Multiagent Reinforcement Learning-Based Adaptive Sampling for Conformational Dynamics of Proteins

Ensemble Adaptive Sampling Scheme: Identifying an Optimal Sampling Strategy via Policy Ranking

Efficient sampling in biomolecular simulations is critical for accurately capturing the complex dynamic behaviors of biological systems. Adaptive sampling techniques aim to improve efficiency by focusing computational resources on the most relevant regions of the phase space. In this work, we present a framework for identifying the optimal sampling policy through metric-driven ranking. Our approach systematically evaluates the policy ensemble and ranks the policies based on their ability to explore the conformational space effectively. Through a series of biomolecular simulation case studies, we demonstrate that the choice of a different adaptive sampling policy at each round significantly outperforms single policy sampling, leading to faster convergence and improved sampling performance. This approach takes an ensemble of adaptive sampling policies and identifies the optimal policy for the next round based on current data. Beyond presenting this ensemble view of adaptive sampling, we also propose two sampling algorithms that approximate this ranking framework on the fly. The modularity of this framework allows incorporation of any adaptive sampling policy, making it versatile and suitable as a comprehensive adaptive sampling scheme.

Mechanistic basis for enhanced strigolactone sensitivity in KAI2 triple mutant

Striga hermonthica is a parasitic weed that destroys billions of dollars' worth of staple crops every year. Its rapid proliferation stems from an enhanced ability to metabolize strigolactones (SLs), plant hormones that direct root branching and shoot growth. Striga's SL receptor, ShHTL7, bears more similarity to the staple crop karrikin receptor karrikin insensitive 2 (KAI2) than to SL receptor D14, though KAI2 variants in plants like Arabidopsis thaliana show minimal SL sensitivity. Recently, studies have indicated that a small number of point mutations to HTL7 residues can confer SL sensitivity to AtKAI2. Here, we analyze both wild-type AtKAI2 and SL-sensitive mutant Var64 through all-atom, long-timescale molecular dynamics simulations to determine the effects of these mutations on receptor function at a molecular level. We demonstrate that the mutations stabilize SL binding by about 2 kcal/mol. They also result in a doubling of the average pocket volume and eliminate the dependence of binding on certain pocket conformational arrangements. Although the probability of certain nonbinding SL-receptor interactions increases in the mutant compared with the wild-type, the rate of binding also increases by a factor of 10. All these changes account for the increased SL sensitivity in mutant KAI2 and suggest mechanisms for increasing the functionality of host crop SL receptors.

Molecular insights into the elevator-type mechanism of the cyanobacterial bicarbonate transporter BicA

Cyanobacteria are responsible for up to 80% of aquatic carbon dioxide fixation and have evolved a specialized carbon concentrating mechanism to increase photosynthetic yield. As such, cyanobacteria are attractive targets for synthetic biology and engineering approaches to address the demands of global energy security, food production, and climate change for an increasing world's population. The bicarbonate transporter BicA is a sodium-dependent, low-affinity, high-flux bicarbonate symporter expressed in the plasma membrane of cyanobacteria. Despite extensive biochemical characterization of BicA, including the resolution of the BicA crystal structure, the dynamic understanding of the bicarbonate transport mechanism remains elusive. To this end, we have collected over 1 ms of all-atom molecular dynamics simulation data of the BicA dimer to elucidate the structural rearrangements involved in the substrate transport process. We further characterized the energetics of the transition of BicA protomers and investigated potential mutations that are shown to decrease the free energy barrier of conformational transitions. In all, our study illuminates a detailed mechanistic understanding of the conformational dynamics of bicarbonate transporters and provides atomistic insights to engineering these transporters for enhanced photosynthetic production.

