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

Deciphering allosteric mechanisms in KRAS activation: insights from GTP-induced conformational dynamics and interaction network reorganization

The conformational dynamics and activation mechanisms of KRAS proteins are of great importance for targeted cancer therapy. However, the detailed molecular mechanics of KRAS activation induced by GTP binding remains unclear. In this study, we systematically investigated how GTP/GDP exchange affects the thermodynamic and kinetic properties of KRAS and explored the activation mechanism using molecular dynamics (MD) simulations, Markov state models (MSMs), and neural relational inference (NRI) models. Our MD simulation results show that GTP binding significantly enhances the conformational flexibility of KRAS, and thus promotes its transition to an active conformation with more open switch I and II regions. MSMs analyses show that KRAS in the GTP-bound state can be transitioned to the active state more efficiently during the simulation than in the GDP-bound state. In addition, NRI model calculations showed that GTP binding enhanced residue-residue interactions within the KRAS protein, especially when the long-range interactions were significantly enhanced. Furthermore, the allosteric signaling pathways from the P-loop to switch I and II as well as the key amino acid sites along the pathways were obtained using a graph-based shortest path analysis. Our results can contribute to a deeper understanding of the mechanism of KRAS allosteric activation and provide a foundation for the development of targeted therapeutic drugs to regulate KRAS activity.

Early intermediates in bacterial RNA polymerase promoter melting visualized by time-resolved cryo-electron microscopy

During formation of the transcription-competent open complex (RPo) by bacterial RNA polymerases (RNAPs), transient intermediates pile up before overcoming a rate-limiting step. Structural descriptions of these interconversions in real time are unavailable. To address this gap, here we use time-resolved cryogenic electron microscopy (cryo-EM) to capture four intermediates populated 120 ms or 500 ms after mixing Escherichia coli σ70-RNAP and the λPR promoter. Cryo-EM snapshots revealed that the upstream edge of the transcription bubble unpairs rapidly, followed by stepwise insertion of two conserved nontemplate strand (nt-strand) bases into RNAP pockets. As the nt-strand 'read-out' extends, the RNAP clamp closes, expelling an inhibitory σ70 domain from the active-site cleft. The template strand is fully unpaired by 120 ms but remains dynamic, indicating that yet unknown conformational changes complete RPo formation in subsequent steps. Given that these events likely describe DNA opening at many bacterial promoters, this study provides insights into how DNA sequence regulates steps of RPo formation.

Information Bottleneck Approach for Markov Model Construction

Markov state models (MSMs) have proven valuable in studying the dynamics of protein conformational changes via statistical analysis of molecular dynamics simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time necessitates defining states that circumvent significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process effectively coarse-grains time and space, integrating out rapid motions within metastable states. Thus, MSMs possess a multiresolution nature, where the granularity of states can be adjusted according to the time-resolution, offering flexibility in capturing system dynamics. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), a framework that unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of the VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multiresolution Markovian models. Through applications to well-validated mini-proteins, SPIB showcases unique advantages compared to competing methods. It autonomously and self-consistently adjusts the number of metastable states based on a specified minimal time resolution, eliminating the need for manual tuning. While maintaining efficacy in dynamical properties, SPIB excels in accurately distinguishing metastable states and capturing numerous well-populated macrostates. This contrasts with existing VAMP-based methods, which often emphasize slow dynamics at the expense of incorporating numerous sparsely populated states. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. With these benefits, we propose SPIB as an easy-to-implement methodology for end-to-end MSM construction.

An Information Bottleneck Approach for Markov Model Construction

Markov state models (MSMs) have proven valuable in studying dynamics of protein conformational changes via statistical analysis of molecular dynamics (MD) simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time necessitates defining states that circumvent significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process effectively coarse-grains time and space, integrating out rapid motions within metastable states. Thus, MSMs possess a multi-resolution nature, where the granularity of states can be adjusted according to the time-resolution, offering flexibility in capturing system dynamics. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), a framework that unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of the VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multi-resolution Markovian models. Through applications to well-validated mini-proteins, SPIB showcases unique advantages compared to competing methods. It autonomously and self-consistently adjusts the number of metastable states based on specified minimal time resolution, eliminating the need for manual tuning. While maintaining efficacy in dynamical properties, SPIB excels in accurately distinguishing metastable states and capturing numerous well-populated macrostates. This contrasts with existing VAMP-based methods, which often emphasize slow dynamics at the expense of incorporating numerous sparsely populated states. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. With these benefits, we propose SPIB as an easy-to-implement methodology for end-to-end MSMs construction.

