A deep autoencoder framework for discovery of metastable ensembles in biomacromolecules

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.

Machine Learning Subtle Conformational Change due to Phosphorylation in Intrinsically Disordered Proteins

Phosphorylation of intrinsically disordered proteins/regions (IDPs/IDRs) has a profound effect in biological functions such as cell signaling, protein folding or unfolding, and long-range allosteric effects. However, here we focus on two IDPs, namely 83-residue IDR transcription factor Ash1 and 92-residue long N-terminal region of CDK inhibitor Sic1 protein, found in Saccharomyces cerevisiae, for which experimental measurements of average conformational properties, namely, radius of gyration and structure factor, indicate negligible changes upon phosphorylation. Here, we show that a judicious dissection of conformational ensemble via combination of unsupervised machine learning and extensive molecular dynamics (MD) trajectories can highlight key differences and similarities among the phosphorylated and wild-type IDP. In particular, we develop Markov state model (MSM) using the latent-space dimensions of an autoencoder, trained using multi-microsecond long MD simulation trajectories. Examination of structural changes among the states, prior to and upon phosphorylation, captured several similarities and differences in their backbone contact maps, secondary structure, and torsion angles. Hydrogen bonding analysis revealed that phosphorylation not only increases the number of hydrogen bonds but also switches the pattern of hydrogen bonding between the backbone and side chain atoms with the phosphorylated residues. We also observe that although phosphorylation introduces salt bridges, there is a loss of the cation-π interaction. Phosphorylation also improved the probability for long-range hydrophobic contacts and also enhanced interaction with water molecules and improved the local structure of water as evident from the geometric order parameters. The observations on these machine-learnt states gave important insights, as it would otherwise be difficult to determine experimentally which is important, if we were to understand the role of phosphorylation of IDPs in their biological functions.

Toward a structural identification of metastable molecular conformations

Interpreting high-dimensional data from molecular dynamics simulations is a persistent challenge. In this paper, we show that for a small peptide, deca-alanine, metastable states can be identified through a neural net based on structural information alone. While processing molecular dynamics data, dimensionality reduction is a necessary step that projects high-dimensional data onto a low-dimensional representation that, ideally, captures the conformational changes in the underlying data. Conventional methods make use of the temporal information contained in trajectories generated through integrating the equations of motion, which forgoes more efficient sampling schemes. We demonstrate that EncoderMap, an autoencoder architecture with an additional distance metric, can find a suitable low-dimensional representation to identify long-lived molecular conformations using exclusively structural information. For deca-alanine, which exhibits several helix-forming pathways, we show that this approach allows us to combine simulations with different biasing forces and yields representations comparable in quality to other established methods. Our results contribute to computational strategies for the rapid automatic exploration of the configuration space of peptides and proteins.

A deep encoder-decoder framework for identifying distinct ligand binding pathways

The pathway(s) that a ligand would adopt en route to its trajectory to the native pocket of the receptor protein act as a key determinant of its biological activity. While Molecular Dynamics (MD) simulations have emerged as the method of choice for modeling protein-ligand binding events, the high dimensional nature of the MD-derived trajectories often remains a barrier in the statistical elucidation of distinct ligand binding pathways due to the stochasticity inherent in the ligand's fluctuation in the solution and around the receptor. Here, we demonstrate that an autoencoder based deep neural network, trained using an objective input feature of a large matrix of residue-ligand distances, can efficiently produce an optimal low-dimensional latent space that stores necessary information on the ligand-binding event. In particular, for a system of L99A mutant of T4 lysozyme interacting with its native ligand, benzene, this deep encoder-decoder framework automatically identifies multiple distinct recognition pathways, without requiring user intervention. The intermediates involve the spatially discrete location of the ligand in different helices of the protein before its eventual recognition of native pose. The compressed subspace derived from the autoencoder provides a quantitatively accurate measure of the free energy and kinetics of ligand binding to the native pocket. The investigation also recommends that while a linear dimensional reduction technique, such as time-structured independent component analysis, can do a decent job of state-space decomposition in cases where the intermediates are long-lived, autoencoder is the method of choice in systems where transient, low-populated intermediates can lead to multiple ligand-binding pathways.

Resolving Protein Conformational Plasticity and Substrate Binding via Machine Learning

A long-standing target in elucidating the biomolecular recognition process is the identification of binding-competent conformations of the receptor protein. However, protein conformational plasticity and the stochastic nature of the recognition processes often preclude the assignment of a specific protein conformation to an individual ligand-bound pose. Here, we demonstrate that a computational framework coined as RF-TICA-MD, which integrates an ensemble decision-tree-based Random Forest (RF) machine learning (ML) technique with an unsupervised dimension reduction approach time-structured independent component analysis (TICA), provides an efficient and unambiguous solution toward resolving protein conformational plasticity and the substrate binding process. In particular, we consider multimicrosecond-long molecular dynamics (MD) simulation trajectories of a ligand recognition process in solvent-inaccessible cavities of archetypal proteins T4 lysozyme and cytochrome P450cam. We show that in a scenario in which clear correspondence between protein conformation and binding-competent macrostates could not be obtained via an unsupervised dimension reduction approach, an a priori decision-tree-based supervised classification of the simulated recognition trajectories via RF would help characterize key amino acid residue pairs of the protein that are deemed sensitive for ligand binding. A subsequent unsupervised dimensional reduction of the selected residue pairs via TICA would then delineate a conformational landscape of protein which is able to demarcate ligand-bound poses from unbound ones. The proposed RF-TICA-MD approach is shown to be data agnostic and found to be robust when using other ML-based classification methods such as XGBoost. As a promising spinoff of the protocol, the framework is found to be capable of identifying distal protein locations which would be allosterically important for ligand binding and would characterize their roles in recognition pathways. A Python implementation of a proposed ML workflow is available in GitHub https://github.com/navjeet0211/rf-tica-md.

