Variational cross-validation of slow dynamical modes in molecular kinetics

Atomic resolution of short-range sliding dynamics of thymine DNA glycosylase along DNA minor-groove for lesion recognition

Thymine DNA glycosylase (TDG), as a repair enzyme, plays essential roles in maintaining the genome integrity by correcting several mismatched/damaged nucleobases. TDG acquires an efficient strategy to search for the lesions among a vast number of cognate base pairs. Currently, atomic-level details of how TDG translocates along DNA as it approaches the lesion site and the molecular mechanisms of the interplay between TDG and DNA are still elusive. Here, by constructing the Markov state model based on hundreds of molecular dynamics simulations with an integrated simulation time of ∼25 μs, we reveal the rotation-coupled sliding dynamics of TDG along a 9 bp DNA segment containing one G·T mispair. We find that TDG translocates along DNA at a relatively faster rate when distant from the lesion site, but slows down as it approaches the target, accompanied by deeply penetrating into the minor-groove, opening up the mismatched base pair and significantly sculpturing the DNA shape. Moreover, the electrostatic interactions between TDG and DNA are found to be critical for mediating the TDG translocation. Notably, several uncharacterized TDG residues are identified to take part in regulating the conformational switches of TDG occurred in the site-transfer process, which warrants further experimental validations.

A critical perspective on Markov state model treatments of protein-protein association using coarse-grained simulations

Atomic-level information is essential to explain the specific interactions governing protein–protein recognition in terms of structure and dynamics. Of particular interest is a characterization of the time-dependent kinetic aspects of protein–protein association and dissociation. A powerful framework to characterize the dynamics of complex molecular systems is provided by Markov State Models (MSMs). The central idea is to construct a reduced stochastic model of the full system by defining a set of conformational featured microstates and determining the matrix of transition probabilities between them. While a MSM framework can sometimes be very effective, different combinations of input featurization and simulation methods can significantly affect the robustness and the quality of the information generated from MSMs in the context of protein association. Here, a systematic examination of a variety of MSMs methodologies is undertaken to clarify these issues. To circumvent the uncertainties caused by sampling issues, we use a simplified coarse-grained model of the barnase–barstar protein complex. A sensitivity analysis is proposed to identify the microstates of an MSM that contribute most to the error in conjunction with the transition-based reweighting analysis method for a more efficient and accurate MSM construction.

Specific PIP2 binding promotes calcium activation of TMEM16A chloride channels

TMEM16A is a widely expressed Ca²⁺-activated Cl⁻ channel that regulates crucial physiological functions including fluid secretion, neuronal excitability, and smooth muscle contraction. There is a critical need to understand the molecular mechanisms of TMEM16A gating and regulation. However, high-resolution TMEM16A structures have failed to reveal an activated state with an unobstructed permeation pathway even with saturating Ca²⁺. This has been attributed to the requirement of PIP₂ for preventing TMEM16A desensitization. Here, atomistic simulations show that specific binding of PIP₂ to TMEM16A can lead to spontaneous opening of the permeation pathway in the Ca²⁺-bound state. The predicted activated state is highly consistent with a wide range of mutagenesis and functional data. It yields a maximal Cl⁻ conductance of ~1 pS, similar to experimental estimates, and recapitulates the selectivity of larger SCN⁻ over Cl⁻. The resulting molecular mechanism of activation provides a basis for understanding the interplay of multiple signals in controlling TMEM16A channel function.

Chen and Jia investigate the synergistic regulating role of Ca²⁺ binding and the signaling lipid PIP₂ in TMEM16A channel gating. Their study is significant as it provides new insights into the activated state of TMEM16A and highlights an example of functional importance of lipids in regulating membrane-associated proteins.

An Appraisal of Computer Simulation Approaches in Elucidating Biomolecular Recognition Pathways

Computer simulation approaches in biomolecular recognition processes have come a long way. In this Perspective, we highlight a series of recent success stories in which computer simulations have played a remarkable role in elucidating the atomic resolution mechanism of kinetic processes of protein-ligand binding in a quantitative fashion. In particular, we show that a robust combination of unbiased simulation, harnessed by a high-fidelity computing environment, and Markov state modeling approaches has been instrumental in revealing novel protein-ligand recognition pathways in multiple systems. We also elucidate the role of recent developments in enhanced sampling approaches in providing the much-needed impetus in accelerating simulation of the ligand recognition process. We identify multiple key issues, including force fields and the sampling bottleneck, which are currently preventing the field from achieving quantitative reconstruction of experimental measurements. Finally, we suggest a possible way forward via adoption of multiscale approaches and coarse-grained simulations as next steps toward efficient elucidation of ligand binding kinetics.

