A two-state model for the dynamics of the pyrophosphate ion release in bacterial RNA polymerase

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.

SARS-CoV-2 RNA-Dependent RNA Polymerase Follows Asynchronous Translocation Pathway for Viral Transcription and Replication

Translocation is one essential step for the SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) to exert viral replication and transcription. Although cryo-EM structures of SARS-CoV-2 RdRp are available, the molecular mechanisms of dynamic translocation remain elusive. Herein, we constructed a Markov state model based on extensive molecular dynamics simulations to elucidate the translocation dynamics of the SARS-CoV-2 RdRp. We identified two intermediates that pinpoint the rate-limiting step of translocation and characterize the asynchronous movement of the template-primer duplex. The 3'-terminal nucleotide in the primer strand lags behind due to the uneven distribution of protein-RNA interactions, while the translocation of the template strand is delayed by the hurdle residue K500. Even so, the two strands share the same "ratchet" to stabilize the polymerase in the post-translocation state, suggesting a Brownian-ratchet model. Overall, our study provides intriguing insights into SARS-CoV-2 replication and transcription, which would open a new avenue for drug discoveries.

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.

Incorporation efficiency and inhibition mechanism of 2'-substituted nucleotide analogs against SARS-CoV-2 RNA-dependent RNA polymerase

The ongoing pandemic caused by SARS-CoV-2 emphasizes the need for effective therapeutics. Inhibition of SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) by nucleotide analogs provides a promising antiviral strategy. One common group of RdRp inhibitors, 2'-modified nucleotides, are reported to exhibit different behaviors in the SARS-CoV-2 RdRp transcription assay. Three of these analogs, 2'-O-methyl UTP, Sofosbuvir, and 2'-methyl CTP, act as effective inhibitors in previous biochemical experiments, while Gemcitabine and ara-UTP show no inhibitory activity. To understand the impact of the 2'-modification on their inhibitory effects, we conducted extensive molecular dynamics simulations and relative binding free energy calculations using the free energy perturbation method on SARS-CoV-2 replication-transcription complex (RTC) with these five nucleotide analogs. Our results reveal that the five nucleotide analogs display comparable binding affinities to SARS-CoV-2 RdRp and they can all be added to the nascent RNA chain. Moreover, we examine how the incorporation of these nucleotide triphosphate (NTP) analogs will impact the addition of the next nucleotide. Our results indicate that 2'-O-methyl UTP can weaken the binding of the subsequent NTP and consequently lead to partial chain termination. Additionally, Sofosbuvir and 2'-methyl CTP can cause immediate termination due to the strong steric hindrance introduced by their bulky 2'-methyl groups. In contrast, nucleotide analogs with smaller substitutions, such as the fluorine atoms and the ara-hydroxyl group in Gemcitabine and ara-UTP, have a marginal impact on the polymerization process. Our findings are consistent with experimental observations, and more importantly, shed light on the detailed molecular mechanism of SARS-CoV-2 RdRp inhibition by 2'-substituted nucleotide analogs, and may facilitate the rational design of antiviral agents to inhibit SARS-CoV-2 RdRp.

Controlled Trafficking of Multiple and Diverse Cations Prompts Nucleic Acid Hydrolysis

Recent in crystallo reaction intermediates have detailed how nucleic acid hydrolysis occurs in the RNA ribonuclease H1 (RNase H1), a fundamental metalloenzyme involved in maintaining the human genome. At odds with the previous characterization, these in crystallo structures unexpectedly captured multiple metal ions (K⁺ and Mg²⁺) transiently bound in the vicinity of the two-metal-ion active site. Using multi-microsecond all-atom molecular dynamics and free-energy simulations, we investigated the functional implications of the dynamic exchange of multiple K⁺ and Mg²⁺ ions at the RNase H1 reaction center. We found that such ions are timely positioned at non-overlapping locations near the active site, at different stages of catalysis, being crucial for both reactants' alignment and leaving group departure. We also found that this cation trafficking is tightly regulated by variations of the solution's ionic strength and is aided by two conserved second-shell residues, E188 and K196, suggesting a mechanism for the cations' recruitment during catalysis. These results indicate that controlled trafficking of multi-cation dynamics, opportunely prompted by second-shell residues, is functionally essential to the complex enzymatic machinery of the RNase H1. These findings revise the current knowledge on the RNase H1 catalysis and open new catalytic possibilities for other similar metalloenzymes including, but not limited to, CRISPR-Cas9, group II intron ribozyme and the human spliceosome.

