Enhanced unbiased sampling of protein dynamics using evolutionary coupling information

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 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. While the probability of certain non-binding SL-receptor interactions increases in the mutant compared with the wild-type, the rate of binding also increases by a factor of ten. All these changes account for the increased SL sensitivity in mutant KAI2, and suggest mechanisms for increasing functionality of host crop SL receptors.

Multiple modes of cholesterol translocation in the human Smoothened receptor

Smoothened (SMO), a member of the G Protein-Coupled Receptor superfamily, mediates Hedgehog signaling and is linked to cancer and birth defects. SMO responds to accessible cholesterol in the ciliary membrane, translocating it via a longitudinal tunnel to its extracellular domain. Reaching a complete mechanistic understanding of the cholesterol translocation process would help in the development of cancer therapies. Experimental data suggests two modes of translocation to support entry of cholesterol from outer and inner membrane leaflets, but the exact mechanism of translocation remains unclear. Using atomistic molecular dynamics simulations (~2 millisecond simulations) and biochemical assays of SMO mutants, we assess the energetic feasibilities of the two modes. We show that the highest energetic barrier for cholesterol translocation from the outer leaflet is lower than that from the inner leaflet. Mutagenesis experiments and complementary simulations of SMO mutants validate the role of critical amino acid residues along the translocation pathways. Our data suggests that cholesterol can take either pathway to enter SMO, thus explaining experimental observations in literature. Thus, our results illuminate the energetics and provide a first molecular description of cholesterol translocation in SMO.

Dynamic Mechanism for Subtype Selectivity of Endocannabinoids

Endocannabinoids are naturally occurring lipid-like molecules that bind to cannabinoid receptors (CB1 and CB2) and regulate many of human bodily functions via the endocannabinoid system. There is a tremendous interest in developing selective drugs that target the CB receptors. However, the biophysical mechanisms responsible for the subtype selectivity for endocannbinoids have not been established. Recent experimental structures of CB receptors show that endocannbinoids potentially bind via membrane using the lipid access channel in the transmembrane region of the receptors. Furthermore, the N-terminus of the receptor could move in and out of the binding pocket thereby modulating both the pocket volume and its residue composition. On the basis of these observations, we propose two hypothesis to explain the selectivity of the endocannabinoid, anandamide for CB1 receptor. First, the selectivity arises from distinct enthalpic ligand-protein interactions along the ligand binding pathway formed due to the movement of N-terminus and subsequent shifts in the binding pocket composition. Second, selectivity arises from the volumetric differences in the binding pocket allowing for differences in ligand conformational entropy. To quantitatively test these hypothesis, we perform extensive molecular dynamics simulations (∼0.9 milliseconds) along with Markov state modeling and deep learning-based VAMP-nets to provide an interpretable characterization of the anandamide binding process to cannabinoid receptors and explain its selectivity for CB1. Our findings reveal that the distinct N-terminus positions along lipid access channels between TM1 and TM7 lead to different binding mechanisms and interactions between anandamide and the binding pocket residues. To validate the critical stabilizing interactions along the binding pathway, relative free energy calculations of anandamide analogs are used. Moreover, the larger CB2 pocket volume increases the entropic effects of ligand binding by allowing higher ligand fluctuations but reduced stable interactions. Therefore, the opposing enthalpy and entropy effects between the receptors shape the endocannabinoid selectivity. Overall, the CB1 selectivity of anandamide is explained by the dominant enthalpy contributions due to ligand-protein interactions in stable binding poses. This study shed lights on potential selectivity mechanisms for endocannabinoids that would aid in the discovery of CB selective drugs.

