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Equilibria, or fixed points, play an important role in dynamical systems across various domains, yet finding them can be computationally challenging. Here, we show how to efficiently compute all equilibrium points of discrete-valued, discrete-time systems on sparse networks. Using graph partitioning, we recursively decompose the original problem into a set of …

Viruses such as the novel coronavirus, SARS-CoV-2, that is wreaking havoc on the world, depend on interactions of its own proteins with those of the human host cells. Relatively small changes in sequence such as between SARS-CoV and SARS-CoV-2 can dramatically change clinical phenotypes of the virus, including transmission rates and severity of the disease. On…

The SARS-CoV-2 nucleocapsid (N) protein is an abundant RNA-binding protein critical for viral genome packaging, yet the molecular details that underlie this process are poorly understood. Here we combine single-molecule spectroscopy with all-atom simulations to uncover the molecular details that contribute to N protein function. N protein contains three dynami…

Understanding the structural determinants of a protein’s biochemical properties, such as activity and stability, is a major challenge in biology and medicine. Comparing computer simulations of protein variants with different biochemical properties is an increasingly powerful means to drive progress. However, success often hinges on dimensionality reduction alg…

SARS-CoV-2 has intricate mechanisms for initiating infection, immune evasion/suppression and replication that depend on the structure and dynamics of its constituent proteins. Many protein structures have been solved, but far less is known about their relevant conformational changes. To address this challenge, over a million citizen scientists banded together …

The hormone oxytocin is commonly administered during childbirth to initiate and strengthen uterine contractions and prevent postpartum hemorrhage. However, patients have wide variation in the oxytocin dose required for a clinical response. To begin to uncover the mechanisms underlying this variability, we screened the 11 most prevalent missense genetic variant…

Understanding the functional role of protein-excited states has important implications in protein design and drug discovery. However, because these states are difficult to find and study, it is still unclear if excited states simply result from thermal fluctuations and generally detract from function or if these states can actually enhance protein function. To…

Understanding molecular kinetics, and particularly protein folding, is a classic grand challenge in molecular biophysics. Network models, such as Markov state models (MSMs), are one potential solution to this problem. MSMs have recently yielded quantitative agreement with experimentally derived structures and folding rates for specific systems, leaving them po…

Simulating protein folding has been a challenging problem for decades due to the long timescales involved (compared with what is possible to simulate) and the challenges of gaining insight from the complex nature of the resulting simulation data. Markov State Models (MSMs) present a means to tackle both of these challenges, yielding simulations on experimental…

Protein folding is an important problem in structural biology with significant medical implications, particularly for misfolding disorders like Alzheimer’s disease. Solving the folding problem will ultimately require a combination of theory and experiment, with theoretical models providing a comprehensive view of folding and experiments grounding these models …