ConfRank: Improving GFN-FF Conformer Ranking with Pairwise Training

Conformer ranking is a crucial task for drug discovery, with methods for generating conformers often based on molecular (meta)dynamics or sophisticated sampling techniques. These methods are constrained by the underlying force computation regarding runtime and energy ranking accuracy, limiting their effectiveness for large-scale screening applications. To address these ranking limitations, we introduce ConfRank, a machine learning-based approach that enhances conformer ranking using pairwise training. We demonstrate its performance using GFN-FF-generated conformer ensembles, leveraging the DimeNet++ architecture trained on pairs of 159 760 uncharged organic compounds from the GEOM data set with r2SCAN-3c reference level. Instead of predicting only on single molecules, this approach captures relative energy differences between conformers, leading to a significant improvement of the overall conformational ranking, outperforming GFN-FF and GFN2-xTB. Thereby, the pairwise RMSD of the relative energy difference of two conformers can be reduced from 5.65 to 0.71 kcal mol-1 on the test data set, allowing to correctly identify up to 81% of all lowest lying conformers correctly (GFN-FF: 10%, GFN2-xTB: 47%). The ConfRank approach is cost-effective, allowing for scalable deployment on both CPU and GPU, achieving runtime accelerations by up to 2 orders of magnitude compared to GFN2-xTB. Out-of-sample investigations on CREST-generated conformer ensembles from the QM9 data set and conformers taken from an extended GMTKN55 data set show promising results for the robustness of this approach. Thereby, ranking correlation coefficient such as Spearman can be improved to 0.90 (GFN-FF: 0.39, GFN2-xTB: 0.84) reducing the probability of an incorrect sign flip in pairwise energy comparison from 32 to 7%. On the extended GMTKN55 subsets the pairwise MAD (RMSD) could be reduced on almost all subsets by up to 62% (58%) with an average improvement of 30% (29%). Moreover, an exemplary case study on vancomycin shows similar performance, indicating applicability to larger (bio)molecular structures. Furthermore, we motivate the usage of the pairwise training approach from a theoretical perspective, highlighting that while pairwise training can lead to a decline in single sample prediction of absolute energies for ML models, it significantly enhances conformer ranking performance. The data and models used in this study are available at https://github.com/grimme-lab/confrank.

Adaptive CVgen: Leveraging reinforcement learning for advanced sampling in protein folding and chemical reactions

Enhanced sampling techniques have traditionally encountered two significant challenges: identifying suitable reaction coordinates and addressing the exploration-exploitation dilemma, particularly the difficulty of escaping local energy minima. Here, we introduce Adaptive CVgen, a universal adaptive sampling framework designed to tackle these issues. Our approach utilizes a set of collective variables (CVs) to comprehensively cover the system's potential evolutionary phase space, generating diverse reaction coordinates to address the first challenge. Moreover, we integrate reinforcement learning strategies to dynamically adjust the generated reaction coordinates, thereby effectively balancing the exploration-exploitation dilemma. We apply this framework to sample the conformational space of six proteins transitioning from completely disordered states to folded states, as well as to model the chemical synthesis process of C60, achieving conformations that perfectly match the standard C60 structure. The results demonstrate Adaptive CVgen's effectiveness in exploring new conformations and escaping local minima, achieving both sampling efficiency and exploration accuracy. This framework holds potential for extending to various related challenges, including protein folding dynamics, drug targeting, and complex chemical reactions, thereby opening promising avenues for application in these fields.

Enhanced Sampling of Biomolecular Slow Conformational Transitions Using Adaptive Sampling and Machine Learning

Biomolecular simulations often suffer from the "time scale problem", hindering the study of rare events occurring over extended time scales. Enhanced sampling techniques aim to alleviate this issue by accelerating conformational transitions, yet they typically necessitate well-defined collective variables (CVs), posing a significant challenge. Machine learning offers promising solutions but typically requires rich training data encompassing the entire free energy surface (FES). In this work, we introduce an automated iterative pipeline designed to mitigate these limitations. Our protocol first utilizes a CV-free count-based adaptive sampling method to generate a data set rich in rare events. From this data set, slow modes are identified using Koopman-reweighted time-lagged independent component analysis (KTICA), which are subsequently leveraged by on-the-fly probability enhanced sampling (OPES) to efficiently explore the FES. The effectiveness of our pipeline is demonstrated and further compared with the common Markov State Model (MSM) approach on two model systems with increasing complexity: alanine dipeptide (Ala2) and deca-alanine (Ala10), underscoring its applicability across diverse biomolecular simulations.

