State predictive information bottleneck

Calculating Protein-Ligand Residence Times through State Predictive Information Bottleneck Based Enhanced Sampling

Understanding drug residence times in target proteins is key to improving drug efficacy and understanding target recognition in biochemistry. While drug residence time is just as important as binding affinity, atomic-level understanding of drug residence times through molecular dynamics (MD) simulations has been difficult primarily due to the extremely long time scales. Recent advances in rare event sampling have allowed us to reach these time scales, yet predicting protein-ligand residence times remains a significant challenge. Here we present a semi-automated protocol to calculate the ligand residence times across 12 orders of magnitude of time scales. In our proposed framework, we integrate a deep learning-based method, the state predictive information bottleneck (SPIB), to learn an approximate reaction coordinate (RC) and use it to guide the enhanced sampling method metadynamics. We demonstrate the performance of our algorithm by applying it to six different protein-ligand complexes with available benchmark residence times, including the dissociation of the widely studied anticancer drug Imatinib (Gleevec) from both wild-type Abl kinase and drug-resistant mutants. We show how our protocol can recover quantitatively accurate residence times, potentially opening avenues for deeper insights into drug development possibilities and ligand recognition mechanisms.

Mechanism of phosphate release from actin filaments

After ATP-actin monomers assemble filaments, the ATP's [Formula: see text]-phosphate is hydrolyzedwithin seconds and dissociates over minutes. We used all-atom molecular dynamics simulations to sample the release of phosphate from filaments and study residues that gate release. Dissociation of phosphate from Mg2+ is rate limiting and associated with an energy barrier of 20 kcal/mol, consistent with experimental rates of phosphate release. Phosphate then diffuses within an internal cavity toward a gate formed by R177, as suggested in prior computational studies and cryo-EM structures. The gate is closed when R177 hydrogen bonds with N111 and is open when R177 forms a salt bridge with D179. Most of the time, interactions of R177 with other residues occlude the phosphate release pathway. Machine learning analysis reveals that the occluding interactions fluctuate rapidly, underscoring the secondary role of backdoor gate opening in Pi release, in contrast with the previous hypothesis that gate opening is the primary event.

Machine Learning Derived Collective Variables for the Study of Protein Homodimerization in Membrane

The accurate calculation of equilibrium constants for protein-protein association is of fundamental importance to quantitative biology and remains an outstanding challenge for computational biophysics. Traditionally, equilibrium constants have been computed from one-dimensional free energy surfaces derived from sampling along a single collective variable. Importantly, recent advances in enhanced sampling methodology have facilitated the characterization of multidimensional free energy landscapes, often exposing multiple thermodynamically important minima missed by more restrictive sampling methods. A key to the effectiveness of this multidimensional sampling approach is the identification of collective variables that effectively define the configurational space of dissociated and associated states. Here we present the application of two machine learning methods for the unbiased determination of collective variables for enhanced sampling and analysis of protein-protein association. Our results both validate prior work, based on intuition derived collective variables, and demonstrate the effectiveness of the machine learning methods for the identification of collective variables for association reactions in complex biomolecular systems.

Information Bottleneck Approach for Markov Model Construction

Markov state models (MSMs) have proven valuable in studying the dynamics of protein conformational changes via statistical analysis of molecular dynamics simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time necessitates defining states that circumvent significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process effectively coarse-grains time and space, integrating out rapid motions within metastable states. Thus, MSMs possess a multiresolution nature, where the granularity of states can be adjusted according to the time-resolution, offering flexibility in capturing system dynamics. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), a framework that unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of the VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multiresolution Markovian models. Through applications to well-validated mini-proteins, SPIB showcases unique advantages compared to competing methods. It autonomously and self-consistently adjusts the number of metastable states based on a specified minimal time resolution, eliminating the need for manual tuning. While maintaining efficacy in dynamical properties, SPIB excels in accurately distinguishing metastable states and capturing numerous well-populated macrostates. This contrasts with existing VAMP-based methods, which often emphasize slow dynamics at the expense of incorporating numerous sparsely populated states. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. With these benefits, we propose SPIB as an easy-to-implement methodology for end-to-end MSM construction.

From Latent Dynamics to Meaningful Representations

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned representation through prior probability distributions. However, such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted toward leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density─a prior driven by statistical mechanics. We show that this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie data set. We show that our algorithm can uniquely identify orthogonal, isometric, and meaningful latent representations.

Mechanism of Phosphate Release from Actin Filaments

After ATP-actin monomers assemble filaments, the ATP's γ-phosphate is hydrolyzed within seconds and dissociates over minutes. We used all-atom molecular dynamics simulations to sample the release of phosphate from filaments and study residues that gate release. Dissociation of phosphate from Mg2+ is rate limiting and associated with an energy barrier of 20 kcal/mol, consistent with experimental rates of phosphate release. Phosphate then diffuses in an internal cavity toward a gate formed by R177 suggested in prior computational studies and cryo-EM structures. The gate is closed when R177 hydrogen bonds with N111 and is open when R177 forms a salt bridge with D179. Most of the time interactions of R177 with other residues occludes the phosphate release pathway. Machine learning analysis reveals that the occluding interactions fluctuate rapidly, underscoring the secondary role of backdoor gate opening in Pi release, in contrast with the previous hypothesis that gate opening is the primary event.

