Progress in deep Markov state modeling: Coarse graining and experimental data restraints

CoVAMPnet: Comparative Markov State Analysis for Studying Effects of Drug Candidates on Disordered Biomolecules

Computational study of the effect of drug candidates on intrinsically disordered biomolecules is challenging due to their vast and complex conformational space. Here, we developed a comparative Markov state analysis (CoVAMPnet) framework to quantify changes in the conformational distribution and dynamics of a disordered biomolecule in the presence and absence of small organic drug candidate molecules. First, molecular dynamics trajectories are generated using enhanced sampling, in the presence and absence of small molecule drug candidates, and ensembles of soft Markov state models (MSMs) are learned for each system using unsupervised machine learning. Second, these ensembles of learned MSMs are aligned across different systems based on a solution to an optimal transport problem. Third, the directional importance of inter-residue distances for the assignment to different conformational states is assessed by a discriminative analysis of aggregated neural network gradients. This final step provides interpretability and biophysical context to the learned MSMs. We applied this novel computational framework to assess the effects of ongoing phase 3 therapeutics tramiprosate (TMP) and its metabolite 3-sulfopropanoic acid (SPA) on the disordered Aβ42 peptide involved in Alzheimer's disease. Based on adaptive sampling molecular dynamics and CoVAMPnet analysis, we observed that both TMP and SPA preserved more structured conformations of Aβ42 by interacting nonspecifically with charged residues. SPA impacted Aβ42 more than TMP, protecting α-helices and suppressing the formation of aggregation-prone β-strands. Experimental biophysical analyses showed only mild effects of TMP/SPA on Aβ42 and activity enhancement by the endogenous metabolization of TMP into SPA. Our data suggest that TMP/SPA may also target biomolecules other than Aβ peptides. The CoVAMPnet method is broadly applicable to study the effects of drug candidates on the conformational behavior of intrinsically disordered biomolecules.

Representation of Protein Dynamics Disentangled by Time-Structure-Based Prior

Representation learning (RL) is a universal technique for deriving low-dimensional disentangled representations from high-dimensional observations, aiding in a multitude of downstream tasks. RL has been extensively applied to various data types, including images and natural language. Here, we analyze molecular dynamics (MD) simulation data of biomolecules in terms of RL. Currently, state-of-the-art RL techniques, mainly motivated by the variational principle, try to capture slow motions in the representation (latent) space. Here, we propose two methods based on an alternative perspective on the disentanglement in the latent space. By disentanglement, we here mean the separation of underlying factors in the simulation data, aiding in detecting physically important coordinates for conformational transitions. The proposed methods introduce a simple prior that imposes temporal constraints in the latent space, serving as a regularization term to facilitate the capture of disentangled representations of dynamics. Comparison with other methods via the analysis of MD simulation trajectories for alanine dipeptide and chignolin validates that the proposed methods construct Markov state models (MSMs) whose implied time scales are comparable to those of the state-of-the-art methods. Using a measure based on total variation, we quantitatively evaluated that the proposed methods successfully disentangle physically important coordinates, aiding the interpretation of folding/unfolding transitions of chignolin. Overall, our methods provide good representations of complex biomolecular dynamics for downstream tasks, allowing for better interpretations of the conformational transitions.

Deep learning to decompose macromolecules into independent Markovian domains

The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the molecular system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large molecular systems the number of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decomposition (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decomposition of the molecular system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decomposition into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large molecular complexes from simulation data.

A Small Molecule Stabilizes the Disordered Native State of the Alzheimer's Aβ Peptide

The stabilization of native states of proteins is a powerful drug discovery strategy. It is still unclear, however, whether this approach can be applied to intrinsically disordered proteins. Here, we report a small molecule that stabilizes the native state of the Aβ42 peptide, an intrinsically disordered protein fragment associated with Alzheimer's disease. We show that this stabilization takes place by a disordered binding mechanism, in which both the small molecule and the Aβ42 peptide remain disordered. This disordered binding mechanism involves enthalpically favorable local π-stacking interactions coupled with entropically advantageous global effects. These results indicate that small molecules can stabilize disordered proteins in their native states through transient non-specific interactions that provide enthalpic gain while simultaneously increasing the conformational entropy of the proteins.

GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules

Finding a low dimensional representation of data from long-timescale trajectories of biomolecular processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of molecular representation results in a higher resolution and a more interpretable Markov model than the standard VAMPNet, enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.

Deeptime: a Python library for machine learning dynamical models from time series data

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under https://deeptime-ml.github.io/.