorems to characterize coexistence and extinction for stochastic, multispecies models with temporal autocorrelations. These characterizations rely on Lyapunov exponents at stationary distributions supporting a subset of species. Applying these methods to classical ecological modules of exploitative competition and apparent competition, I determine how autocorrelated temporal fluctuations alter ecological outcomes. For example, if survivorships of competing species fluctuate, then negative autocorrelations promote coexistence while positive autocorrelations lead to stochastic priority effects. In contrast, positively autocorrelated fluctuations in attack rates of a shared predator can mediate coexistence, while negatively autocorrelated fluctuations generate stochastic priority effects. These results highlight the importance of temporal autocorrelations in structuring ecological communities.

April 7, 2022

Speaker: William Duncan, Montana State University

Title: Interaction of Homeostasis Singularities in Input-Output Networks.

Abstract: Biological systems often arise from networks with a distinguished input parameter, I, and output node, o. Homeostasis, the property that the output does not vary much as the input changes over an interval, is often of interest in these systems. Recently, it was shown that input-output networks can be decomposed into subnetworks so that the input-output function x_o(I) is homeostatic if and only if one of the subnetworks is homeostasis inducing. If exactly one subnetwork is homeostasis inducing, then simple homeostasis (x_o'(I) = 0 and x_o''(I) non-zero) occurs. A priori, when varying a parameter so that two simple homeostasis points come together, a cubic singularity (x_o'(I) = x_o''(I) = 0 and x_o'''(I) non-zero) is expected. In this talk I will discuss the surprising result that higher order degeneracies occur when a parameter is varied so that two subnetworks are homeostasis inducing. There are two possibilities: (1) a quartic homeostasis point, which suggests a wide homeostatic plateau, occurs, or (2) homeostasis is obstructed by a bifurcation. Both possibilities are a co-dimension 2 phenomenon in a general system, but the network structure allows them to be attained by varying a single parameter. I will give graph theoretic conditions for determining whether (1) or (2) occurs and show that a non-standard degeneracy occurs in the bifurcation case.

April 14, 2022

Speaker: Gheorghe Craciun, University of Wisconsin - Madison

Title: Mathematical Analysis of Biochemical Reaction Networks.

Abstract: The reliable operation of biochemical systems is due to complex interactions between its constitutive parts, which give these systems the ability to produce specific functional properties. These functional properties have mathematical counterparts. For example, cellular decision and differentiation is related to the existence of multiple basins of attraction, i.e., multistability, while robustness is related to persistence and global stability. On the other hand, the task of determining the capacity for multistability, persistence, and global stability in mathematical and computational models gives rise to very challenging mathematical problems. These challenges create great opportunities in both directions: for mathematical and computational contributions to understanding biochemical systems, but also for using biology-inspired ideas in the development of new mathematical methods, tools, and directions. To illustrate these ideas we will discuss several examples, including: (i) how a classification of positive and negative feedbacks allows us to analyze biochemical switches, and (ii) recent progress toward understanding robustness in biochemical systems. We will also point out interesting connections to some classical mathematical problems: Hilbert’s 16th problem, the Jacobian Conjecture, and Boltzmann’s H-theorem.