One Descriptor to Fold Them All: Harnessing Intuition and Machine Learning to Identify Transferable Lasso Peptide Reaction Coordinates

Identifying optimal reaction coordinates for complex conformational changes and protein folding remains an outstanding challenge. This study combines collective variable (CV) discovery based on chemical intuition and machine learning with enhanced sampling to converge the folding free energy landscape of lasso peptides, a unique class of natural products with knot-like tertiary structures. This knotted scaffold imparts remarkable stability, making lasso peptides resistant to proteolytic degradation, thermal denaturation, and extreme pH conditions. Although their direct synthesis would enable therapeutic design, it has not yet been possible due to the improbable occurrence of spontaneous lasso folding. Thus, simulations characterizing the folding propensity are needed to identify strategies for increasing access to the lasso architecture by stabilizing the pre-lasso ensemble before isopeptide bond formation. Herein, harmonic linear discriminant analysis (HLDA) is combined with metadynamics-enhanced sampling to discover CVs capable of distinguishing the pre-lasso fold and converging the folding propensity. Intuitive CVs are compared to iterative rounds of HLDA to identify CVs that not only accomplish these goals for one lasso peptide but also seem to be transferable to others, establishing a protocol for the identification of folding reaction coordinates for lasso peptides.

Data-Driven Path Collective Variables

Identifying optimal collective variables to model transformations using atomic-scale simulations is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables that can be thought of as a data-driven generalization of the path collective variable concept. It consists of a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model and the association of Li+ and F- in water. For the former, we show that global descriptors such as the permutation invariant vector allow reaching an accuracy far from the one achieved via simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.

Calculating Protein-Ligand Residence Times Through State Predictive Information Bottleneck based Enhanced Sampling

Understanding drug residence times in target proteins is key to improving drug efficacy and understanding target recognition in biochemistry. While drug residence time is just as important as binding affinity, atomic-level understanding of drug residence times through molecular dynamics (MD) simulations has been difficult primarily due to the extremely long timescales. Recent advances in rare event sampling have allowed us to reach these timescales, yet predicting protein-ligand residence times remains a significant challenge. Here we present a semi-automated protocol to calculate the ligand residence times across 12 orders of magnitudes of timescales. In our proposed framework, we integrate a deep learning-based method, the state predictive information bottleneck (SPIB), to learn an approximate reaction coordinate (RC) and use it to guide the enhanced sampling method metadynamics. We demonstrate the performance of our algorithm by applying it to six different protein-ligand complexes with available benchmark residence times, including the dissociation of the widely studied anti-cancer drug Imatinib (Gleevec) from both wild-type Abl kinase and drug-resistant mutants. We show how our protocol can recover quantitatively accurate residence times, potentially opening avenues for deeper insights into drug development possibilities and ligand recognition mechanisms.

Kinetic Ensemble of Tau Protein through the Markov State Model and Deep Learning Analysis

The ordered assembly of Tau protein into filaments characterizes Alzheimer's and other neurodegenerative diseases, and thus, stabilization of Tau protein is a promising avenue for tauopathies therapy. To dissect the underlying aggregation mechanisms on Tau, we employ a set of molecular simulations and the Markov state model to determine the kinetics of ensemble of K18. K18 is the microtubule-binding domain of Tau protein and plays a vital role in the microtubule assembly, recycling processes, and amyloid fibril formation. Here, we efficiently explore the conformation of K18 with about 150 μs lifetimes in silico. Our results observe that all four repeat regions (R1-R4) are very dynamic, featuring frequent conformational conversion and lacking stable conformations, and the R2 region is more flexible than the R1, R3, and R4 regions. Additionally, it is worth noting that residues 300-310 in R2-R3 and residues 319-336 in R3 tend to form sheet structures, indicating that K18 has a broader functional role than individual repeat monomers. Finally, the simulations combined with Markov state models and deep learning reveal 5 key conformational states along the transition pathway and provide the information on the microsecond time scale interstate transition rates. Overall, this study offers significant insights into the molecular mechanism of Tau pathological aggregation and develops novel strategies for both securing tauopathies and advancing drug discovery.

Exploring Kinase Asp-Phe-Gly (DFG) Loop Conformational Stability with AlphaFold2-RAVE

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular, cancers. The ubiquitousness and structural similarities of kinases make specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved Asp-Phe-Gly (DFG) motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticeably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learned order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations (Meller, A.; Bhakat, S.; Solieva, S.; Bowman, G. R. Accelerating Cryptic Pocket Discovery Using AlphaFold. J. Chem. Theory Comput. 2023, 19, 4355-4363).

