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

Collective Variables and Facilitated Conformational Opening during Translocation of Human Mitochondrial RNA Polymerase (POLRMT) from Atomic Simulations

Collective variable (CV) identification is challenging in complex dynamical systems. To study the translocation of a single-subunit RNA polymerase (RNAP) during human mitochondrial transcription, we employed all-atom molecular dynamics (MD) as a vehicle to illustrate CV refinement in conformational samplings and dimension reduction analyses. RNAP translocation is an essential mechanical step of transcription elongation that dictates gene expression. The translocation generally follows from polymerization product release and proceeds to initial binding or preinsertion of incoming nucleotides. The human mitochondrial DNA-dependent RNAP (or POLRMT) plays a critical role in cellular metabolism and can be a key molecular off-target in the design of nucleotide analogue antiviral and antitumor drugs due to its structural similarities with many viral RNAPs or RNA-dependent RNA polymerases (RdRps). While POLRMT shares particularly high structural similarity with bacteriophage T7 RNAP, previous experimental studies and our current simulations suggest that POLRMT's mechanochemical coupling mechanisms may be distinct. In the current work, we modeled POLRMT elongation complexes and performed equilibrium MD simulations on the pre- and post-translocation models, with extensive samplings around two potential translocation paths (with or without coupling to the fingers subdomain conformational change). We then compared time-lagged independent component analysis (tICA) and the neural network implementation of the variational approach for Markov processes (VAMPnets) as dimensional reduction methods on selected atomic coordinate sets to best represent the sampled features from the MD simulations. Our results indicate that POLRMT translocation is likely coupled with NTP binding to enable fingers subdomain opening at post-translocation which would otherwise be nonstabilized, or the translocations may proceed futilely without the fingers opening for incoming NTP initial binding or incorporation. The time scale of the coupled translocation reaches over hundreds of microseconds, as predicted by the VAMPnets analyses. Such a time scale seems to match a last postcatalytic kinetic step suggested for the POLRMT elongation cycle by previous experimental measurements. Our MD simulation studies combining atomic coordinate refinements and dimension reduction analyses on top of extensive conformational samplings thus suggest a variation of Brownian ratcheting in POLRMT translocation, as if the Brownian motions of translocation are coupled with NTP binding, which captures transient fingers subdomain opening to couple the translocation with a sustained fingers opening.

AMUSET-TICA: A Tensor-Based Approach for Identifying Slow Collective Variables in Biomolecular Dynamics

Elucidating collective variables (CVs) for biomolecular dynamics is crucial for understanding numerous biological processes. By leveraging the tensor-train data structure, a multilinear version of the AMUSE (Algorithm for Multiple Unknown Signals) algorithm for Koopman approximation (AMUSEt) was recently developed to identify CVs for biomolecular dynamics. To find slow CVs, AMUSEt transforms input features (e.g., pairwise atomic distances) into nonlinear basis functions (e.g., Gaussian functions) and encodes these nonlinear basis functions within a tensor-train structure via time-lagged correlation functions. Due to the need to fit these tensor-train data structures into computer memory, AMUSEt can handle only a limited number of input features. Consequently, AMUSEt relies on manually selecting and ranking features based on physical intuition to fully capture the slow dynamics. However, when applied to complex biological systems with numerous features, this selection and ranking process becomes increasingly challenging. To address this challenge, here we present AMUSET-TICA (AMUSEt-based Time-lagged Independent Component Analysis), a CV-identification method using time-structure-independent components (tICs) as the input features for AMUSEt. The key insight of AMUSET-TICA lies in its highly effective embedding of high-dimensional atomistic protein conformations, achieved by expanding orthogonal tICs into overlapping Gaussian basis functions through a tensor-product data structure. This eliminates the need for manually selecting and ranking input features for a wide range of biomolecular systems. We demonstrate that AMUSET-TICA consistently and significantly outperforms AMUSEt and tICA in identifying slow CVs for three different biomolecular systems: alanine dipeptide, the N-terminal domain of L9 (NTL9), and the FIP35 WW domain. For all these systems, the CVs generated by AMUSET-TICA accurately describe the slowest dynamical modes underlying these biological conformational changes. Furthermore, we show that AMUSET-TICA achieves performance comparable to deep-learning approaches like VAMPnets in identifying the slowest dynamical modes, while being significantly more computationally efficient in terms of CPU time. In addition, the CVs yielded by AMUSET-TICA provide insights into the folding mechanisms of NTL9 and the FIP35 WW domain, including CV3 and CV4 of the WW domain, which capture its two parallel folding pathways. We expect AMUSET-TICA can be widely applied to facilitate the investigation of biomolecular dynamics.