Transient interactions modulate the affinity of NF-κB transcription factors for DNA

The dimeric nuclear factor kappa B (NF-κB) transcription factors (TFs) regulate gene expression by binding to a variety of κB DNA elements with conserved G:C-rich flanking sequences enclosing a degenerate central region. Toward defining mechanistic principles of affinity regulated by degeneracy, we observed an unusual dependence of the affinity of RelA on the identity of the central base pair, which appears to be noncontacted in the complex crystal structures. The affinity of κB sites with A or T at the central position is ~10-fold higher than with G or C. The crystal structures of neither the complexes nor the free κB DNAs could explain the differences in affinity. Interestingly, differential dynamics of several residues were revealed in molecular dynamics simulation studies, where simulation replicates totaling 148 μs were performed on NF-κB:DNA complexes and free κB DNAs. Notably, Arg187 and Arg124 exhibited selectivity in transient interactions that orchestrated a complex interplay among several DNA-interacting residues in the central region. Binding and simulation studies with mutants supported these observations of transient interactions dictating specificity. In combination with published reports, this work provides insights into the nuanced mechanisms governing the discriminatory binding of NF-κB family TFs to κB DNA elements and sheds light on cancer pathogenesis of cRel, a close homolog of RelA.

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.

Early intermediates in bacterial RNA polymerase promoter melting visualized by time-resolved cryo-electron microscopy

During formation of the transcription-competent open complex (RPo) by bacterial RNA polymerases (RNAP), transient intermediates pile up before overcoming a rate-limiting step. Structural descriptions of these interconversions in real time are unavailable. To address this gap, time-resolved cryo-electron microscopy (cryo-EM) was used to capture four intermediates populated 120 or 500 milliseconds (ms) after mixing Escherichia coli σ70-RNAP and the λPR promoter. Cryo-EM snapshots revealed the upstream edge of the transcription bubble unpairs rapidly, followed by stepwise insertion of two conserved nontemplate strand (nt-strand) bases into RNAP pockets. As nt-strand "read-out" extends, the RNAP clamp closes, expelling an inhibitory σ70 domain from the active-site cleft. The template strand is fully unpaired by 120 ms but remains dynamic, indicating yet unknown conformational changes load it in subsequent steps. Because these events likely describe DNA opening at many bacterial promoters, this study provides needed insights into how DNA sequence regulates steps of RPo formation.

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.

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

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

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

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

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

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

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

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

Clamp Interactions with +3/+6 Duplex and Upstream-to-Downstream Allosteric Effects in Late Steps of Forming a Stable RNA Polymerase-Promoter Open Complex

Stable 37 °C open complexes (OC) of E. coli RNA polymerase (RNAP) at λP_R and T7A1 promoters form at similar rates but have very different lifetimes. To understand the downstream interactions responsible for OC lifetime, how promoter sequence directs them and when they form, we report lifetimes of stable OC and unstable late (I₂) intermediates for promoters with different combinations of λP_R (L) and T7A1 (T) discriminators, core promoters and UP elements. I₂ lifetimes are similarly short, while stable OC lifetimes differ greatly, determined largely by the discriminator and modulated by core-promoter and UP elements. The free energy change ΔG₃^o for I₂ → stable OC is approximately -4 kcal more favorable for L-discriminator than for T-discriminator promoters. Downstream-truncation at +6 (DT+6) greatly destabilizes OC at L-discriminator but not T-discriminator promoters, making all ΔG₃^o values similar (approximately -4 kcal). Urea reduces OC lifetime greatly by affecting ΔG₃^o. We deduce that urea acts by disfavoring coupled folding of key elements of the β'-clamp, that I₂ is an open-clamp OC, and that clamp-closing in I₂ → stable OC involves coupled folding. Differences in ΔG₃^o between downstream-truncated and full-length promoters yield contributions to ΔG₃^o from interactions with downstream mobile elements (DME) including β-lobe and β'-jaw, more favorable for L-discriminator than for T-discriminator promoters. We deduce how competition between far-downstream DNA and σ⁷⁰ region 1.1 affects ΔG₃^o values. We discuss variant-specific ΔG₃^o contributions in terms of the allosteric network by which differences in discriminator and -10 sequence are sensed and transmitted downstream to affect DME-duplex interactions in I₂ → stable OC.