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.

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.

The Mechanisms of Substrate Selection, Catalysis, and Translocation by the Elongating RNA Polymerase

Multi-subunit DNA-dependent RNA polymerases synthesize all classes of cellular RNAs, ranging from short regulatory transcripts to gigantic messenger RNAs. RNA polymerase has to make each RNA product in just one try, even if it takes millions of successive nucleotide addition steps. During each step, RNA polymerase selects a correct substrate, adds it to a growing chain, and moves one nucleotide forward before repeating the cycle. However, RNA synthesis is anything but monotonous: RNA polymerase frequently pauses upon encountering mechanical, chemical and torsional barriers, sometimes stepping back and cleaving off nucleotides from the growing RNA chain. A picture in which these intermittent dynamics enable processive, accurate, and controllable RNA synthesis is emerging from complementary structural, biochemical, computational, and single-molecule studies. Here, we summarize our current understanding of the mechanism and regulation of the on-pathway transcription elongation. We review the details of substrate selection, catalysis, proofreading, and translocation, focusing on rate-limiting steps, structural elements that modulate them, and accessory proteins that appear to control RNA polymerase translocation.

C, Da LT, Yu J. A Viral T7 RNA Polymerase Ratcheting Along DNA With Fidelity Control

RNA polymerase (RNAP) from bacteriophage T7 is a representative single-subunit viral RNAP that can transcribe with high promoter activities without assistances from transcription factors. We accordingly studied this small transcription machine computationally as a model system to understand underlying mechanisms of mechano-chemical coupling and fidelity control in the RNAP transcription elongation. Here we summarize our computational work from several recent publications to demonstrate first how T7 RNAP translocates via Brownian alike motions along DNA right after the catalytic product release. Then we show how the backward translocation motions are prevented at post-translocation upon successful nucleotide incorporation, which is also subject to stepwise nucleotide selection and acts as a pawl for "selective ratcheting". The structural dynamics and energetics features revealed from our atomistic molecular dynamics (MD) simulations and related analyses on the single-subunit T7 RNAP thus provided detailed and quantitative characterizations on the Brownian-ratchet working scenario of a prototypical transcription machine with sophisticated nucleotide selectivity for fidelity control. The presented mechanisms can be more or less general for structurally similar viral or mitochondrial RNAPs and some of DNA polymerases, or even for the RNAP engine of the more complicated transcription machinery in higher organisms.

Mechanism of Mg2+-Accompanied Product Release in Sugar Nucleotidyltransferases

The nucleotidyl transfer reaction, catalyzed by sugar nucleotidyltransferases (SNTs), is assisted by two active site Mg²⁺ ions. While studying this reaction using X-ray crystallography, we captured snapshots of the pyrophosphate (product) as it exits along a pocket. Surprisingly, one of the active site Mg²⁺ ions remains coordinated to the exiting pyrophosphate. This hints at the participation of Mg²⁺ in the process of product release, besides its role in catalyzing nucleotidyl transfer. These observations are further supported by enhanced sampling molecular dynamics simulations. Free energy computations suggest that the product release is likely to be rate limiting in SNTs, and the origin of the high free energy barrier for product release could be traced back to the "slow" conformational change of an Arg residue at the exit end of the pocket. These results establish a dual role for Mg²⁺, and propose a general mechanism of product release during the nucleotidyl transfer by SNTs.

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.

Improving the productivity of monodisperse polyhedral cages by the rational design of kinetic self-assembly pathways

Hollow polyhedral cages hold great potential for application in nanotechnological and biomedical fields. Understanding the formation mechanism of these self-assembled structures could provide guidance for the rational design of the desired polyhedral cages. Here, by constructing kinetic network models from extensive coarse-grained molecular dynamics simulations, we elucidated the formation mechanism of the dodecahedral cage, which is formed by the self-assembly of patchy particles. We found that the dodecahedral cage is formed through increasing the aggregate size followed by structure rearrangement. Based on this mechanistic understanding, we improved the productivity of the dodecahedral cage through the rational design of the patch arrangement of patchy particles, which promotes the structural rearrangement process. Our results demonstrate that it should be a feasible strategy to achieve the rational design of the desired nanostructures via the kinetic analysis. We anticipate that this methodology could be extended to other self-assembly systems for the fabrication of functional nanomaterials.