Targeting Bacterial RNA Polymerase: Harnessing Simulations and Machine Learning to Design Inhibitors for Drug-Resistant Pathogens

The increase in antimicrobial resistance presents a major challenge in treating bacterial infections, underscoring the need for innovative drug discovery approaches and novel inhibitors. Bacterial RNA polymerase (RNAP) has emerged as a crucial target for antibiotic development due to its essential role in transcription. RNAP is a molecular motor, and its function relies heavily on the dynamic shifts between multiple conformational states. While biochemical and structural experimental methods offer crucial insights into static RNAP-drug interactions, they fall short in capturing the dynamics at a molecular level. By integrating experimental data with advanced computational techniques like Markov State Models (MSMs), Generalized Master Equation (GME) Models and other machine-learning models constructed from molecular dynamics (MD) simulations, researchers can elucidate novel cryptic pockets that open transiently for antibiotic compounds and gain a more nuanced and comprehensive understanding of RNAP-drug interactions. This integrated approach not only deepens our fundamental knowledge but also enables more targeted and efficient antibiotic design strategies. In this Perspective, we highlight how this synergy between experimental and computational methods has the potential to open new pathways for innovative drug design and combination therapies that may help turn the tide in the ongoing battle against antibiotic-resistant bacteria.

RNA Polymerase II Activity Control of Gene Expression and Involvement in Disease

Gene expression is dependent on RNA Polymerase II (Pol II) activity in eukaryotes. In addition to determining the rate of RNA synthesis for all protein coding genes, Pol II serves as a platform for the recruitment of factors and regulation of co-transcriptional events, from RNA processing to chromatin modification and remodeling. The transcriptome can be shaped by changes in Pol II kinetics affecting RNA synthesis itself or because of alterations to co-transcriptional events that are responsive to or coupled with transcription. Genetic, biochemical, and structural approaches to Pol II in model organisms have revealed critical insights into how Pol II works and the types of factors that regulate it. The complexity of Pol II regulation generally increases with organismal complexity. In this review, we describe fundamental aspects of how Pol II activity can shape gene expression, discuss recent advances in how Pol II elongation is regulated on genes, and how altered Pol II function is linked to human disease and aging.

Structural basis of transcription: RNA polymerase II substrate binding and metal coordination using a free-electron laser

Catalysis and translocation of multisubunit DNA-directed RNA polymerases underlie all cellular mRNA synthesis. RNA polymerase II (Pol II) synthesizes eukaryotic pre-mRNAs from a DNA template strand buried in its active site. Structural details of catalysis at near-atomic resolution and precise arrangement of key active site components have been elusive. Here, we present the free-electron laser (FEL) structures of a matched ATP-bound Pol II and the hyperactive Rpb1 T834P bridge helix (BH) mutant at the highest resolution to date. The radiation-damage-free FEL structures reveal the full active site interaction network, including the trigger loop (TL) in the closed conformation, bonafide occupancy of both site A and B Mg2+, and, more importantly, a putative third (site C) Mg2+ analogous to that described for some DNA polymerases but not observed previously for cellular RNA polymerases. Molecular dynamics (MD) simulations of the structures indicate that the third Mg2+ is coordinated and stabilized at its observed position. TL residues provide half of the substrate binding pocket while multiple TL/BH interactions induce conformational changes that could allow translocation upon substrate hydrolysis. Consistent with TL/BH communication, a FEL structure and MD simulations of the T834P mutant reveal rearrangement of some active site interactions supporting potential plasticity in active site function and long-distance effects on both the width of the central channel and TL conformation, likely underlying its increased elongation rate at the expense of fidelity.

