Paul Robustelli

Performing all-atom molecular dynamics simulations of intrinsically disordered proteins with replica exchange solute tempering All-atom molecular dynamics (MD) computer simulations are a valuable tool for characterizing the conformational ensembles of intrinsically disordered proteins (IDPs). IDP conformational ensembles are ...

Brought to you by post-doctoral scholars Korey Reid and Jaya Krishna Koneru.

Paper: arxiv.org/abs/2505.01860

Tutorial + Code: github.com/paulrobustel...

We hope you find it helpful!

Performing all-atom molecular dynamics simulations of intrinsically disordered proteins with replica exchange solute tempering All-atom molecular dynamics (MD) computer simulations are a valuable tool for characterizing the conformational ensembles of intrinsically disordered proteins (IDPs). IDP conformational ensembles are ...

Want to run and analyze MD simulations of a disordered protein?

Check out our step-by-step guide (+ tutorial with code) for preparing, running and analyzing replica exchange solute tempering (REST2) simulations of IDPs with @gromacs.bsky.social and @plumed.org on arxiv!

arxiv.org/abs/2505.01860

Thanks Grant!

Characterizing structural and kinetic ensembles of intrinsically disordered proteins using writhe The biological functions of intrinsically disordered proteins (IDPs) are governed by the conformational states they adopt in solution and the kinetics of transitions between these states. We apply wri...

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

Paper: www.biorxiv.org/content/10.1...

Code:
github.com/paulrobustel...

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

...generative models you can switch from D- to L-amino acids. 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.

...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).

Why do this? A DDPM trained with an E(3)-equivariant model can invert the chirality of generated structures. In all-atom...

..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.bsky.social on this. To construct message passing NN layers between atoms, Tommy derived a writhe-graph Laplacian..

...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). He thought it would be cool to show you could leverage this symmetry to train an SE(3)-equivariant NN...

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. Tommy saw that if you take a mirror reflection of a protein conformation the...

GitHub - paulrobustelli/Sisk_IDP_Writhe_2025: Code Accompanying "Characterizing structural and kinetic ensembles of of intrinsically disordered proteins using writhe" Code Accompanying "Characterizing structural and kinetic ensembles of of intrinsically disordered proteins using writhe" - paulrobustelli/Sisk_IDP_Writhe_2025

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:

github.com/paulrobustel...

Now we can take this MSM workflow and build a very nice 5-macrostate MSM from 315us of Abeta42 MD simulations from @tlhr.bsky.social and Vendruscolo lab coworkers (www.nature.com/articles/s43...), without using any of the elegant ML tricks of their original paper.

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.

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

Now let's look at how many discrete conformational 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.

BLAMMO. Writhe captures more kinetic variance, meaning it describes slower dynamics, better than distances at almost all length scales. Even better, if you use writhe computed at multiple length scales you capture even more kinetic variance. We call these combos "multiscale writhe descriptors"

..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) of the slowest modes at different lag times and compare to interresidue distances

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.

Now we're going to use tCCA to asses how well writhe describes..

Polymers (and IDPs) have different timescale fluctuations at different length scales. We compare writhe matrices computed with different segment lengths for a folded conformation of HP35, and show that they are sensitive to different structural features. We analyze a folding trajectory of HP35...

Here is an illustration of how to compute writhe in a geometric fashion. You can project the apparent crossings of two segments to define a spherical quadrangle, and use this the accurately calculate writhe. Tommy wrote a python package to do this real fast

github.com/paulrobustel...

You can think of a writhe matrix as having a radial component that describes the distance between segments, with an additional angular component, that describes the relative orientations of each segment. It has the distance information of a contact map, with additional info on segment orientations

We set out to see if we can understand IDP ensembles and dynamics using writhe. Instead of using inter-residue distances (or contact maps), we're going to describe IDP conformations using "writhe matrices", that describe the crossings of all segments of a protein at a desired segment length

We're inspired by work in the late 70s by Harold Scheraga using differential geometry to describe polymer conformations (pubs.acs.org/doi/epdf/10....) and a Michael Levit 1983 JMB classic (www.sciencedirect.com/science/arti...) calculating writhe of protein conformations using discrete segments.

If want to use topology, geometry and Markov state models to describe the conformational ensembles and dynamics of IDPs (and who doesn't?) with a little deep learning spice, this one is for you.

So what is this writhe business? Writhe describes the orientations of curves in 3D space.

Presenting one of my favorite manuscripts I've ever worked on:

"Characterizing structural and kinetic ensembles of intrinsically disordered proteins using writhe"

www.biorxiv.org/content/10.1...

by Tommy Sisk, with a generative modeling component done in collaboration with @smnlssn.bsky.social

…of all our labs, and to plan our next steps with the exciting new IDP drug biotechs Nuage Therapeutics and @bindresearch.org to translate our research to help discover new medicines that target IDPs.

Watch this space, the next 5 years will be even more exciting!

I came to UCL, the Pasteur Institute, and IRB Barcelona in December 2019 and presented my research vision for my lab @dartmouthartsci.bsky.social.

Those days, proposing to discover IDP drugs was seen as “controversial” (at best) and its an absolute joy to share and discuss the collective progress…

Thanks to my hosts @bonomimax.bsky.social, @xsalvatella1.bsky.social, @fabferrage.bsky.social, @rcrehuet.bsky.social & Gabi Heller for a wonderful sabbatical science tour of Barcelona, Paris and London! Until next time!

As an American who’s immigrant grandfather grew up in a New Jersey home with a dirt floor, I can’t quite explain the feeling I have when I walk past the pantheon to spend the afternoon discussing magnetic resonance with Parisian intellectuals.

Thanks @fabferrage.bsky.social for a great visit!

Thats awesome, but we really think of this as more of a do-si-dos preprint.