The meeting will have a broad agenda in a general area of mathematical modeling of living systems (MMLS). Representatives of the four newly established NSF-Simons Math Biology Centers will be invited to interact with Simons Fellows in MMLS. Talks will be given by both representatives of the Centers as well as by four Simons Investigators.
Strings, Trees, and RNA Folding
The math-bio interface has many facets, distinguished by both the biological applications as well as the mathematical motivations. We discuss here the problem of RNA folding which lies at the intersection of discrete mathematics and molecular biology. As will be illustrated, combinatorial models, methods, and analyses yield insight into the structure, and therefore function, of RNA molecules. Since RNA mediates DNA expression through gene splicing, editing, and regulation, this advances our understanding at a critical juncture from genome to phenome.
Looking for a place for Theory
(Joint work with Laura Bagamery and Ethan Garner)
The budding yeast, Saccharomyces cerevisiae, both in nature and the laboratory, experiences two very different environments: brief periods with abundant nutrients and long periods of starvation. Our investigations suggest that they cope with this unpredictable alternation by adopting two different strategies: fast (F), reproducing as fast as possible by avoiding the cost of accumulating reserve nutrients (storage carbohydrates) and ways of utilizing them efficiently (mitochondria), or slow (S), replicating more slowly and accumulating these resources in order to better survive transitions to environments with worse or no nutrients. The two different strategies are revealed by suddenly removing glucose, yeast’s preferred carbon source, and requiring them to grow on amino acids, which cells must respire to produce ATP. When glucose is removed, the mitochondria of F cells collapse into a spherical aggregate, their cytoplasmic pH falls and remains low, and they remain arrested for many hours before dispersing their mitochondria into tubular network and resuming growth. S cells retain a normal distribution of mitochondria, suffer a smaller drop in pH, and resume growth after little or no lag. We can quantitatively model the transition between these two states, find mutations that lock cells in one or the other, and are searching for the physiological circuits that allow cells to exist in two heritable states and explain how they switch between them.
Qing Nie and Arthur Lander
Multiscale Cell Fate Through the Lens of Single Cells
Of the many abilities that cells in multicellular organisms display, one of the most interesting is the ability to adopt or change fate, i.e. to stably become a particular cell type. Signals from other cells, the environment, or disease agents can all influence cell fate decisions. Recent technological breakthroughs, which have made it possible to gather data at the single cell level in previously unimaginable quantities, are providing a wealth of information relevant to how cell fate decisions are made. From this information is emerging a view of cell fate that is more dynamic, stochastic, and complex than previously recognized. Furthermore, the wide range of time- and space-scales associated with cell-cell communication, cell signaling, gene expression, and cell growth, indicate the need for new computational tools and multiscale models to describe and explain the complexity of cell fate dynamics. In this talk we will present, using multiple biological examples, our recent efforts within the Center to use single-cell RNA-seq data and spatial imaging to gain insight into cell fate control in development, regeneration, and tumor formation. We will also present several new computational tools and mathematical modeling methods that we have been developing for the study of cell fate processes from the perspective of single cells.
Current Research at the NSF-Simons Center for Quantitative Biology
Research at the NSF-Simons Center for Quantitative Biology aims to transform our understanding of animal growth and development by applying mathematical analysis and modeling. Five vibrant research programs in the Center are composed of collaborative teams of mathematical and life scientists from Northwestern University. The Center deploys three fundamental mathematical disciplines: dynamical systems theory; stochastic processes; and dimensional reduction. These approaches are highly suited to the real-world features of growth and development. Experimental focus is on established laboratory model organisms: Drosophila melanogaster, Caenorhabditis elegans, Xenopus laevis, and Mus musculus. Three research studies at varying stages of maturity will be highlighted.
Deep Learning and Proteins
Modeling Learning in the Brain
We are interested in the field of neuroscience, especially insofar as it addresses the questions of learning and memory. Learning is thought to change the connections between the neurons in the brain, a process called synaptic plasticity. Using mathematical and computational tools, we model synaptic plasticity across different time scales that reproduces experimental findings. We then study the role of synaptic plasticity, by constructing networks of artificial neurons with plastic synapses. We are working to tight collaboration with experimental laboratories, which measure connectivity changes and behavioral learning.
Complex life above a certain size would not be possible without a circulatory system. Plants, fungi and animals have developed vascular systems of striking complexity to solve the problem of nutrient delivery, waste removal, and information exchange. These vascular systems are frequently not static, but respond to environmental cues and continuously alter the diameters of their vessels. Inspired by recent findings that hemodynamic fluctuations in the cortex can persist even in the absence of neuronal input extrinsic to the vascular network, we present a network model that can support self-sustained oscillations without a time varying external input. In addition, modelling network development during growth, we discuss how a hierarchically organized vascular system can develop under constant or variable flow and with limited genetic information. We show how time-dependent flow can stabilize anastomoses and lead to a topology dominated by cycles, and discuss the spectrum of phenotypes that optimize trade-offs between competing evolutionary pressures.
Universality Classes in the Evolutionary Dynamics of Expanding Populations
Reaction-diffusion waves describe diverse natural phenomena from crystal growth in physics to range expansions in biology. Two classes of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Recently, we examined how demographic fluctuations change as the density-dependence of growth or dispersal dynamics is tuned to transition from pulled to pushed waves. We found three regimes with the variance of the fluctuations decreasing inversely with the population size, as a power law, or logarithmically. These scalings reflect distinct genealogical structures of the expanding population, which change from the Kingman coalescent in pushed waves to the Bolthausen-Sznitman coalescent in pulled waves. The genealogies and the scaling exponents are model-independent and are fully determined by the ratio of the wave velocity to the geometric mean of dispersal and growth rates at the leading edge. Our theory predicts that positive density-dependence in growth or dispersal could dramatically alter evolution in expanding populations even when its contribution to the expansion velocity is small. On a technical side, our work highlights potential pitfalls in the commonly-used method to approximate stochastic dynamics and shows how to avoid them.