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.

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.

Structural basis of transcription: RNA Polymerase II substrate binding and metal coordination at 3.0 Å using a free-electron laser

Catalysis and translocation of multi-subunit DNA-directed RNA polymerases underlie all cellular mRNA synthesis. RNA polymerase II (Pol II) synthesizes eukaryotic pre-mRNAs from a DNA template strand buried in its active site. Structural details of catalysis at near atomic resolution and precise arrangement of key active site components have been elusive. Here we present the free electron laser (FEL) structure of a matched ATP-bound Pol II, revealing the full active site interaction network at the highest resolution to date, including the trigger loop (TL) in the closed conformation, bonafide occupancy of both site A and B Mg2+, and a putative third (site C) Mg2+ analogous to that described for some DNA polymerases but not observed previously for cellular RNA polymerases. Molecular dynamics (MD) simulations of the structure indicate that the third Mg2+ is coordinated and stabilized at its observed position. TL residues provide half of the substrate binding pocket while multiple TL/bridge helix (BH) interactions induce conformational changes that could propel translocation upon substrate hydrolysis. Consistent with TL/BH communication, a FEL structure and MD simulations of the hyperactive Rpb1 T834P bridge helix mutant reveals rearrangement of some active site interactions supporting potential plasticity in active site function and long-distance effects on both the width of the central channel and TL conformation, likely underlying its increased elongation rate at the expense of fidelity.

GraphVAMPnets for uncovering slow collective variables of self-assembly dynamics

Uncovering slow collective variables (CVs) of self-assembly dynamics is important to elucidate its numerous kinetic assembly pathways and drive the design of novel structures for advanced materials through the bottom-up approach. However, identifying the CVs for self-assembly presents several challenges. First, self-assembly systems often consist of identical monomers, and the feature representations should be invariant to permutations and rotational symmetries. Physical coordinates, such as aggregate size, lack high-resolution detail, while common geometric coordinates like pairwise distances are hindered by the permutation and rotational symmetry challenges. Second, self-assembly is usually a downhill process, and the trajectories often suffer from insufficient sampling of backward transitions that correspond to the dissociation of self-assembled structures. Popular dimensionality reduction methods, such as time-structure independent component analysis, impose detailed balance constraints, potentially obscuring the true dynamics of self-assembly. In this work, we employ GraphVAMPnets, which combines graph neural networks with a variational approach for Markovian process (VAMP) theory to identify the slow CVs of the self-assembly processes. First, GraphVAMPnets bears the advantages of graph neural networks, in which the graph embeddings can represent self-assembly structures in high-resolution while being invariant to permutations and rotational symmetries. Second, it is built upon VAMP theory, which studies Markov processes without forcing detailed balance constraints, which addresses the out-of-equilibrium challenge in the self-assembly process. We demonstrate GraphVAMPnets for identifying slow CVs of self-assembly kinetics in two systems: the aggregation of two hydrophobic molecules and the self-assembly of patchy particles. We expect that our GraphVAMPnets can be widely applied to molecular self-assembly.

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.

Characterization of RNA polymerase II trigger loop mutations using molecular dynamics simulations and machine learning