A kinetic ensemble of the Alzheimer's Aβ peptide

The conformational and thermodynamic properties of disordered proteins are commonly described in terms of structural ensembles and free energy landscapes. To provide information on the transition rates between the different states populated by these proteins, it would be desirable to generalize this description to kinetic ensembles. Approaches based on the theory of stochastic processes can be particularly suitable for this purpose. Here, we develop a Markov state model and apply it to determine a kinetic ensemble of Aβ42, a disordered peptide associated with Alzheimer's disease. Through the Google Compute Engine, we generated 315-µs all-atom molecular dynamics trajectories. Using a probabilistic-based definition of conformational states in a neural network approach, we found that Aβ42 is characterized by inter-state transitions on the microsecond timescale, exhibiting only fully unfolded or short-lived, partially folded states. Our results illustrate how kinetic ensembles provide effective information about the structure, thermodynamics and kinetics of disordered proteins.

Markov State Models to Elucidate Ligand Binding Mechanism

Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.

Confronting pitfalls of AI-augmented molecular dynamics using statistical physics

Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.

Accelerated Estimation of Long-Timescale Kinetics from Weighted Ensemble Simulation via Non-Markovian "Microbin" Analysis

The weighted ensemble (WE) simulation strategy provides unbiased sampling of nonequilibrium processes, such as molecular folding or binding, but the extraction of rate constants relies on characterizing steady-state behavior. Unfortunately, WE simulations of sufficiently complex systems will not relax to steady state on observed simulation times. Here, we show that a postsimulation clustering of molecular configurations into "microbins" using methods developed in the Markov State Model (MSM) community can yield unbiased kinetics from WE data before steady-state convergence of the WE simulation itself. Because WE trajectories are directional and not equilibrium distributed, the history-augmented MSM (haMSM) formulation can be used, which yields the mean first-passage time (MFPT) without bias for arbitrarily small lag times. Accurate kinetics can be obtained while bypassing the often prohibitive convergence requirements of the nonequilibrium weighted ensemble. We validate the method in a simple diffusive process on a two-dimensional (2D) random energy landscape and then analyze atomistic protein folding simulations using WE molecular dynamics. We report significant progress toward the unbiased estimation of protein folding times and pathways, though key challenges remain.

Elucidating molecular mechanisms of functional conformational changes of proteins via Markov state models

Functional conformational changes of proteins can facilitate numerous biological events in cells. The Markov state model (MSM) built from molecular dynamics simulations provide a powerful approach to study them. We here introduce a protocol that is tailor-made for constructing MSMs to study the functional conformational changes of proteins. In this protocol, one of the important steps is to select proper molecular features that can collectively describe the slowest timescales of conformational changes of interest. We recommend spectral oASIS, the modified version of oASIS, as a promising approach for automatic feature selection. Recently developed deep learning methods could also serve efficient approaches for selecting features and finding collective variables. Using DNA repair enzymes and RNA polymerases as examples, we review recent applications of MSMs to elucidate molecular mechanisms of functional conformational changes. Finally, we discuss remaining challenges and future perspectives for constructing MSMs to study functional conformational changes of proteins.

Integrated Variational Approach to Conformational Dynamics: A Robust Strategy for Identifying Eigenfunctions of Dynamical Operators

One approach to analyzing the dynamics of a physical system is to search for long-lived patterns in its motions. This approach has been particularly successful for molecular dynamics data, where slowly decorrelating patterns can indicate large-scale conformational changes. Detecting such patterns is the central objective of the variational approach to conformational dynamics (VAC), as well as the related methods of time-lagged independent component analysis and Markov state modeling. In VAC, the search for slowly decorrelating patterns is formalized as a variational problem solved by the eigenfunctions of the system's transition operator. VAC computes solutions to this variational problem by optimizing a linear or nonlinear model of the eigenfunctions using time series data. Here, we build on VAC's success by addressing two practical limitations. First, VAC can give poor eigenfunction estimates when the lag time parameter is chosen poorly. Second, VAC can overfit when using flexible parametrizations such as artificial neural networks with insufficient regularization. To address these issues, we propose an extension that we call integrated VAC (IVAC). IVAC integrates over multiple lag times before solving the variational problem, making its results more robust and reproducible than VAC's.

