Event type: Seminar

I will present a general model of continuous-time opinion dynamics for an arbitrary number of agents that sense or communicate over a network and form real-valued opinions about an arbitrary number of options. Drawing from biology, physics, and social psychology, an attention parameter is introduced to modulate social influence and a saturation function to bound inter-agent and intra-agent opinion exchanges. This yields simply parameterized dynamics that exhibit the range of opinion formation behaviors predicted by model-independent bifurcation theory but not exhibited by linear models or existing nonlinear models. Behaviors include rapid and reliable formation of multistable consensus and dissensus states, even in homogeneous networks, as well as ultra-sensitivity to inputs, robustness to uncertainty, flexible transitions between consensus and dissensus, and opinion cascades. Augmenting the opinion dynamics with feedback dynamics for the attention parameter results in tunable thresholds that govern sensitivity and robustness. The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision making and dynamic task allocation. This is joint work with Alessio Franci (UNAM, Mexico) and Anastasia Bizyaeva (Princeton). The talk is based on version 2 of the paper “A General Model of Opinion Dynamics with Tunable Sensitivity”, which will be available on Tuesday October 13, 2020 here: https://arxiv.org/abs/2009.04332v2

In the domain of computational/theoretical neuroscience a recently revived question is about the complexity of neural data. This question can be tackled by studying the dimensionality of such data: is neural activity high or low dimensional? How does the geometrical structure of neural activity depend on behavior, learning or the underlying connectivity? In my talk I will show how it is possible to link these three aspects (animal behavior, learning and underlying network connectivity) to the geometrical properties of neural data, with an emphasis on dimensionality phenomena. My results depart from neural recordings and aim at building understanding of neural dynamics by means of theoretical and computational tools. Such tools are mainly borrowed from the domain of neural networks dynamics, using a blend of large scale dynamical systems and statistical physics approaches.

Wild-type zebrafish (Danio rerio) are characterized by black and yellow stripes, which form on their body and fins due to the self-organization of thousands of pigment cells. Mutant zebrafish and sibling species in the Danio genus, on the other hand, feature altered, variable patterns, including spots and labyrinth curves. The longterm goal of my work is to better link genotype, cell behavior, and phenotype by helping to identify the specific alterations to cell interactions that lead to these different fish patterns. Using a phenomenological approach, we develop agent-based models to describe the behavior of individual cells and simulate pattern formation on growing domains. In this talk, I will overview our models and highlight how topological techniques can be used to quantitatively compare our simulations with in vivo images. I will also discuss future directions related to taking a more mechanistic approach to modeling cell behavior in zebrafish.

Fertilization is one of the fundamental processes of living systems. Here I will address marine external fertilization and comment on recent work on mammals. I will show experiments that substantiate that sea urchin sperms exhibit chemotaxis as they swim towards the ovum. They are guided by flagellum internal [Ca2+] concentration fluctuations triggered by the binding of chemicals from the oocyte surroundings. Based on experiment, I present a family of logical regulatory networks for the [Ca2+] fluctuation signaling-pathway that reproduce previously observed electrophysiological behaviors and provide predictions, which have been confirmed with new experiments. These studies give insight on the operation of drugs that control sperm navigation. In this systems biology approach, global properties of the [Ca2+] discrete regulatory network dynamics such as

Ring-shaped contractile structures play important roles in biological processes including wound healing and cell division. Many of these contractile structures rely on motor proteins called myosins for constriction. We investigate force generation by the Type II myosins NMY-1 and NMY-2 in ring channels, contractile structures in developing oocytes of the nematode worm C. elegans, as our model system. By exploiting the ring channel’s circular geometry, we derive a second order ODE to describe the evolution of the radius of the ring channel. By comparing our model predictions to experimental depletion of NMY-1 and NMY-2, we show that these myosins act antagonistically to each other, with NMY-1 exerting force orthogonally and NMY-2 exerting force tangentially to the ring channel opening. Stochastic simulations are currently being used to determine how NMY-1 and NMY-2 may be producing these antagonistic forces, with new tools from topological data analysis identifying persistent ring-like structures in the simulation data.