Catalysis and fidelity of multisubunit RNA polymerases rely on a highly conserved active site domain called the trigger loop (TL), which achieves roles in transcription through conformational changes and interaction with NTP substrates. The mutations of TL residues cause distinct effects on catalysis including hypo- and hyperactivity and altered fidelity. We applied molecular dynamics simulation (MD) and machine learning (ML) techniques to characterize TL mutations in the Saccharomyces cerevisiae RNA Polymerase II (Pol II) system. We did so to determine relationships between individual mutations and phenotypes and to associate phenotypes with MD simulated structural alterations. Using fitness values of mutants under various stress conditions, we modeled phenotypes along a spectrum of continual values. We found that ML could predict the phenotypes with 0.68 R2 correlation from amino acid sequences alone. It was more difficult to incorporate MD data to improve predictions from machine learning, presumably because MD data is too noisy and possibly incomplete to directly infer functional phenotypes. However, a variational auto-encoder model based on the MD data allowed the clustering of mutants with different phenotypes based on structural details. Overall, we found that a subset of loss-of-function (LOF) and lethal mutations tended to increase distances of TL residues to the NTP substrate, while another subset of LOF and lethal substitutions tended to confer an increase in distances between TL and bridge helix (BH). In contrast, some of the gain-of-function (GOF) mutants appear to cause disruption of hydrophobic contacts among TL and nearby helices.

Transient-State Kinetic Analysis of the RNA Polymerase II Nucleotide Incorporation Mechanism

Eukaryotic RNA polymerase II (Pol II) is an essential enzyme that lies at the core of eukaryotic biology. Due to its pivotal role in gene expression, Pol II has been subjected to a substantial number of investigations. We aim to further our understanding of Pol II nucleotide incorporation by utilizing transient-state kinetic techniques to examine Pol II single nucleotide addition on the millisecond time scale. We analyzed Saccharomyces cerevisiae Pol II incorporation of ATP or an ATP analog, Sp-ATP-α-S. Here we have measured the rate constants governing individual steps of the Pol II transcription cycle in the presence of ATP or Sp-ATP-α-S. These results suggest that Pol II catalyzes nucleotide incorporation by binding the next cognate nucleotide and immediately catalyzes bond formation and bond formation is either followed by a conformational change or pyrophosphate release. By comparing our previously published RNA polymerase I (Pol I) and Pol I lacking the A12 subunit (Pol I ΔA12) results that we collected under the same conditions with the identical technique, we show that Pol II and Pol I ΔA12 exhibit similar nucleotide addition mechanisms. This observation indicates that removal of the A12 subunit from Pol I results in a Pol II like enzyme. Taken together, these data further our collective understanding of Pol II's nucleotide incorporation mechanism and the evolutionary divergence of RNA polymerases across the three domains of life.

Unveiling the "Template-Dependent" Inhibition on the Viral Transcription of SARS-CoV-2

Remdesivir is one nucleotide analogue prodrug capable to terminate RNA synthesis in SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) by two distinct mechanisms. Although the "delayed chain termination" mechanism has been extensively investigated, the "template-dependent" inhibitory mechanism remains elusive. In this study, we have demonstrated that remdesivir embedded in the template strand seldom directly disrupted the complementary NTP incorporation at the active site. Instead, the translocation of remdesivir from the +2 to the +1 site was hindered due to the steric clash with V557. Moreover, we have elucidated the molecular mechanism characterizing the drug resistance upon V557L mutation. Overall, our studies have provided valuable insight into the "template-dependent" inhibitory mechanism exerted by remdesivir on SARS-CoV-2 RdRp and paved venues for an alternative antiviral strategy for the COVID-19 pandemic. As the "template-dependent" inhibition occurs across diverse viral RdRps, our findings may also shed light on a common acting mechanism of inhibitors.

DNA Deformation Exerted by Regulatory DNA-Binding Motifs in Human Alkyladenine DNA Glycosylase Promotes Base Flipping