ivis Dimensionality Reduction Framework for Biomacromolecular Simulations

Molecular dynamics (MD) simulations have been widely applied to study macromolecules including proteins. However, the high dimensionality of the data sets produced by simulations makes thorough analysis difficult and further hinders a deeper understanding of biomacromolecules. To gain more insights into the protein structure-function relations, appropriate dimensionality reduction methods are needed to project simulations onto low-dimensional spaces. Linear dimensionality reduction methods, such as principal component analysis (PCA) and time-structure-based independent component analysis (t-ICA), could not preserve sufficient structural information. Though better than linear methods, nonlinear methods, such as t-distributed stochastic neighbor embedding (t-SNE), still suffer from the limitations in avoiding system noise and keeping inter-cluster relations. ivis is a novel deep learning-based dimensionality reduction method originally developed for single-cell data sets. Here, we applied this framework for the study of light, oxygen, and voltage (LOV) domains of diatom Phaeodactylum tricornutum aureochrome 1a (PtAu1a). Compared with other methods, ivis is shown to be superior in constructing a Markov state model (MSM), preserving information of both local and global distances, and maintaining similarity between high and low dimensions with the least information loss. Moreover, the ivis framework is capable of providing new perspectives for deciphering residue-level protein allostery through the feature weights in the neural network. Overall, ivis is a promising member of the analysis toolbox for proteins.

Target search and recognition mechanisms of glycosylase AlkD revealed by scanning FRET-FCS and Markov state models

DNA glycosylase repairs DNA damage to maintain the genome integrity, and thus it is essential for the survival of all organisms. However, it remains a long-standing puzzle how glycosylase diffuses along the genomic DNA to locate the sparse and aberrant lesion sites efficiently and accurately in the genome containing numerous base pairs. Previously, only the high-speed–low-accuracy search mode has been characterized experimentally, while the low-speed–high-accuracy mode is undetectable. Here, we observed the low-speed mode of glycosylase AlkD translocating, and further dissected its molecular mechanisms. To achieve this, we developed an integrated platform by combining scanning FRET-FCS with Markov state model. We expect that this platform can be widely applied to investigate other glycosylases and DNA-binding proteins.

DNA glycosylase is responsible for repairing DNA damage to maintain the genome stability and integrity. However, how glycosylase can efficiently and accurately recognize DNA lesions across the enormous DNA genome remains elusive. It has been hypothesized that glycosylase translocates along the DNA by alternating between a fast but low-accuracy diffusion mode and a slow but high-accuracy mode when searching for DNA lesions. However, the slow mode has not been successfully characterized due to the limitation in the spatial and temporal resolutions of current experimental techniques. Using a newly developed scanning fluorescence resonance energy transfer (FRET)–fluorescence correlation spectroscopy (FCS) platform, we were able to observe both slow and fast modes of glycosylase AlkD translocating on double-stranded DNA (dsDNA), reaching the temporal resolution of microsecond and spatial resolution of subnanometer. The underlying molecular mechanism of the slow mode was further elucidated by Markov state model built from extensive all-atom molecular dynamics simulations. We found that in the slow mode, AlkD follows an asymmetric diffusion pathway, i.e., rotation followed by translation. Furthermore, the essential role of Y27 in AlkD diffusion dynamics was identified both experimentally and computationally. Our results provided mechanistic insights on how conformational dynamics of AlkD–dsDNA complex coordinate different diffusion modes to accomplish the search for DNA lesions with high efficiency and accuracy. We anticipate that the mechanism adopted by AlkD to search for DNA lesions could be a general one utilized by other glycosylases and DNA binding proteins.

Ligand-bound glutamine binding protein assumes multiple metastable binding sites with different binding affinities

Protein dynamics plays key roles in ligand binding. However, the microscopic description of conformational dynamics-coupled ligand binding remains a challenge. In this study, we integrate molecular dynamics simulations, Markov state model (MSM) analysis and experimental methods to characterize the conformational dynamics of ligand-bound glutamine binding protein (GlnBP). We show that ligand-bound GlnBP has high conformational flexibility and additional metastable binding sites, presenting a more complex energy landscape than the scenario in the absence of ligand. The diverse conformations of GlnBP demonstrate different binding affinities and entail complex transition kinetics, implicating a concerted ligand binding mechanism. Single molecule fluorescence resonance energy transfer measurements and mutagenesis experiments are performed to validate our MSM-derived structure ensemble as well as the binding mechanism. Collectively, our study provides deeper insights into the protein dynamics-coupled ligand binding, revealing an intricate regulatory network underlying the apparent binding affinity.