Tutorial on how to build non-Markovian dynamic models from molecular dynamics simulations for studying protein conformational changes

Protein conformational changes play crucial roles in their biological functions. In recent years, the Markov State Model (MSM) constructed from extensive Molecular Dynamics (MD) simulations has emerged as a powerful tool for modeling complex protein conformational changes. In MSMs, dynamics are modeled as a sequence of Markovian transitions among metastable conformational states at discrete time intervals (called lag time). A major challenge for MSMs is that the lag time must be long enough to allow transitions among states to become memoryless (or Markovian). However, this lag time is constrained by the length of individual MD simulations available to track these transitions. To address this challenge, we have recently developed Generalized Master Equation (GME)-based approaches, encoding non-Markovian dynamics using a time-dependent memory kernel. In this Tutorial, we introduce the theory behind two recently developed GME-based non-Markovian dynamic models: the quasi-Markov State Model (qMSM) and the Integrative Generalized Master Equation (IGME). We subsequently outline the procedures for constructing these models and provide a step-by-step tutorial on applying qMSM and IGME to study two peptide systems: alanine dipeptide and villin headpiece. This Tutorial is available at https://github.com/xuhuihuang/GME_tutorials. The protocols detailed in this Tutorial aim to be accessible for non-experts interested in studying the biomolecular dynamics using these non-Markovian dynamic models.

A slow feature analysis approach for the optimization of collective variables

Molecular dynamics simulations have become increasingly important in understanding the microscopic mechanisms of various molecular systems. However, the high energy barriers in complicated molecules often make it difficult to observe events of interest within a reasonable timescale. To address this issue, researchers have developed a variety of enhanced sampling methods to explore configuration space by adding bias potentials along the slowly changing collective variables (CVs). In this study, we have developed a new tool that combines slow feature analysis and biasing-enhanced sampling methods to identify effective CVs and enhance the sampling efficiency of configuration space. We have demonstrated the effectiveness of this tool through three general examples.

Is the Local Ion Density Sufficient to Drive NaCl Nucleation from the Melt and Aqueous Solution?

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling of all-atom molecular dynamics with deep-learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in an aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, although fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Our protocol proposed here enables robust nucleation analysis and phase sampling and could offer insights into nucleation mechanisms for generic small molecules in different environments.

Reaction coordinate flows for model reduction of molecular kinetics

In this work, we introduce a flow based machine learning approach called reaction coordinate (RC) flow for the discovery of low-dimensional kinetic models of molecular systems. The RC flow utilizes a normalizing flow to design the coordinate transformation and a Brownian dynamics model to approximate the kinetics of RC, where all model parameters can be estimated in a data-driven manner. In contrast to existing model reduction methods for molecular kinetics, RC flow offers a trainable and tractable model of reduced kinetics in continuous time and space due to the invertibility of the normalizing flow. Furthermore, the Brownian dynamics-based reduced kinetic model investigated in this work yields a readily discernible representation of metastable states within the phase space of the molecular system. Numerical experiments demonstrate how effectively the proposed method discovers interpretable and accurate low-dimensional representations of given full-state kinetics from simulations.

Thermodynamically Optimized Machine-Learned Reaction Coordinates for Hydrophobic Ligand Dissociation

Ligand unbinding is mediated by its free energy change, which has intertwined contributions from both energy and entropy. It is important, but not easy, to quantify their individual contributions to the free energy profile. We model hydrophobic ligand unbinding for two systems, a methane particle and a C60 fullerene, both unbinding from hydrophobic pockets in all-atom water. Using a modified deep learning framework, we learn a thermodynamically optimized reaction coordinate to describe the hydrophobic ligand dissociation for both systems. Interpretation of these reaction coordinates reveals the roles of entropic and enthalpic forces as the ligand and pocket sizes change. In both cases, we observe that the free-energy barrier to unbinding is dominated by entropy considerations. Furthermore, the process of methane unbinding is driven by methane solvation, while fullerene unbinding is driven first by pocket wetting and then fullerene wetting. For both solutes, the direct importance of the distance from the binding pocket to the learned reaction coordinate is present, but low. Our framework and subsequent feature important analysis thus give useful thermodynamic insight into hydrophobic ligand dissociation problems that are otherwise difficult to glean.

Analyzing Molecular Dynamics Trajectories Thermodynamically through Artificial Intelligence

Molecular dynamics simulations produce trajectories that correspond to vast amounts of structure when exploring biochemical processes. Extracting valuable information, e.g., important intermediate states and collective variables (CVs) that describe the major movement modes, from molecular trajectories to understand the underlying mechanisms of biological processes presents a significant challenge. To achieve this goal, we introduce a deep learning approach, coined DIKI (deep identification of key intermediates), to determine low-dimensional CVs distinguishing key intermediate conformations without a-priori assumptions. DIKI dynamically plans the distribution of latent space and groups together similar conformations within the same cluster. Moreover, by incorporating two user-defined parameters, namely, coarse focus knob and fine focus knob, to help identify conformations with low free energy and differentiate the subtle distinctions among these conformations, resolution-tunable clustering was achieved. Furthermore, the integration of DIKI with a path-finding algorithm contributes to the identification of crucial intermediates along the lowest free-energy pathway. We postulate that DIKI is a robust and flexible tool that can find widespread applications in the analysis of complex biochemical processes.