Human alkyladenine DNA glycosylase (AAG) is a key enzyme that corrects a broad range of alkylated and deaminated nucleobases to maintain genomic integrity. When encountering the lesions, AAG adopts a base-flipping strategy to extrude the target base from the DNA duplex to its active site, thereby cleaving the glycosidic bond. Despite its functional importance, the detailed mechanism of such base extrusion and how AAG distinguishes the lesions from an excess of normal bases both remain elusive. Here, through the Markov state model constructed on extensive all-atom molecular dynamics simulations, we find that the alkylated nucleobase (N3-methyladenine, 3MeA) everts through the DNA major groove. Two key AAG motifs, the intercalation and E131-N146 motifs, play active roles in bending/pressing the DNA backbone and widening the DNA minor groove during 3MeA eversion. In particular, the intercalated residue Y162 is involved in buckling the target site at the early stage of 3MeA eversion. Our traveling-salesman based automated path searching algorithm further revealed that a non-target normal adenine tends to be trapped in an exo site near the active site, which however barely exists for a target base 3MeA. Collectively, these results suggest that the Markov state model combined with traveling-salesman based automated path searching acts as a promising approach for studying complex conformational changes of biomolecules and dissecting the elaborate mechanism of target recognition by this unique enzyme.

Alternative role of motif B in template dependent polymerase inhibition

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) relies on the central molecular machine RNA-dependent RNA polymerase (RdRp) for the viral replication and transcription. Remdesivir at the template strand has been shown to effectively inhibit the RNA synthesis in SARS-CoV-2 RdRp by deactivating not only the complementary UTP incorporation but also the next nucleotide addition. How-ever, the underlying molecular mechanism of the second inhibitory point remains unclear. In this work, we have performed molecular dynamics simulations and demonstrated that such inhibition has not directly acted on the nucleotide addition at the active site. Instead, the translocation of Remdesivir from + 1 to − 1 site is hindered thermodynamically as the post-translocation state is less stable than the pre-translocation state due to the motif B residue G683. Moreover, another conserved residue S682 on motif B further hinders the dynamic translocation of Remdesivir due to the steric clash with the 1′-cyano substitution. Overall, our study has unveiled an alternative role of motif B in mediating the translocation when Remdesivir is present in the template strand and complemented our understanding about the inhibitory mechanisms exerted by Remdesivir on the RNA synthesis in SARS-CoV-2 RdRp.

Dynamics of peptide loading into major histocompatibility complex class I molecules chaperoned by TAPBPR

Major histocompatibility complex class I (MHC-I) molecules display antigenic peptides on the cell surface for T cell receptor scanning, thereby activating the immune response. Peptide loading into MHC-I molecules is thus a critical step during the antigen presentation process. Chaperone TAP-binding protein related (TAPBPR) plays a critical role in promoting high-affinity peptide loading into MHC-I, by discriminating against the low-affinity ones. However, the complete peptide loading dynamics into TAPBPR-bound MHC-I is still elusive. Here, we constructed kinetic network models based on hundreds of short-time MD simulations with an aggregated simulation time of ∼21.7 μs, and revealed, at atomic level, four key intermediate states of one antigenic peptide derived from melanoma-associated MART-1/Melan-A protein during its loading process into TAPBPR-bound MHC-I. We find that the TAPBPR binding at the MHC-I pocket-F can substantially reshape the distant pocket-B via allosteric regulations, which in turn promotes the following peptide N-terminal loading. Intriguingly, the partially loaded peptide could profoundly weaken the TAPBPR-MHC stability, promoting the dissociation of the TAPBPR scoop-loop (SL) region from the pocket-F to a more solvent-exposed conformation. Structural inspections further indicate that the peptide loading could remotely affect the SL binding site through both allosteric perturbations and direct contacts. In addition, another structural motif of TAPBPR, the jack hairpin region, was also found to participate in mediating the peptide editing. Our study sheds light on the detailed molecular mechanisms underlying the peptide loading process into TAPBPR-bound MHC-I and pinpoints the key structural factors responsible for dictating the peptide-loading dynamics.

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.

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.