Zhang, Wu, Feng et al. show that ligand-bound glutamine binding protein assumes multiple metastable binding sites, presenting a more dynamic energy landscape than its ligand-free form. This study provides insights into the ligand-binding mechanisms coupled with protein dynamics that underly the apparent binding affinity.

Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator

Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.

Laplacian score and genetic algorithm based automatic feature selection for Markov State Models in adaptive sampling based molecular dynamics

Adaptive sampling molecular dynamics based on Markov State Models use short parallel MD simulations to accelerate simulations, and are proven to identify hidden conformers. The accuracy of the predictions provided by it depends on the features extracted from the simulated data that is used to construct it. The identification of the most important features in the trajectories of the simulated system has a considerable effect on the results.

Methods

In this study, we use a combination of Laplacian scoring and genetic algorithms to obtain an optimized feature subset for the construction of the MSM. The approach is validated on simulations of three protein folding complexes, and two protein ligand binding complexes.

Results

Our experiments show that this approach produces better results when the number of samples is significantly lesser than the number of features extracted. We also observed that this method mitigates over fitting that occurs due to high dimensionality of large biosystems with shorter simulation times.

How Anionic Lipids Affect Spatiotemporal Properties of KRAS4B on Model Membranes

RAS proteins are small membrane-anchored GTPases that regulate key cellular signaling networks. It has been recently shown that different anionic lipid types can affect the spatiotemporal properties of RAS through dimerization/clustering and signaling fidelity. To understand the effects of anionic lipids on key spatiotemporal properties of RAS, we dissected 1 ms of data from all-atom molecular dynamics simulations for KRAS4B on two model anionic lipid membranes that have 30% of POPS mixed with neutral POPC and 8% of PIP2 mixed with POPC. We unveiled the orientation space of KRAS4B, whose kinetics were slower and more distinguishable on the membrane containing PIP2 than the membrane containing POPS. Particularly, the PIP2-mixed membrane can differentiate a third kinetic orientation state from the other two known orientation states. We observed that each orientation state may yield different binding modes with an RAF kinase, which is required for activating the MAPK/ERK signaling pathway. However, an overall occluded probability, for which RAF kinases cannot bind KRAS4B, remains unchanged on the two different membranes. We identified rare fast diffusion modes of KRAS4B that appear coupled with orientations exposed to cytosolic RAF. Particularly, on the membrane having PIP2, we found nonlinear correlations between the orientation states and the conformations of the cationic farnesylated hypervariable region, which acts as an anchor in the membrane. Using diffusion coefficients estimated from the all-atom simulations, we quantified the effect of PIP2 and POPS on the KRAS4B dimerization via Green's function reaction dynamics simulations, in which the averaged dimerization rate is 12.5% slower on PIP2-mixed membranes.

Markov State Model of Lassa Virus Nucleoprotein Reveals Large Structural Changes during the Trimer to Monomer Transition

Lassa virus contains a nucleoprotein (NP) that encapsulates the viral genomic RNA forming the ribonucleoprotein (RNP). The NP forms trimers that do not bind RNA, but a structure of only the NP N-terminal domain was co-crystallized with RNA bound. These structures suggested a model in which the NP forms a trimer to keep the RNA gate closed, but then is triggered to undergo a change to a form competent for RNA binding. Here, we investigate the scenario in which the trimer is disrupted to observe whether monomeric NP undergoes significant conformational changes. From multi-microsecond molecular dynamics simulations and an adaptive sampling scheme to sample the conformational space, a Markov state model (MSM) is constructed. The MSM reveals an energetically favorable conformational change, with the most significant changes occurring at the domain interface. These results support a model in which significant structural reorganization of the NP is required for RNP formation.

Fragment Pose Prediction Using Non-equilibrium Candidate Monte Carlo and Molecular Dynamics Simulations

Part of early stage drug discovery involves determining how molecules may bind to the target protein. Through understanding where and how molecules bind, chemists can begin to build ideas on how to design improvements to increase binding affinities. In this retrospective study, we compare how computational approaches like docking, molecular dynamics (MD) simulations, and a non-equilibrium candidate Monte Carlo (NCMC)-based method (NCMC + MD) perform in predicting binding modes for a set of 12 fragment-like molecules, which bind to soluble epoxide hydrolase. We evaluate each method's effectiveness in identifying the dominant binding mode and finding additional binding modes (if any). Then, we compare our predicted binding modes to experimentally obtained X-ray crystal structures. We dock each of the 12 small molecules into the apo-protein crystal structure and then run simulations up to 1 μs each. Small and fragment-like molecules likely have smaller energy barriers separating different binding modes by virtue of relatively fewer and weaker interactions relative to drug-like molecules and thus likely undergo more rapid binding mode transitions. We expect, thus, to see more rapid transitions between binding modes in our study. Following this, we build Markov State Models to define our stable ligand binding modes. We investigate if adequate sampling of ligand binding modes and transitions between them can occur at the microsecond timescale using traditional MD or a hybrid NCMC+MD simulation approach. Our findings suggest that even with small fragment-like molecules, we fail to sample all the crystallographic binding modes using microsecond MD simulations, but using NCMC+MD, we have better success in sampling the crystal structure while obtaining the correct populations.