Cyclopamine modulates smoothened receptor activity in a binding position dependent manner

Cyclopamine, a natural alkaloid, can act as an agonist when it binds to the Cysteine-Rich Domain (CRD) of Smoothened receptor and as an antagonist when it binds to the Transmembrane Domain (TMD). To study the effect of cyclopamine binding to each site experimentally, mutations in the other site are required. Hence, simulations are critical for understanding the WT activity due to binding at different sites. Using multi-milliseconds long aggregate MD simulations combined with Markov state models and machine learning, we explore the dynamic behavior of cyclopamine's interactions with different domains of WT SMO. A higher population of the active state at equilibrium, a lower free energy barrier of ~2 kcal/mol, and expansion of hydrophobic tunnel to facilitate cholesterol transport agrees with cyclopamine's agonistic behavior when bound to CRD. A higher population of the inactive state at equilibrium, a higher free energy barrier of ~4 kcal/mol and restricted hydrophobic tunnel shows cyclopamine's antagonistic behavior when bound to TMD. With cyclopamine bound to both sites, there is a slightly larger inactive population at equilibrium and an increased free energy barrier (~3.5 kcal/mol) exhibiting an overall weak antagonistic effect. These findings show cyclopamine's domain-specific modulation of SMO regulates Hedgehog signaling and cholesterol transport.

Energetics of substrate transport in proton-dependent oligopeptide transporters

The PepT So transporter mediates the transport of peptides across biological membranes. Despite advancements in structural biology, including cryogenic electron microscopy structures resolving PepT So in different states, the molecular basis of peptide recognition and transport by PepT So is not fully elucidated. In this study, we employed molecular dynamics simulations, Markov State Models (MSMs), and Transition Path Theory (TPT) to investigate the transport mechanism of an alanine-alanine peptide (Ala-Ala) through the PepT So transporter. Our simulations revealed conformational changes and key intermediate states involved in peptide translocation. We observed that the presence of the Ala-Ala peptide substrate lowers the free energy barriers associated with transition to the inward-facing state. Furthermore, we elucidated the proton transport model and analyzed the pharmacophore features of intermediate states, providing insights for rational drug design. These findings highlight the significance of substrate binding in modulating the conformational dynamics of PepT So and identify critical residues that facilitate transport.

Functional regulation of aquaporin dynamics by lipid bilayer composition

With the diversity of lipid-protein interactions, any observed membrane protein dynamics or functions directly depend on the lipid bilayer selection. However, the implications of lipid bilayer choice are seldom considered unless characteristic lipid-protein interactions have been previously reported. Using molecular dynamics simulation, we characterize the effects of membrane embedding on plant aquaporin SoPIP2;1, which has no reported high-affinity lipid interactions. The regulatory impacts of a realistic lipid bilayer, and nine different homogeneous bilayers, on varying SoPIP2;1 dynamics are examined. We demonstrate that SoPIP2;1's structure, thermodynamics, kinetics, and water transport are altered as a function of each membrane construct's ensemble properties. Notably, the realistic bilayer provides stabilization of non-functional SoPIP2;1 metastable states. Hydrophobic mismatch and lipid order parameter calculations further explain how lipid ensemble properties manipulate SoPIP2;1 behavior. Our results illustrate the importance of careful bilayer selection when studying membrane proteins. To this end, we advise cautionary measures when performing membrane protein molecular dynamics simulations.

Collective Variable-Based Enhanced Sampling: From Human Learning to Machine Learning

Enhanced-sampling algorithms relying on collective variables (CVs) are extensively employed to study complex (bio)chemical processes that are not amenable to brute-force molecular simulations. The selection of appropriate CVs characterizing the slow movement modes is of paramount importance for reliable and efficient enhanced-sampling simulations. In this Perspective, we first review the application and limitations of CVs obtained from chemical and geometrical intuition. We also introduce path-sampling algorithms, which can identify path-like CVs in a high-dimensional free-energy space. Machine-learning algorithms offer a viable approach to finding suitable CVs by analyzing trajectories from preliminary simulations. We discuss both the performance of machine-learning-derived CVs in enhanced-sampling simulations of experimental models and the challenges involved in applying these CVs to realistic, complex molecular assemblies. Moreover, we provide a prospective view of the potential advancements of machine-learning algorithms for the development of CVs in the field of enhanced-sampling simulations.