A Deep Learning-Driven Sampling Technique to Explore the Phase Space of an RNA Stem-Loop

The folding and unfolding of RNA stem-loops are critical biological processes; however, their computational studies are often hampered by the ruggedness of their folding landscape, necessitating long simulation times at the atomistic scale. Here, we adapted DeepDriveMD (DDMD), an advanced deep learning-driven sampling technique originally developed for protein folding, to address the challenges of RNA stem-loop folding. Although tempering- and order parameter-based techniques are commonly used for similar rare-event problems, the computational costs or the need for a priori knowledge about the system often present a challenge in their effective use. DDMD overcomes these challenges by adaptively learning from an ensemble of running MD simulations using generic contact maps as the raw input. DeepDriveMD enables on-the-fly learning of a low-dimensional latent representation and guides the simulation toward the undersampled regions while optimizing the resources to explore the relevant parts of the phase space. We showed that DDMD estimates the free energy landscape of the RNA stem-loop reasonably well at room temperature. Our simulation framework runs at a constant temperature without external biasing potential, hence preserving the information on transition rates, with a computational cost much lower than that of the simulations performed with external biasing potentials. We also introduced a reweighting strategy for obtaining unbiased free energy surfaces and presented a qualitative analysis of the latent space. This analysis showed that the latent space captures the relevant slow degrees of freedom for the RNA folding problem of interest. Finally, throughout the manuscript, we outlined how different parameters are selected and optimized to adapt DDMD for this system. We believe this compendium of decision-making processes will help new users adapt this technique for the rare-event sampling problems of their interest.

The Arabidopsis AtSWEET13 transporter discriminates sugars by selective facial and positional substrate recognition

Transporters are targeted by endogenous metabolites and exogenous molecules to reach cellular destinations, but it is generally not understood how different substrate classes exploit the same transporter's mechanism. Any disclosure of plasticity in transporter mechanism when treated with different substrates becomes critical for developing general selectivity principles in membrane transport catalysis. Using extensive molecular dynamics simulations with an enhanced sampling approach, we select the Arabidopsis sugar transporter AtSWEET13 as a model system to identify the basis for glucose versus sucrose molecular recognition and transport. Here we find that AtSWEET13 chemical selectivity originates from a conserved substrate facial selectivity demonstrated when committing alternate access, despite mono-/di-saccharides experiencing differing degrees of conformational and positional freedom throughout other stages of transport. However, substrate interactions with structural hallmarks associated with known functional annotations can help reinforce selective preferences in molecular transport.

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

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

Interplay between phosphorylation and oligomerization tunes the conformational ensemble of SWEET transporters

SWEET sugar transporters are desirable biotechnological targets for improving plant growth. One engineering strategy includes modulating how SWEET transporters are regulated. Phosphorylation and oligomerization have been shown to positively regulate SWEET function, leading to increased sugar transport activity. However, constitutive phosphorylation may not be beneficial to plant health under basal conditions. Structural and mechanistic understanding of the interplay between phosphorylation and oligomerization in functional regulation of SWEETs remains limited. Using extensive molecular dynamics simulations coupled with Markov state models, we demonstrate the thermodynamic and kinetic effects of SWEET phosphorylation and oligomerization using OsSWEET2b as a model. We report that the beneficial effects of these SWEET regulatory mechanisms bias outward-facing states and improved extracellular gating, which complement published experimental findings. Our results offer molecular insights to SWEET regulation and may guide engineering strategies throughout the SWEET transport family.

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.

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.

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.

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.

Protein Function Analysis through Machine Learning

Machine learning (ML) has been an important arsenal in computational biology used to elucidate protein function for decades. With the recent burgeoning of novel ML methods and applications, new ML approaches have been incorporated into many areas of computational biology dealing with protein function. We examine how ML has been integrated into a wide range of computational models to improve prediction accuracy and gain a better understanding of protein function. The applications discussed are protein structure prediction, protein engineering using sequence modifications to achieve stability and druggability characteristics, molecular docking in terms of protein-ligand binding, including allosteric effects, protein-protein interactions and protein-centric drug discovery. To quantify the mechanisms underlying protein function, a holistic approach that takes structure, flexibility, stability, and dynamics into account is required, as these aspects become inseparable through their interdependence. Another key component of protein function is conformational dynamics, which often manifest as protein kinetics. Computational methods that use ML to generate representative conformational ensembles and quantify differences in conformational ensembles important for function are included in this review. Future opportunities are highlighted for each of these topics.