Transcriptional Pausing as a Mediator of Bacterial Gene Regulation

Cellular life depends on transcription of DNA by RNA polymerase to express genetic information. RNA polymerase has evolved not just to read information from DNA and write it to RNA but also to sense and process information from the cellular and extracellular environments. Much of this information processing occurs during transcript elongation, when transcriptional pausing enables regulatory decisions. Transcriptional pauses halt RNA polymerase in response to DNA and RNA sequences and structures at locations and times that help coordinate interactions with small molecules and transcription factors important for regulation. Four classes of transcriptional pause signals are now evident after decades of study: elemental pauses, backtrack pauses, hairpin-stabilized pauses, and regulator-stabilized pauses. In this review, I describe current understanding of the molecular mechanisms of these four classes of pause signals, remaining questions about how RNA polymerase responds to pause signals, and the many exciting directions now open to understand pausing and the regulation of transcript elongation on a genome-wide scale. Expected final online publication date for the Annual Review of Microbiology, Volume 75 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

Markov models from the square root approximation of the Fokker-Planck equation: calculating the grid-dependent flux

Molecular dynamics (MD) are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the MD as a stochastic process and analyses the dominant eigenfunctions of the associated Fokker-Planck operator, or of closely related transfer operators. So far, the calculation of the discretized operators requires extensive MD simulations. The square-root approximation of the Fokker-Planck equation is a method to calculate transition rates as a ratio of the Boltzmann densities of neighboring grid cells times a flux, and can in principle be calculated without a simulation. In a previous work we still used MD simulations to determine the flux. Here, we propose several methods to calculate the exact or approximate flux for various grid types, and thus estimate the rate matrix without a simulation. Using model potentials we test computational efficiency of the methods, and the accuracy with which they reproduce the dominant eigenfunctions and eigenvalues. For these model potentials, rate matrices with up to [Formula: see text] states can be obtained within seconds on a single high-performance compute server if regular grids are used.

1'-Ribose cyano substitution allows Remdesivir to effectively inhibit nucleotide addition and proofreading during SARS-CoV-2 viral RNA replication

COVID-19 has recently caused a global health crisis and an effective interventional therapy is urgently needed. Remdesivir is one effective inhibitor for SARS-CoV-2 viral RNA replication. It supersedes other NTP analogues because it not only terminates the polymerization activity of RNA-dependent RNA polymerase (RdRp), but also inhibits the proofreading activity of intrinsic exoribonuclease (ExoN). Even though the static structure of Remdesivir binding to RdRp has been solved and biochemical experiments have suggested it to be a "delayed chain terminator", the underlying molecular mechanisms is not fully understood. Here, we performed all-atom molecular dynamics (MD) simulations with an accumulated simulation time of 24 microseconds to elucidate the inhibitory mechanism of Remdesivir on nucleotide addition and proofreading. We found that when Remdesivir locates at an upstream site in RdRp, the 1'-cyano group experiences electrostatic interactions with a salt bridge (Asp865-Lys593), which subsequently halts translocation. Our findings can supplement the current understanding of the delayed chain termination exerted by Remdesivir and provide an alternative molecular explanation about Remdesivir's inhibitory mechanism. Such inhibition also reduces the likelihood of Remdesivir to be cleaved by ExoN acting on 3'-terminal nucleotides. Furthermore, our study also suggests that Remdesivir's 1'-cyano group can disrupt the cleavage site of ExoN via steric interactions, leading to a further reduction in the cleavage efficiency. Our work provides plausible and novel mechanisms at the molecular level of how Remdesivir inhibits viral RNA replication, and our findings may guide rational design for new treatments of COVID-19 targeting viral replication.

Molecular motor traffic with a slow binding site

We discuss how the presence of a slow binding site in molecular motor traffic gives rise to defect-induced "traffic jams" that have properties different from those of the well-studied boundary-induced jams that originate from an imbalance between initiation and termination. To this end we analyze in detail the stationary distribution of a lattice gas model for traffic of molecular motors with a defect. In particular, we obtain analytically the exact spatial distribution of motors, the probability distribution of the random position of the molecular traffic jam and we report unexpected spatial anticorrelations between local molecular motor densities near the defect.