Binding Position Dependent Modulation of Smoothened Activity by Cyclopamine

Cyclopamine is a natural alkaloid that is known to act as an agonist when it binds to the Cysteine Rich Domain (CRD) of the Smoothened receptor and as an antagonist when it binds to the Transmembrane Domain (TMD). To study the effect of cyclopamine binding to each binding site experimentally, mutations in the other site are required. Hence, simulations are critical for understanding the WT activity due to binding at different sites. Additionally, there is a possibility that cyclopamine could bind to both sites simultaneously especially at high concentration, the implications of which remain unknown. We performed three independent sets of simulations to observe the receptor activation with cyclopamine bound to each site independently (CRD, TMD) and bound to both sites simultaneously. Using multi-milliseconds long aggregate MD simulations combined with Markov state models and machine learning, we explored the dynamic behavior of cyclopamine's interactions with different domains of WT SMO. A higher population of the active state at equilibrium, a lower activation free energy barrier of ~ 2 kcal/mol, and expansion of the hydrophobic tunnel to facilitate cholesterol transport agrees with the cyclopamine's agonistic behavior when bound to the CRD of SMO. A higher population of the inactive state at equilibrium, a higher free energy barrier of ~ 4 kcal/mol and restricted the hydrophobic tunnel to impede cholesterol transport showed cyclopamine's antagonistic behavior when bound to TMD. With cyclopamine bound to both sites, there was a slightly larger inactive population at equilibrium and an increased free energy barrier (~ 3.5 kcal/mol). The tunnel was slightly larger than when solely bound to TMD, and showed a balance between agonism and antagonism with respect to residue movements exhibiting an overall weak antagonistic effect.

Adaptive Sampling Methods for Molecular Dynamics in the Era of Machine Learning

Molecular dynamics (MD) simulations are fundamental computational tools for the study of proteins and their free energy landscapes. However, sampling protein conformational changes through MD simulations is challenging due to the relatively long time scales of these processes. Many enhanced sampling approaches have emerged to tackle this problem, including biased sampling and path-sampling methods. In this Perspective, we focus on adaptive sampling algorithms. These techniques differ from other approaches because the thermodynamic ensemble is preserved and the sampling is enhanced solely by restarting MD trajectories at particularly chosen seeds rather than introducing biasing forces. We begin our treatment with an overview of theoretically transparent methods, where we discuss principles and guidelines for adaptive sampling. Then, we present a brief summary of select methods that have been applied to realistic systems in the past. Finally, we discuss recent advances in adaptive sampling methodology powered by deep learning techniques, as well as their shortcomings.

Computational methods in glaucoma research: Current status and future outlook

Advancements in computational techniques have transformed glaucoma research, providing a deeper understanding of genetics, disease mechanisms, and potential therapeutic targets. Systems genetics integrates genomic and clinical data, aiding in identifying drug targets, comprehending disease mechanisms, and personalizing treatment strategies for glaucoma. Molecular dynamics simulations offer valuable molecular-level insights into glaucoma-related biomolecule behavior and drug interactions, guiding experimental studies and drug discovery efforts. Artificial intelligence (AI) technologies hold promise in revolutionizing glaucoma research, enhancing disease diagnosis, target identification, and drug candidate selection. The generalized protocols for systems genetics, MD simulations, and AI model development are included as a guide for glaucoma researchers. These computational methods, however, are not separate and work harmoniously together to discover novel ways to combat glaucoma. Ongoing research and progresses in genomics technologies, MD simulations, and AI methodologies project computational methods to become an integral part of glaucoma research in the future.

Functional Regulation of Aquaporin Dynamics by Lipid Bilayer Composition

With the diversity of lipid-protein interactions, any observed membrane protein dynamics or functions directly depend on the lipid bilayer selection. However, the implications of lipid bilayer choice are seldom considered unless characteristic lipid-protein interactions have been previously reported. Using molecular dynamics simulation, we characterize the effects of membrane embedding on plant aquaporin SoPIP2;1, which has no reported high-affinity lipid interactions. The regulatory impacts of a realistic lipid bilayer, and nine different homogeneous bilayers, on varying SoPIP2;1 dynamics were examined. We demonstrate that SoPIP2;1s structure, thermodynamics, kinetics, and water transport are altered as a function of each membrane construct's ensemble properties. Notably, the realistic bilayer provides stabilization of non-functional SoPIP2;1 metastable states. Hydrophobic mismatch and lipid order parameter calculations further explain how lipid ensemble properties manipulate SoPIP2;1 behavior. Our results illustrate the importance of careful bilayer selection when studying membrane proteins. To this end, we advise cautionary measures when performing membrane protein molecular dynamics simulations.