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

Machine learning is increasingly applied to improve the efficiency and accuracy of molecular dynamics (MD) simulations. Although the growth of distributed computer clusters has allowed researchers to obtain higher amounts of data, unbiased MD simulations have difficulty sampling rare states, even under massively parallel adaptive sampling schemes. To address this issue, several algorithms inspired by reinforcement learning (RL) have arisen to promote exploration of the slow collective variables (CVs) of complex systems. Nonetheless, most of these algorithms are not well-suited to leverage the information gained by simultaneously sampling a system from different initial states (e.g., a protein in different conformations associated with distinct functional states). To fill this gap, we propose two algorithms inspired by multiagent RL that extend the functionality of closely related techniques (REAP and TSLC) to situations where the sampling can be accelerated by learning from different regions of the energy landscape through coordinated agents. Essentially, the algorithms work by remembering which agent discovered each conformation and sharing this information with others at the action-space discretization step. A stakes function is introduced to modulate how different agents sense rewards from discovered states of the system. The consequences are three-fold: (i) agents learn to prioritize CVs using only relevant data, (ii) redundant exploration is reduced, and (iii) agents that obtain higher stakes are assigned more actions. We compare our algorithm with other adaptive sampling techniques (least counts, REAP, TSLC, and AdaptiveBandit) to show and rationalize the gain in performance.

Integration of machine learning with computational structural biology of plants

Computational structural biology of proteins has developed rapidly in recent decades with the development of new computational tools and the advancement of computing hardware. However, while these techniques have widely been used to make advancements in human medicine, these methods have seen less utilization in the plant sciences. In the last several years, machine learning methods have gained popularity in computational structural biology. These methods have enabled the development of new tools which are able to address the major challenges that have hampered the wide adoption of the computational structural biology of plants. This perspective examines the remaining challenges in computational structural biology and how the development of machine learning techniques enables more in-depth computational structural biology of plants.

Dual Role of Strigolactone Receptor Signaling Partner in Inhibiting Substrate Hydrolysis

Plant branch and root growth relies on metabolism of the strigolactone (SL) hormone. The interaction between the SL molecule, Oryza sativa DWARF14 (D14) SL receptor, and D3 F-box protein has been shown to play a critical role in SL perception. Previously, it was believed that D3 only interacts with the closed form of D14 to induce downstream signaling, but recent experiments indicate that D3, as well as its C-terminal helix (CTH), can interact with the open form as well to inhibit strigolactone signaling. Two hypotheses for the CTH induced inhibition are that either the CTH affects the conformational ensemble of D14 by stabilizing catalytically inactive states or the CTH interacts with SLs in a way that prevents them from entering the binding pocket. In this study, we have performed molecular dynamics (MD) simulations to assess the validity of these hypotheses. We used an apo system with only D14 and the CTH to test the active site conformational stability and a holo system with D14, the CTH, and an SL molecule to test the interaction between the SL and CTH. Our simulations show that the CTH affects both active site conformation and the ability of SLs to move into the binding pocket. In the apo system, the CTH allosterically stabilized catalytic residues into their inactive conformation. In the holo system, significant interactions between SLs and the CTH hindered the ability of SLs to enter the D14 binding pocket. These two mechanisms account for the observed decrease in SL binding to D14 and subsequent ligand hydrolysis in the presence of the CTH.

Distinct Binding Mechanisms for Allosteric Sodium Ion in Cannabinoid Receptors

The therapeutic potential of cannabinoid receptors is not fully explored due to psychoactive side effects and lack of selectivity associated with orthosteric ligands. Allosteric modulators have the potential to become selective therapeutics for cannabinoid receptors. Biochemical experiments have shown the effects of the allosteric Na⁺ binding on cannabinoid receptor activity. However, the Na⁺ coordination site and binding pathway are still unknown. Here, we perform molecular dynamic simulations to explore Na⁺ binding in the cannabinoid receptors, CB₁ and CB₂. Simulations reveal that Na⁺ binds to the primary binding site from different extracellular sites for CB₁ and CB₂. A distinct secondary Na⁺ coordination site is identified in CB₁ that is not present in CB₂. Furthermore, simulations also show that intracellular Na⁺ could bind to the Na⁺ binding site in CB₁. Constructed Markov state models show that the standard free energy of Na⁺ binding is similar to the previously calculated free energy for other class A GPCRs.

