Mitochondrial networks through the lens of mathematics.

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.

Extending chemical perturbations of the ubiquitin fitness landscape in a classroom setting reveals new constraints on sequence tolerance.

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 timescales. 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. Collectively, our experiments have identified eight new sensitizing conditions for Lys63 and 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.

Understanding the antagonism of retinoblastoma protein dephosphorylation by PNUTS provides insights into the PP1 regulatory code.

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.