2026 National Institute for Theory and Mathematics in Biology Annual Meeting

Danny Abrams
Northwestern University

Modeling and Analysis of Synchronous Signaling in Biological Systems

Self-organization is a hallmark of biological systems. It is characterized by the spontaneous appearance of collective order that arises merely from local interaction among individuals—no leader is needed. In this talk, I will focus on two particular species where synchronous signaling emerges in the context of mating: Pteroptyx malaccae fireflies, which synchronize their flashes, and Austruca perplexa fiddler crabs, which synchronize the waving of their major claws. In these two systems, the individuals remain predominantly immobile while synchronizing, making their behavior both trackable and tractable. This allows us to pose mathematical models and test them against observations, yielding insight into the mechanisms by which biological synchrony can occur and important clues about its adaptive value.
 

Stefano Allesina
University of Chicago

One Hundred Years of Lotka-Volterra Models
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Over the past century, the Generalized Lotka–Volterra (GLV) model has grown from a mathematical curiosity to a cornerstone of theoretical ecology. Here we celebrate the enduring legacy of Lotka and Volterra by tracing how their model has progressively shaped our understanding of ecological dynamics, even as fundamental questions remain open. Along this trajectory, the GLV model has emerged as a common framework linking ecology, evolutionary biology, and infectious disease dynamics, and as a bridge between theory and experiment. Its distinctive balance of tractability and realism has made it a natural arena for studying complex phenomena such as ecological assembly and the behavior of large communities. The same features have attracted researchers from mathematics and physics, sparking advances such as the analysis of GLV models with random parameters. By weaving together these developments and highlighting future directions, we aim to guide the GLV model into its next century.
 

Alasdair Hastewell
National Institute for Theory and Mathematics in Biology

Discovering Insights Into Biological Dynamics Using Data-Driven Modeling
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Living organisms are complex, multi-scale, spatiotemporal dynamical systems. Recent advances in quantitative live imaging enable tracking biological dynamics at unprecedented resolution, yet challenges remain, as important variables are often unmeasured or noisy. To translate high-dimensional, dynamic biological imaging data into interpretable low-dimensional representations and mechanistic models, we introduce a framework that combines geometry-aware spectral mode representations with wavelet analysis and model selection. I will demonstrate the approach’s flexibility by applying it to tracking data on cilia dynamics in single-celled algae and to jump takeoff kinematics in Amazonian jumping spiders to characterize the behavioral complexity and mechanisms of locomotion. When not all important dynamical variables are observed, the applicability of these model-discovery methods is challenged by model non-uniqueness. Using differential algebraic techniques, we quantify the set of indistinguishable models, which has implications for mechanistic insights from data and for strategies to make model selection algorithms robust to real biological data.
 

Andrea Liu
University of Pennsylvania

Insights Into Global Epistasis in Proteins From Tunable Matter

Proteins have long been modeled as mechanical networks of nodes connected by springs. We have studied the inverse problem, of starting with mechanical networks and then tuning their properties to introduce protein function. We focus on allostery, where binding of a small molecule to the protein triggers a conformational change that enables binding or unbinding of another small molecule. Here I will describe what our approach brings to protein allostery, including a relation between structure and function and insight into the phenomenon of global epistasis, where the non-additivity of mutations can have a global contribution, arising from the cost landscape in which the mutation occurs.
 

Sergei Maslov
University of Illinois at Urbana-Champaign

Crossfeeding Dynamics in Energy-Limited and Auxotrophic Microbial Communities

Microorganisms in many environments survive by sharing nutrients with each other in a process called crossfeeding. Some microbes are extremely slow-growing (taking weeks or years to divide instead of hours), while others are auxotrophs that have lost the ability to make essential nutrients and must obtain them from neighboring species. I will describe two distinct modeling approaches for understanding crossfeeding: (1) a thermodynamic consumer-resource model for slow-growing communities in energy-limited environments (George, Wang & Maslov, ISME J, 2023) and (2) a higher-order interaction model for auxotrophic communities dependent on essential resource exchange (Wang & Maslov, Cell Systems, in press).

The thermodynamic model is applicable to slow-growing communities in which metabolic byproducts from reactions close to thermodynamic equilibrium create crossfeeding networks. We derive the principle of maximum free energy dissipation in this model and demonstrate how functional convergence emerges despite taxonomic differences in crossfeeding partnerships. The model successfully predicts functional convergence in anaerobic digesters, showing how crossfeeding networks stabilize at low dilution rates.

The auxotroph model examines communities where organisms are genetically unable to synthesize essential nutrients (e.g. amino acids) and must rely on crossfeeding from other species. Using graphical and algebraic methods, our approach reveals how amino acid crossfeeding creates higher-order interaction networks that enhance community resilience to environmental fluctuations through metabolic complementarity. Applied to experimental data from synthetic E. coli communities, the model accurately predicted the survival of 3 out of 4 strains in a 14-member auxotroph community, correctly identifying key mutualistic crossfeeding partnerships.
 

Jasmine Nirody
University of Chicago

Adaptive Bacterial Motility Across Species and Scales

Bacteria live complicated lives: they swim through fluids of varying viscosity as well as interact with surfaces and other bacteria. We explore how bacteria make use of adaptive dynamics at both the level of whole-cell swimming behavior and at the level of the molecular machine underlying swimming, the bacterial flagellar motor. (1) Observed bacterial motility patterns are a convolution of the underlying control program and constraints from the environment. Using microfluidic experiments and mathematical modeling, we demonstrate how various bacterial species have tuned their motility strategies facilitate movement through their environments, from ‘run-and-tumble’ in the gut-dwelling E. coli to ‘push-pull-wrap’ in the squid symbiont Vibrio fischeri. (2) We characterize mechanosensitive remodeling in bacterial flagella that facilitates movement through complex, dynamic mechanical environments. We use magnetic tweezers to manipulate external torque on the bacterial flagellar motor, and present a model for the dynamics of load-dependent assembly in the flagellar motor. We illustrate how this nanomachine allows bacteria to adapt to changes in their surroundings. Together, our results reveal conserved principles of adaptive motility across bacterial species and length scales.
 

Lior Pachter
California Institute of Technology

The Systems Biology of a Single Cell
 

Mercedes Pascual
New York University and the Santa Fe Institute

Toward a Theory of Strain Hyper-Diversity in Host-Pathogen Systems
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Growing genomic evidence is revealing large strain diversity within populations of microbes encoded by multigene families and accessory genomes. One process of interest in explaining diversity patterns is competition for hosts via cross-immunity, which sets the stage for negative frequency-dependent selection (NFDS, an advantage of the rare and a disadvantage of the common) in transmission dynamics. Starting with literature results on the emergence of niches in mathematical models of competition for fixed and typically low trait spaces, I contrast the biology of pathogens whose vast strain diversity is defined in large combinatorial spaces of antigenic variation. I rely on the malaria parasite Plasmodium falciparum under high transmission as an example for this purpose, and present results of a stochastic computational (agent-based) model on the role of NFDS in strain diversity and its structure. With a simplified, more analytical tractable PDE model, I argue that the feedback of ecology and evolution which generates a large trait space matters to system resilience. I end with some potential implications and generalizations of these ideas to other eco-evolutionary systems.