Molecular basis of the activation and dissociation of dimeric PYL2 receptor in abscisic acid signaling

Phytohormone abscisic acid (ABA) is essential for plant responses to biotic and abiotic stresses. Dimeric receptors are a class of PYR1/PYL/RCAR (pyrabactin resistance 1/PYR1-like/regulatory component of ABA receptors) ABA receptors that are important for various ABA responses. While extensive experimental and computational studies have investigated these receptors, it remains not fully understood how ABA leads to their activation and dissociation for interaction with downstream protein phosphatase 2C (PP2C). Here, we study the activation and the homodimeric association processes of the PYL2 receptor as well as its heterodimeric association with protein phosphatase 2C 16 (HAB1) using molecular dynamics simulations. Free energy landscapes from ∼223 μs simulations show that dimerization substantially constrains PYL2 conformational plasticity and stabilizes the inactive state, resulting in lower ABA affinity. Also, we establish the thermodynamic model for competitive binding between homodimeric PYL2 association and heterodimeric PYL2-HAB1 association in the absence and presence of ABA. Our results suggest that the binding of ABA destabilizes the PYL2 complex and further stabilizes PYL2-HAB1 association, thereby promoting PYL2 dissociation. Overall, this study explains several key aspects on the activation of dimeric ABA receptors, which provide new avenues for selective regulation of these receptors.

Role of substrate recognition in modulating strigolactone receptor selectivity in witchweed

Witchweed, or Striga hermonthica, is a parasitic weed that destroys billions of dollars' worth of crops globally every year. Its germination is stimulated by strigolactones exuded by its host plants. Despite high sequence, structure, and ligand-binding site conservation across different plant species, one strigolactone receptor in witchweed, ShHTL7, uniquely exhibits a picomolar EC50 for downstream signaling. Previous biochemical and structural analyses have hypothesized that this unique ligand sensitivity can be attributed to a large binding pocket volume in ShHTL7 resulting in enhanced ability to bind substrates, but additional structural details of the substrate-binding process would help explain its role in modulating the ligand selectivity. Using long-timescale molecular dynamics simulations, we demonstrate that mutations at the entrance of the binding pocket facilitate a more direct ligand-binding pathway to ShHTL7, whereas hydrophobicity at the binding pocket entrance results in a stable “anchored” state. We also demonstrate that several residues on the D-loop of AtD14 stabilize catalytically inactive conformations. Finally, we show that strigolactone selectivity is not modulated by binding pocket volume. Our results indicate that while ligand binding is not the sole modulator of strigolactone receptor selectivity, it is a significant contributing factor. These results can be used to inform the design of selective antagonists for strigolactone receptors in witchweed.

Impact of Increased Membrane Realism on Conformational Sampling of Proteins

The realism and accuracy of lipid bilayer simulations through molecular dynamics (MD) are heavily dependent on the lipid composition. While the field is pushing toward implementing more heterogeneous and realistic membrane compositions, a lack of high-resolution lipidomic data prevents some membrane protein systems from being modeled with the highest level of realism. Given the additional diversity of real-world cellular membranes and protein-lipid interactions, it is still not fully understood how altering membrane complexity affects modeled membrane protein functions or if it matters over long-timescale simulations. This is especially true for organisms whose membrane environments have little to no computational study, such as the plant plasma membrane. Tackling these issues in tandem, a generalized, realistic, and asymmetric plant plasma membrane with more than 10 different lipid species is constructed herein. Classical MD simulations of pure membrane constructs were performed to evaluate how altering the compositional complexity of the membrane impacted the plant membrane properties. The apo form of a plant sugar transporter, OsSWEET2b, was inserted into membrane models where lipid diversity was calculated in either a size-dependent or size-independent manner. An adaptive sampling simulation regime validated by Markov-state models was performed to capture the gating dynamics of OsSWEET2b in each of these membrane constructs. In comparison to previous OsSWEET2b simulations performed in a pure POPC bilayer, we confirm that simulations performed within a native-like membrane composition alter the stabilization of apo OsSWEET2b conformational states by ∼1 kcal/mol. The free-energy barriers of intermediate conformational states decrease when realistic membrane complexity is simplified, albeit roughly within sampling error, suggesting that protein-specific responses to membranes differ due to altered packing caused by compositional fluctuations. This work serves as a case study where a more realistic bilayer composition makes unbiased conformational sampling easier to achieve than with simplified bilayers.