Compact and complete description of non-Markovian dynamics

Generalized master equations provide a theoretically rigorous framework to capture the dynamics of processes ranging from energy harvesting in plants and photovoltaic devices to qubit decoherence in quantum technologies and even protein folding. At their center is the concept of memory. The explicit time-nonlocal description of memory is both protracted and elaborate. When physical intuition is at a premium, one would desire a more compact, yet complete, description. Here, we demonstrate how and when the time-convolutionless formalism constitutes such a description. In particular, by focusing on the dissipative dynamics of the spin-boson and Frenkel exciton models, we show how to: easily construct the time-local generator from reference reduced dynamics, elucidate the dependence of its existence on the system parameters and the choice of reduced observables, identify the physical origin of its apparent divergences, and offer analysis tools to diagnose their severity and circumvent their deleterious effects. We demonstrate that, when applicable, the time-local approach requires as little information as the more commonly used time-nonlocal scheme, with the important advantages of providing a more compact description, greater algorithmic simplicity, and physical interpretability. We conclude by introducing the discrete-time analog and a straightforward protocol to employ it in cases where the reference dynamics have limited resolution. The insights we present here offer the potential for extending the reach of dynamical methods, reducing both their cost and conceptual complexity.

Automated Path Searching Reveals the Mechanism of Hydrolysis Enhancement by T4 Lysozyme Mutants

Bacteriophage T4 lysozyme (T4L) is a glycosidase that is widely applied as a natural antimicrobial agent in the food industry. Due to its wide applications and small size, T4L has been regarded as a model system for understanding protein dynamics and for large-scale protein engineering. Through structural insights from the single conformation of T4L, a series of mutations (L99A,G113A,R119P) have been introduced, which have successfully raised the fractional population of its only hydrolysis-competent excited state to 96%. However, the actual impact of these substitutions on its dynamics remains unclear, largely due to the lack of highly efficient sampling algorithms. Here, using our recently developed travelling-salesman-based automated path searching (TAPS), we located the minimum-free-energy path (MFEP) for the transition of three T4L mutants from their ground states to their excited states. All three mutants share a three-step transition: the flipping of F114, the rearrangement of α0/α1 helices, and final refinement. Remarkably, the MFEP revealed that the effects of the mutations are drastically beyond the expectations of their original design: (a) the G113A substitution not only enhances helicity but also fills the hydrophobic Cavity I and reduces the free energy barrier for flipping F114; (b) R119P barely changes the stability of the ground state but stabilizes the excited state through rarely reported polar contacts S117_OG:N132_ND2, E11_OE1:R145_NH1, and E11_OE2:Q105_NE2; (c) the residue W138 flips into Cavity I and further stabilizes the excited state for the triple mutant L99A,G113A,R119P. These novel insights that were unexpected in the original mutant design indicated the necessity of incorporating path searching into the workflow of rational protein engineering.

DNA opening during transcription initiation by RNA polymerase II in atomic detail

RNA polymerase II (RNAP II) synthesizes RNA by reading the DNA code. During transcription initiation, RNAP II opens the double-stranded DNA to expose the DNA template to the active site. The molecular interactions driving and controlling DNA opening are not well understood. We used all-atom steered molecular dynamics simulations to derive a continuous pathway of DNA opening in human RNAP II, involving a 55 Å DNA strand displacement and a nearly 360° DNA helix rotation. To drive such large-scale transitions, we used a combination of RMSD-based collective variables, a newly designed rotational coordinate, and a path collective variable. The simulations reveal extensive interactions of the DNA with three conserved protein loops near the active site, namely with the rudder, fork loop 1, and fork loop 2. According to the simulations, DNA-protein interactions support DNA opening by a twofold mechanism; they catalyze DNA opening by attacking Watson-Crick hydrogen bonds, and they stabilize the open DNA bubble by the formation of a wide set of DNA-protein salt bridges.

