Rapid equilibrium sampling initiated from nonequilibrium data

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.

An encompassed representation of timescale hierarchies in first-order reaction network

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.

Understanding the Fast-Triggering Unfolding Dynamics of FK-11 upon Photoexcitation of Azobenzene

Photoswitchable molecules can control the activity and functions of biomolecules by triggering conformational changes. However, it is still challenging to fully understand such fast-triggering conformational evolution from nonequilibrium to equilibrium distribution at the molecular level. Herein, we successfully simulated the unfolding of the FK-11 peptide upon the photoinduced trans-to-cis isomerization of azobenzene based on the Markov state model. We found that the ensemble of FK-11 contains five conformational states, constituting two unfolding pathways. More intriguingly, we observed the microsecond-scale conformational propagation of the FK-11 peptide from the fully folded state to the equilibrium populations of the five states. The computed CD spectra match well with the experimental data, validating our simulation method. Overall, our study not only offers a protocol to study the photoisomerization-induced conformational changes of enzymes but also could orientate the rational design of a photoswitchable molecule to manipulate biological functions.

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

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

PopShift: A Thermodynamically Sound Approach to Estimate Binding Free Energies by Accounting for Ligand-Induced Population Shifts from a Ligand-Free Markov State Model

Obtaining accurate binding free energies from in silico screens has been a long-standing goal for the computational chemistry community. However, accuracy and computational cost are at odds with one another, limiting the utility of methods that perform this type of calculation. Many methods achieve massive scale by explicitly or implicitly assuming that the target protein adopts a single structure, or undergoes limited fluctuations around that structure, to minimize computational cost. Others simulate each protein-ligand complex of interest, accepting lower throughput in exchange for better predictions of binding affinities. Here, we present the PopShift framework for accounting for the ensemble of structures a protein adopts and their relative probabilities. Protein degrees of freedom are enumerated once, and then arbitrarily many molecules can be screened against this ensemble. Specifically, we use Markov state models (MSMs) as a compressed representation of a protein's thermodynamic ensemble. We start with a ligand-free MSM and then calculate how addition of a ligand shifts the populations of each protein conformational state based on the strength of the interaction between that protein conformation and the ligand. In this work we use docking to estimate the affinity between a given protein structure and ligand, but any estimator of binding affinities could be used in the PopShift framework. We test PopShift on the classic benchmark pocket T4 Lysozyme L99A. We find that PopShift is more accurate than common strategies, such as docking to a single structure and traditional ensemble docking─producing results that compare favorably with alchemical binding free energy calculations in terms of RMSE but not correlation─and may have a more favorable computational cost profile in some applications. In addition to predicting binding free energies and ligand poses, PopShift also provides insight into how the probability of different protein structures is shifted upon addition of various concentrations of ligand, providing a platform for predicting affinities and allosteric effects of ligand binding. Therefore, we expect PopShift will be valuable for hit finding and for providing insight into phenomena like allostery.

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.

Integrative generalized master equation: A method to study long-timescale biomolecular dynamics via the integrals of memory kernels

The generalized master equation (GME) provides a powerful approach to study biomolecular dynamics via non-Markovian dynamic models built from molecular dynamics (MD) simulations. Previously, we have implemented the GME, namely the quasi Markov State Model (qMSM), where we explicitly calculate the memory kernel and propagate dynamics using a discretized GME. qMSM can be constructed with much shorter MD trajectories than the MSM. However, since qMSM needs to explicitly compute the time-dependent memory kernels, it is heavily affected by the numerical fluctuations of simulation data when applied to study biomolecular conformational changes. This can lead to numerical instability of predicted long-time dynamics, greatly limiting the applicability of qMSM in complicated biomolecules. We present a new method, the Integrative GME (IGME), in which we analytically solve the GME under the condition when the memory kernels have decayed to zero. Our IGME overcomes the challenges of the qMSM by using the time integrations of memory kernels, thereby avoiding the numerical instability caused by explicit computation of time-dependent memory kernels. Using our solutions of the GME, we have developed a new approach to compute long-time dynamics based on MD simulations in a numerically stable, accurate and efficient way. To demonstrate its effectiveness, we have applied the IGME in three biomolecules: the alanine dipeptide, FIP35 WW-domain, and Taq RNA polymerase. In each system, the IGME achieves significantly smaller fluctuations for both memory kernels and long-time dynamics compared to the qMSM. We anticipate that the IGME can be widely applied to investigate biomolecular conformational changes.