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

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.

Quantifying the Relevance of Long-Range Forces for Crystal Nucleation in Water

Understanding nucleation from aqueous solutions is of fundamental importance in a multitude of fields, ranging from materials science to biophysics. The complex solvent-mediated interactions in aqueous solutions hamper the development of a simple physical picture, elucidating the roles of different interactions in nucleation processes. In this work, we make use of three complementary techniques to disentangle the role played by short- and long-range interactions in solvent-mediated nucleation. Specifically, the first approach we utilize is the local molecular field (LMF) theory to renormalize long-range Coulomb electrostatics. Second, we use well-tempered metadynamics to speed up rare events governed by short-range interactions. Third, the deep learning-based State Predictive Information Bottleneck approach is employed in analyzing the reaction coordinate of the nucleation processes obtained from the LMF treatment coupled with well-tempered metadynamics. We find that the two-step nucleation mechanism can largely be captured by the short-range interactions, while the long-range interactions further contribute to the stability of the primary crystal state under ambient conditions. Furthermore, by analyzing the reaction coordinate obtained from the combined LMF-metadynamics treatment, we discern the fluctuations on different time scales, highlighting the need for long-range interactions when accounting for metastability.

Improved Sampling of Adaptive Path Collective Variables by Stabilized Extended-System Dynamics

Because of the complicated multistep nature of many biocatalytic reactions, an a priori definition of reaction coordinates is difficult. Therefore, we apply enhanced sampling algorithms along with adaptive path collective variables (PCVs), which converge to the minimum free energy path (MFEP) during the simulation. We show how PCVs can be combined with the highly efficient well-tempered metadynamics extended-system adaptive biasing force (WTM-eABF) hybrid sampling algorithm, offering dramatically increased sampling efficiency due to its fast adaptation to path updates. For this purpose, we address discontinuities of PCVs that can arise due to path shortcutting or path updates with a novel stabilization algorithm for extended-system methods. In addition, we show how the convergence of simulations can be further accelerated by utilizing the multistate Bennett's acceptance ratio (MBAR) estimator. These methods are applied to the first step of the enzymatic reaction mechanism of pseudouridine synthases, where the ability of path WTM-eABF to efficiently explore intricate molecular transitions is demonstrated.

Entropy and Energy Profiles of Chemical Reactions

The description of chemical processes at the molecular level is often facilitated by the use of reaction coordinates or collective variables (CVs). The CV measures the progress of the reaction and allows the construction of profiles that track how specific properties evolve as the reaction progresses. Whereas CVs are routinely used, especially alongside enhanced sampling techniques, the links among reaction profiles, thermodynamic state functions, and reaction rate constants are not rigorously exploited. Here, we report a unified treatment of such reaction profiles. Tractable expressions are derived for the free-energy, internal-energy, and entropy profiles as functions of only the CV. We demonstrate the ability of this treatment to extract quantitative insight from the entropy and internal-energy profiles of various real-world physicochemical processes, including intramolecular organic reactions, ionic transport in superionic electrolytes, and molecular transport in nanoporous materials.

Open-Source Machine Learning in Computational Chemistry

The field of computational chemistry has seen a significant increase in the integration of machine learning concepts and algorithms. In this Perspective, we surveyed 179 open-source software projects, with corresponding peer-reviewed papers published within the last 5 years, to better understand the topics within the field being investigated by machine learning approaches. For each project, we provide a short description, the link to the code, the accompanying license type, and whether the training data and resulting models are made publicly available. Based on those deposited in GitHub repositories, the most popular employed Python libraries are identified. We hope that this survey will serve as a resource to learn about machine learning or specific architectures thereof by identifying accessible codes with accompanying papers on a topic basis. To this end, we also include computational chemistry open-source software for generating training data and fundamental Python libraries for machine learning. Based on our observations and considering the three pillars of collaborative machine learning work, open data, open source (code), and open models, we provide some suggestions to the community.

AlphaFold2-RAVE: From Sequence to Boltzmann Ranking

While AlphaFold2 is rapidly being adopted as a new standard in protein structure predictions, it is limited to single structures. This can be insufficient for the inherently dynamic world of biomolecules. In this Letter, we propose AlphaFold2-RAVE, an efficient protocol for obtaining Boltzmann-ranked ensembles from sequence. The method uses structural outputs from AlphaFold2 as initializations for artificial intelligence-augmented molecular dynamics. We release the method as an open-source code and demonstrate results on different proteins.

