2025 National Institute for Theory and Mathematics in Biology Annual Meeting

The second NITMB Annual Meeting at the Simons Foundation was held on April 3-4th 2025. It was a great opportunity for mathematicians and biologists to convene and learn about important new advances in mathematical biology. The NITMB was founded in 2023 to create an international nexus for scientists working at the interface between mathematics and biology, two disciplines that only sporadically have overlapped to promote common interests. Sponsored by an equal partnership between the Simons Foundation and the National Science Foundation, the NITMB is a joint partnership between Northwestern University and the University of Chicago. As such, the institute is located in downtown Chicago, where it supports a broad variety of convening programs, as well as research aimed at better integrating mathematics with biology. NITMB research aims to broaden the use of mathematics in biological research to advance understanding of living systems. Its research also aims to develop new mathematics that is inspired by biology, which in turn, may become applied to harness new discoveries in biology.

Over 100 people attended the meeting in-person, including 50 trainees. The meeting brought together pure and applied mathematicians, computer scientists, theoretical physicists, and empirical biologists. Although most attendees were faculty and trainees from the NITMB, the meeting also included people from around the United States and Europe. The meeting was comprised of a poster session that catalyzed new interactions between disciplines, a session of 20 lightning talks, and seven full-length talks, all of which were enthusiastically received with vigorous questions and engagement.

Eric Siggia (Rockefeller University) kicked off the meeting by talking about his theoretical studies of animal development. Cells in an embryo undergo transitions in their identity, becoming progressively more restricted in what final differentiated state they can adopt. Conrad Waddington likened it to a ball rolling down a hill, following valleys that bifurcate. This Waddington’s landscape has become a cliché in modern embryology. Dr Siggia’s work aims to provide precise and rigorous meaning to the process. Working closely with experimental colleagues, he is gaining a dynamical systems perspective to development. Mammalian embryonic stem cells can be induced to develop in vitro in ways that remarkably resemble what happens in an intact embryo. Dr Siggia leverages this simple minimal system to understand the mysteries of development.

Rebecca Willett (University of Chicago) spoke about a new and powerful method for model selection. Model selection is the process of choosing a model from a class of candidate data-driven models. However, absent strong assumptions, typical approaches to this problem are highly unstable. If a single data point is removed from the training set, a different model may be selected. Dr Willett presented a new approach to stabilizing model selection with theoretical stability guarantees. In the first step, the data is “bagged” into a subgroup that is used to train a model. This bagging or bootstrapping is repeated many times, yielding a set of potential models. From these, the “best-fit” model is selected using an “inflated” argmax operation. This 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 results in a collection of selected models that overlap with the original collection. Dr Willett illustrated the utility of this method in a model selection problem focused on the MNIST garment dataset. Since the method is generalizable to any form of model, Dr. Willett’s work promises to be a powerful method to robustly select models throughout biology.

James Fitzgerald (Northwestern University) talked about his theoretical studies of the nervous system. Neuronal activity is heterogeneous in response to a specific stimulus; some neurons emit action potentials and others are silent. This activity emerges from the network of synaptic interactions between neurons. Many different patterns of synaptic connectivity could underlie the same functional response properties. Dr Fitzgerald described his efforts to link neural network structure to function by building and characterizing mathematical ensembles of neural network models. By comparing the possibilities to available connectivity data, he builds biologically realistic neural network models. His approach seeks to learn what is shared by all possibile models, making experimental predictions that rigorously test neural network models. Dr Fitzgerald explained each of these applications to illustrate how ensemble modeling provides a general framework for understanding how brains work.

Mary Silber (University of Chicago) spoke about mathematical modeling of pattern-forming 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 plant life involves feedbacks that drive the formation of regularly-spaced bands of vegetation interspersed by exposed soil. 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 planet. Dr Silber uses a PDE framework to model the consumer-resource interactions between vegetation and soil moisture, with soil water replenished by rainstorms that are modeled as impulses to the system. She uses 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. Storm variability impacts vegetation pattern formation, which gives insight into the potential resilience of these dryland ecosystems in the face of climate change.

The second day of the meeting started with Sebastien Roch (University of Wisconsin) speaking about inference modeling the tree of life with genome sequences. 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 differentially within the genomes of evolving populations. These differential processes include hybrid speciation, horizontal gene transfer, gene duplication and loss, and incomplete lineage sorting. These 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 DNA 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. Dr Roch discussed the challenges and opportunities in this area via a few recent results involving the tree of birds.

Rosemary Braun (Northwestern University) spoke about how organisms tell time on a circadian 24-hour cycle. She presented work on the fruit fly clock and how study of transients can provide a deeper understanding of clock function. Dr Braun also talked about the clock in a cyanobacteria, which has one of the simplest known circadian clocks. It is a molecular oscillator comprised of 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. However, as the cell grows and divides, new KaiC molecules are synthesized. Yet the cell-level clock maintains its approximate 24h rhythm despite the obvious fluctuations in phosphorylated and unphosphorylated KaiC. How does the cell deal with this heterogeneity? Dr Brain proposed models for this mechanism, with the ultimate goal of predicting the limits of growth on the cell’s ability to keep time.

The meeting was concluded by Shmuel Weinberger (University of Chicago) who talked about topology and how it might be used on biological problems. Considering networks of molecules (genes, RNAs or proteins) Dr Weinberger discussed the topological properties of them. In particular, there might arise interesting deformations on a manifold that represent biological features such as enzymatic activity. This topological analysis also suggests why life evolved with limits that are not intuitively obvious. Dr Weinberger also touched on collaborative work using geometry to study form in the fruit fly.

Rosemary Braun
Northwestern University

Keeping Accurate Time in a fluctuating World
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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
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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
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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
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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
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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.

Lightning Talks
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