Pathways of hLL-3717-29 Aggregation Give Insight into the Mechanism of α-Amyloid Formation

α-amyloids present a novel self-assembly principle that can be utilized to prepare functional biomaterials. Evidence of α-amyloid formation in the active core of the human LL-37 protein (comprising residues 17 to 29) was associated with this peptide's membranolytic property. Though mechanistic pathways of β-amyloid formation are known, such studies are scarce in α-amyloids. Modern computational techniques allow such mechanistic studies in molecular detail. Here, we propose aggregation pathways in hLL-3717-29 through molecular dynamics simulations. We first identified oligomers among peptides based on a distance criterion. The distribution of oligomers was then used to build Markov state models from which pathways were obtained using the framework of transition path theory. We checked the structural stability of the peptides during oligomerization, which is crucial from their functional point of view. We also investigated the key residues that participate in oligomer formation, the interactions between them, and the effect of residue mutations on the binding free energy of the peptides. Our findings suggest that larger oligomers are produced from the association of smaller and intermediate oligomers. The peptides retain their helical structure during aggregation with transient occurrences of 3-10 helix and turns. Hydrophobic interactions are vital in the aggregation of these peptides with Ile24 playing a crucial role. Mutation of this residue to alanine decreases the peptides' binding free energy, resulting in reduced aggregation tendency.

Folding@home: Achievements from over 20 years of citizen science herald the exascale era

Simulations of biomolecules have enormous potential to inform our understanding of biology but require extremely demanding calculations. For over 20 years, the Folding@home distributed computing project has pioneered a massively parallel approach to biomolecular simulation, harnessing the resources of citizen scientists across the globe. Here, we summarize the scientific and technical advances this perspective has enabled. As the project's name implies, the early years of Folding@home focused on driving advances in our understanding of protein folding by developing statistical methods for capturing long-timescale processes and facilitating insight into complex dynamical processes. Success laid a foundation for broadening the scope of Folding@home to address other functionally relevant conformational changes, such as receptor signaling, enzyme dynamics, and ligand binding. Continued algorithmic advances, hardware developments such as graphics processing unit (GPU)-based computing, and the growing scale of Folding@home have enabled the project to focus on new areas where massively parallel sampling can be impactful. While previous work sought to expand toward larger proteins with slower conformational changes, new work focuses on large-scale comparative studies of different protein sequences and chemical compounds to better understand biology and inform the development of small-molecule drugs. Progress on these fronts enabled the community to pivot quickly in response to the COVID-19 pandemic, expanding to become the world's first exascale computer and deploying this massive resource to provide insight into the inner workings of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus and aid the development of new antivirals. This success provides a glimpse of what is to come as exascale supercomputers come online and as Folding@home continues its work.

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

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

Memory Unlocks the Future of Biomolecular Dynamics: Transformative Tools to Uncover Physical Insights Accurately and Efficiently

Conformational changes underpin function and encode complex biomolecular mechanisms. Gaining atomic-level detail of how such changes occur has the potential to reveal these mechanisms and is of critical importance in identifying drug targets, facilitating rational drug design, and enabling bioengineering applications. While the past two decades have brought Markov state model techniques to the point where practitioners can regularly use them to glimpse the long-time dynamics of slow conformations in complex systems, many systems are still beyond their reach. In this Perspective, we discuss how including memory (i.e., non-Markovian effects) can reduce the computational cost to predict the long-time dynamics in these complex systems by orders of magnitude and with greater accuracy and resolution than state-of-the-art Markov state models. We illustrate how memory lies at the heart of successful and promising techniques, ranging from the Fokker-Planck and generalized Langevin equations to deep-learning recurrent neural networks and generalized master equations. We delineate how these techniques work, identify insights that they can offer in biomolecular systems, and discuss their advantages and disadvantages in practical settings. We show how generalized master equations can enable the investigation of, for example, the gate-opening process in RNA polymerase II and demonstrate how our recent advances tame the deleterious influence of statistical underconvergence of the molecular dynamics simulations used to parameterize these techniques. This represents a significant leap forward that will enable our memory-based techniques to interrogate systems that are currently beyond the reach of even the best Markov state models. We conclude by discussing some current challenges and future prospects for how exploiting memory will open the door to many exciting opportunities.

Building insightful, memory-enriched models to capture long-time biochemical processes from short-time simulations

The ability to predict and understand complex molecular motions occurring over diverse timescales ranging from picoseconds to seconds and even hours in biological systems remains one of the largest challenges to chemical theory. Markov state models (MSMs), which provide a memoryless description of the transitions between different states of a biochemical system, have provided numerous important physically transparent insights into biological function. However, constructing these models often necessitates performing extremely long molecular simulations to converge the rates. Here, we show that by incorporating memory via the time-convolutionless generalized master equation (TCL-GME) one can build a theoretically transparent and physically intuitive memory-enriched model of biochemical processes with up to a three order of magnitude reduction in the simulation data required while also providing a higher temporal resolution. We derive the conditions under which the TCL-GME provides a more efficient means to capture slow dynamics than MSMs and rigorously prove when the two provide equally valid and efficient descriptions of the slow configurational dynamics. We further introduce a simple averaging procedure that enables our TCL-GME approach to quickly converge and accurately predict long-time dynamics even when parameterized with noisy reference data arising from short trajectories. We illustrate the advantages of the TCL-GME using alanine dipeptide, the human argonaute complex, and FiP35 WW domain.

