Menger_Curvature : a MDAKit implementation to decipher the dynamics, curvatures and flexibilities of polymeric backbones at the residue level

Characterizing the dynamics of the backbone of flexible polymers such as Intrinsically Disordered Regions and Proteins (IDRs and IDPs) has proven to be a significant challenge in molecular dynamics (MD) simulations due to the high conformational variability. The widely-used mobility metric Root-Mean-Squared Fluctuations (RMSF) is powerless to provide information as defining a relevant reference structure is often not possible. We previously introduced a new flexibility metric to remedy this gap : the Local Flexibilities (LFs), derived -alongside the Local Curvatures (LCs)- from the Proteic Menger Curvatures (PMCs). Here we present a numba accelerated implementation for any polymer of the calculation of Menger curvatures as a MDAKit from the widely-used MDAnalysis package. We perform a benchmark with the RMSF and another flexibility metric derived from Proteic Blocks (PBs), the Equivalent Number of PBs (Neq), and show that the PMCs are an order of magnitude faster to compute on a modern CPU chip. We applied all 3 flexibility metrics to a β III-tubulin monomer as an example, as tubulins are known to possess the entire range of proteic elements, from α -helix and β -sheets to a flexible loop and a disordered C-terminal tail (CTT). RMSF, LFs and Neq all succeed in identifying the flexible loops and the CTT, although the RMSF requires a system-specific alignment to do so. We believe that Menger curvatures will prove to be a valuable metric to study protein dynamics and polymers in general. The MDAKit package Menger_Curvature is readily available at https://github.com/EtienneReboul/menger_curvature