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The serine/threonine protein phosphatase 1 (PP1) dephosphorylates hundreds of key biological targets by associating with nearly 200 regulatory proteins to form highly specific holoenzymes. However, how these proteins direct PP1 specificity and the ability to predict how these PP1 interacting proteins bind PP1 from sequence alone is still missing. PP1 nuclear targeting subunit (PNUTS) is a PP1 targeting protein that, with PP1, plays a central role in the nucleus, where it regulates chromatin decondensation, RNA processing, and the phosphorylation state of fundamental cell cycle proteins, including the retinoblastoma protein (Rb), p53, and MDM2. The molecular function of PNUTS in these processes is completely unknown. Here, we show that PNUTS, which is intrinsically disordered in its free form, interacts strongly with PP1 in a highly extended manner. Unexpectedly, PNUTS blocks one of PP1's substrate binding grooves while leaving the active site accessible. This interaction site, which we have named the arginine site, allowed us to define unique PP1 binding motifs, which advances our ability to predict how more than a quarter of the known PP1 regulators bind PP1. Additionally, the structure shows how PNUTS inhibits the PP1-mediated dephosphorylation of critical substrates, especially Rb, by blocking their binding sites on PP1, insights that are providing strategies for selectively enhancing Rb activity.

While the COVID-19 pandemic continues to impact public health worldwide significantly, the use of antiviral drugs and therapies has dramatically reduced the instances of severe disease and death. More broadly, the unprecedented use of antivirals also provides hope for preventing and mitigating similar viral outbreaks in the future. Here we ask: What are the comparative impact of antiviral therapeutics targeting different stages of the viral lifecycle? How do antiviral therapeutics impact the viral population in the bloodstream, or in other words, the viral load in high and low-immunity individuals? To address these questions, we use a model of viral quasispecies dynamics to examine the efficacy of antiviral strategies targeting three critical aspects of the viral life cycle, fecundity, reproduction rate, or infection rate. We find a linear relationship of the viral load with the change in fecundity and a power law with the change in the reproduction rate of the virus, with the viral load decreasing as the fecundity and the reproduction rates are decreased. Interestingly, however, for antivirals that target the infection rate, the viral load changes non-monotonically with the change in infection rate; the viral population initially increases and then decreases as the infection rate is decreased. The initial increase is especially pronounced for individuals with low immunity. By examining the viral population inside cells for such cases, we found that the therapeutics are only effective in such individuals if they stop the infection process entirely. Otherwise, the viral population inside cells does not go extinct. Our results predict the effectiveness of different antiviral strategies for COVID-19 and similar viral diseases and provide insights into the susceptibility of individuals with low immunity to effects like long covid. Competing Interest Statement The authors have declared no competing interest. Footnotes * Fixed an error in the author names listed online. The pdf of the manuscript did not have this error. Added acknowledgment to the funding agency that partially supported the work.

We use computational modeling to study within-host viral infection and evolution. In our model, viruses exhibit variable binding to cells, with better infection and replication countered by a stronger immune response and a high rate of mutation. By varying host conditions (permissivity to viral entry T and immune clearance intensity A) for large numbers of cells and viruses, we study the dynamics of how viral populations evolve from initial infection to steady state and obtain a phase diagram of the range of cell and viral responses. We find three distinct replicative strategies corresponding to three physiological classes of viral infections: acute, chronic, and opportunistic. We show similarities between our findings and the behavior of real viral infections such as common flu, hepatitis, and SARS-CoV-2019. The phases associated with the three strategies are separated by a phase transition of primarily first order, in addition to a crossover region. Our simulations also reveal a wide range of physical phenomena, including metastable states, periodicity, and glassy dynamics. Lastly, our results suggest that the resolution of acute viral disease in patients whose immunity cannot be boosted can only be achieved by significant inhibition of viral infection and replication. Competing Interest Statement The authors have declared no competing interest.

Mitochondria often form branching membrane networks distributed throughout the cell interior. In many, though not all, cell types, these networks are observed to consist of one large connected component together with many smaller fragments. Why does this pattern arise? Does it reflect a specific biological function, an external biophysical constraint, or something simpler? Using results from extremal graph theory, we prove a new theorem which suggests that, under a sufficiently broad sampling of the space of mitochondria-like graphs, the predominance of three-way junctions makes the appearance of a large component likely. This suggests that, in some settings, a large component may serve as a useful null model for mitochondrial network structure rather than requiring a dedicated explanation. More broadly, our result points towards testable predictions, since systematic deviations from this baseline may help reveal additional constraints or mechanisms shaping mitochondrial morphology.