Nucleotide addition and cleavage by RNA polymerase II: Coordination of two catalytic reactions using a single active site

RNA polymerase II (Pol II) incorporates complementary ribonucleotides into the growing RNA chain one at a time via the nucleotide addition cycle. The nucleotide addition cycle, however, is prone to misincorporation of noncomplementary nucleotides. Thus, to ensure transcriptional fidelity, Pol II backtracks and then cleaves the misincorporated nucleotides. These two reverse reactions, nucleotide addition and cleavage, are catalyzed in the same active site of Pol II, which is different from DNA polymerases or other endonucleases. Recently, substantial progress has been made to understand how Pol II effectively performs its dual role in the same active site. Our review highlights these recent studies and provides an overall model of the catalytic mechanisms of Pol II. In particular, RNA extension follows the two-metal-ion mechanism, and several Pol II residues play important roles to facilitate the catalysis. In sharp contrast, the cleavage reaction is independent of any Pol II residues. Interestingly, Pol II relies on its residues to recognize the misincorporated nucleotides during the backtracking process, prior to cleavage. In this way, Pol II efficiently compartmentalizes its two distinct catalytic functions using the same active site. Lastly, we also discuss a new perspective on the potential third Mg²⁺ in the nucleotide addition and intrinsic cleavage reactions.

Computational investigations on target-site searching and recognition mechanisms by thymine DNA glycosylase during DNA repair process

DNA glycosylase, as one member of DNA repair machineries, plays an essential role in correcting mismatched/damaged DNA nucleotides by cleaving the N-glycosidic bond between the sugar and target nucleobase through the base excision repair (BER) pathways. Efficient corrections of these DNA lesions are critical for maintaining genome integrity and preventing premature aging and cancers. The target-site searching/recognition mechanisms and the subsequent conformational dynamics of DNA glycosylase, however, remain challenging to be characterized using experimental techniques. In this review, we summarize our recent studies of sequential structural changes of thymine DNA glycosylase (TDG) during the DNA repair process, achieved mostly by molecular dynamics (MD) simulations. Computational simulations allow us to reveal atomic-level structural dynamics of TDG as it approaches the target-site, and pinpoint the key structural elements responsible for regulating the translocation of TDG along DNA. Subsequently, upon locating the lesions, TDG adopts a base-flipping mechanism to extrude the mispaired nucleobase into the enzyme active-site. The constructed kinetic network model elucidates six metastable states during the base-extrusion process and suggests an active role of TDG in flipping the intrahelical nucleobase. Finally, the molecular mechanism of product release dynamics after catalysis is also summarized. Taken together, we highlight to what extent the computational simulations advance our knowledge and understanding of the molecular mechanism underlying the conformational dynamics of TDG, as well as the limitations of current theoretical work.

Early aggregation mechanism of Aβ16-22 revealed by Markov state models

Aβ_16-22 is believed to have critical role in early aggregation of full length amyloids that are associated with the Alzheimer's disease and can aggregate to form amyloid fibrils. However, the early aggregation mechanism is still unsolved. Here, multiple long-term molecular dynamics simulations combining with Markov state model were used to probe the early oligomerization mechanism of Aβ_16-22 peptides. The identified dimeric form adopted either globular random-coil or extended β-strand like conformations. The observed dimers of these variants shared many overall conformational characteristics but differed in several aspects at detailed level. In all cases, the most common type of secondary structure was intermolecular antiparallel β-sheets. The inter-state transitions were very frequent ranges from few to hundred nanoseconds. More strikingly, those states which contain fraction of β secondary structure and significant amount of extended coiled structures, therefore exposed to the solvent, were majorly participated in aggregation. The assembly of low-energy dimers, in which the peptides form antiparallel β sheets, occurred by multiple pathways with the formation of an obligatory intermediates. We proposed that these states might facilitate the Aβ_16-22 aggregation through a significant component of the conformational selection mechanism, because they might increase the aggregates population by promoting the inter-chain hydrophobic and the hydrogen bond contacts. The formation of early stage antiparallel β sheet structures is critical for oligomerization, and at the same time provided a flat geometry to seed the ordered β-strand packing of the fibrils. Our findings hint at reorganization of this part of the molecule as a potentially critical step in Aβ aggregation and will insight into early oligomerization for large β amyloids.

RPnet: a reverse-projection-based neural network for coarse-graining metastable conformational states for protein dynamics

The Markov State Model (MSM) is a powerful tool for modeling long timescale dynamics based on numerous short molecular dynamics (MD) simulation trajectories, which makes it a useful tool for elucidating the conformational changes of biological macromolecules. By partitioning the phase space into discretized states and estimating the probabilities of inter-state transitions based on short MD trajectories, one can construct a kinetic network model that could be used to extrapolate long-timescale kinetics if the Markovian condition is met. However, meeting the Markovian condition often requires hundreds or even thousands of states (microstates), which greatly hinders the comprehension of the conformational dynamics of complex biomolecules. Kinetic lumping algorithms can coarse grain numerous microstates into a handful of metastable states (macrostates), which would greatly facilitate the elucidation of biological mechanisms. In this work, we have developed a reverse-projection-based neural network (RPnet) to lump microstates into macrostates, by making use of a physics-based loss function that is based on the projection operator framework of conformational dynamics. By recognizing that microstate and macrostate transition modes can be related through a projection process, we have developed a reverse-projection scheme to directly compare the microstate and macrostate dynamics. Based on this reverse-projection scheme, we designed a loss function that allows the effective assessment of the quality of a given kinetic lumping. We then make use of a neural network to efficiently minimize this loss function to obtain an optimized set of macrostates. We have demonstrated the power of our RPnet in analyzing the dynamics of a numerical 2D potential, alanine dipeptide, and the clamp opening of an RNA polymerase. In all these systems, we have illustrated that our method could yield comparable or better results than competing methods in terms of state partitioning and reproduction of slow dynamics. We expect that our RPnet holds promise in analyzing the conformational dynamics of biological macromolecules.