Dimeric allostery mechanism of the plant circadian clock photoreceptor ZEITLUPE

In Arabidopsis thaliana, the Light-Oxygen-Voltage (LOV) domain containing protein ZEITLUPE (ZTL) integrates light quality, intensity, and duration into regulation of the circadian clock. Recent structural and biochemical studies of ZTL indicate that the protein diverges from other members of the LOV superfamily in its allosteric mechanism, and that the divergent allosteric mechanism hinges upon conservation of two signaling residues G46 and V48 that alter dynamic motions of a Gln residue implicated in signal transduction in all LOV proteins. Here, we delineate the allosteric mechanism of ZTL via an integrated computational approach that employs atomistic simulations of wild type and allosteric variants of ZTL in the functional dark and light states, together with Markov state and supervised machine learning classification models. This approach has unveiled key factors of the ZTL allosteric mechanisms, and identified specific interactions and residues implicated in functional allosteric changes. The final results reveal atomic level insights into allosteric mechanisms of ZTL function that operate via a non-trivial combination of population-shift and dynamics-driven allosteric pathways.

UMAP as a Dimensionality Reduction Tool for Molecular Dynamics Simulations of Biomacromolecules: A Comparison Study

Proteins are the molecular machines of life. The multitude of possible conformations that proteins can adopt determines their free-energy landscapes. However, the inherently high dimensionality of a protein free-energy landscape poses a challenge to deciphering how proteins perform their functions. For this reason, dimensionality reduction is an active field of research for molecular biologists. The uniform manifold approximation and projection (UMAP) is a dimensionality reduction method based on a fuzzy topological analysis of data. In the present study, the performance of UMAP is compared with that of other popular dimensionality reduction methods such as t-distributed stochastic neighbor embedding (t-SNE), principal component analysis (PCA), and time-structure independent components analysis (tICA) in the context of analyzing molecular dynamics simulations of the circadian clock protein VIVID. A good dimensionality reduction method should accurately represent the data structure on the projected components. The comparison of the raw high-dimensional data with the projections obtained using different dimensionality reduction methods based on various metrics showed that UMAP has superior performance when compared with linear reduction methods (PCA and tICA) and has competitive performance and scalable computational cost.

How do antiporters exchange substrates across the cell membrane? An atomic-level description of the complete exchange cycle in NarK

Major facilitator superfamily (MFS) proteins operate via three different mechanisms: uniport, symport, and antiport. Despite extensive investigations, the molecular understanding of antiporters is less advanced than that of other transporters due to the complex coupling between two substrates and the lack of distinct structures. We employ extensive all-atom molecular dynamics simulations to dissect the complete substrate exchange cycle of the bacterial NO₃^-/NO₂^- antiporter, NarK. We show that paired basic residues in the binding site prevent the closure of unbound protein and ensure the exchange of two substrates. Conformational transition occurs only in the presence of substrate, which weakens the electrostatic repulsion and stabilizes the transporter. Furthermore, we propose a state-dependent substrate exchange model, in which the relative spacing between the paired basic residues determines whether NO₃^- and NO₂^- bind simultaneously or sequentially. Overall, this work presents a general working model for the antiport mechanism within the MFS.

Extensible and Scalable Adaptive Sampling on Supercomputers

The accurate sampling of protein dynamics is an ongoing challenge despite the utilization of high-performance computer (HPC) systems. Utilizing only "brute force" molecular dynamics (MD) simulations requires an unacceptably long time to solution. Adaptive sampling methods allow a more effective sampling of protein dynamics than standard MD simulations. Depending on the restarting strategy, the speed up can be more than 1 order of magnitude. One challenge limiting the utilization of adaptive sampling by domain experts is the relatively high complexity of efficiently running adaptive sampling on HPC systems. We discuss how the ExTASY framework can set up new adaptive sampling strategies and reliably execute resulting workflows at scale on HPC platforms. Here, the folding dynamics of four proteins are predicted with no a priori information.