Harnessing complexity in molecular self-assembly using computer simulations

In molecular self-assembly, hundreds of thousands of freely-diffusing molecules associate to form ordered and functional architectures in the absence of an actuator. This intriguing phenomenon plays a critical role in biology and has become a powerful tool for the fabrication of advanced nanomaterials. Due to the limited spatial and temporal resolutions of current experimental techniques, computer simulations offer a complementary strategy to explore self-assembly with atomic resolution. Here, we review recent computational studies focusing on both thermodynamic and kinetic aspects. As we shall see, thermodynamic approaches based on modeling and statistical mechanics offer initial guidelines to design nanostructures with modest computational effort. Computationally more intensive analyses based on molecular dynamics simulations and kinetic network models (KNMs) reach beyond it, opening the door to the rational design of self-assembly pathways. Current limitations of these methodologies are discussed. We anticipate that the synergistic use of thermodynamic and kinetic analyses based on computer simulations will provide an important contribution to the de novo design of self-assembly.

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.

Mechanism of NTP Binding to the Active Site of T7 RNA Polymerase Revealed by Free-Energy Simulation

In genetic transcription, molecular dynamic details and energetics of NTP binding to the active site of RNA polymerase (RNAP) are poorly understood. In this article, we investigated the NTP binding process in T7 RNAP using all-atom MD simulation combined with the umbrella sampling technique. Based on our simulations, a two-step mechanism was proposed to explain NTP binding: first, substrate NTP in aqueous solution, which carries a magnesium ion, diffuses through a secondary channel of RNAP to attain a pore region, where it undergoes conformational changes to give a correct orientation; next, the NTP establishes initial basepairing contacts with the template nucleoside (TN). Our free-energy calculations suggest that both steps are spontaneous. This mechanism can easily explain the problem of NTP binding with different orientations. Moreover, it is found that the nascent NTP:TN basepair is fragile and easily broken by thermal disturbance. Therefore, we speculate that the fingers domain will be triggered to close, so as to create a steady environment for the next chemical step. The observations from the work provide valuable information for comprehensively understanding the mechanism of the basic step in genetic transcription.

Kinetics of nucleotide entry into RNA polymerase active site provides mechanism for efficiency and fidelity

During transcription, RNA polymerase II elongates RNA by adding nucleotide triphosphates (NTPs) complementary to a DNA template. Structural studies have suggested that NTPs enter and exit the active site via the narrow secondary pore but details have remained unclear. A kinetic model is presented that integrates molecular dynamics simulations with experimental data. Previous simulations of trigger loop dynamics and the dynamics of matched and mismatched NTPs in and near the active site were combined with new simulations describing NTP exit from the active site via the secondary pore. Markov state analysis was applied to identify major states and estimate kinetic rates for transitions between those states. The kinetic model predicts elongation and misincorporation rates in close agreement with experiment and provides mechanistic hypotheses for how NTP entry and exit via the secondary pore is feasible and a key feature for achieving high elongation and low misincorporation rates during RNA elongation.

Elucidating Mechanisms of Molecular Recognition Between Human Argonaute and miRNA Using Computational Approaches

MicroRNA (miRNA) and Argonaute (AGO) protein together form the RNA-induced silencing complex (RISC) that plays an essential role in the regulation of gene expression. Elucidating the underlying mechanism of AGO-miRNA recognition is thus of great importance not only for the in-depth understanding of miRNA function but also for inspiring new drugs targeting miRNAs. In this chapter we introduce a combined computational approach of molecular dynamics (MD) simulations, Markov state models (MSMs), and protein-RNA docking to investigate AGO-miRNA recognition. Constructed from MD simulations, MSMs can elucidate the conformational dynamics of AGO at biologically relevant timescales. Protein-RNA docking can then efficiently identify the AGO conformations that are geometrically accessible to miRNA. Using our recent work on human AGO2 as an example, we explain the rationale and the workflow of our method in details. This combined approach holds great promise to complement experiments in unraveling the mechanisms of molecular recognition between large, flexible, and complex biomolecules.