Machine Learning Generation of Dynamic Protein Conformational Ensembles

Machine learning has achieved remarkable success across a broad range of scientific and engineering disciplines, particularly its use for predicting native protein structures from sequence information alone. However, biomolecules are inherently dynamic, and there is a pressing need for accurate predictions of dynamic structural ensembles across multiple functional levels. These problems range from the relatively well-defined task of predicting conformational dynamics around the native state of a protein, which traditional molecular dynamics (MD) simulations are particularly adept at handling, to generating large-scale conformational transitions connecting distinct functional states of structured proteins or numerous marginally stable states within the dynamic ensembles of intrinsically disordered proteins. Machine learning has been increasingly applied to learn low-dimensional representations of protein conformational spaces, which can then be used to drive additional MD sampling or directly generate novel conformations. These methods promise to greatly reduce the computational cost of generating dynamic protein ensembles, compared to traditional MD simulations. In this review, we examine recent progress in machine learning approaches towards generative modeling of dynamic protein ensembles and emphasize the crucial importance of integrating advances in machine learning, structural data, and physical principles to achieve these ambitious goals.

Distinct activation mechanisms regulate subtype selectivity of Cannabinoid receptors

Design of cannabinergic subtype selective ligands is challenging because of high sequence and structural similarities of cannabinoid receptors (CB₁ and CB₂). We hypothesize that the subtype selectivity of designed selective ligands can be explained by the ligand binding to the conformationally distinct states between cannabinoid receptors. Analysis of ~ 700 μs of unbiased simulations using Markov state models and VAMPnets identifies the similarities and distinctions between the activation mechanism of both receptors. Structural and dynamic comparisons of metastable intermediate states allow us to observe the distinction in the binding pocket volume change during CB₁ and CB₂ activation. Docking analysis reveals that only a few of the intermediate metastable states of CB₁ show high affinity towards CB₂ selective agonists. In contrast, all the CB₂ metastable states show a similar affinity for these agonists. These results mechanistically explain the subtype selectivity of these agonists by deciphering the activation mechanism of cannabinoid receptors.

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.

Thirty years of molecular dynamics simulations on posttranslational modifications of proteins

Posttranslational modifications (PTMs) are an integral component to how cells respond to perturbation. While experimental advances have enabled improved PTM identification capabilities, the same throughput for characterizing how structural changes caused by PTMs equate to altered physiological function has not been maintained. In this Perspective, we cover the history of computational modeling and molecular dynamics simulations which have characterized the structural implications of PTMs. We distinguish results from different molecular dynamics studies based upon the timescales simulated and analysis approaches used for PTM characterization. Lastly, we offer insights into how opportunities for modern research efforts on in silico PTM characterization may proceed given current state-of-the-art computing capabilities and methodological advancements.

Conformational Stability and Denaturation Processes of Proteins Investigated by Electrophoresis under Extreme Conditions

The functional structure of proteins results from marginally stable folded conformations. Reversible unfolding, irreversible denaturation, and deterioration can be caused by chemical and physical agents due to changes in the physicochemical conditions of pH, ionic strength, temperature, pressure, and electric field or due to the presence of a cosolvent that perturbs the delicate balance between stabilizing and destabilizing interactions and eventually induces chemical modifications. For most proteins, denaturation is a complex process involving transient intermediates in several reversible and eventually irreversible steps. Knowledge of protein stability and denaturation processes is mandatory for the development of enzymes as industrial catalysts, biopharmaceuticals, analytical and medical bioreagents, and safe industrial food. Electrophoresis techniques operating under extreme conditions are convenient tools for analyzing unfolding transitions, trapping transient intermediates, and gaining insight into the mechanisms of denaturation processes. Moreover, quantitative analysis of electrophoretic mobility transition curves allows the estimation of the conformational stability of proteins. These approaches include polyacrylamide gel electrophoresis and capillary zone electrophoresis under cold, heat, and hydrostatic pressure and in the presence of non-ionic denaturing agents or stabilizers such as polyols and heavy water. Lastly, after exposure to extremes of physical conditions, electrophoresis under standard conditions provides information on irreversible processes, slow conformational drifts, and slow renaturation processes. The impressive developments of enzyme technology with multiple applications in fine chemistry, biopharmaceutics, and nanomedicine prompted us to revisit the potentialities of these electrophoretic approaches. This feature review is illustrated with published and unpublished results obtained by the authors on cholinesterases and paraoxonase, two physiologically and toxicologically important enzymes.