Structural insights into tetraspanin CD9 function

Tetraspanins play critical roles in various physiological processes, ranging from cell adhesion to virus infection. The members of the tetraspanin family have four membrane-spanning domains and short and large extracellular loops, and associate with a broad range of other functional proteins to exert cellular functions. Here we report the crystal structure of CD9 and the cryo-electron microscopic structure of CD9 in complex with its single membrane-spanning partner protein, EWI-2. The reversed cone-like molecular shape of CD9 generates membrane curvature in the crystalline lipid layers, which explains the CD9 localization in regions with high membrane curvature and its implications in membrane remodeling. The molecular interaction between CD9 and EWI-2 is mainly mediated through the small residues in the transmembrane region and protein/lipid interactions, whereas the fertilization assay revealed the critical involvement of the LEL region in the sperm-egg fusion, indicating the different dependency of each binding domain for other partner proteins.

Tetraspanins play critical roles in various physiological processes, ranging from cell adhesion to virus infection. Here authors report the crystal structure of CD9 and the cryo-electron microscopic structure of CD9 in complex with its single membrane-spanning partner protein, EWI-2.

Machine Learning for Molecular Simulation

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.

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.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.

Molecular Basis of the Glucose Transport Mechanism in Plants

The SWEET family belongs to a class of transporters in plants that undergoes large conformational changes to facilitate transport of sugar molecules across the cell membrane (SWEET, Sugars Will Eventually Be Exported Transporter). However, the structures of their functionally relevant conformational states in the transport cycle have not been reported. In this study, we have characterized the conformational dynamics and complete transport cycle of glucose in the OsSWEET2b transporter using extensive molecular dynamics simulations. Using Markov state models, we estimated the free energy barrier associated with different states as well as for the glucose transport mechanism. SWEETs undergo a structural transition to outward-facing (OF), occluded (OC), and inward-facing (IF) and strongly support an alternate access transport mechanism. The glucose diffuses freely from outside to inside the cell without causing major conformational changes which means that the conformations of glucose unbound and bound snapshots are exactly the same for OF, OC, and IF states. We identified a network of hydrophobic core residues at the center of the transporter that restricts the glucose entry to the cytoplasmic side and acts as an intracellular hydrophobic gate. The mechanistic predictions from molecular dynamics simulations are validated using site-directed mutagenesis experiments. Our simulation also revealed hourglass-like intermediate states making the pore radius narrower at the center. This work provides new fundamental insights into how substrate-transporter interactions actively change the free energy landscape of the transport cycle to facilitate enhanced transport activity.

Structural basis for the homotypic fusion of chlamydial inclusions by the SNARE-like protein IncA

Many intracellular bacteria, including Chlamydia, establish a parasitic membrane-bound organelle inside the host cell that is essential for the bacteria’s survival. Chlamydia trachomatis forms inclusions that are decorated with poorly characterized membrane proteins known as Incs. The prototypical Inc, called IncA, enhances Chlamydia pathogenicity by promoting the homotypic fusion of inclusions and shares structural and functional similarity to eukaryotic SNAREs. Here, we present the atomic structure of the cytoplasmic domain of IncA, which reveals a non-canonical four-helix bundle. Structure-based mutagenesis, molecular dynamics simulation, and functional cellular assays identify an intramolecular clamp that is essential for IncA-mediated homotypic membrane fusion during infection.

Chlamydia trachomatis forms membrane-bound inclusions inside the host cell that are decorated with IncA, a SNARE-like protein that promotes the fusion of inclusions. Here, Cingolani et al. show that the protein folds into a non-canonical four-helix bundle and identify an intramolecular clamp required for membrane fusion.

Variational selection of features for molecular kinetics

The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long time-scale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of 12 fast-folding protein simulations and show that our procedure leads to more efficient model selection.

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.