An Efficient Path Classification Algorithm Based on Variational Autoencoder to Identify Metastable Path Channels for Complex Conformational Changes

Conformational changes (i.e., dynamic transitions between pairs of conformational states) play important roles in many chemical and biological processes. Constructing the Markov state model (MSM) from extensive molecular dynamics (MD) simulations is an effective approach to dissect the mechanism of conformational changes. When combined with transition path theory (TPT), MSM can be applied to elucidate the ensemble of kinetic pathways connecting pairs of conformational states. However, the application of TPT to analyze complex conformational changes often results in a vast number of kinetic pathways with comparable fluxes. This obstacle is particularly pronounced in heterogeneous self-assembly and aggregation processes. The large number of kinetic pathways makes it challenging to comprehend the molecular mechanisms underlying conformational changes of interest. To address this challenge, we have developed a path classification algorithm named latent-space path clustering (LPC) that efficiently lumps parallel kinetic pathways into distinct metastable path channels, making them easier to comprehend. In our algorithm, MD conformations are first projected onto a low-dimensional space containing a small set of collective variables (CVs) by time-structure-based independent component analysis (tICA) with kinetic mapping. Then, MSM and TPT are constructed to obtain the ensemble of pathways, and a deep learning architecture named the variational autoencoder (VAE) is used to learn the spatial distributions of kinetic pathways in the continuous CV space. Based on the trained VAE model, the TPT-generated ensemble of kinetic pathways can be embedded into a latent space, where the classification becomes clear. We show that LPC can efficiently and accurately identify the metastable path channels in three systems: a 2D potential, the aggregation of two hydrophobic particles in water, and the folding of the Fip35 WW domain. Using the 2D potential, we further demonstrate that our LPC algorithm outperforms the previous path-lumping algorithms by making substantially fewer incorrect assignments of individual pathways to four path channels. We expect that LPC can be widely applied to identify the dominant kinetic pathways underlying complex conformational changes.

From Deep Mutational Mapping of Allosteric Protein Landscapes to Deep Learning of Allostery and Hidden Allosteric Sites: Zooming in on "Allosteric Intersection" of Biochemical and Big Data Approaches

The recent advances in artificial intelligence (AI) and machine learning have driven the design of new expert systems and automated workflows that are able to model complex chemical and biological phenomena. In recent years, machine learning approaches have been developed and actively deployed to facilitate computational and experimental studies of protein dynamics and allosteric mechanisms. In this review, we discuss in detail new developments along two major directions of allosteric research through the lens of data-intensive biochemical approaches and AI-based computational methods. Despite considerable progress in applications of AI methods for protein structure and dynamics studies, the intersection between allosteric regulation, the emerging structural biology technologies and AI approaches remains largely unexplored, calling for the development of AI-augmented integrative structural biology. In this review, we focus on the latest remarkable progress in deep high-throughput mining and comprehensive mapping of allosteric protein landscapes and allosteric regulatory mechanisms as well as on the new developments in AI methods for prediction and characterization of allosteric binding sites on the proteome level. We also discuss new AI-augmented structural biology approaches that expand our knowledge of the universe of protein dynamics and allostery. We conclude with an outlook and highlight the importance of developing an open science infrastructure for machine learning studies of allosteric regulation and validation of computational approaches using integrative studies of allosteric mechanisms. The development of community-accessible tools that uniquely leverage the existing experimental and simulation knowledgebase to enable interrogation of the allosteric functions can provide a much-needed boost to further innovation and integration of experimental and computational technologies empowered by booming AI field.

Exploring and Learning the Universe of Protein Allostery Using Artificial Intelligence Augmented Biophysical and Computational Approaches

Allosteric mechanisms are commonly employed regulatory tools used by proteins to orchestrate complex biochemical processes and control communications in cells. The quantitative understanding and characterization of allosteric molecular events are among major challenges in modern biology and require integration of innovative computational experimental approaches to obtain atomistic-level knowledge of the allosteric states, interactions, and dynamic conformational landscapes. The growing body of computational and experimental studies empowered by emerging artificial intelligence (AI) technologies has opened up new paradigms for exploring and learning the universe of protein allostery from first principles. In this review we analyze recent developments in high-throughput deep mutational scanning of allosteric protein functions; applications and latest adaptations of Alpha-fold structural prediction methods for studies of protein dynamics and allostery; new frontiers in integrating machine learning and enhanced sampling techniques for characterization of allostery; and recent advances in structural biology approaches for studies of allosteric systems. We also highlight recent computational and experimental studies of the SARS-CoV-2 spike (S) proteins revealing an important and often hidden role of allosteric regulation driving functional conformational changes, binding interactions with the host receptor, and mutational escape mechanisms of S proteins which are critical for viral infection. We conclude with a summary and outlook of future directions suggesting that AI-augmented biophysical and computer simulation approaches are beginning to transform studies of protein allostery toward systematic characterization of allosteric landscapes, hidden allosteric states, and mechanisms which may bring about a new revolution in molecular biology and drug discovery.