Theoretical Study of Macrocyclic Host Molecules: From Supramolecular Recognition to Self-Assembly

Supramolecular chemistry focuses on molecular recognition and self-assembly of various building blocks through weak non-covalent interactions, including anion-π, hydrogen bond (HB), hydrophobic interactions, van der Waals (vdW) interactions, etc, which...

Critical role of backbone coordination in the mRNA recognition by RNA induced silencing complex

Despite its functional importance, the molecular mechanism underlying target mRNA recognition by Argonaute (Ago) remains largely elusive. Based on extensive all-atom molecular dynamics simulations, we constructed quasi-Markov State Model (qMSM) to reveal the dynamics during recognition at position 6-7 in the seed region of human Argonaute 2 (hAgo2). Interestingly, we found that the slowest mode of motion therein is not the gRNA-target base-pairing, but the coordination of the target phosphate groups with a set of positively charged residues of hAgo2. Moreover, the ability of Helix-7 to approach the PIWI and MID domains was found to reduce the effective volume accessible to the target mRNA and therefore facilitate both the backbone coordination and base-pair formation. Further mutant simulations revealed that alanine mutation of the D358 residue on Helix-7 enhanced a trap state to slow down the loading of target mRNA. Similar trap state was also observed when wobble pairs were introduced in g6 and g7, indicating the role of Helix-7 in suppressing non-canonical base-paring. Our study pointed to a general mechanism for mRNA recognition by eukaryotic Agos and demonstrated the promise of qMSM in investigating complex conformational changes of biomolecular systems.

Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning

Markov state models (MSMs) based on molecular dynamics (MD) simulations are routinely employed to study protein folding, however, their application to functional conformational changes of biomolecules is still limited. In the past few years, the field of computational chemistry has experienced a surge of advancements stemming from machine learning algorithms, and MSMs have not been left out. Unlike global processes, such as protein folding, the application of MSMs to functional conformational changes is challenging because they mostly consist of localized structural transitions. Therefore, it is critical to properly select a subset of structural features that can describe the slowest dynamics of these functional conformational changes. To address this challenge, we recommend several automatic feature selection methods such as Spectral-OASIS. To identify states in MSMs, the chosen features can be subject to dimensionality reduction methods such as TICA or deep learning based VAMPNets to project MD conformations onto a few collective variables for subsequent clustering. Another challenge for the application of MSMs to the study of functional conformational changes is the ability to comprehend their biophysical mechanisms, as MSMs built for these processes often require a large number of states. We recommend the recently developed quasi-MSMs (qMSMs) to address this issue. Compared to MSMs, qMSMs encode the non-Markovian dynamics via the generalized master equation and can significantly reduce the number of states. As a result, qMSMs can be built with a handful of states to facilitate the interpretation of functional conformational changes. In the wake of machine learning, we believe that the rapid advancement in the MSM methodology will lead to their wider application in studying functional conformational changes of biomolecules.

Temperature-dependent kinetic pathways of heterogeneous ice nucleation competing between classical and non-classical nucleation

Ice nucleation on the surface plays a vital role in diverse areas, ranging from physics and cryobiology to atmospheric science. Compared to ice nucleation in the bulk, the water-surface interactions present in heterogeneous ice nucleation complicate the nucleation process, making heterogeneous ice nucleation less comprehended, especially the relationship between the kinetics and the structures of the critical ice nucleus. Here we combine Markov State Models and transition path theory to elucidate the ensemble pathways of heterogeneous ice nucleation. Our Markov State Models reveal that the classical one-step and non-classical two-step nucleation pathways can surprisingly co-exist with comparable fluxes at T = 230 K. Interestingly, we find that the disordered mixing of rhombic and hexagonal ice leads to a favorable configurational entropy that stabilizes the critical nucleus, facilitating the non-classical pathway. In contrast, the favorable energetics promotes the formation of hexagonal ice, resulting in the classical pathway. Furthermore, we discover that, at elevated temperatures, the nucleation process prefers to proceed via the classical pathway, as opposed to the non-classical pathway, since the potential energy contributions override the configurational entropy compensation. This study provides insights into the mechanisms of heterogeneous ice nucleation and sheds light on the rational designs to control crystallization processes.