Adaptive partitioning by local density-peaks: An efficient density-based clustering algorithm for analyzing molecular dynamics trajectories

We present an efficient density-based adaptive-resolution clustering method APLoD for analyzing large-scale molecular dynamics (MD) trajectories. APLoD performs the k-nearest-neighbors search to estimate the density of MD conformations in a local fashion, which can group MD conformations in the same high-density region into a cluster. APLoD greatly improves the popular density peaks algorithm by reducing the running time and the memory usage by 2-3 orders of magnitude for systems ranging from alanine dipeptide to a 370-residue Maltose-binding protein. In addition, we demonstrate that APLoD can produce clusters with various sizes that are adaptive to the underlying density (i.e., larger clusters at low-density regions, while smaller clusters at high-density regions), which is a clear advantage over other popular clustering algorithms including k-centers and k-medoids. We anticipate that APLoD can be widely applied to split ultra-large MD datasets containing millions of conformations for subsequent construction of Markov State Models. © 2016 Wiley Periodicals, Inc.

Understanding the core of RNA interference: The dynamic aspects of Argonaute-mediated processes

At the core of RNA interference, the Argonaute proteins (Ago) load and utilize small guide nucleic acids to silence mRNAs or cleave foreign nucleic acids in a sequence specific manner. In recent years, based on extensive structural studies of Ago and its interaction with the nucleic acids, considerable progress has been made to reveal the dynamic aspects of various Ago-mediated processes. Here we review these novel insights into the guide-strand loading, duplex unwinding, and effects of seed mismatch, with a focus on two representative Agos, the human Ago 2 (hAgo2) and the bacterial Thermus thermophilus Ago (TtAgo). In particular, comprehensive molecular simulation studies revealed that although sharing similar overall structures, the two Agos have vastly different conformational landscapes and guide-strand loading mechanisms because of the distinct rigidity of their L1-PAZ hinge. Given the central role of the PAZ motions in regulating the exposure of the nucleic acid binding channel, these findings exemplify the importance of protein motions in distinguishing the overlapping, yet distinct, mechanisms of Ago-mediated processes in different organisms.

Nanoscale Engineering of Designer Cellulosomes

Biocatalysts showcase the upper limit obtainable for high-speed molecular processing and transformation. Efforts to engineer functionality in synthetic nanostructured materials are guided by the increasing knowledge of evolving architectures, which enable controlled molecular motion and precise molecular recognition. The cellulosome is a biological nanomachine, which, as a fundamental component of the plant-digestion machinery from bacterial cells, has a key potential role in the successful development of environmentally-friendly processes to produce biofuels and fine chemicals from the breakdown of biomass waste. Here, the progress toward so-called "designer cellulosomes", which provide an elegant alternative to enzyme cocktails for lignocellulose breakdown, is reviewed. Particular attention is paid to rational design via computational modeling coupled with nanoscale characterization and engineering tools. Remaining challenges and potential routes to industrial application are put forward.

Elucidation of the Dynamics of Transcription Elongation by RNA Polymerase II using Kinetic Network Models