The mammalian cell surface is highly permeable to water. The cell can also actively control the water flux across the cell surface by pumping solutes (mostly ions), and thereby controlling the cell water content and the cell volume. In this talk, we will explore how the cell also uses active water fluxes to move and change cell shape. The same players in the cell volume control system are involved in driving cell movement, especially in high viscosity environments. Mathematical modeling shows that the water-driven cell movement is energetically costly, but is necessary when the hydraulic environment is viscous. Finally, we will discuss how epithelial cell layers such as the kidney tubule pump water and generate mechanical force.

Recent findings suggest that cancer cells can acquire transient resistant phenotypes via epigenetic modifications and other non-genetic mechanisms. Although these resistant phenotypes are eventually relinquished by individual cells, they can temporarily ’save’ the tumor from extinction and enable the emergence of more permanent resistance mechanisms. These observations have generated interest in the potential of epigenetic therapies for long-term tumor control or eradication. In this talk, I will discuss some mathematical models for exploring how phenotypic switching at the single-cell level affects resistance evolution in cancer. As an example, we will explore the role of MGMT promoter methylation in driving resistance to temozolomide in glioblastoma.

Many membrane-bound T cell receptors have long, unstructured cytoplasmic tails that contain tyrosine sites. These sites can serve as regulators of receptor activation when phosphorylated or dephosphorylated, while also serving as docking sites for cytosolic enzymes. Interactions between receptors then involve the in-membrane diffusion of the receptor proteins, and reactions between proteins tethered to the receptors’ tails (and hence diffusing within the three-dimensional cytosolic space near the membrane). We develop a particle-based stochastic reaction-diffusion model based on the Convergent Reaction-Diffusion Master Equation to study the combined diffusion of individual receptors within the cell membrane, and chemical reactions between proteins bound to receptor tails. The model suggests a switch-like behavior in the dependence of the fraction of activated receptors on both receptor diffusivity, and on the molecular reach at which two receptor tails can interact. A simplified, analytically solvable model is developed to approximate the more complicated multi-particle system, and used to illustrate how the switch-like behavior arises.

Classical population dynamics problems assume constant unchanging environments. However, realistic environments fluctuate in both space and time. My lecture will focus on the analysis of population dynamics in environments that shift spatially, due either to advective flow (eg., river population dynamics) or to changing environmental conditions (eg., climate change). The emphasis will be on the analysis of nonlinear advection-diffusion-reaction equations and related models in the case where there is strong advection and environments are heterogeneous. I will use methods of spreading speed analysis, net reproductive rate and inside dynamics to understand qualitative outcomes. Applications will be made to river populations and to the genetic structure of populations subject to climate change.

Many-body problem of celestial mechanics revolutionized applied mathematics and continues to provide inspiration. Math/physical communities are much less aware that there are numerous example of fascinating many-body problems of classical mechanics arising in live cells at drastically different scales: instead of years and millions of kilometers, in the cell we deal with minutes and microns. Another big difference is: rather than Newtonian mechanics in empty space, when acceleration is proportional to force, in the cells filled with viscous cytoplasm, we deal with Aristotelian mechanics, in which velocity is proportional to force. Yet another difference is a great diversity of complex inter-body forces in the cell, compared to pleasingly simple gravitational force of celestial mechanics. Because of this diversity, in cell biology we often need to solve the ill-posed inverse problem – reverse-engineering forces from the observed patterns and movements – contrasted with the well-posed direct problem of predicting patterns and movements from known forces. I will discuss two many-body problems of cell biology – assembly of mitotic spindle from two centrosomes and tens of chromosomes, and nuclei positioning in multi-nucleated muscle cells. Three approaches – solutions of ODEs of ‘particle’ models, solutions of PDEs of continuous approximation, and energy minimization, complemented by computer screening – shed light on the molecular origins of the intracellular forces that ensure proper and robust cellular architecture.