Assessing the Performance of Traveling-salesman based Automated Path Searching (TAPS) on Complex Biomolecular Systems

Though crucial for understanding the function of large biomolecular systems, locating the minimum free energy paths (MFEPs) between their key conformational states is far from trivial due to their high-dimensional nature. Most existing path-searching methods require a static collective variable space as input, encoding intuition or prior knowledge of the transition mechanism. Such information is, however, hardly available a priori and expensive to validate. To alleviate this issue, we have previously introduced a Traveling-salesman based Automated Path Searching method (TAPS) and demonstrated its efficiency on simple peptide systems. Having implemented a parallel version of this method, here we assess the performance of TAPS on three realistic systems (tens to hundreds of residues) in explicit solvents. We show that TAPS successfully located the MFEP for the ground/excited state transition of the T4 lysozyme L99A variant, consistent with previous findings. TAPS also helped identifying the important role of the two polar contacts in directing the loop-in/loop-out transition of the mitogen-activated protein kinase kinase (MEK1), which explained previous mutant experiments. Remarkably, at a minimal cost of 126 ns sampling, TAPS revealed that the Ltn40/Ltn10 transition of lymphotactin needs no complete unfolding/refolding of its β-sheets and that five polar contacts are sufficient to stabilize the various partially unfolded intermediates along the MFEP. These results present TAPS as a general and promising tool for studying the functional dynamics of complex biomolecular systems.

A comprehensive mechanism for 5-carboxylcytosine-induced transcriptional pausing revealed by Markov state models

RNA polymerase II (Pol II) surveils the genome, pausing as it encounters DNA lesions and base modifications and initiating signals for DNA repair among other important regulatory events. Recent work suggests that Pol II pauses at 5-carboxycytosine (5caC), an epigenetic modification of cytosine, because of a specific hydrogen bond between the carboxyl group of 5caC and a specific residue in fork loop 3 of Pol II. This hydrogen bond compromises productive NTP binding and slows down elongation. Apart from this specific interaction, the carboxyl group of 5caC can potentially interact with numerous charged residues in the cleft of Pol II. However, it is not clear how other interactions between Pol II and 5caC contribute to pausing. In this study, we use Markov state models (a type of kinetic network models) built from extensive molecular dynamics simulations to comprehensively study the impact of 5caC on Pol II translocation. We describe two translocation intermediates with specific interactions that prevent the template base from loading into the Pol II active site. In addition to the previously observed state with 5caC constrained by fork loop 3, we discovered a new intermediate state with a hydrogen bond between 5caC and fork loop 2. Surprisingly, we find that 5caC may curb translocation by suppressing kinking of the helix bordering the active site (the bridge helix) because its high flexibility is critical to translocation. Our work provides new insights into how epigenetic modifications of genomic DNA can modulate Pol II translocation, inducing pauses in transcription.

Role of bacterial RNA polymerase gate opening dynamics in DNA loading and antibiotics inhibition elucidated by quasi-Markov State Model

To initiate transcription, the holoenzyme (RNA polymerase [RNAP] in complex with σ factor) loads the promoter DNA via the flexible loading gate created by the clamp and β-lobe, yet their roles in DNA loading have not been characterized. We used a quasi-Markov State Model (qMSM) built from extensive molecular dynamics simulations to elucidate the dynamics of Thermus aquaticus holoenzyme's gate opening. We showed that during gate opening, β-lobe oscillates four orders of magnitude faster than the clamp, whose opening depends on the Switch 2's structure. Myxopyronin, an antibiotic that binds to Switch 2, was shown to undergo a conformational selection mechanism to inhibit clamp opening. Importantly, we reveal a critical but undiscovered role of β-lobe, whose opening is sufficient for DNA loading even when the clamp is partially closed. These findings open the opportunity for the development of antibiotics targeting β-lobe of RNAP. Finally, we have shown that our qMSMs, which encode non-Markovian dynamics based on the generalized master equation formalism, hold great potential to be widely applied to study biomolecular dynamics.

On the advantages of exploiting memory in Markov state models for biomolecular dynamics

Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.

A novel multiscale scheme to accelerate atomistic simulations of bio-macromolecules by adaptively driving coarse-grained coordinates

All-atom molecular dynamics (MD) simulations of bio-macromolecules can yield relatively accurate results while suffering from the limitation of insufficient conformational sampling. On the other hand, the coarse-grained (CG) MD simulations efficiently accelerate conformational changes in biomolecules but lose atomistic details and accuracy. Here, we propose a novel multiscale simulation method called the adaptively driving multiscale simulation (ADMS)-it efficiently accelerates biomolecular dynamics by adaptively driving virtual CG atoms on the fly while maintaining the atomistic details and focusing on important conformations of the original system with irrelevant conformations rarely sampled. Herein, the "adaptive driving" is based on the short-time-averaging response of the system (i.e., an approximate free energy surface of the original system), without requiring the construction of the CG force field. We apply the ADMS to two peptides (deca-alanine and Ace-GGPGGG-Nme) and one small protein (HP35) as illustrations. The simulations show that the ADMS not only efficiently captures important conformational states of biomolecules and drives fast interstate transitions but also yields, although it might be in part, reliable protein folding pathways. Remarkably, a ∼100-ns explicit-solvent ADMS trajectory of HP35 with three CG atoms realizes folding and unfolding repeatedly and captures the important states comparable to those from a 398-µs standard all-atom MD simulation.