RNA polymerase II (Pol II) is an essential enzyme that catalyzes transcription with high efficiency and fidelity in eukaryotic cells. During transcription elongation, Pol II catalyzes the nucleotide addition cycle (NAC) to synthesize mRNA using DNA as the template. The transitions between the states of the NAC require conformational changes of both the protein and nucleotides. Although X-ray structures are available for most of these states, the dynamics of the transitions between states are largely unknown. Molecular dynamics (MD) simulations can predict structure-based molecular details and shed light on the mechanisms of these dynamic transitions. However, the employment of MD simulations on a macromolecule (tens to hundreds of nanoseconds) such as Pol II is challenging due to the difficulty of reaching biologically relevant timescales (tens of microseconds or even longer). For this challenge to be overcome, kinetic network models (KNMs), such as Markov State Models (MSMs), have become a popular approach to access long-timescale conformational changes using many short MD simulations. We describe here our application of KNMs to characterize the molecular mechanisms of the NAC of Pol II. First, we introduce the general background of MSMs and further explain procedures for the construction and validation of MSMs by providing some technical details. Next, we review our previous studies in which we applied MSMs to investigate the individual steps of the NAC, including translocation and pyrophosphate ion release. In particular, we describe in detail how we prepared the initial conformations of Pol II elongation complex, performed MD simulations, extracted MD conformations to construct MSMs, and further validated them. We also summarize our major findings on molecular mechanisms of Pol II elongation based on these MSMs. In addition, we have included discussions regarding various key points and challenges for applications of MSMs to systems as large as the Pol II elongation complex. Finally, to study the overall NAC, we combine the individual steps of the NAC into a five-state KNM based on a nonbranched Brownian ratchet scheme to explain the single-molecule optical tweezers experimental data. The studies complement experimental observations and provide molecular mechanisms for the transcription elongation cycle. In the long term, incorporation of sequence-dependent kinetic parameters into KNMs has great potential for identifying error-prone sequences and predicting transcription dynamics in genome-wide transcriptomes.

Unfolding mechanism of thrombin-binding aptamer revealed by molecular dynamics simulation and Markov State Model

Thrombin-binding aptamer (TBA) with the sequence 5′GGTTGGTGTGGTTGG3′ could fold into G-quadruplex, which correlates with functionally important genomic regionsis. However, unfolding mechanism involved in the structural stability of G-quadruplex has not been satisfactorily elucidated on experiments so far. Herein, we studied the unfolding pathway of TBA by a combination of molecular dynamics simulation (MD) and Markov State Model (MSM). Our results revealed that the unfolding of TBA is not a simple two-state process but proceeds along multiple pathways with multistate intermediates. One high flux confirms some observations from NMR experiment. Another high flux exhibits a different and simpler unfolding pathway with less intermediates. Two important intermediate states were identified. One is similar to the G-triplex reported in the folding of G-quadruplex, but lack of H-bonding between guanines in the upper plane. More importantly, another intermediate state acting as a connector to link the folding region and the unfolding one, was the first time identified, which exhibits higher population and stability than the G-triplex-like intermediate. These results will provide valuable information for extending our understanding the folding landscape of G-quadruplex formation.

Bridging the Missing Link between Structure and Fidelity of the RNA-Dependent RNA Polymerase from Poliovirus through Free Energy Simulations

RNA-dependent RNA polymerases (RdRps) are enzymes catalyzing RNA replication from a RNA template. Active-site closure in RdRps, normally induced by correct nucleotide triphosphate (NTP) binding, is a prerequisite for the cycle of nucleotide incorporation. So, a complete understanding of polymerase function (in particular polymerase fidelity) of a RdRp requires more complete knowledge of active-site closure in the RdRp. In this work, based on solved crystal structures, we have built different models for the RNA-dependent RNA polymerase from poliovirus (termed PV 3D(pol)). Through MD simulations and free energy calculations of these PV 3D(pol) models, we have revealed the dynamic correlation between motif A and motif D and between motif A and incoming NTP, have deepened our understanding of polymerase fidelity from dynamic aspects, and have provided an explanation to the puzzle that arises from different observations based on kinetic studies and structural data.

A Jump-from-Cavity Pyrophosphate Ion Release Assisted by a Key Lysine Residue in T7 RNA Polymerase Transcription Elongation