From free-energy profiles to activation free energies

Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the “free-energy” analog of the minimum potential energy path and to take the activation free energy, [Formula: see text], as the difference between the maximum at the transition state and the minimum at R. We show that this approximation can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different [Formula: see text]. We derive an exact expression for the activation free energy that avoids this ambiguity. We find [Formula: see text] to be a combination of the probability of the system being in the reactant state, the probability density on the dividing surface, and the thermal de Broglie wavelength associated with the transition. We apply our formalism to simple analytic models and realistic chemical systems and show that the FEP-based approximation applies only at low temperatures for CVs with a small effective mass. Most chemical reactions occur on complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, [Formula: see text] is quite sensitive.

Statistically optimal analysis of the extended-system adaptive biasing force (eABF) method

The extended-system adaptive biasing force (eABF) method and its newer variants offer rapid exploration of the configuration space of chemical systems. Instead of directly applying the ABF bias to collective variables, they are harmonically coupled to fictitious particles, which separates the problem of enhanced sampling from that of free energy estimation. The prevalent analysis method to obtain the potential of mean force (PMF) from eABF is thermodynamic integration. However, besides the PMF, most information is lost as the unbiased probability of visited configurations is never recovered. In this contribution, we show how statistical weights of individual frames can be computed using the Multistate Bennett's Acceptance Ratio (MBAR), putting the post-processing of eABF on one level with other frequently used sampling methods. In addition, we apply this formalism to the prediction of nuclear magnetic resonance shieldings, which are very sensitive to molecular geometries and often require extensive sampling. The results show that the combination of enhanced sampling by means of extended-system dynamics with the MBAR estimator is a highly useful tool for the calculation of ensemble properties. Furthermore, the extension of the presented scheme to the recently published Gaussian-accelerated molecular dynamics eABF hybrid is straightforward and approximation free.

Interrogating RNA-Small Molecule Interactions with Structure Probing and Artificial Intelligence-Augmented Molecular Simulations

While there is increasing interest in the study of RNA as a therapeutic target, efforts to understand RNA-ligand recognition at the molecular level lag far behind our understanding of protein-ligand recognition. This problem is complicated due to the more than 10 orders of magnitude in time scales involved in RNA dynamics and ligand binding events, making it not straightforward to design experiments or simulations. Here, we make use of artificial intelligence (AI)-augmented molecular dynamics simulations to directly observe ligand dissociation for cognate and synthetic ligands from a riboswitch system. The site-specific flexibility profiles from our simulations are compared with in vitro measurements of flexibility using selective 2' hydroxyl acylation analyzed by primer extension and mutational profiling (SHAPE-MaP). Our simulations reproduce known relative binding affinity profiles for the cognate and synthetic ligands, and pinpoint how both ligands make use of different aspects of riboswitch flexibility. On the basis of our dissociation trajectories, we also make and validate predictions of pairs of mutations for both the ligand systems that would show differing binding affinities. These mutations are distal to the binding site and could not have been predicted solely on the basis of structure. The methodology demonstrated here shows how molecular dynamics simulations with all-atom force-fields have now come of age in making predictions that complement existing experimental techniques and illuminate aspects of systems otherwise not trivial to understand.

Learning Efficient, Collective Monte Carlo Moves with Variational Autoencoders

Discovering meaningful collective variables for enhancing sampling, via applied biasing potentials or tailored MC move sets, remains a major challenge within molecular simulation. While recent studies identifying collective variables with variational autoencoders (VAEs) have focused on the encoding and latent space discovered by a VAE, the impact of the decoding and its ability to act as a generative model remains unexplored. We demonstrate how VAEs may be used to learn (on-the-fly and with minimal human intervention) highly efficient, collective Monte Carlo moves that accelerate sampling along the learned collective variable. In contrast to many machine learning-based efforts to bias sampling and generate novel configurations, our methods result in exact sampling in the ensemble of interest and do not require reweighting. In fact, we show that the acceptance rates of our moves approach unity for a perfect VAE model. While this is never observed in practice, VAE-based Monte Carlo moves still enhance sampling of new configurations. We demonstrate, however, that the form of the encoding and decoding distributions, in particular the extent to which the decoder reflects the underlying physics, greatly impacts the performance of the trained VAE.

Quantifying Energetic and Entropic Pathways in Molecular Systems

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Finally, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.

Information Thermodynamics of the Transition-Path Ensemble

The reaction coordinate describing a transition between reactant and product is a fundamental concept in the theory of chemical reactions. Within transition-path theory, a quantitative definition of the reaction coordinate is found in the committor, which is the probability that a trajectory initiated from a given microstate first reaches the product before the reactant. Here we develop an information-theoretic origin for the committor and show how selecting transition paths from a long ergodic equilibrium trajectory induces entropy production which exactly equals the information that system dynamics provide about the reactivity of trajectories. This equality of entropy production and dynamical information generation also holds at the level of arbitrary individual coordinates, providing parallel measures of the coordinate's relevance to the reaction, each of which is maximized by the committor.