TLmutation: Predicting the Effects of Mutations Using Transfer Learning

A reccurring challenge in bioinformatics is predicting the phenotypic consequence of amino acid variation in proteins. With the recent advancements in sequencing techniques, sufficient genomic data has become available to train models that predict the evolutionary statistical energies, but there is still inadequate experimental data to directly predict functional effects. One approach to overcome this data scarcity is to apply transfer learning and train more models with available data sets. In this study, we propose a set of transfer learning algorithms we call TLmutation, which implements a supervised transfer learning algorithm that transfers knowledge from survival data of a protein to a particular function of that protein. This is followed by an unsupervised transfer learning algorithm that extends the knowledge to a homologous protein. We explore the application of our algorithms in three cases. First, we test the supervised transfer on 17 previously published deep mutagenesis data sets to complete and refine missing data points. We further investigate these data sets to identify which mutations build better predictors of variant functions. In the second case, we apply the algorithm to predict higher-order mutations solely from single point mutagenesis data. Finally, we perform the unsupervised transfer learning algorithm to predict mutational effects of homologous proteins from experimental data sets. These algorithms are generalized to transfer knowledge between Markov random field models. We show the benefit of our transfer learning algorithms to utilize informative deep mutational data and provide new insights into protein variant functions. As these algorithms are generalized to transfer knowledge between Markov random field models, we expect these algorithms to be applicable to other disciplines.

FingerprintContacts: Predicting Alternative Conformations of Proteins from Coevolution

Proteins are dynamic molecules which perform diverse molecular functions by adopting different three-dimensional structures. Recent progress in residue-residue contacts prediction opens up new avenues for the de novo protein structure prediction from sequence information. However, it is still difficult to predict more than one conformation from residue-residue contacts alone. This is due to the inability to deconvolve the complex signals of residue-residue contacts, i.e., spatial contacts relevant for protein folding, conformational diversity, and ligand binding. Here, we introduce a machine learning based method, called FingerprintContacts, for extending the capabilities of residue-residue contacts. This algorithm leverages the features of residue-residue contacts, that is, (1) a single conformation outperforms the others in the structural prediction using all the top ranking residue-residue contacts as structural constraints and (2) conformation specific contacts rank lower and constitute a small fraction of residue-residue contacts. We demonstrate the capabilities of FingerprintContacts on eight ligand binding proteins with varying conformational motions. Furthermore, FingerprintContacts identifies small clusters of residue-residue contacts which are preferentially located in the dynamically fluctuating regions. With the rapid growth in protein sequence information, we expect FingerprintContacts to be a powerful first step in structural understanding of protein functional mechanisms.

Correlation functions, mean first passage times, and the Kemeny constant

Markov processes are widely used models for investigating kinetic networks. Here, we collate and present a variety of results pertaining to kinetic network models in a unified framework. The aim is to lay out explicit links between several important quantities commonly studied in the field, including mean first passage times (MFPTs), correlation functions, and the Kemeny constant. We provide new insights into (i) a simple physical interpretation of the Kemeny constant, (ii) a relationship to infer equilibrium distributions and rate matrices from measurements of MFPTs, and (iii) a protocol to reduce the dimensionality of kinetic networks based on specific requirements that the MFPTs in the coarse-grained system should satisfy. We prove that this protocol coincides with the one proposed by Hummer and Szabo [J. Phys. Chem. B 119, 9029 (2014)], and it leads to a variational principle for the Kemeny constant. Finally, we introduce a modification of this protocol, which preserves the Kemeny constant. Our work underpinning the theoretical aspects of kinetic networks will be useful in applications including milestoning and path sampling algorithms in molecular simulations.

Adaptive Markov state model estimation using short reseeding trajectories

In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on slow time scales. A promising approach to enhanced sampling of MSMs is to use "adaptive" methods, in which new MD trajectories are "seeded" preferentially from previously identified states. Here, we investigate the performance of various MSM estimators applied to reseeding trajectory data, for both a simple 1D free energy landscape and mini-protein folding MSMs of WW domain and NTL9(1-39). Our results reveal the practical challenges of reseeding simulations and suggest a simple way to reweight seeding trajectory data to better estimate both thermodynamic and kinetic quantities.

