2025 National Institute for Theory and Mathematics in Biology Annual Meeting

Rosemary Braun
Northwestern University

Keeping Accurate Time in a Fuctuating World

​

The cyanobacteria Synechococcus elongatus has one of the simplest known circadian clocks: a molecular oscillator comprising three proteins, one of which [KaiC] cycles through four phosphorylation states with an approximate 24-hour period. For this to be useful at the cell level, the phosphorylation states of many KaiC molecules must be approximately synchronized. Obviously, both the forward drive of the cycle and the synchronization mechanism operate out of equilibrium, incurring an energetic cost to maintain both. But there is something even more puzzling: as the cell elongates and divides, new KaiC molecules are synthesized, yet the cell-level clock maintains its approximate 24h rhythm despite fluctuations in local concentrations of phosphorylated and unphosphorylated KaiC. How does the cell deal with this heterogeneity, and at what energetic cost? We propose models for his mechanism, with the ultimate goal of predicting the limits of growth on the cell’s ability to keep time.
 

James Fitzgerald
Northwestern University

Ensemble Modeling of Biological Neural Networks

​

Neuronal activity patterns provide the physical substrates for perception, cognition, and behavior. This activity in turn emerges from the network of synaptic interactions between neurons. A mechanistic understanding of brain function thus requires that neuroscientists be able to link functional patterns of neuronal activity to structural patterns of synaptic connectivity. Here, I will describe my lab’s efforts to link neural network structure and function by building and characterizing mathematical ensembles of neural network models. Our approach embraces the fact that many different patterns of synaptic connectivity could underlie the same functional response properties. By figuring out what is shared by all possibilities, we make experimental predictions that rigorously test neural network models. By comparing the possibilities to available connectivity data, we build biologically realistic neural network models. And by hypothesizing that biology dynamically explores its possibilities, we develop novel theories of learning and memory. This talk will explain each of these applications to illustrate how ensemble modeling provides a general framework for understanding how brains work.
 

Sebastien Roch
University of Wisconsin–Madison

Complex Discrete Probability Models in Evolutionary Biology: Challenges and Opportunities

 

The reconstruction of species phylogenies from genomic data is a key step in modern evolutionary studies. This task is complicated by the fact that genes evolve under biological phenomena that produce discordant histories. These include hybrid speciation, horizontal gene transfer, gene duplication and loss, and incomplete lineage sorting, all of which can be modeled using random gene tree distributions building on well-studied discrete stochastic processes (branching processes, the coalescent, random rearrangements, etc.). Gene trees are in turn estimated from molecular sequences using Markov models on trees. The rigorous analysis of the resulting complex models can help guide the design of new reconstruction methods with computational and statistical guarantees. I will illustrate the challenges and opportunities in this area via a few recent results. No biology background will be assumed.
 

Eric Siggia
Rockefeller University

Geometry and Genetics

​

The application of quantitative methods to biological problems faces the choice of how much detail to include and the generality of the conclusions. The middle ground entails some use phenomenology, a well-regarded approach in physics. Genetic screens have uncovered most of the genes responsible for development from egg to adult. But overlaid is the phenomenon of canalization in development that is a license to develop models that are quantitative and dynamic yet do not begin from an enumeration of the relevant genes. Modern mathematics (i.e., post 1960), ‘dynamical systems’ so called, has many similarities to experimental embryology and allows the enumeration of categories of dynamical behaviors by geometric methods. Examples from stem cell differentiation, and the embryos of model organisms will illustrate how systems with a few variables can be fit to cell state transitions. Phenomenology of the sort envisioned is essential to bridge the scales from cell to tissue to embryo, by breaking the system into blocks that can be separately parameterized.
 

Mary Silber
University of Chicago

Self-Organized Vegetation Patterns in Drylands

​

Drylands are water-limited ecosystems, where the water arrives via rare, discrete, and unpredictable rainstorms. One strategy for concentrating this resource where it is needed by the consumers involves feedbacks that drive the formation of regularly-spaced bands of vegetation. These bands form transverse to gentle slopes and can capture rain run-off. Such large-scale vegetation patterns, readily observed via satellite images, have been found in semi-arid and arid regions around the globe. We use a PDE framework to model the consumer-resource interactions between biomass and soil moisture, with soil water replenished by rainstorms that we model as impulses to the system. We use this framework to explore the impact of storm variability on vegetation pattern formation by introducing randomness into the timing and the total amount of water deposited by each storm. We investigate how storm variability impacts vegetation pattern formation, which may give insight into the resilience of these dryland ecosystems in the face of climate change.
 

Shmuel Weinberger
University of Chicago

Persistent Homology of Function Spaces and Geometric Metaphors in Biology

The first goal of the talk is to explain what the first clause of the title means, and to describe some recent results that are suggested by (elementary) biochemistry. This will include (or at least motivate) the solution to a problem raised by Misha Gromov in the 1970s. A second goal will be to reflect on two common geometric metaphors that arise in biology, the landscape and the network in the hopes of spurring some conversation. Finally, I will discuss some questions this perspective gives rise to. A part of the talk will be based on joint work with Rich Carthew, Lorenzo Orechia, Sam Riesenfeld, Ryan Robinett, and Evan Gibbs — most of it (i.e., the math) is based on joint work with Jonathan Block and Fedya Manin.
 

Rebecca Willett
University of Chicago

Stabilizing Black-Box Model Selection

​

Model selection is the process of choosing from a class of candidate models given data. For instance, we may wish to select which set of features best predict a label or response or select an equation that hypothesizes a model of a dynamic biological process. However, absent strong assumptions, typical approaches to these problems are highly unstable: if a single data point is removed from the training set, a different model may be selected. In this talk, I will present a new approach to stabilizing model selection with theoretical stability guarantees that leverages a combination of bagging and an “inflated” argmax operation. Our method selects a small collection of models that all fit the data, and it is stable in that, with high probability, the removal of any training point will result in a collection of selected models that overlap with the original collection. We illustrate this method in a model selection problem focused on identifying how competition in an ecosystem influences species’ abundances and a graph estimation problem using cell-signaling data from proteomics. In these settings, the proposed method yields stable, compact, and accurate collections of selected models, outperforming a variety of benchmarks. This is joint work with Melissa Adrian and Jake Soloff.