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.

A Two-Ended Data-Driven Accelerated Sampling Method for Exploring the Transition Pathways between Two Known States of Protein

Conformational transitions of protein between different states are often associated with their biological functions. These dynamic processes, however, are usually not easy to be well characterized by experimental measurements, mainly because of inadequate temporal and spatial resolution. Meantime, sampling of configuration space with molecular dynamics (MD) simulations is still a challenge. Here we proposed a robust two-ended data-driven accelerated (teDA2) conformational sampling method, which drives the structural change in an adaptively updated feature space without introducing a bias potential. teDA2 was applied to explore adenylate kinase (ADK), a model with well characterized "open" and "closed" states. A single conformational transition event of ADK could be achieved within only a few or tens of nanoseconds sampled with teDA2. By analyzing hundreds of transition events, we reproduced different mechanisms and the associated pathways for domain motion of ADK reported in the literature. The multiroute characteristic of ADK was confirmed by the fact that some metastable states identified with teDA2 resemble available crystal structures determined at different conditions. This feature was further validated with Markov state modeling with independent MD simulations. Therefore, our work provides strong evidence for the conformational plasticity of protein, which is mainly due to the inherent degree of flexibility. As a reliable and efficient enhanced sampling protocol, teDA2 could be used to study the dynamics between functional states of various biomolecular machines.

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.

Hierarchical Ensembles of Intrinsically Disordered Proteins at Atomic Resolution in Molecular Dynamics Simulations

Intrinsically disordered proteins (IDPs) constitute a large fraction of the human proteome and are critical in the regulation of cellular processes. A detailed understanding of the conformational dynamics of IDPs could help to elucidate their roles in health and disease. However, the inherent flexibility of IDPs makes structural studies and their interpretation challenging. Molecular dynamics (MD) simulations could address this challenge in principle, but inaccuracies in the simulation models and the need for long simulations have stymied progress. To overcome these limitations, we adopt a hierarchical approach that builds on the "flexible-meccano" model reported by Bernadó et al. (J. Am. Chem. Soc. 2005, 127, 17968-17969). First, we exhaustively sample small IDP fragments in all-atom simulations to capture their local structures. Then, we assemble the fragments into full-length IDPs to explore the stereochemically possible global structures of IDPs. The resulting ensembles of three-dimensional structures of full-length IDPs are highly diverse, much more so than in standard MD simulation. For the paradigmatic IDP α-synuclein, our ensemble captures both the local structure, as probed by nuclear magnetic resonance spectroscopy, and its overall dimension, as obtained from small-angle X-ray scattering in solution. By generating representative and meaningful starting ensembles, we can begin to exploit the massive parallelism afforded by current and future high-performance computing resources for atomic-resolution characterization of IDPs.

Opening dynamics of HIV-1 gp120 upon receptor binding is dictated by a key hydrophobic core

HIV-1 entry is mediated firstly by the molecular recognition between the viral glycoprotein gp120 and its receptor CD4 on host T-cells. As a key antigen that can be targeted by neutralizing antibodies, gp120 has been a focus for extensive studies with efforts to understand its structural properties and conformational dynamics upon receptor binding. An atomistic-level revelation of gp120 opening dynamics activated by CD4, however, is still unknown. Here, by constructing a Markov State Model (MSM) based on hundreds of Molecular Dynamics (MD) simulations with an aggregated simulation time of ∼20 microseconds (μs), we identify the key metastable states of gp120 during its opening dynamics upon CD4 binding. The MSM provides a clear dynamic model whereby the identified metastable states coexist and can reach an equilibrium. More importantly, a hydrophobic core flanked by variable loops (V1V2 and V3) and the β20/21 region plays an essential role in triggering the gp120 opening. Any destabilizing effects introduced into the hydrophobic core, therefore, can be expected to promote transition of gp120 to an open state. Moreover, the variable loops demonstrate high flexibilities in fully open gp120. In particular, the V3 region is capable of exploring both closed and open conformations, even with the V1/V2 loops largely adopting an open form. In addition, the bridging sheet formation in gp120 is likely induced by the incoming co-receptor/antibody recognitions, since the V1/V2 structure is highly heterogeneous so that the bridging-sheet formed conformation is not the most populated state. Our studies provide deep insights into the dynamic features of gp120 and its molecular recognitions to the broadly neutralizing antibodies, which guides future attempts to design more effective gp120 immunogens.

