SUMMARY: Here we present EpiGraph, an image analysis tool that quantifies epithelial organization. Our method combines computational geometry and graph theory to measure the degree of order of any packed tissue. EpiGraph goes beyond the traditional polygon distribution analysis, capturing other organizational traits that improve the characterization of epithelia. EpiGraph can objectively compare the rearrangements of epithelial cells during development and homeostasis to quantify how the global ensemble is affected. Importantly, it has been implemented in the open-access platform Fiji. This makes EpiGraph very user friendly, with no programming skills required. AVAILABILITY AND IMPLEMENTATION: EpiGraph is available at https://imagej.net/EpiGraph and the code is accessible (https://github.com/ComplexOrganizationOfLivingMatter/Epigraph) under GPLv3 license. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Sumoylation, the covalent attachment of SUMO (Small Ubiquitin-Like Modifier) to proteins, differs from other Ubl (Ubiquitin-like) pathways. In sumoylation, E2 ligase Ubc9 can function without E3 enzymes, albeit with lower reaction efficiency. Here, we study the mechanism through which E3 ligase RanBP2 triggers target recognition and catalysis by E2 Ubc9. Two mechanisms were proposed for sumoylation. While in both the first step involves Ubc9 conjugation to SUMO, the subsequent sequence of events differs: in the first E2-SUMO forms a complex with the target and E3, followed by SUMO transfer to the target. In the second, Ubc9-SUMO binds to the target and facilitates SUMO transfer without E3. Using dynamic correlations obtained from explicit solvent molecular dynamic simulations we illustrate the key roles played by allostery in both mechanisms. Pre-existence of conformational states explains the experimental observations that sumoylation can occur without E3, even though at a reduced rate. Furthermore, we propose a mechanism for enhancement of sumoylation by E3. Analysis of the conformational ensembles of the complex of E2 conjugated to SUMO illustrates that the E2 enzyme is already largely pre-organized for target binding and catalysis; E3 binding shifts the equilibrium and enhances these pre-existing populations. We further observe that E3 binding regulates allosterically the key residues in E2, Ubc9 Asp100/Lys101 E2, for the target recognition.