Molecular Mechanism of Brassinosteroid Perception by the Plant Growth Receptor BRI1

Brassinosteroids (BRs) are essential phytohormones, which bind to the plant receptor, BRI1, to regulate various physiological processes. The molecular mechanism of the perception of BRs by the ectodomain of BRI1 remains not fully understood. It also remains elusive why a substantial difference in biological activity exists between the BRs. In this work, we study the binding mechanisms of the two most bioactive BRs, brassinolide (BLD) and castasterone (CAT), using molecular dynamics simulations. We report free-energy landscapes of the binding processes of both ligands, as well as detailed ligand binding pathways. Our results suggest that CAT has a lower binding affinity compared to BLD due to its inability to form hydrogen-bonding interactions with a tyrosine residue in the island domain of BRI1. We uncover a conserved nonproductive binding state for both BLD and CAT, which is more stable for CAT and may further contribute to the bioactivity difference. Finally, we validate past observations about the conformational restructuring and ordering of the island domain upon BLD binding. Overall, this study provides new insights into the fundamental mechanism of the perception of the two most bioactive BRs, which may create new avenues for genetic and agrochemical control of their signaling cascade.

Structural characterization of the PCV2d virus-like particle at 3.3 Å resolution reveals differences to PCV2a and PCV2b capsids, a tetranucleotide, and an N-terminus near the icosahedral 3-fold axes

Porcine circovirus 2 (PCV2) has a major impact on the swine industry. Eight PCV2 genotypes (a-h) have been identified using capsid sequence analysis. PCV2d has been designated as the emerging genotype. The cryo-electron microscopy molecular envelope of PCV2d virus-like particles identifies differences between PCV2a, b and d genotypes that accompany the emergence of PCV2b from PCV2a, and PCV2d from PCV2b. These differences indicate that sequence analysis of genotypes is insufficient, and that it is important to determine the PCV2 capsid structure as the virus evolves. Structure-based sequence comparison demonstrate that each genotype possesses a unique combination of amino acids located on the surface of the capsid that undergo substitution. We also demonstrate that the capsid N-terminus moves in response to increasing amount of nucleic acid packaged into the capsid. Furthermore, we model a tetranucleotide between the 5- and 2-fold axes of symmetry that appears to be responsible for capsid stability.

The dynamic conformational landscape of the protein methyltransferase SETD8

Elucidating the conformational heterogeneity of proteins is essential for understanding protein function and developing exogenous ligands. With the rapid development of experimental and computational methods, it is of great interest to integrate these approaches to illuminate the conformational landscapes of target proteins. SETD8 is a protein lysine methyltransferase (PKMT), which functions in vivo via the methylation of histone and nonhistone targets. Utilizing covalent inhibitors and depleting native ligands to trap hidden conformational states, we obtained diverse X-ray structures of SETD8. These structures were used to seed distributed atomistic molecular dynamics simulations that generated a total of six milliseconds of trajectory data. Markov state models, built via an automated machine learning approach and corroborated experimentally, reveal how slow conformational motions and conformational states are relevant to catalysis. These findings provide molecular insight on enzymatic catalysis and allosteric mechanisms of a PKMT via its detailed conformational landscape.

Our cells contain thousands of proteins that perform many different tasks. Such tasks often involve significant changes in the shape of a protein that allow it to interact with other proteins or ligands. Understanding these shape changes can be an essential step for predicting and manipulating how proteins work or designing new drugs. Some changes in protein shape happen quickly, whereas others take longer. Existing experimental approaches generally only capture some, but not all, of the different shapes an individual protein adopts.

A family of proteins known as protein lysine methyltransferases (PKMTs) help to regulate the activities of other proteins by adding small tags called methyl groups to specific positions on their target proteins. PKMTs play important roles in many life processes including in activating genes, maintaining stem cells and controlling how organs develop.