Pseudomonas aeruginosa SutA wedges RNAP lobe domain open to facilitate promoter DNA unwinding

Pseudomonas aeruginosa (Pae) SutA adapts bacteria to hypoxia and nutrition-limited environment during chronic infection by increasing transcription activity of an RNA polymerase (RNAP) holoenzyme comprising the stress-responsive σ factor σ^S (RNAP-σ^S). SutA shows no homology to previously characterized RNAP-binding proteins. The structure and mode of action of SutA remain unclear. Here we determined cryo-EM structures of Pae RNAP-σ^S holoenzyme, Pae RNAP-σ^S holoenzyme complexed with SutA, and Pae RNAP-σ^S transcription initiation complex comprising SutA. The structures show SutA pinches RNAP-β protrusion and facilitates promoter unwinding by wedging RNAP-β lobe open. Our results demonstrate that SutA clears an energetic barrier to facilitate promoter unwinding of RNAP-σ^S holoenzyme.

SutA is a transcription factor which increases transcription activity of an RNA polymerase (RNAP). Here, authors present cryo-EM structures of SutA-bound RNAP-σ^S holoenzyme and SutA-bound transcription initiation complex, which reveals SutA wedging the RNAP-β lobe open to aid unwinding.

Correlation-Based Feature Selection to Identify Functional Dynamics in Proteins

To interpret molecular dynamics simulations of biomolecular systems, systematic dimensionality reduction methods are commonly employed. Among others, this includes principal component analysis (PCA) and time-lagged independent component analysis (TICA), which aim to maximize the variance and the time scale of the first components, respectively. A crucial first step of such an analysis is the identification of suitable and relevant input coordinates (the so-called features), such as backbone dihedral angles and interresidue distances. As typically only a small subset of those coordinates is involved in a specific biomolecular process, it is important to discard the remaining uncorrelated motions or weakly correlated noise coordinates. This is because they may exhibit large amplitudes or long time scales and therefore will be erroneously considered important by PCA and TICA, respectively. To discriminate collective motions underlying functional dynamics from uncorrelated motions, the correlation matrix of the input coordinates is block-diagonalized by a clustering method. This strategy avoids possible bias due to presumed functional observables and conformational states or variation principles that maximize variance or time scales. Considering several linear and nonlinear correlation measures and various clustering algorithms, it is shown that the combination of linear correlation and the Leiden community detection algorithm yields excellent results for all considered model systems. These include the functional motion of T4 lysozyme to demonstrate the successful identification of collective motion, as well as the folding of the villin headpiece to highlight the physical interpretation of the correlated motions in terms of a functional mechanism.

Rotational Mechanism of FO Motor in the F-Type ATP Synthase Driven by the Proton Motive Force

In FOF1 ATP synthase, driven by the proton motive force across the membrane, the FO motor rotates the central rotor and induces conformational changes in the F1 motor, resulting in ATP synthesis. Recently, many near-atomic resolution structural models have been obtained using cryo-electron microscopy. Despite high resolution, however, static information alone cannot elucidate how and where the protons pass through the FO and how proton passage is coupled to FO rotation. Here, we review theoretical and computational studies based on FO structure models. All-atom molecular dynamics (MD) simulations elucidated changes in the protonation/deprotonation of glutamate-the protein-carrier residue-during rotation and revealed the protonation states that form the "water wire" required for long-range proton hopping. Coarse-grained MD simulations unveiled a free energy surface based on the protonation state and rotational angle of the rotor. Hybrid Monte Carlo and MD simulations showed how proton transfer is coupled to rotation.

