I'm thrilled to share our group's first foray into deep learning and Markov state models: "Folding-upon-binding pathways of an intrinsically disordered protein from a deep Markov state model" from intrepid graduate student Tommy Sisk!

We set out to see if MSMs could provide new insights into the folding-upon-binding pathways of a partially helical fragment of the measles virus nucleoprotein NTAIL binding the X domain (XD) of the measles phosphoprotein observed in a previous MD study

In the previous study, we utilized a 1D reaction coordinate approach to characterize the 36 binding and 36 unbinding events observed in a 200us unbiased MD simulation of NTAIL and XD with the a99BS-disp force field.

Starting with a reaction coordinate defined by the fraction of native intermolecular contacts (Q), we optimized a new reaction coordinate (R) to calculate a transition state ensemble which was heterogenous and defined by a few key contacts

Tommy got started by building a conventional MSM using tICA, but this time considering all intermolecular contacts, to capture the role of non-native intermolecular contacts, together with helical order parameters (Sa) that describes the helical character of 7-residue fragments

Unsatisfied with a well validated 7-state hidden MSM (HMSM), Tommy was eager to start exploring the latest methods for deep-learning MSMs - Deep reversible VAMPnets (developed by @andreasmardt and @FrankNoeBerlin) to see if we could obtain a higher resolution mechanistic model.

Tommy had an idea to use a multi-input neural net architecture to merge molecular features with different dimensionalities. He used convolutional layers to transform intermolecular distance matrices, and dense layers to transform helical order parameters before aggregating

Using this approach, we obtained a kinetically meaningful latest space (which we think looks like a hammerhead shark). Repeatedly training an unconstrained VAMPnet we consistently arrived at the same 12 states.

Next we applied physical constraints to learn a 12-state deep MSM that validates well. This higher resolution MSMs differentiates additional states and provides several insights that our conventional HMSM from tICA did not resolve.

Notably, we resolve 2 distinct encounter complexes (ECs) and an off-pathway kinetic trap where the tICA HMSM (and the JACS reaction coordinate study) identified a single heterogenous EC. In one EC, NTAIL is highly helical and binds "upside-down" while the other has little ...

...helical content and samples all rotational orientations. We wondered if the more helical EC might proceed to the native state through a conformational selection pathway, while the less helical EC proceeds through an induced-fit pathway, but the MSM shows this is not the case.

Lastly, we dissected the nature of the kinetic barriers between native-like bound states. These states share a core of native contacts and stable NTAIL helices, and are differentiated by the subsequent formation and breakage of non-native contacts that facilitate the formation..

...of additional helical turns and native contacts. Our deep MSM provides an atomically detailed description of the conformational states of a dynamic and heterogenous, or “fuzzy”, protein complex, and identifies the interactions that produce conformational frustration.

We think that using convolutional neural network layers to describe distance matrices may be a generally powerful technique for building MSMs of IDPs, based on the fuzziness of their intra-and-intermolecular interactions, and are exploring this approach in other systems.

I want to note that Tommy arrived in the group 2-years ago with no experience with IDPs, MSMs, deep learning or python, and initiated and executed this entire project on his own, teaching himself everything as he went along. All his code is here: