2024 National Institute for Theory and Mathematics in Biology Annual Meeting and Retreat

Accompanied by a 4.8-magnitude earthquake and preceding a continent-spanning total solar eclipse by three days, the first NITMB Annual Meeting at the Simons Foundation was held on April 4–5th 2024. Foremost in excitement, though, was the 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.

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Almost 100 people attended the meeting in-person, including 27 trainees, with another 10 trainees and faculty in virtual attendance. 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, and eight talks, all of which were enthusiastically received with vigorous questions and engagement.

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Daniel Fisher (Stanford University) kicked off the meeting by talking about his theoretical studies of microbial evolution. Inspired by the laboratory evolution experiments done by Richard Lenski on the bacterium Escherichia coli, Dr. Fisher presented two mathematically based models of evolution. The first model was a numerical analysis of how a population of cells evolves in isolation over time when environmental conditions are invariant. The theory of neutral evolution states that stochastic mutation and genetic drift are responsible for the genetic variation at the population level under such circumstances. Dr. Fisher found that, instead, selection of new mutants with small effects on cell fitness could theoretically account for continual evolution of the population to quasi-steady states, as had been observed in the lab evolution experiments. Dr. Fisher also modeled evolution of co-existing populations of bacteria and a virus that infects the bacteria. Again, he found that there was continual evolution of the two populations, but the dynamics were chaotic in nature. This discovery resonates with empirical observations of fluctuating host-pathogen population dynamics in the natural world.

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Yogesh Goyal (Northwestern University) spoke about his own work on cell evolution, but in his case, understanding how tumor cells evolve under selection during anti-cancer drug treatments. Inspired by the landmark mathematical analysis of bacterial mutagenesis by Luria and Delbrück in 1943, Dr. Goyal described his use of cutting-edge genomic methods to tag and monitor thousands of cancer cell lineages before and after drug selection. He found that rare cells in the population exist before selection that are drug resistant once exposed to the selective agent. Resistance is not genetic in origin but is pre-determined by molecular differences in the initial state of cells. Remarkably, cells as they divide retain a memory of this initial state for several generations. The nature of these molecular states and their memory mechanism remain to be elucidated. Dr. Goyal’s work exemplifies how mathematical dimension reduction can provide insights into the mysterious high-dimensional states of a cancer cell.

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Brent Doiron (University of Chicago) talked about his theoretical studies of the nervous system. Neuronal activity is very heterogeneous in response to a specific stimulus; some neurons emit many action potentials and others are silent. Further, trial-to-trial fluctuations of neuronal activity occupy a low dimensional space, owing to correlated activity of neurons within a population. Using techniques from the theory of random matrices, Dr. Doiron linked these two aspects of neuronal response and showed that the more heterogeneous neuronal firing rates are, the lower dimensional is their population trial-to-trial variability. This prediction was validated for multiple datasets from numerous brain areas in rodents, primates and humans. Dr. Doiron presented a simple theory in which a more heterogeneous neuronal code leads to better fine-discrimination performance, particularly when the brain is in more heightened states of information processing.

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Niall Mangan (Northwestern University) spoke on her work applying mathematics to discover dynamic models to describe time-series from biological networks. Machine learning often does not provide mechanistic insights whereas heuristic model selection based on information theory is often limited in model sampling. Dr. Mangan described an approach to use sparse optimization to select a subset of nonlinear dynamic network models. Since many biological networks have abundant nonlinearities, this approach is especially attractive to discover novel interactions controlling dynamic behavior. The sparse optimization algorithm discovers the most parsimonious models from a combinatorically large set of nonlinear network models (for a simple 3-species system 109 models). Dr. Mangan applied this innovative data-driven approach to time-series data from a hibernating mammal and successfully found models consistent with metabolic regulation. 

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Arvind Murugan (University of Chicago) related a theoretical study of how mechanisms emerged to enhance biological fidelity beyond the limits set by equilibrium thermodynamics. Processive biochemical reactions often inject chemical energy at each step so that enzymes catalyze the reactions with orders-of-magnitude greater fidelity than if at equilibrium. This is known as kinetic proofreading. Dr. Murugan described how errors in the processive reaction generate a temporal delay such that if the reaction is optimized for speed, it will naturally evolve a kinetic proofreading mechanism. Thus, the costs in time and energetics for having kinetic proofreading would be offset by reactions occurring at greater speed, and therefore possibly greater fitness. This plausible mechanism for how proofreading evolved in DNA replication and protein synthesis was expanded upon by Dr. Murugan to include its generality to cell-scale and other higher-scale phenomena as well.

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The second day of the meeting started with Paul François (Université de Montréal) speaking about complex dynamical systems in development and immunology. Dr. François described using a combination of first-principle theoretical modeling with simple machine-learning autoencoders to build tractable models of biological dynamics. This allowed Dr. François to discover a small number of latent variables acting within each system of study. By inferring dynamics of the latent variables, a latent space could be described for the system. Dr. François applied his modeling to a simple gene regulatory network acting in the fruit fly embryo, and found two latent variables that describe the system. He also modeled the complex cytokine responses of immune T cells when exposed to various antigens, and found the latent space captured key modalities of T cell response. The latent space is consistent with T cell receptors responding to antigens using a kinetic proofreading mechanism to accurately discriminate between different types of antigens.

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Stephanie Palmer (University of Chicago) spoke about how the nervous system encodes predictive features that are most useful for fast and effective movements. Dr. Palmer found that predictive computation begins even at the earliest stages of the visual system, in the retina. Using data from the salamander retina, Dr. Palmer applied techniques in statistical physics and information theory to assess how the retina achieves predictive computation. She compared this to predictive computation performed by fruit flies in flight, observing parallels and differences with the salamander system. Dr. Palmer also discussed using an autoencoder model to characterize the latent space of retinal processing when stimulated by a variety of dynamic natural scenes, yielding a low representation of time in the natural scenes.

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The meeting was concluded by Richard Carthew (Northwestern University) who talked about how growth can distort the genotype-to-phenotype map. Dr. Carthew discussed how slowing animal growth will often suppress defects in cell fate specification caused by mutation. Conversely, accelerating growth will often enhance such mutationally-driven defects. These effects are not specific to particular body systems or stages of development. Dr. Carthew described a simple and general model of developmental gene expression using a control theoretic framework that made predictions about expression dynamics when subjected to growth variation. These predictions were validated by experiments in the fruit fly. The study highlights a deep connection existing between growth and development.