Identification of kinetic order parameters for non-equilibrium dynamics

A popular approach to analyze the dynamics of high-dimensional many-body systems, such as macromolecules, is to project the trajectories onto a space of slowly varying collective variables, where subsequent analyses are made, such as clustering or estimation of free energy profiles or Markov state models. However, existing "dynamical" dimension reduction methods, such as the time-lagged independent component analysis (TICA), are only valid if the dynamics obeys detailed balance (microscopic reversibility) and typically require long, equilibrated simulation trajectories. Here, we develop a dimension reduction method for non-equilibrium dynamics based on the recently developed Variational Approach for Markov Processes (VAMP) by Wu and Noé. VAMP is illustrated by obtaining a low-dimensional description of a single file ion diffusion model and by identifying long-lived states from molecular dynamics simulations of the KcsA channel protein in an external electrochemical potential. This analysis provides detailed insights into the coupling of conformational dynamics, the configuration of the selectivity filter, and the conductance of the channel. We recommend VAMP as a replacement for the less general TICA method.

On the removal of initial state bias from simulation data

Classical atomistic simulations of biomolecules play an increasingly important role in molecular life science. The structure of current computing architectures favors methods that run multiple trajectories at once without requiring extensive communication between them. Many advanced sampling strategies in the field fit this mold. These approaches often rely on an adaptive logic and create ensembles of comparatively short trajectories whose starting points are not distributed according to the correct Boltzmann weights. This type of bias is notoriously difficult to remove, and Markov state models (MSMs) are one of the few strategies available for recovering the correct kinetics and thermodynamics from these ensembles of trajectories. In this contribution, we analyze the performance of MSMs in the thermodynamic reweighting task for a hierarchical set of systems. We show that MSMs can be rigorous tools to recover the correct equilibrium distribution for systems of sufficiently low dimensionality. This is conditional upon not tampering with local flux imbalances found in the data. For a real-world application, we find that a pure likelihood-based inference of the transition matrix produces the best results. The removal of the bias is incomplete, however, and for this system, all tested MSMs are outperformed by an alternative albeit less general approach rooted in the ideas of statistical resampling. We conclude by formulating some recommendations for how to address the reweighting issue in practice.

Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study

One of the fundamental events in protein folding is α-helix formation, which involves sequential development of a series of helical hydrogen bonds between the backbone C═O group of residues i and the -NH group of residues i + 4. While we now know a great deal about α-helix folding dynamics, a key question that remains to be answered is where the productive helical nucleation event occurs. Statistically, a helical nucleus (or the first helical hydrogen-bond) can form anywhere within the peptide sequence in question; however, the one that leads to productive folding may only form at a preferred location. This consideration is based on the fact that the α-helical structure is inherently asymmetric, due to the specific alignment of the helical hydrogen bonds. While this hypothesis is plausible, validating it is challenging because there is not an experimental observable that can be used to directly pinpoint the location of the productive nucleation process. Therefore, in this study we combine several techniques, including peptide cross-linking, laser-induced temperature-jump infrared spectroscopy, and molecular dynamics simulations, to tackle this challenge. Taken together, our experimental and simulation results support an α-helix folding mechanism wherein the productive nucleus is formed at the N-terminus, which propagates toward the C-terminal end of the peptide to yield the folded structure. In addition, our results show that incorporation of a cross-linker can lead to formation of differently folded conformations, underscoring the need for all-atom simulations to quantitatively assess the proposed cross-linking design.

Note: Variational encoding of protein dynamics benefits from maximizing latent autocorrelation

As deep Variational Auto-Encoder (VAE) frameworks become more widely used for modeling biomolecular simulation data, we emphasize the capability of the VAE architecture to concurrently maximize the time scale of the latent space while inferring a reduced coordinate, which assists in finding slow processes as according to the variational approach to conformational dynamics. We provide evidence that the VDE framework [Hernández et al., Phys. Rev. E 97, 062412 (2018)], which uses this autocorrelation loss along with a time-lagged reconstruction loss, obtains a variationally optimized latent coordinate in comparison with related loss functions. We thus recommend leveraging the autocorrelation of the latent space while training neural network models of biomolecular simulation data to better represent slow processes.