Dynamics of the excised base release in thymine DNA glycosylase during DNA repair process

Thymine DNA glycosylase (TDG) initiates base excision repair by cleaving the N-glycosidic bond between the sugar and target base. After catalysis, the release of excised base is a requisite step to terminate the catalytic cycle and liberate the TDG for the following enzymatic reactions. However, an atomistic-level understanding of the dynamics of the product release process in TDG remains unknown. Here, by employing molecular dynamics simulations combined with the Markov State Model, we reveal the dynamics of the thymine release after the excision at microseconds timescale and all-atom resolution. We identify several key metastable states of the thymine and its dominant releasing pathway. Notably, after replacing the TDG residue Gly142 with tyrosine, the thymine release is delayed compared to the wild-type (wt) TDG, as supported by our potential of mean force (PMF) calculations. These findings warrant further experimental tests to potentially trap the excised base in the active site of TDG after the catalysis, which had been unsuccessful by previous attempts. Finally, we extended our studies to other TDG products, including the uracil, 5hmU, 5fC and 5caC bases in order to compare the product release for different targeting bases in the TDG–DNA complex.

Fast-Folding Pathways of the Thrombin-Binding Aptamer G-Quadruplex Revealed by a Markov State Model

G-quadruplex structures participate in many important cellular processes. For a better understanding of their functions, knowledge of the mechanism by which they fold into the functional native structures is necessary. In this work, we studied the folding process of the thrombin-binding aptamer G-quadruplex. Enabled by a computational paradigm that couples an advanced sampling method and a Markov state model, four folding intermediates were identified, including an antiparallel G-hairpin, two G-triplex structures, and a double-hairpin conformation. Likewise, a misfolded structure with a nonnative distribution of syn/anti guanines was also observed. Based on these states, a transition path analysis revealed three fast-folding pathways, along which the thrombin-binding aptamer would fold to the native state directly, with no evidence of potential nonnative competing conformations. The results also showed that the TGT-loop plays an important role in the folding process. The findings of this research may provide general insight about the folding of other G-quadruplex structures.

Advanced Methods for Accessing Protein Shape-Shifting Present New Therapeutic Opportunities

A protein is a dynamic shape-shifter whose function is determined by the set of structures it adopts. Unfortunately, atomically detailed structures are only available for a few conformations of any given protein, and these structures have limited explanatory and predictive power. Here, we provide a brief historical perspective on protein dynamics and introduce recent advances in computational and experimental methods that are providing unprecedented access to protein shape-shifting. Next, we focus on how these tools are revealing the mechanism of allosteric communication and features like cryptic pockets; both of which present new therapeutic opportunities. A major theme is the importance of considering the relative probabilities of different structures and the control one can exert over protein function by modulating this balance.

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.

Simulation of spontaneous G protein activation reveals a new intermediate driving GDP unbinding

Activation of heterotrimeric G proteins is a key step in many signaling cascades. However, a complete mechanism for this process, which requires allosteric communication between binding sites that are ~30 Å apart, remains elusive. We construct an atomically detailed model of G protein activation by combining three powerful computational methods: metadynamics, Markov state models (MSMs), and CARDS analysis of correlated motions. We uncover a mechanism that is consistent with a wide variety of structural and biochemical data. Surprisingly, the rate-limiting step for GDP release correlates with tilting rather than translation of the GPCR-binding helix 5. β-Strands 1 - 3 and helix 1 emerge as hubs in the allosteric network that links conformational changes in the GPCR-binding site to disordering of the distal nucleotide-binding site and consequent GDP release. Our approach and insights provide foundations for understanding disease-implicated G protein mutants, illuminating slow events in allosteric networks, and examining unbinding processes with slow off-rates.

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.

An efficient Bayesian kinetic lumping algorithm to identify metastable conformational states via Gibbs sampling

Markov State Model (MSM) has become a popular approach to study the conformational dynamics of complex biological systems in recent years. Built upon a large number of short molecular dynamics simulation trajectories, MSM is able to predict the long time scale dynamics of complex systems. However, to achieve Markovianity, an MSM often contains hundreds or thousands of states (microstates), hindering human interpretation of the underlying system mechanism. One way to reduce the number of states is to lump kinetically similar states together and thus coarse-grain the microstates into macrostates. In this work, we introduce a probabilistic lumping algorithm, the Gibbs lumping algorithm, to assign a probability to any given kinetic lumping using the Bayesian inference. In our algorithm, the transitions among kinetically distinct macrostates are modeled by Poisson processes, which will well reflect the separation of time scales in the underlying free energy landscape of biomolecules. Furthermore, to facilitate the search for the optimal kinetic lumping (i.e., the lumped model with the highest probability), a Gibbs sampling algorithm is introduced. To demonstrate the power of our new method, we apply it to three systems: a 2D potential, alanine dipeptide, and a WW protein domain. In comparison with six other popular lumping algorithms, we show that our method can persistently produce the lumped macrostate model with the highest probability as well as the largest metastability. We anticipate that our Gibbs lumping algorithm holds great promise to be widely applied to investigate conformational changes in biological macromolecules.