Super enhancers-Functional cores under the 3D genome

Complex biochemical reactions take place in the nucleus all the time. Transcription machines must follow the rules. The chromatin state, especially the three-dimensional structure of the genome, plays an important role in gene regulation and expression. The super enhancers are important for defining cell identity in mammalian developmental processes and human diseases. It has been shown that the major components of transcriptional activation complexes are recruited by super enhancer to form phase-separated condensates. We summarize the current knowledge about super enhancer in the 3D genome. Furthermore, a new related transcriptional regulation model from super enhancer is outlined to explain its role in the mammalian cell progress.

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.

Nucleotide Loading Modes of Human RNA Polymerase II as Deciphered by Molecular Simulations

Mapping the route of nucleoside triphosphate (NTP) entry into the sequestered active site of RNA polymerase (RNAP) has major implications for elucidating the complete nucleotide addition cycle. Constituting a dichotomy that remains to be resolved, two alternatives, direct NTP delivery via the secondary channel (CH2) or selection to downstream sites in the main channel (CH1) prior to catalysis, have been proposed. In this study, accelerated molecular dynamics simulations of freely diffusing NTPs about RNAPII were applied to refine the CH2 model and uncover atomic details on the CH1 model that previously lacked a persuasive structural framework to illustrate its mechanism of action. Diffusion and binding of NTPs to downstream DNA, and the transfer of a preselected NTP to the active site, are simulated for the first time. All-atom simulations further support that CH1 loading is transcription factor IIF (TFIIF) dependent and impacts catalytic isomerization. Altogether, the alternative nucleotide loading systems may allow distinct transcriptional landscapes to be expressed.

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.

Structure and Function of RNA Polymerases and the Transcription Machineries

In all living organisms, the flow of genetic information is a two-step process: first DNA is transcribed into RNA, which is subsequently used as template for protein synthesis during translation. In bacteria, archaea and eukaryotes, transcription is carried out by multi-subunit RNA polymerases (RNAPs) sharing a conserved architecture of the RNAP core. RNAPs catalyse the highly accurate polymerisation of RNA from NTP building blocks, utilising DNA as template, being assisted by transcription factors during the initiation, elongation and termination phase of transcription. The complexity of this highly dynamic process is reflected in the intricate network of protein-protein and protein-nucleic acid interactions in transcription complexes and the substantial conformational changes of the RNAP as it progresses through the transcription cycle.In this chapter, we will first briefly describe the early work that led to the discovery of multisubunit RNAPs. We will then discuss the three-dimensional organisation of RNAPs from the bacterial, archaeal and eukaryotic domains of life, highlighting the conserved nature, but also the domain-specific features of the transcriptional apparatus. Another section will focus on transcription factors and their role in regulating the RNA polymerase throughout the different phases of the transcription cycle. This includes a discussion of the molecular mechanisms and dynamic events that govern transcription initiation, elongation and termination.

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.

8-Oxo-guanine DNA damage induces transcription errors by escaping two distinct fidelity control checkpoints of RNA polymerase II

RNA polymerase II (Pol II) has an intrinsic fidelity control mechanism to maintain faithful genetic information transfer during transcription. 8-Oxo-guanine (8OG), a commonly occurring damaged guanine base, promotes misincorporation of adenine into the RNA strand. Recent structural work has shown that adenine can pair with the syn conformation of 8OG directly upstream of the Pol II active site. However, it remains unknown how 8OG is accommodated in the active site as a template base for the incoming ATP. Here, we used molecular dynamics (MD) simulations to investigate two consecutive steps that may contribute to the adenine misincorporation by Pol II. First, the mismatch is located in the active site, contributing to initial incorporation of adenine. Second, the mismatch is in the adjacent upstream position, contributing to extension from the mismatched bp. These results are supported by an in vitro transcription assay, confirming that 8OG can induce adenine misincorporation. Our simulations further suggest that 8OG forms a stable bp with the mismatched adenine in both the active site and the adjacent upstream position. This stability predominantly originates from hydrogen bonding between the mismatched adenine and 8OG in a noncanonical syn conformation. Interestingly, we also found that an unstable bp present directly upstream of the active site, such as adenine paired with 8OG in the canonical anti conformation, largely disrupts the stability of the active site. Our findings have uncovered two main factors contributing to how 8OG induces transcriptional errors and escapes Pol II transcriptional fidelity control checkpoints.