Pyrophosphate ion (PPi) release during transcription elongation is a signature step in each nucleotide addition cycle. The kinetics and energetics of the process as well as how it proceeds with substantial conformational changes of the polymerase complex determine the mechano-chemical coupling mechanism of the transcription elongation. Here we investigated detailed dynamics of the PPi release process in a single-subunit RNA polymerase (RNAP) from bacteriophage T7, implementing all-atom molecular dynamics (MD) simulations. We obtained a jump-from-cavity kinetic model of the PPi release utilizing extensive nanosecond MD simulations. We found that the PPi release in T7 RNAP is initiated by the PPi dissociation from two catalytic aspartic acids, followed by a comparatively slow jump-from-cavity activation process. Combining with a number of microsecond long MD simulations, we also found that the activation process is hindered by charged residue associations as well as by local steric and hydrogen bond interactions. On the other hand, the activation is greatly assisted by a highly flexible lysine residue Lys472 that swings its side chain to pull PPi out. The mechanism can apply in general to single subunit RNA and DNA polymerases with similar molecular structures and conserved key residues. Remarkably, the flexible lysine or arginine residue appears to be a universal module that assists the PPi release even in multi-subunit RNAPs with charge facilitated hopping mechanisms. We also noticed that the PPi release is not tightly coupled to opening motions of an O-helix on the fingers domain of T7 RNAP according to the microsecond MD simulations. Our study thus supports the Brownian ratchet scenario of the mechano-chemical coupling in the transcription elongation of the single-subunit polymerase.

A critical residue selectively recruits nucleotides for t7 RNA polymerase transcription fidelity control

Nucleotide selection is essential for fidelity control in gene replication and transcription. Recent work on T7 RNA polymerase suggested that a small posttranslocation free energy bias stabilizes Tyr(639) in the active site to aid nucleotide selection. However, it was not clear exactly how Tyr(639) assists the selection. Here we report a molecular-dynamics simulation study revealing atomistic detail of this critical selectivity. The study shows first that Tyr(639) blocks the active site at posttranslocation by marginally stacking to the end basepair of the DNA-RNA hybrid. The study then demonstrates that at the nucleotide preinsertion state, a cognate RNA nucleotide does not affect the local Tyr(639) stabilization, whereas a noncognate nucleotide substantially stabilizes Tyr(639) so that Tyr(639) keeps blocking the active site. As a result, further nucleotide insertion into the active site, which requires moving Tyr(639) out of the site, would be hindered for the noncognate nucleotide, but not for the cognate nucleotide. In particular, we note that water molecules assist the ribose recognition in the RNA nucleotide preinsertion, and help Tyr(639) stacking to the end basepair in the case of a DNA nucleotide. It was also seen that a base-mismatched nucleotide at preinsertion directly grabs Tyr(639) for the active site stabilization. We also find that in a mutant polymerase Y639F the strong stabilization of residue 639 in the active site cannot establish upon the DNA nucleotide preinsertion. The finding explains the reduced differentiation between ribo- and deoxyribonucleotides that has been recorded experimentally for the mutant polymerase.

Structural Model of RNA Polymerase II Elongation Complex with Complete Transcription Bubble Reveals NTP Entry Routes

The RNA polymerase II (Pol II) is a eukaryotic enzyme that catalyzes the synthesis of the messenger RNA using a DNA template. Despite numerous biochemical and biophysical studies, it remains elusive whether the “secondary channel” is the only route for NTP to reach the active site of the enzyme or if the “main channel” could be an alternative. On this regard, crystallographic structures of Pol II have been extremely useful to understand the structural basis of transcription, however, the conformation of the unpaired non-template DNA part of the full transcription bubble (TB) is still unknown. Since diffusion routes of the nucleoside triphosphate (NTP) substrate through the main channel might overlap with the TB region, gaining structural information of the full TB is critical for a complete understanding of Pol II transcription process. In this study, we have built a structural model of Pol II with a complete transcription bubble based on multiple sources of existing structural data and used Molecular Dynamics (MD) simulations together with structural analysis to shed light on NTP entry pathways. Interestingly, we found that although both channels have enough space to allow NTP loading, the percentage of MD conformations containing enough space for NTP loading through the secondary channel is twice higher than that of the main channel. Further energetic study based on MD simulations with NTP loaded in the channels has revealed that the diffusion of the NTP through the main channel is greatly disfavored by electrostatic repulsion between the NTP and the highly negatively charged backbones of nucleotides in the non-template DNA strand. Taken together, our results suggest that the secondary channel is the major route for NTP entry during Pol II transcription.