Single glucose molecule transport process revealed by force tracing and molecular dynamics simulations

Transporting individual molecules across cell membranes is a fundamental process in cellular metabolism. Although the crystal diffraction technique has greatly contributed to our understanding of the structures of the involved transporters, a description of the dynamic transport mechanism at the single-molecule level has been extremely elusive. In this study, we applied atomic force microscopy (AFM)-based force tracing to directly monitor the transport of a single molecule, d-glucose, across living cell membranes. Our results show that the force to transport a single molecule of d-glucose across cell membranes is 37 ± 9 pN, and the corresponding transport interval is approximately 20 ms, while the average speed is approximately 0.3 μm s^-1. Furthermore, our calculated force profile from molecular dynamics simulations showed quantitatively good agreement with the force tracing observation and revealed detailed information regarding the glucose transport path, indicating that two salt bridges, K38/E299 and K300/E426, play critical roles during glucose transport across glucose transporter 1 (GLUT1). This role was further verified using biological experiments that disrupted these two bridges and measured the uptake of glucose into the cells. Our approaches led to the first unambiguous description of the glucose transport process across cell membranes at the single-molecule level and demonstrated the biological importance of the two salt bridges for transporting glucose across GLUT1.

A new class of enhanced kinetic sampling methods for building Markov state models

Markov state models (MSMs) and other related kinetic network models are frequently used to study the long-timescale dynamical behavior of biomolecular and materials systems. MSMs are often constructed bottom-up using brute-force molecular dynamics (MD) simulations when the model contains a large number of states and kinetic pathways that are not known a priori. However, the resulting network generally encompasses only parts of the configurational space, and regardless of any additional MD performed, several states and pathways will still remain missing. This implies that the duration for which the MSM can faithfully capture the true dynamics, which we term as the validity time for the MSM, is always finite and unfortunately much shorter than the MD time invested to construct the model. A general framework that relates the kinetic uncertainty in the model to the validity time, missing states and pathways, network topology, and statistical sampling is presented. Performing additional calculations for frequently-sampled states/pathways may not alter the MSM validity time. A new class of enhanced kinetic sampling techniques is introduced that aims at targeting rare states/pathways that contribute most to the uncertainty so that the validity time is boosted in an effective manner. Examples including straightforward 1D energy landscapes, lattice models, and biomolecular systems are provided to illustrate the application of the method. Developments presented here will be of interest to the kinetic Monte Carlo community as well.

Focused conformational sampling in proteins

A detailed understanding of the conformational dynamics of biological molecules is difficult to obtain by experimental techniques due to resolution limitations in both time and space. Computer simulations avoid these in theory but are often too short to sample rare events reliably. Here we show that the progress index-guided sampling (PIGS) protocol can be used to enhance the sampling of rare events in selected parts of biomolecules without perturbing the remainder of the system. The method is very easy to use as it only requires as essential input a set of several features representing the parts of interest sufficiently. In this feature space, new states are discovered by spontaneous fluctuations alone and in unsupervised fashion. Because there are no energetic biases acting on phase space variables or projections thereof, the trajectories PIGS generates can be analyzed directly in the framework of transition networks. We demonstrate the possibility and usefulness of such focused explorations of biomolecules with two loops that are part of the binding sites of bromodomains, a family of epigenetic "reader" modules. This real-life application uncovers states that are structurally and kinetically far away from the initial crystallographic structures and are also metastable. Representative conformations are intended to be used in future high-throughput virtual screening campaigns.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

MELD-Path Efficiently Computes Conformational Transitions, Including Multiple and Diverse Paths

The molecular actions of proteins occur along reaction coordinates. Current computer methods have limited ability to explore them. We describe a fast protocol called MELD-path that (1) efficiently samples relevant conformational states via MELD, an accelerator of Molecular Dynamics (MD), (2) seeds multiple short MD trajectories from MELD states, and then (3) constructs Markov State Models (MSM) that give the routes and kinetics. We tested the method against extensive (multi μs) MD simulations of the right-handed- to left-handed-helix transition of a 9-mer peptide of AIB, the symmetry of which allows us to establish convergence. MELD-path finds all the metastable states, their correct relative populations, and the full ensemble of routes, not just a single assumed route. For this transition, we find a very broad route structure. MELD-path is highly parallelizable and efficient, yielding the full route map in a few days of computation. We believe MELD-path could be a general and rapid way to explore mechanistic processes in biomolecules on the computer.

Elucidation of the conformational dynamics of multi-body systems by construction of Markov state models

Constructing Markov State Models (MSMs) based on short molecular dynamics simulations is a powerful computational technique to complement experiments in predicting long-time kinetics of biomolecular processes at atomic resolution. Even though the MSM approach has been widely applied to study one-body processes such as protein folding and enzyme conformational changes, the majority of biological processes, e.g. protein-ligand recognition, signal transduction, and protein aggregation, essentially involve multiple entities. Here we review the attempts at constructing MSMs for multi-body systems, point out the challenges therein and discuss recent algorithmic progresses that alleviate these challenges. In particular, we describe an automatic kinetics based partitioning method that achieves optimal definition of the conformational states in a multi-body system, and discuss a novel maximum-likelihood approach that efficiently estimates the slow uphill kinetics utilizing pre-computed equilibrium populations of all states. We expect that these new algorithms and their combinations may boost investigations of important multi-body biological processes via the efficient construction of MSMs.