Simulations of the regulatory ACT domain of human phenylalanine hydroxylase (PAH) unveil its mechanism of phenylalanine binding

Phenylalanine hydroxylase (PAH) regulates phenylalanine (Phe) levels in mammals to prevent neurotoxicity resulting from high Phe concentrations as observed in genetic disorders leading to hyperphenylalaninemia and phenylketonuria. PAH senses elevated Phe concentrations by transient allosteric Phe binding to a protein-protein interface between ACT domains of different subunits in a PAH tetramer. This interface is present in an activated PAH (A-PAH) tetramer and absent in a resting-state PAH (RS-PAH) tetramer. To investigate this allosteric sensing mechanism, here we used the GROMACS molecular dynamics simulation suite on the Folding@home computing platform to perform extensive molecular simulations and Markov state model (MSM) analysis of Phe binding to ACT domain dimers. These simulations strongly implicated a conformational selection mechanism for Phe association with ACT domain dimers and revealed protein motions that act as a gating mechanism for Phe binding. The MSMs also illuminate a highly mobile hairpin loop, consistent with experimental findings also presented here that the PAH variant L72W does not shift the PAH structural equilibrium toward the activated state. Finally, simulations of ACT domain monomers are presented, in which spontaneous transitions between resting-state and activated conformations are observed, also consistent with a mechanism of conformational selection. These mechanistic details provide detailed insight into the regulation of PAH activation and provide testable hypotheses for the development of new allosteric effectors to correct structural and functional defects in PAH.

Free Energy Landscape of the Complete Transport Cycle in a Key Bacterial Transporter

PepT_So is a proton-coupled bacterial symporter, from the major facilitator superfamily (MFS), which transports di-/tripeptide molecules. The recently obtained crystal structure of PepT_So provides an unprecedented opportunity to gain an understanding of functional insights of the substrate transport mechanism. Binding of the proton and peptide molecule induces conformational changes into occluded (OC) and outward-facing (OF) states, which we are able to characterize using molecular dynamics (MD) simulations. The structural knowledge of the OC and OF state is important to fully understand the major energy barrier associated with the transport cycle. In order to gain functional insight into the interstate dynamics, we performed extensive all atom MD simulations. The Markov state model was constructed to identify the free energy barriers between the states, and kinetic information on intermediate pathways was obtained using the transition pathway theory (TPT). TPT shows that the OF state is obtained by the movement of TM1 and TM7 at the extracellular side approximately 12-16 Å away from each other, and the inward movement of TM4 and TM10 at the intracellular halves to 3-4 Å characterizes the OC state. Helix distance distributions obtained from MD simulations were compared with experimental double electron-electron resonance spectroscopy and were found to be in excellent agreement with previous studies. We also predicted the optimal positions for placement of methane thiosulfonate spin label probes to capture the slowest protein dynamics. Our finding sheds light on the conformational cycle of this key membrane transporter and the functional relationships between the multiple intermediate states.

Assessment and optimization of collective variables for protein conformational landscape: GB1 β-hairpin as a case study

Collective variables (CVs), when chosen judiciously, can play an important role in recognizing rate-limiting processes and rare events in any biomolecular systems. However, high dimensionality and inherent complexities associated with such biochemical systems render the identification of an optimal CV a challenging task, which in turn precludes the elucidation of an underlying conformational landscape in sufficient details. In this context, a relevant model system is presented by a 16-residue β-hairpin of GB1 protein. Despite being the target of numerous theoretical and computational studies for understanding the protein folding, the set of CVs optimally characterizing the conformational landscape of the β-hairpin of GB1 protein has remained elusive, resulting in a lack of consensus on its folding mechanism. Here we address this by proposing a pair of optimal CVs which can resolve the underlying free energy landscape of the GB1 hairpin quite efficiently. Expressed as a linear combination of a number of traditional CVs, the optimal CV for this system is derived by employing the recently introduced time-structured independent component analysis approach on a large number of independent unbiased simulations. By projecting the replica-exchange simulated trajectories along these pair of optimized CVs, the resulting free energy landscape of this system is able to resolve four distinct well-separated metastable states encompassing the extensive ensembles of folded, unfolded, and molten globule states. Importantly, the optimized CVs were found to be capable of automatically recovering a novel partial helical state of this protein, without needing to explicitly invoke helicity as a constituent CV. Furthermore, a quantitative sensitivity analysis of each constituent in the optimized CV provided key insights on the relative contributions of the constituent CVs in the overall free energy landscapes. Finally, the kinetic pathways connecting these metastable states, constructed using a Markov state model, provide an optimum description of the underlying folding mechanism of the peptide. Taken together, this work offers a quantitatively robust approach toward comprehensive mapping of the underlying folding landscape of a quintessential model system along its optimized CV.