Multidimensional minimum-work control of a 2D Ising model

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and thus decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations, and significantly reducing resistance and hence work.

Transition rate theory, spectral analysis, and reactive paths

The kinetics of a dynamical system dominated by two metastable states is examined from the perspective of the activated-dynamics reactive flux formalism, Markov state eigenvalue spectral decomposition, and committor-based transition path theory. Analysis shows that the different theoretical formulations are consistent, clarifying the significance of the inherent microscopic lag-times that are implicated, and that the most meaningful one-dimensional reaction coordinate in the region of the transition state is along the gradient of the committor in the multidimensional subspace of collective variables. It is shown that the familiar reactive flux activated dynamics formalism provides an effective route to calculate the transition rate in the case of a narrow sharp barrier but much less so in the case of a broad flat barrier. In this case, the standard reactive flux correlation function decays very slowly to the plateau value that corresponds to the transmission coefficient. Treating the committor function as a reaction coordinate does not alleviate all issues caused by the slow relaxation of the reactive flux correlation function. A more efficient activated dynamics simulation algorithm may be achieved from a modified reactive flux weighted by the committor. Simulation results on simple systems are used to illustrate the various conceptual points.

Accelerating All-Atom Simulations and Gaining Mechanistic Understanding of Biophysical Systems through State Predictive Information Bottleneck

An effective implementation of enhanced sampling algorithms for molecular dynamics simulations requires a priori knowledge of the approximate reaction coordinate describing the relevant mechanisms in the system. In this work, we focus on the recently developed artificial intelligence-based State Predictive Information Bottleneck (SPIB) approach and demonstrate how SPIB can learn such a reaction coordinate as a deep neural network even from undersampled trajectories. We exemplify its usefulness by achieving more than 40 times acceleration in simulating two model biophysical systems through well-tempered metadynamics performed by biasing along the SPIB-learned reaction coordinate. These include left- to right-handed chirality transitions in a synthetic helical peptide (Aib)₉ and permeation of a small benzoic acid molecule through a synthetic, symmetric phospholipid bilayer. In addition to significantly accelerating the dynamics and achieving back and forth movement between different metastable states, the SPIB-based reaction coordinate gives mechanistic insights into the processes driving these two important problems.

Explaining reaction coordinates of alanine dipeptide isomerization obtained from deep neural networks using Explainable Artificial Intelligence (XAI)

A method for obtaining appropriate reaction coordinates is required to identify transition states distinguishing product and reactant in complex molecular systems. Recently, abundant research has been devoted to obtaining reaction coordinates using artificial neural networks from deep learning literature, where many collective variables are typically utilized in the input layer. However, it is difficult to explain the details of which collective variables contribute to the predicted reaction coordinates owing to the complexity of the nonlinear functions in deep neural networks. To overcome this limitation, we used Explainable Artificial Intelligence (XAI) methods of the Local Interpretable Model-agnostic Explanation (LIME) and the game theory-based framework known as Shapley Additive exPlanations (SHAP). We demonstrated that XAI enables us to obtain the degree of contribution of each collective variable to reaction coordinates that is determined by nonlinear regressions with deep learning for the committor of the alanine dipeptide isomerization in vacuum. In particular, both LIME and SHAP provide important features to the predicted reaction coordinates, which are characterized by appropriate dihedral angles consistent with those previously reported from the committor test analysis. The present study offers an AI-aided framework to explain the appropriate reaction coordinates, which acquires considerable significance when the number of degrees of freedom increases.

Multitask Machine Learning of Collective Variables for Enhanced Sampling of Rare Events

Computing accurate reaction rates is a central challenge in computational chemistry and biology because of the high cost of free energy estimation with unbiased molecular dynamics. In this work, a data-driven machine learning algorithm is devised to learn collective variables with a multitask neural network, where a common upstream part reduces the high dimensionality of atomic configurations to a low dimensional latent space and separate downstream parts map the latent space to predictions of basin class labels and potential energies. The resulting latent space is shown to be an effective low-dimensional representation, capturing the reaction progress and guiding effective umbrella sampling to obtain accurate free energy landscapes. This approach is successfully applied to model systems including a 5D Müller Brown model, a 5D three-well model, the alanine dipeptide in vacuum, and an Au(110) surface reconstruction unit reaction. It enables automated dimensionality reduction for energy controlled reactions in complex systems, offers a unified and data-efficient framework that can be trained with limited data, and outperforms single-task learning approaches, including autoencoders.

Computing Rates and Understanding Unbinding Mechanisms in Host-Guest Systems

The long time scale associated with ligand residence times renders their computation challenging. Therefore, the influence of factors like solvation and steric hindrance on residence times is not fully understood. Here, we demonstrate in a set of model host-guest systems that the recently developed Gaussian mixture based enhanced sampling allows residence times to be computed and enables an understanding of their unbinding mechanism. We observe that guest unbinding often proceeds via a series of intermediate states that can be labeled by the number of water molecules present in the binding cavity. In several cases the residence time is correlated to the water trapping times in the cavity.

