Event category: Spring 2021

The observed gait of a swimmer arises from the interplay of internal force generation, the passive elastic properties of its body, and environmental features such as fluid viscosity, boundaries, and obstacles. One could question whether optimal swimming of a fish occurs when it is actuated at a frequency near a natural frequency determined by its material bending rigidity. We will share some insights that we have gained using computational models of a few systems that range from the Stokes regime to others where inertial forces are important.

Boolean networks are a common modeling tool for studying the phenotypic changes that cells undergo in response stimuli. Examples include cell differentiation during embryogenesis, metastasis of cancer cells, and apoptosis. In these models, genes and proteins are represented by nodes in a network, and each node is assigned a Boolean activity variable that evolves in discrete time-steps such that the attractors of the resulting dynamics correspond to phenotypes of interest. In this talk, I will focus on the techniques we use to analyze these discrete dynamical systems. These techniques rely on the construction and iterative reduction of an auxiliary network that encodes dynamical information as graph structure (an example is diagrammed in the accompanying figure). Our goals include finding all attractors, identifying key feedback loops that govern attractor selection, and driving the system to a desired attractor from an arbitrary initial state. I will briefly cover several recent applications of these methods to empirical and statistical models. I will also discuss ways in which these discrete models — and the techniques we use to analyze them — are related to their ODE counterparts.

I am a cancer researcher working on a framework for a new mathematical model of metastasis. The reason for making a new model is that, in mice, metastases can grow from cells that are still normal at the time of arriving to the future metastasis site. If the same happens in humans, it would be pretty important for cancer therapy. First, it would explain why anti-cancer therapies fail to prevent metastases in some patients: if the cells are yet non-malignant at the time of therapy, they would be spared by the treatment. Second, it may be possible to identify improved treatments based on the ability to kill these non-malignant cells. I hypothesize that dissemination of non-malignant epithelial cells occurs in parallel with tumor cells, and subsequent transformation at the ectopic sites is a source of some metastases. This scenario ties together two contradictory observations: that metastases are associated with large and rapidly growing primary tumors, while metastatic tumors themselves often take a long time to appear. During my recent sabbatical at the Institut des Hautes Etudes Scientifiques, together with Misha Gromov and his colleagues I started to interrogate publicly available data on mutation rates and/or profiles from cancer patients and healthy individuals to determine whether the earliest common ancestor predicted using phylogenetic methods in some primary-metastasis pairs has features of a non-malignant cell.

Predicting a previously unseen example from training examples is unsolvable without additional assumptions about the nature of the task at hand. A learner’s performance depends crucially on how its internal assumptions, or inductive biases, align with the task. I will present a theory that describes the inductive biases of neural networks using kernel methods and statistical mechanics. This theory elucidates an inductive bias to explain data with “simple functions, which are identified by solving a related kernel eigenfunction problem on the data distribution. This notion of simplicity allows us to characterize whether a network is compatible with a learning task, facilitating good generalization performance from a small number of training examples. I will present applications of this theory to artificial and biological neural systems, and real datasets.

Our airways are continuously exposed to potentially harmful particles like dust and viruses. The first line of defence against these pathogens is a network of millions of cilia, whip-like organelles that pump flows by beating over a thousand times per minute. In this talk, I will first discuss the connection between local ciliary architecture and the topology of the flows they generate. We image the mouse airway from the sub-cellular (nm) to the organ scales (mm), characterising quantitatively its ciliary arrangement and the resulting flows. Interestingly, we find that disorder in the ciliary alignment can actually be beneficial for this pathogen clearance [1]. Second, I would also like to discuss how systems can be driven out of equilibrium by such active carpets. Combining techniques from statistical and fluid mechanics, I will demonstrate how we can derive the diffusivity of particles near an active carpet, and how we can generalise Fick’s laws to describe their non-equilibrium transport [2]. These results may be used for designing self-cleaning materials, much like our airways. [1] Ramirez San-Juan, Mathijssen et al., “Multi-scale spatial heterogeneity enhances particle clearance in airway ciliary arrays”, Nature Physics 16, 958–964 (2020) [2] Guzman-Lastra, Löwen & Mathijssen, “Active carpets drive non-equilibrium diffusion and enhanced molecular fluxes”, in press, Nature Communications (2021) Note: We also have an informal discussion session after the seminar. Please stay in the Zoom seminar room to chat together with Professor Arnold Mathijssen!

Inherent fluctuations may play an important role in biochemical and biophysical systems when the system involves some species with low copy numbers. This talk will present the recent work on the stochastic modeling of reaction-diffusion processes in glucose metabolism. The first part of the talk introduces a compartment-based model for a simple glycolytic pathway using a continuous-time Markov jump process, which describes system features at different scales of interest. Then, we will see how the multiscale approximate method reduces the model complexity. We will briefly discuss how the compartment size in the spatial domain can affect the spatial patterns of the system. In the second part of the talk, I will show another example for glucose metabolism where we see different-sized enzyme complexes. We hypothesized that the size of multienzyme complexes is related to their functional roles. We will see two models: one using a system of differential equations and the other using the Langevin dynamics.

A 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 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. This is joint work with Viviana Zlochiver, Stacie Kroboth (Advocate Aurora Research Institute), and John Jurkiewicz (graduate student at UWM).

We describe a spatial Moran model that captures mechanical interactions and directional growth in spatially extended populations. The model is analytically tractable and completely solvable under a mean-field approximation and can elucidate the mechanisms that drive the formation of population-level patterns. As an example, we model a population of E. coli growing in a rectangular microfluidic trap. We show that spatial patterns can arise because of a tug-of-war between boundary effects and growth rate modulations due to cell-cell interactions: Cells align parallel to the long side of the trap when boundary effects dominate. However, when cell​-cell interactions exceed a critical value, cells align orthogonally to the trap’s long side. This modeling approach and analysis can be extended to directionally growing cells in a variety of domains to provide insight into how local and global interactions shape collective behavior. As an example, we discuss how our model reveals how changes to a cell-shape describing parameter may manifest at the population level of the microbial collective. Specifically, we discuss mechanisms revealed by our model on how we may be able to control spatiotemporal patterning by modifying cell shape of a given strain in a multi-strain microbial consortium.

It is well known that relocation strategies in ecology and in economics can make the difference between extinction and persistence. In this talk I present a unifying model for the dynamics of ecological populations and street vendors, an important part of many informal economies. I discuss the effects of chemotactic movement of populations subject to the Allee Effect by discussing the existence of equilibrium solutions subject to various boundary conditions and the evolution problem when the chemotaxis effect is small. On an interesting note, I present numerical simulations, which show that in fact chemotaxis can help overcome the Allee effect as well as some partial analytical results in this direction on a bounded domain. We can make this precise in unbounded domains. I will conclude by making a connection to the Ideal Free Distribution and other movement strategies under competition.

Contact networks on which epidemic spreading occurs vary over time. Epidemic processes on such temporal networks are complicated by complexity of both network structure and temporal dimensions. We discuss two mathematical modeling topics on “temporal network epidemiology. First, we analyze how concurrency, i.e., the number of partnerships that an individual (i.e., node of the network) simultaneously owns affects the epidemic threshold. We particularly use a temporal network model with which we can vary the degree of concurrency while preserving the structure of the aggregate, static network. Second, we analyze the epidemic threshold and dynamics when each node switches between a high-activity state and a low-activity state in a Markovian manner. This assumption facilitates theoretical analyses and also allows us to produce distributions of inter-event times resembling heavy-tailed distributions, which are prevalent in empirical data. We argue that it is not the tail of the distribution but the small values of inter-event time that impact epidemic dynamics.