Elucidating the inhibition of peptidoglycan biosynthesis in Staphylococcus aureus by albocycline, a macrolactone isolated from Streptomyces maizeus

Antibiotic resistance is a serious threat to global public health, and methicillin-resistant Staphylococcus aureus (MRSA) is a poignant example. The macrolactone natural product albocycline, derived from various Streptomyces strains, was recently identified as a promising antibiotic candidate for the treatment of both MRSA and vancomycin-resistant S. aureus (VRSA), which is another clinically relevant and antibiotic resistant strain. Moreover, it was hypothesized that albocycline's antimicrobial activity was derived from the inhibition of peptidoglycan (i.e., bacterial cell wall) biosynthesis. Herein, preliminary mechanistic studies are performed to test the hypothesis that albocycline inhibits MurA, the enzyme that catalyzes the first step of peptidoglycan biosynthesis, using a combination of biological assays alongside molecular modeling and simulation studies. Computational modeling suggests albocycline exists as two conformations in solution, and computational docking of these conformations to an ensemble of simulated receptor structures correctly predicted preferential binding to S. aureus MurA-the enzyme that catalyzes the first step of peptidoglycan biosynthesis-over Escherichia coli (E. coli) MurA. Albocycline isolated from the producing organism (Streptomyces maizeus) weakly inhibited S. aureus MurA (IC50 of 480 μM) but did not inhibit E. coli MurA. The antimicrobial activity of albocycline against resistant S. aureus strains was superior to that of vancomycin, preferentially inhibiting Gram-positive organisms. Albocycline was not toxic to human HepG2 cells in MTT assays. While these studies demonstrate that albocycline is a promising lead candidate against resistant S. aureus, taken together they suggest that MurA is not the primary target, and further work is necessary to identify the major biological target.

Variational encoding of complex dynamics

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.

Towards simple kinetic models of functional dynamics for a kinase subfamily

Kinases are ubiquitous enzymes involved in the regulation of critical cellular pathways. However, in silico modelling of the conformational ensembles of these enzymes is difficult due to inherent limitations and the cost of computational approaches. Recent algorithmic advances combined with homology modelling and parallel simulations have enabled researchers to address this computational sampling bottleneck. Here, we present the results of molecular dynamics studies for seven Src family kinase (SFK) members: Fyn, Lyn, Lck, Hck, Fgr, Yes and Blk. We present a sequence invariant extension to Markov state models, which allows us to quantitatively compare the structural ensembles of the seven kinases. Our findings indicate that in the absence of their regulatory partners, SFK members have similar in silico dynamics with active state populations ranging from 4 to 40% and activation timescales in the hundreds of microseconds. Furthermore, we observe several potentially druggable intermediate states, including a pocket next to the adenosine triphosphate binding site that could potentially be targeted via a small-molecule inhibitor.

Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes-beyond the capabilities of linear dimension reduction techniques.

Computer Simulations Predict High Structural Heterogeneity of Functional State of NMDA Receptors

N-methyl-D-aspartate receptors (NMDARs)-i.e., transmembrane proteins expressed in neurons-play a central role in the molecular mechanisms of learning and memory formation. It is unclear how the known atomic structures of NMDARs determined by x-ray crystallography and electron cryomicroscopy (18 published Protein Data Bank entries) relate to the functional states of NMDARs inferred from electrophysiological recordings (multiple closed, open, preopen, etc. states). We address this problem by using molecular dynamics simulations at atomic resolution, a method successfully applied in the past to much smaller biomolecules. Our simulations predict that several conformations of NMDARs with experimentally determined geometries, including four "nonactive" electron cryomicroscopy structures, rapidly interconvert on submicrosecond timescales and therefore may correspond to the same functional state of the receptor (specifically, one of the closed states). This conclusion is not trivial because these conformational transitions involve changes in certain interatomic distances as large as tens of Å. The simulations also predict differences in the conformational dynamics of the apo and holo (i.e., agonist and coagonist bound) forms of the receptor on the microsecond timescale. To our knowledge, five new conformations of NMDARs, with geometries joining various features from different known experimental structures, are also predicted by the model. The main limitation of this work stems from its limited sampling (30 μs of aggregate length of molecular dynamics trajectories). Though this level significantly exceeds the sampling in previous simulations of parts of NMDARs, it is still much lower than the sampling recently achieved for smaller biomolecules (up to a few milliseconds), thus precluding, in particular, the observation of transitions between different functional states of NMDARs. Despite this limitation, such computational predictions may guide further experimental studies on the structure, dynamics, and function of NMDARs, for example by suggesting optimal locations of spectroscopic probes. Overall, atomic resolution simulations provide, to our knowledge, a novel perspective on the structure and dynamics of NMDARs, complementing information obtained by experimental methods.

Note: MSM lag time cannot be used for variational model selection

The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note, we discuss why the lag time of the operator being approximated must be held constant in the variational approach.