Efficient Interrogation of the Kinetic Barriers Demarcating Catalytic States of a Tyrosine Kinase with Optimal Physical Descriptors and Mixture Models

Computer simulations are increasingly used to access thermo-kinetic information underlying structural transformation of protein kinases. Such information are necessary to probe their roles in disease progression and interactions with drug targets. However, the investigations are frequently challenged by forbiddingly high computational expense, and by the lack of standard protocols for the design of low dimensional physical descriptors that encode system features important for transitions. Here, we consider the demarcating characteristics of the different states of Abelson tyrosine kinase associated with distinct catalytic activity to construct a set of physically meaningful, orthogonal collective variables that preserve the slow modes of the system. Independent sampling of each metastable state is followed by the estimation of global partition function along the appropriate physical descriptors using the modified Expectation Maximized Molecular Dynamics method. The resultant free energy barriers are in excellent agreement with experimentally known rate-limiting dynamics and activation energy computed with conventional enhanced sampling methods. We discuss possible directions for further development and applications.

Long-time-step molecular dynamics can retard simulation of protein-ligand recognition process

Molecular dynamics (MD) simulation of biologically relevant processes at realistic time scale and atomistic precision is generally limited by prohibitively large computational cost, due to its restriction of using an ultrashort integration time step (1-2 fs). A popular numerical recipe to reduce the associated computational burden is adopting schemes that would allow relatively longer-time-step for MD propagation. Here, we explore the perceived potential of one of the most frequently used long-time-step protocols, namely the hydrogen mass repartitioning (HMR) approach, in alleviating the computational overhead associated with simulation of the kinetic process of protein-ligand recognition events. By repartitioning the mass of heavier atoms to their linked hydrogen atoms, HMR leverages around twofold longer time step than regular simulation, holding promise of significant performance boost. However, our probe into direct simulation of the protein-ligand recognition event, one of the computationally most challenging processes, shows that long-time-step HMR MD simulations do not necessarily translate to a computationally affordable solution. Our investigations spanning cumulative 176 μs in three independent proteins (T4 lysozyme, sensor domain of MopR, and galectin-3) show that long-time-step HMR-based MD simulations can catch the ligand in its act of recognizing the native cavity. But, as a major caveat, the ligand is found to require significantly longer time to identify buried native protein cavity in an HMR MD simulation than regular simulation, thereby defeating the purpose of its usage for performance upgrade. A molecular analysis shows that the longer time required by a ligand to recognize the protein in HMR is rooted in faster diffusion of the ligand, which reduces the survival probability of decisive on-pathway metastable intermediates, thereby slowing down the eventual recognition process at the native cavity. Together, the investigation stresses careful assessment of pitfalls of long-time-step algorithms before attempting to utilize them for higher performance for biomolecular recognition simulations.

LAST: Latent Space-Assisted Adaptive Sampling for Protein Trajectories

Molecular dynamics (MD) simulation is widely used to study protein conformations and dynamics. However, conventional simulation suffers from being trapped in some local energy minima that are hard to escape. Thus, most of the computational time is spent sampling in the already visited regions. This leads to an inefficient sampling process and further hinders the exploration of protein movements in affordable simulation time. The advancement of deep learning provides new opportunities for protein sampling. Variational autoencoders are a class of deep learning models to learn a low-dimensional representation (referred to as the latent space) that can capture the key features of the input data. Based on this characteristic, we proposed a new adaptive sampling method, latent space-assisted adaptive sampling for protein trajectories (LAST), to accelerate the exploration of protein conformational space. This method comprises cycles of (i) variational autoencoder training, (ii) seed structure selection on the latent space, and (iii) conformational sampling through additional MD simulations. The proposed approach is validated through the sampling of four structures of two protein systems: two metastable states of Escherichia coli adenosine kinase (ADK) and two native states of Vivid (VVD). In all four conformations, seed structures were shown to lie on the boundary of conformation distributions. Moreover, large conformational changes were observed in a shorter simulation time when compared with structural dissimilarity sampling (SDS) and conventional MD (cMD) simulations in both systems. In metastable ADK simulations, LAST explored two transition paths toward two stable states, while SDS explored only one and cMD neither. In VVD light state simulations, LAST was three times faster than cMD simulation with a similar conformational space. Overall, LAST is comparable to SDS and is a promising tool in adaptive sampling. The LAST method is publicly available at https://github.com/smu-tao-group/LAST to facilitate related research.

Chasing collective variables using temporal data-driven strategies

The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N'-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.

Machine learning approaches for biomolecular, biophysical, and biomaterials research

A fluent conversation with a virtual assistant, person-tailored news feeds, and deep-fake images created within seconds-all those things that have been unthinkable for a long time are now a part of our everyday lives. What these examples have in common is that they are realized by different means of machine learning (ML), a technology that has fundamentally changed many aspects of the modern world. The possibility to process enormous amount of data in multi-hierarchical, digital constructs has paved the way not only for creating intelligent systems but also for obtaining surprising new insight into many scientific problems. However, in the different areas of biosciences, which typically rely heavily on the collection of time-consuming experimental data, applying ML methods is a bit more challenging: Here, difficulties can arise from small datasets and the inherent, broad variability, and complexity associated with studying biological objects and phenomena. In this Review, we give an overview of commonly used ML algorithms (which are often referred to as "machines") and learning strategies as well as their applications in different bio-disciplines such as molecular biology, drug development, biophysics, and biomaterials science. We highlight how selected research questions from those fields were successfully translated into machine readable formats, discuss typical problems that can arise in this context, and provide an overview of how to resolve those encountered difficulties.