Machine Learning at the Interface of Polymer Science and Biology: How Far Can We Go?

This Perspective outlines recent progress and future directions for using machine learning (ML), a data-driven method, to address critical questions in the design, synthesis, processing, and characterization of biomacromolecules. The achievement of these tasks requires the navigation of vast and complex chemical and biological spaces, difficult to accomplish with reasonable speed. Using modern algorithms and supercomputers, quantum physics methods are able to examine systems containing a few hundred interacting species and determine the probability of finding them in a particular region of phase space, thereby anticipating their properties. Likewise, modern approaches in chemistry and biomolecular simulation, supported by high performance computing, have culminated in producing data sets of escalating size and intrinsically high complexity. Hence, using ML to extract relevant information from these fields is of paramount importance to advance our understanding of chemical and biomolecular systems. At the heart of ML approaches lie statistical algorithms, which by evaluating a portion of a given data set, identify, learn, and manipulate the underlying rules that govern the whole data set. The assembly of a quality model to represent the data followed by the predictions and elimination of error sources are the key steps in ML. In addition to a growing infrastructure of ML tools to address complex problems, an increasing number of aspects related to our understanding of the fundamental properties of biomacromolecules are exposed to ML. These fields, including those residing at the interface of polymer science and biology (i.e., structure determination, de novo design, folding, and dynamics), strive to adopt and take advantage of the transformative power offered by approaches in the ML domain, which clearly has the potential of accelerating research in the field of biomacromolecules.

Influence of Long-Range Forces on the Transition States and Dynamics of NaCl Ion-Pair Dissociation in Water

We study NaCl ion-pair dissociation in a dilute aqueous solution using computer simulations both for the full system with long-range Coulomb interactions and for a well-chosen reference system with short-range intermolecular interactions. Analyzing results using concepts from Local Molecular Field (LMF) theory and the recently proposed AI-based analysis tool "State predictive information bottleneck" (SPIB), we show that the system with short-range interactions can accurately reproduce the transition rate for the dissociation process, the dynamics for moving between the underlying metastable states, and the transition state ensemble. Contributions from long-range interactions can be largely neglected for these processes because long-range forces from the direct interionic Coulomb interactions are almost completely canceled (>90%) by those from solvent interactions over the length scale where the transition takes place. Thus, for this important monovalent ion-pair system, short-range forces alone are able to capture detailed consequences of the collective solvent motion, allowing the use of physically suggestive and computationally efficient short-range models for the dissociation event. We believe that the framework here should be applicable to disentangling mechanisms for more complex processes such as multivalent ion disassociation, where previous work has suggested that long-range contributions may be more important.

Accelerated Simulations of Molecular Systems through Learning of Effective Dynamics

Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the time scales necessary to capture the structural evolution of biomolecules remains a daunting task. In this work, we present a novel framework to advance simulation time scales by up to 3 orders of magnitude by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müller-Brown potential, the Trp cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations, i.e., collective variables, and can generate, at any instant, all-atom molecular trajectories consistent with the collective variables. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.

Making High-Dimensional Molecular Distribution Functions Tractable through Belief Propagation on Factor Graphs

Molecular dynamics (MD) simulations provide a wealth of high-dimensional data at all-atom and femtosecond resolution but deciphering mechanistic information from this data is an ongoing challenge in physical chemistry and biophysics. Theoretically speaking, joint probabilities of the equilibrium distribution contain all thermodynamic information, but they prove increasingly difficult to compute and interpret as the dimensionality increases. Here, inspired by tools in probabilistic graphical modeling, we develop a factor graph trained through belief propagation that helps factorize the joint probability into an approximate tractable form that can be easily visualized and used. We validate the study through the analysis of the conformational dynamics of two small peptides with five and nine residues. Our validations include testing the conditional dependency predictions through an intervention scheme inspired by Judea Pearl. Second, we directly use the belief propagation-based approximate probability distribution as a high-dimensional static bias for enhanced sampling, where we achieve spontaneous back-and-forth motion between metastable states that is up to 350 times faster than unbiased MD. We believe this work opens up useful ways to thinking about and dealing with high-dimensional molecular simulations.

Attention-based generative models for de novo molecular design

Attention mechanisms have led to many breakthroughs in sequential data modeling but have yet to be incorporated into any generative algorithms for molecular design. Here we explore the impact of adding self-attention layers to generative β-VAE models and show that those with attention are able to learn a complex "molecular grammar" while improving performance on downstream tasks such as accurately sampling from the latent space ("model memory") or exploring novel chemistries not present in the training data. There is a notable relationship between a model's architecture, the structure of its latent memory and its performance during inference. We demonstrate that there is an unavoidable tradeoff between model exploration and validity that is a function of the complexity of the latent memory. However, novel sampling schemes may be used that optimize this tradeoff. We anticipate that attention will play an important role in future molecular design algorithms that can make efficient use of the detailed molecular substructures learned by the transformer.