We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

Actin filament assembly by the actin-related protein (Arp) 2/3 complex is necessary to build many cellular structures, including lamellipodia at the leading edge of motile cells and phagocytic cups, and to move endosomes and intracellular pathogens. The crucial role of the Arp2/3 complex in cellular processes requires precise spatiotemporal regulation of its activity. While binding of nucleation-promoting factors (NPFs) has long been considered essential to Arp2/3 complex activity, we recently showed that phosphorylation of the Arp2 subunit is also necessary for Arp2/3 complex activation. Using molecular dynamics simulations and biochemical assays with recombinant Arp2/3 complex, we now show how phosphorylation of Arp2 induces conformational changes permitting activation. The simulations suggest that phosphorylation causes reorientation of Arp2 relative to Arp3 by destabilizing a network of salt-bridge interactions at the interface of the Arp2, Arp3, and ARPC4 subunits. Simulations also suggest a gain-of-function ARPC4 mutant that we show experimentally to have substantial activity in the absence of NPFs. We propose a model in which a network of auto-inhibitory salt-bridge interactions holds the Arp2 subunit in an inactive orientation. These auto-inhibitory interactions are destabilized upon phosphorylation of Arp2, allowing Arp2 to reorient to an activation-competent state.

Post-translational phosphorylation is a ubiquitous mechanism for modulating protein activity and protein-protein interactions. In this work, we examine how phosphorylation can modulate the conformation of a protein by changing the energy landscape. We present a molecular mechanics method in which we phosphorylate proteins in silico and then predict how the conformation of the protein will change in response to phosphorylation. We apply this method to a test set comprised of proteins with both phosphorylated and non-phosphorylated crystal structures, and demonstrate that it is possible to predict localized phosphorylation-induced conformational changes, or the absence of conformational changes, with near-atomic accuracy in most cases. Examples of proteins used for testing our methods include kinases and prokaryotic response regulators. Through a detailed case study of cyclin-dependent kinase 2, we also illustrate how the computational methods can be used to provide new understanding of how phosphorylation drives conformational change, why substituting Glu or Asp for a phosphorylated amino acid does not always mimic the effects of phosphorylation, and how a phosphatase can "capture" a phosphorylated amino acid. This work illustrates how computational methods can be used to elucidate principles and mechanisms of post-translational phosphorylation, which can ultimately help to bridge the gap between the number of known sites of phosphorylation and the number of structures of phosphorylated proteins.