Allosteric couplings upon binding of RfaH to transcription elongation complexes

In every domain of life, NusG-like proteins bind to the elongating RNA polymerase (RNAP) to support processive RNA synthesis and to couple transcription to ongoing cellular processes. Structures of factor-bound transcription elongation complexes (TECs) reveal similar contacts to RNAP, consistent with a shared mechanism of action. However, NusG homologs differ in their regulatory roles, modes of recruitment, and effects on RNA synthesis. Some of these differences could be due to conformational changes in RNAP and NusG-like proteins, which cannot be captured in static structures. Here, we employed hydrogen-deuterium exchange mass spectrometry to investigate changes in local and non-local structural dynamics of Escherichia coli NusG and its paralog RfaH, which have opposite effects on expression of xenogenes, upon binding to TEC. We found that NusG and RfaH regions that bind RNAP became solvent-protected in factor-bound TECs, whereas RNAP regions that interact with both factors showed opposite deuterium uptake changes when bound to NusG or RfaH. Additional changes far from the factor-binding site were observed only with RfaH. Our results provide insights into differences in structural dynamics exerted by NusG and RfaH during binding to TEC, which may explain their different functional outcomes and allosteric regulation of transcriptional pausing by RfaH.

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

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

Harnessing Reversed Allosteric Communication: A Novel Strategy for Allosteric Drug Discovery

Allostery is a fundamental and extensive mechanism of intramolecular signal transmission. Allosteric drugs possess several unique pharmacological advantages over traditional orthosteric drugs, including greater selectivity, better physicochemical properties, and lower off-target toxicity. However, owing to the complexity of allosteric regulation, experimental approaches for the development of allosteric modulators are traditionally serendipitous. Recently, the reversed allosteric communication theory has been proposed, providing a feasible tool for the unbiased detection of allosteric sites. Herein, we review the latest research on the reversed allosteric communication effect using the examples of sirtuin 6, epidermal growth factor receptor, 3-phosphoinositide-dependent protein kinase 1, and Related to A and C kinases (RAC) serine/threonine protein kinase B and recapitulate the methodologies of reversed allosteric communication strategy. The novel reversed allosteric communication strategy greatly expands the horizon of allosteric site identification and allosteric mechanism exploration and is expected to accelerate an end-to-end framework for drug discovery.

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

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

Modeling DNA Opening in the Eukaryotic Transcription Initiation Complexes via Coarse-Grained Models

Recently, the molecular mechanisms of transcription initiation have been intensively studied. Especially, the cryo-electron microscopy revealed atomic structure details in key states in the eukaryotic transcription initiation. Yet, the dynamic processes of the promoter DNA opening in the pre-initiation complex remain obscured. In this study, based on the three cryo-electron microscopic yeast structures for the closed, open, and initially transcribing complexes, we performed multiscale molecular dynamics (MD) simulations to model structures and dynamic processes of DNA opening. Combining coarse-grained and all-atom MD simulations, we first obtained the atomic model for the DNA bubble in the open complexes. Then, in the MD simulation from the open to the initially transcribing complexes, we found a previously unidentified intermediate state which is formed by the bottleneck in the fork loop 1 of Pol II: The loop opening triggered the escape from the intermediate, serving as a gatekeeper of the promoter DNA opening. In the initially transcribing complex, the non-template DNA strand passes a groove made of the protrusion, the lobe, and the fork of Rpb2 subunit of Pol II, in which several positively charged and highly conserved residues exhibit key interactions to the non-template DNA strand. The back-mapped all-atom models provided further insights on atomistic interactions such as hydrogen bonding and can be used for future simulations.

Transcription initiation at a consensus bacterial promoter proceeds via a 'bind-unwind-load-and-lock' mechanism

Transcription initiation starts with unwinding of promoter DNA by RNA polymerase (RNAP) to form a catalytically competent RNAP-promoter complex (RPo). Despite extensive study, the mechanism of promoter unwinding has remained unclear, in part due to the transient nature of intermediates on path to RPo. Here, using single-molecule unwinding-induced fluorescence enhancement to monitor promoter unwinding, and single-molecule fluorescence resonance energy transfer to monitor RNAP clamp conformation, we analyse RPo formation at a consensus bacterial core promoter. We find that the RNAP clamp is closed during promoter binding, remains closed during promoter unwinding, and then closes further, locking the unwound DNA in the RNAP active-centre cleft. Our work defines a new, ‘bind-unwind-load-and-lock’, model for the series of conformational changes occurring during promoter unwinding at a consensus bacterial promoter and provides the tools needed to examine the process in other organisms and at other promoters.

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.