Stationary RNA polymerase fluctuations during transcription elongation

We study fluctuation effects of nonsteric molecular interactions between RNA polymerase (RNAP) motors that move simultaneously on the same DNA track during transcription elongation. Based on a stochastic model that allows for the exact analytical computation of the stationary distribution of RNAPs as a function of their density, interaction strength, nucleoside triphosphate concentration, and rate of pyrophosphate release we predict an almost geometric headway distribution of subsequent RNAP transcribing on the same DNA segment. The localization length which characterizes the decay of the headway distribution depends directly only the average density of RNAP and the interaction strength, but not on specific single-RNAP properties. Density correlations are predicted to decay exponentially with the distance (in units of DNA base pairs), with a correlation length that is significantly shorter than the localization length.

Estimation of the infinitesimal generator by square-root approximation

In recent years, for the analysis of molecular processes, the estimation of time-scales and transition rates has become fundamental. Estimating the transition rates between molecular conformations is-from a mathematical point of view-an invariant subspace projection problem. We present a method to project the infinitesimal generator acting on function space to a low-dimensional rate matrix. This projection can be performed in two steps. First, we discretize the conformational space in a Voronoi tessellation, then the transition rates between adjacent cells is approximated by the geometric average of the Boltzmann weights of the Voronoi cells. This method demonstrates that there is a direct relation between the potential energy surface of molecular structures and the transition rates of conformational changes. We will show also that this approximation is correct and converges to the generator of the Smoluchowski equation in the limit of infinitely small Voronoi cells. We present results for a two dimensional diffusion process and alanine dipeptide as a high-dimensional system.

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.

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.

GENESIS 1.1: A hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms

GENeralized-Ensemble SImulation System (GENESIS) is a software package for molecular dynamics (MD) simulation of biological systems. It is designed to extend limitations in system size and accessible time scale by adopting highly parallelized schemes and enhanced conformational sampling algorithms. In this new version, GENESIS 1.1, new functions and advanced algorithms have been added. The all-atom and coarse-grained potential energy functions used in AMBER and GROMACS packages now become available in addition to CHARMM energy functions. The performance of MD simulations has been greatly improved by further optimization, multiple time-step integration, and hybrid (CPU + GPU) computing. The string method and replica-exchange umbrella sampling with flexible collective variable choice are used for finding the minimum free-energy pathway and obtaining free-energy profiles for conformational changes of a macromolecule. These new features increase the usefulness and power of GENESIS for modeling and simulation in biological research. © 2017 Wiley Periodicals, Inc.

Nucleotide Selectivity at a Preinsertion Checkpoint of T7 RNA Polymerase Transcription Elongation

Nucleotide selection is crucial for transcription fidelity control, in particular, for viral T7 RNA polymerase (RNAP) lack of proofreading activity. It has been recognized that multiple kinetic checkpoints exist prior to full nucleotide incorporation. In this work, we implemented intensive atomistic molecular dynamics (MD) simulations to quantify how strong the nucleotide selection is at the initial checkpoint of an elongation cycle of T7 RNAP. The incoming nucleotides bind into a preinsertion site where a critical tyrosine residue locates nearby to assist the nucleotide selection. We calculated the relative binding free energy between a noncognate nucleotide and a cognate one at a preinsertion configuration via alchemical simulations, showing that a small selection free energy or the binding free energy difference (∼3 k_BT) exists between the two nucleotides. Indeed, another preinsertion configuration favored by the noncognate nucleotides was identified, which appears to be off path for further nucleotide insertion and additionally assists the nucleotide selection. By chemical master equation (CME) approach, we show that the small selection free energy at the preinsertion site along with the off-path noncognate nucleotide filtering can help substantially to reduce the error rate and to maintain the elongation rate high in the T7 RNAP transcription.

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.