Presenting one of my favorite manuscripts I've ever worked on:. "Characterizing structural and kinetic ensembles of intrinsically disordered proteins using writhe" . by @DartmouthChem student Tommy Sisk, with a generative modeling component done in collaboration with @smnlssn

The @ml4ngp meeting in Vilnius has been fantastic!.

Brought to you by post-doctoral scholars Korey Reid and Jaya Krishna Koneru. Paper: Tutorial + Code:

Want to run and analyze MD simulations of a disordered protein?. Check out our step-by-step practical guide (+ tutorial with code) for preparing, running and analyzing replica exchange solute tempering (REST2) simulations of IDPs with @GMX_TWEET and @plumed_org on arxiv!

Thanks for coming on this writhe journey and congrats to Tommy on this beautiful work! Links again:. Paper: Code:.

We think this means that Writhe could be a useful feature for training generative models of IDP conformations and assessing their topological complexity, to ultimately produce models that are in closer agreement with all-atom MD.

As proof-of-principle, we show that if you train DDPMs with Writhe-PaiNN on a single long timescale MD trajectory, you can accurately describe the populations of chiral chain crossings seen in that simulations, whereas a DDPM trained with PaiNN can't distinguish their populations

It also means that if you model IDPs with chiral chain crossings in popular 1-bead per residue coarse grain (CG) models, you won't capture differences in populations of chain crossings with different writhe.

Why do this? A DDPM trained with an E(3)-equivariant model can invert the chirality of generated structures. In all-atom generative models you can switch from D- to L-amino acids.

To construct message passing NN layers between atoms, Tommy derived a writhe-graph Laplacian and incorporated this into the E(3)-equivariant, polarizable atom interaction network (PaiNN), to develop Writhe-PaiNN, augmenting its symmetry from E(3) to SE(3).

He thought it would be cool to show you could leverage this symmetry to train an SE(3)-equivariant NN that could be used to sample IDP conformations in a score-based denoising diffusion probabilistic model (DDPM). He packed his bags and headed off to Sweden to work with @smnlssn.

Tommy saw that if you take a mirror reflection of a protein conformation the inter-residue distances of reflected conformation are the same (invariant to parity) while the writhe of the mirror image is distinguished exactly by a change in sign (odd parity).

But there's more. Tommy loves neural networks (NNs) and generative models, which need to be trained using NN architectures that conserve or exclude certain geometric and symmetry properties of coordinate data.

We think that this means writhe could be a general and robust tool to describe IDP conformational ensembles and build MSMs of IDPs! . All the code you need to try this out on your system is here:.

Lucky break? Nope! We see this for all our IDP simulations scanning many sets of MSM hyper-parameters.

If we build an MSM from these projections, we see that the largest implied time scale (ITS) of the writhe MSM converges to a substantially larger value than the largest ITS of the inter-residue distance MSM.

Let's look at how many discrete states we identify from writhe tCCA projections (or reaction coordinates) and distance tCCA projections for a 30us IDP simulation. Here, we see that writhe computed at single segment length (no cheating) identifies more states than distances.

Even better, if you use writhe computed at multiple length scales you capture even more kinetic variance. We call these combos "multiscale writhe descriptors".

of the slowest modes at different lag times and compare to inter-residue distances. BLAMMO. Writhe captures more kinetic variance, meaning it describes slower dynamics, better than distances at almost all length scales.

Now we're going to use tCCA to asses how well writhe describes the slowest motions in equilibrium MD simulations of 5 IDPs and a fast folding protein. We're going to perform tCCA using writhe from different segment lengths, and compute the kinetic variance (aka VAMP-2 score). .

We analyze a folding trajectory of HP35 by performing time-lagged canonical correlation analysis (tCCA) using writhe values computed at different segment lengths as inputs. We look at projections on the slowest mode and see that the resolve different processes. Neat-O.