In eukaryotic cells, the RNA polymerase II (Pol II) is a central enzyme that reads the genetic information encoded in the DNA template to synthetize a messenger RNA. To perform its function, Pol II needs to have the substrate nucleoside triphosphate (NTP) diffuse into its deeply buried active site. Despite numerous efforts, the NTP entry routes remain elusive: NTP could diffuse only through the secondary channel, or also via the main channel. The structural information of the transcription bubble is essential to study this process, however, the unpaired non-template DNA of the transcription bubble is absent in the available X-ray crystal structures. In this regard, we have built a structural model of the Pol II elongation complex with reconstructed transcription bubble using existing experimental data. We then performed Molecular Dynamics (MD) simulations and applied structural analysis to study the routes of NTP diffusion. We found that sterically the probability of NTP loading through the secondary channel is more than twice that of the main channel. Further analysis of the non-bonded energetic contributions to NTP diffusion suggests that NTP diffusion through the main channel is greatly disfavored by the electrostatic repulsion between the substrate and negatively charged backbones of nucleotides in the non-template strand of the transcription bubble. Altogether, our findings suggest that the secondary channel is the more favorable NTP diffusion route for Pol II transcription elongation.

Free energy landscape of activation in a signalling protein at atomic resolution

The interconversion between inactive and active protein states, traditionally described by two static structures, is at the heart of signaling. However, how folded states interconvert is largely unknown due to the inability to experimentally observe transition pathways. Here we explore the free energy landscape of the bacterial response regulator NtrC by combining computation and NMR, and discover unexpected features underlying efficient signaling. We find that functional states are defined purely in kinetic and not structural terms. The need of a well-defined conformer, crucial to the active state, is absent in the inactive state, which comprises a heterogeneous collection of conformers. The transition between active and inactive states occurs through multiple pathways, facilitated by a number of nonnative transient hydrogen bonds, thus lowering the transition barrier through both entropic and enthalpic contributions. These findings may represent general features for functional conformational transitions within the folded state.

Ligand induced change of β2 adrenergic receptor from active to inactive conformation and its implication for the closed/open state of the water channel: insight from molecular dynamics simulation, free energy calculation and Markov state model analysis

The reported crystal structures of β2 adrenergic receptor (β2AR) reveal that the open and closed states of the water channel are correlated with the inactive and active conformations of β2AR. However, more details about the process by which the water channel states are affected by the active to inactive conformational change of β2AR remain illusive. In this work, molecular dynamics simulations are performed to study the dynamical inactive and active conformational change of β2AR induced by inverse agonist ICI 118,551. Markov state model analysis and free energy calculation are employed to explore the open and close states of the water channel. The simulation results show that inverse agonist ICI 118,551 can induce water channel opening during the conformational transition of β2AR. Markov state model (MSM) analysis proves that the energy contour can be divided into seven states. States S1, S2 and S5, which represent the active conformation of β2AR, show that the water channel is in the closed state, while states S4 and S6, which correspond to the intermediate state conformation of β2AR, indicate the water channel opens gradually. State S7, which represents the inactive structure of β2AR, corresponds to the full open state of the water channel. The opening mechanism of the water channel is involved in the ligand-induced conformational change of β2AR. These results can provide useful information for understanding the opening mechanism of the water channel and will be useful for the rational design of potent inverse agonists of β2AR.

Five checkpoints maintaining the fidelity of transcription by RNA polymerases in structural and energetic details

Transcriptional fidelity, which prevents the misincorporation of incorrect nucleoside monophosphates in RNA, is essential for life. Results from molecular dynamics (MD) simulations of eukaryotic RNA polymerase (RNAP) II and bacterial RNAP with experimental data suggest that fidelity may involve as many as five checkpoints. Using MD simulations, the effects of different active site NTPs in both open and closed trigger loop (TL) structures of RNAPs are compared. Unfavorable initial binding of mismatched substrates in the active site with an open TL is proposed to be the first fidelity checkpoint. The leaving of an incorrect substrate is much easier than a correct one energetically from the umbrella sampling simulations. Then, the closing motion of the TL, required for catalysis, is hindered by the presence of mismatched NTPs. Mismatched NTPs also lead to conformational changes in the active site, which perturb the coordination of magnesium ions and likely affect the ability to proceed with catalysis. This step appears to be the most important checkpoint for deoxy-NTP discrimination. Finally, structural perturbations in the template DNA and the nascent RNA in the presence of mismatches likely hinder nucleotide addition and provide the structural foundation for backtracking followed by removing erroneously incorporated nucleotides during proofreading.