It is important for cells to properly control the activity of PKMTs because too much, or too little, activity can promote cancers and neurological diseases. For example, genetic mutations that increase the levels of a PKMT known as SETD8 appear to promote the progression of some breast cancers and childhood leukemia. There is a pressing need to develop new drugs that can inhibit SETD8 and other PKMTs in human patients. However, these efforts are hindered by the lack of understanding of exactly how the shape of PKMT proteins change as they operate in cells.

Chen, Wiewiora et al. used a technique called X-ray crystallography to generate structural models of the human SETD8 protein in the presence or absence of native or foreign ligands. These models were used to develop computer simulations of how the shape of SETD8 changes as it operates. Further computational analysis and laboratory experiments revealed how slow changes in the shape of SETD8 contribute to the ability of the protein to attach methyl groups to other proteins.

This work is a significant stepping-stone to developing a complete model of how the SETD8 protein works, as well as understanding how genetic mutations may affect the protein’s role in the body. The next step is to refine the model by integrating data from other approaches including biophysical models and mathematical calculations of the energy associated with the shape changes, with a long-term goal to better understand and then manipulate the function of SETD8.

Quantitative comparison of adaptive sampling methods for protein dynamics

Adaptive sampling methods, often used in combination with Markov state models, are becoming increasingly popular for speeding up rare events in simulation such as molecular dynamics (MD) without biasing the system dynamics. Several adaptive sampling strategies have been proposed, but it is not clear which methods perform better for different physical systems. In this work, we present a systematic evaluation of selected adaptive sampling strategies on a wide selection of fast folding proteins. The adaptive sampling strategies were emulated using models constructed on already existing MD trajectories. We provide theoretical limits for the sampling speed-up and compare the performance of different strategies with and without using some a priori knowledge of the system. The results show that for different goals, different adaptive sampling strategies are optimal. In order to sample slow dynamical processes such as protein folding without a priori knowledge of the system, a strategy based on the identification of a set of metastable regions is consistently the most efficient, while a strategy based on the identification of microstates performs better if the goal is to explore newer regions of the conformational space. Interestingly, the maximum speed-up achievable for the adaptive sampling of slow processes increases for proteins with longer folding times, encouraging the application of these methods for the characterization of slower processes, beyond the fast-folding proteins considered here.

Coevolutionary Analysis of Protein Sequences for Molecular Modeling

Thanks to the explosion of genomic sequencing, coevolutionary analysis of protein sequences has gained great and ever-increasing popularity in the last decade, and it is currently an important and well-established tool in structural bioinformatics and computational biology. This chapter concisely introduces the theoretical foundation and the practical aspects of coevolutionary analysis, as well as discusses the molecular modeling strategies to exploit its results in the study of protein structure, dynamics, and interactions. We present here a complete pipeline from sequence extraction to contact prediction through two examples, focusing on the predictions of inter-residue contacts in a single protein domain and on the analysis of a multi-domain protein that undergoes functional, large-scale conformational transitions.

SAXS-guided Enhanced Unbiased Sampling for Structure Determination of Proteins and Complexes

Molecular simulations can be utilized to predict protein structure ensembles and dynamics, though sufficient sampling of molecular ensembles and identification of key biologically relevant conformations remains challenging. Low-resolution experimental techniques provide valuable structural information on biomolecule at near-native conditions, which are often combined with molecular simulations to determine and refine protein structural ensembles. In this study, we demonstrate how small angle x-ray scattering (SAXS) information can be incorporated in Markov state model-based adaptive sampling strategy to enhance time efficiency of unbiased MD simulations and identify functionally relevant conformations of proteins and complexes. Our results show that using SAXS data combined with additional information, such as thermodynamics and distance restraints, we are able to distinguish otherwise degenerate structures due to the inherent ambiguity of SAXS pattern. We further demonstrate that adaptive sampling guided by SAXS and hybrid information can significantly reduce the computation time required to discover target structures. Overall, our findings demonstrate the potential of this hybrid approach in predicting near-native structures of proteins and complexes. Other low-resolution experimental information can be incorporated in a similar manner to collectively enhance unbiased sampling and improve the accuracy of structure prediction from simulation.