This paper addresses the increasing need for comprehensive mathematical descriptions of cell organization by examining the algebraic structure of mitochondrial network dynamics. Mitochondria are cellular structures involved in metabolism that take the form of a network of membrane-based tubes that undergo continuous re-arrangement by a set of morphological processes, including fission and fusion, carried out by protein-based machinery. Because of their network structure, mitochondria can be represented as graphs, and the morphological operations that take place in the cell, referred to as mitochondrial dynamics, can be represented by changes to the graphs. Prior studies have classified mitochondrial graphs based on graph-theoretic features, but an alternative approach is to focus not on the graphs themselves but on the set of morphological operations inducing mitochondrial dynamics, since this may provide a simpler representation. Moreover, the operations are what determine the graphs that will be generated in a biological system. Here we show that mitochondrial dynamics on a single connected mitochondrion constitute a groupoid that includes the automorphism group of each mitochondria graph. For multi-component mitochondria we define a graph structure that encapsulates the structure of mitochondrial dynamics. Using these formalisms we define a distance metric for similarity between mitochondrial structures based on an edit distance. In the course of defining these structures we provide a mathematical motivation for new experimental questions regarding mitochondrial fusion and the impacts of cell division on mitochondrial morphology. This work points to a general strategy for formulating a cell structure state-space, based not on the shapes of cellular structures, but on relations between the dynamic operations that produce them.

Although the primary protein sequence of ubiquitin (Ub) is extremely stable over evolutionary time, it is highly tolerant to mutation during selection experiments performed in the laboratory. We have proposed that this discrepancy results from the difference between fitness under laboratory culture conditions and the selective pressures in changing environments over evolutionary time scales. Building on our previous work (Mavor et al. 2016), we used deep mutational scanning to determine how twelve new chemicals reveal novel mutational sensitivities of ubiquitin residues. We found sensitization of Lys63 in eight new conditions. In total, our experiments have uncovered a highly sensitizing condition for every position in Ub except Ser57 and Gln62. By determining the Ubiquitin fitness landscape under different chemical constraints, our work helps to resolve the inconsistencies between deep mutational scanning experiments and sequence conservation over evolutionary timescales.

Although the primary protein sequence of ubiquitin (Ub) is extremely stable over evolutionary time, it is highly tolerant to mutation during selection experiments performed in the laboratory. We have proposed that this discrepancy results from the difference between fitness under laboratory culture conditions and the selective pressures in changing environments over evolutionary time scales. Building on our previous work (Mavor et al 2016), we used deep mutational scanning to determine how twelve new chemicals (3-Amino-1,2,4-triazole, 5-fluorocytosine, Amphotericin B, CaCl2, Cerulenin, Cobalt Acetate, Menadione, Nickel Chloride, p-fluorophenylalanine, Rapamycin, Tamoxifen, and Tunicamycin) reveal novel mutational sensitivities of ubiquitin residues. We found sensitization of Lys63 in eight new conditions. In total, our experiments have uncovered a sensitizing condition for every position in Ub except Ser57 and Gln62. By determining the Ubiquitin fitness landscape under different chemical constraints, our work helps to resolve the inconsistencies between deep mutational scanning experiments and sequence conservation over evolutionary timescales. Mavor D, Barlow KA, Thompson S, Barad BA, Bonny AR, Cario CL, Gaskins G, Liu Z, Deming L, Axen SD, Caceres E, Chen W, Cuesta A, Gate R, Green EM, Hulce KR, Ji W, Kenner LR, Mensa B, Morinishi LS, Moss SM, Mravic M, Muir RK, Niekamp S, Nnadi CI, Palovcak E, Poss EM, Ross TD, Salcedo E, See S, Subramaniam M, Wong AW, Li J, Thorn KS, Conchúir SÓ, Roscoe BP, Chow ED, DeRisi JL, Kortemme T, Bolon DN, Fraser JS. Determination of Ubiquitin Fitness Landscapes Under Different Chemical Stresses in a Classroom Setting. eLife. 2016. We organized a project-based course that used deep mutational scanning in multiple chemical conditions to resolve the inconsistencies between tolerance to mutations in laboratory conditions and sequence conservation over evolutionary timescales.