Quantitatively characterizing the ligand binding mechanisms of choline binding protein using Markov state model analysis

Protein-ligand recognition plays key roles in many biological processes. One of the most fascinating questions about protein-ligand recognition is to understand its underlying mechanism, which often results from a combination of induced fit and conformational selection. In this study, we have developed a three-pronged approach of Markov State Models, Molecular Dynamics simulations, and flux analysis to determine the contribution of each model. Using this approach, we have quantified the recognition mechanism of the choline binding protein (ChoX) to be ∼90% conformational selection dominant under experimental conditions. This is achieved by recovering all the necessary parameters for the flux analysis in combination with available experimental data. Our results also suggest that ChoX has several metastable conformational states, of which an apo-closed state is dominant, consistent with previous experimental findings. Our methodology holds great potential to be widely applied to understand recognition mechanisms underlining many fundamental biological processes.

Markov state models of biomolecular conformational dynamics

It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges.

Quantitative comparison of alternative methods for coarse-graining biological networks

Markov models and master equations are a powerful means of modeling dynamic processes like protein conformational changes. However, these models are often difficult to understand because of the enormous number of components and connections between them. Therefore, a variety of methods have been developed to facilitate understanding by coarse-graining these complex models. Here, we employ Bayesian model comparison to determine which of these coarse-graining methods provides the models that are most faithful to the original set of states. We find that the Bayesian agglomerative clustering engine and the hierarchical Nyström expansion graph (HNEG) typically provide the best performance. Surprisingly, the original Perron cluster cluster analysis (PCCA) method often provides the next best results, outperforming the newer PCCA+ method and the most probable paths algorithm. We also show that the differences between the models are qualitatively significant, rather than being minor shifts in the boundaries between states. The performance of the methods correlates well with the entropy of the resulting coarse-grainings, suggesting that finding states with more similar populations (i.e., avoiding low population states that may just be noise) gives better results.

THEORETICAL INVESTIGATIONS ON ELUCIDATING FUNDAMENTAL MECHANISMS OF CATALYSIS AND DYNAMICS INVOLVED IN TRANSCRIPTION BY RNA POLYMERASE

RNA polymerase is the enzyme that synthesizes RNA during the transcription process. To understand its mechanism, structural studies have provided us pictures of the series of steps necessary to add a new nucleotide to the nascent RNA chain, the steps altogether known as the nucleotide addition cycle (NAC). However, these static snapshots do not provide dynamic information of these processes involved in NAC, such as the conformational changes of the protein and the atomistic details of the catalysis. Computational studies have made efforts to fill these knowledge gaps. In this review, we provide examples of different computational approaches that have improved our understanding of the transcription elongation process for RNA polymerase, such as normal mode analysis, molecular dynamic (MD) simulations, Markov state models (MSMs). We also point out some unsolved questions that could be addressed using computational tools in the future.

Localized frustration and binding-induced conformational change in recognition of 5S RNA by TFIIIA zinc finger

Protein TFIIIA is composed of nine tandemly arranged Cys2His2 zinc fingers. It can bind either to the 5S RNA gene as a transcription factor or to the 5S RNA transcript as a chaperone. Although structural and biochemical data provided valuable information on the recognition between the TFIIIIA and the 5S DNA/RNA, the involved conformational motions and energetic factors contributing to the binding affinity and specificity remain unclear. In this work, we conducted MD simulations and MM/GBSA calculations to investigate the binding-induced conformational changes in the recognition of the 5S RNA by the central three zinc fingers of TFIIIA and the energetic factors that influence the binding affinity and specificity at an atomistic level. Our results revealed drastic interdomain conformational changes between these three zinc fingers, involving the exposure/burial of several crucial DNA/RNA binding residues, which can be related to the competition between DNA and RNA for the binding of TFIIIA. We also showed that the specific recognition between finger 4/finger 6 and the 5S RNA introduces frustrations to the nonspecific interactions between finger 5 and the 5S RNA, which may be important to achieve optimal binding affinity and specificity.