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.

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.

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.

Disease mutations and phosphorylation alter the allosteric pathways involved in autoinhibition of protein phosphatase 2A.

Mutations in protein phosphatase 2A (PP2A) are connected to intellectual disability and cancer. It has been hypothesized that these mutations might disrupt the autoinhibition and phosphorylation-induced activation of PP2A. Since they are located far from both the active and substrate binding sites, it is unclear how they exert their effect. We performed allosteric pathway analysis based on molecular dynamics simulations and combined it with biochemical experiments to investigate the autoinhibition of PP2A. In the wild type (WT), the C-arm of the regulatory subunit B56δ obstructs the active and substrate binding sites exerting a dual autoinhibition effect. We find that the disease mutant, E198K, severely weakens the allosteric pathways that stabilize the C-arm in the WT. Instead, the strongest allosteric pathways in E198K take a different route that promotes exposure of the substrate binding site. To facilitate the allosteric pathway analysis, we introduce a path clustering algorithm for lumping pathways into channels. We reveal remarkable similarities between the allosteric channels of E198K and those in phosphorylation-activated WT, suggesting that the autoinhibition can be alleviated through a conserved mechanism. In contrast, we find that another disease mutant, E200K, which is in spatial proximity of E198, does not repartition the allosteric pathways leading to the substrate binding site; however, it may still induce exposure of the active site. This finding agrees with our biochemical data, allowing us to predict the activity of PP2A with the phosphorylated B56δ and provide insight into how disease mutations in spatial proximity alter the enzymatic activity in surprisingly different mechanisms.

Surface Plasmon Enabling Nitrogen Fixation in Pure Water through a Dissociative Mechanism under Mild Conditions.

Nitrogen fixation in a simulated natural environment (i.e., near ambient pressure, room temperature, pure water, and incident light) would provide a desirable approach to future nitrogen conversion. As the N≡N triple bond has a thermodynamically high cleavage energy, nitrogen reduction under such mild conditions typically undergoes associative alternating or distal pathways rather than following a dissociative mechanism. Here, we report that surface plasmon can supply sufficient energy to activate N2 through a dissociative mechanism in the presence of water and incident light, as evidenced by in situ synchrotron radiation-based infrared spectroscopy and near ambient pressure X-ray photoelectron spectroscopy. Theoretical simulation indicates that the electric field enhanced by surface plasmon, together with plasmonic hot electrons and interfacial hybridization, may play a critical role in N≡N dissociation. Specifically, AuRu core-antenna nanostructures with broadened light adsorption cross section and active sites achieve an ammonia production rate of 101.4 µmol g-1 h-1 without any sacrificial agent at room temperature and 2 atm pressure. This work highlights the significance of surface plasmon to activation of inert molecules, serving as a promising platform for developing novel catalytic systems.

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.

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.

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules.

The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl-, [ClO]- (a two-site anion), and [NO2]- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

Efficient photoelectrochemical CO2 conversion for selective acetic acid production.

Amidst the development of photoelectrochemical (PEC) CO2 conversion toward practical application, the production of high-value chemicals beyond C1 compounds under mild conditions is greatly desired yet challenging. Here, through rational PEC device design by combining Au-loaded and N-doped TiO2 plate nanoarray photoanode with Zn-doped Cu2O dark cathode, efficient conversion of CO2 to CH3COOH has been achieved with an outstanding Faradaic efficiency up to 58.1% (91.5% carbon selectivity) at 0.5 V vs. Ag/AgCl. Temperature programmed desorption and in situ Raman spectra reveal that the Zn-dopant in Cu2O plays multiple roles in selective catalytic CO2 conversion, including local electronic structure manipulation and active site modification, which together promote the formation of intermediate *CH2/*CH3 for C-C coupling. Apart from that, it is also unveiled that the sufficient electron density provided by the Au-loaded and N-doped TiO2 plate nanoarray photoanode plays an equally important role by initiating multi-electron CO2 reduction. This work provides fresh insights into the PEC system design to reach the multi-electron reduction reaction and facilitate the C-C coupling reaction toward high-value multicarbon (C2+) chemical production via CO2 conversion.

General synthesis of single-atom catalysts with high metal loading using graphene quantum dots.

Transition-metal single-atom catalysts present extraordinary activity per metal atomic site, but suffer from low metal-atom densities (typically less than 5 wt% or 1 at.%), which limits their overall catalytic performance. Here we report a general method for the synthesis of single-atom catalysts with high transition-metal-atom loadings of up to 40 wt% or 3.8 at.%, representing several-fold improvements compared to benchmarks in the literature. Graphene quantum dots, later interweaved into a carbon matrix, were used as a support, providing numerous anchoring sites and thus facilitating the generation of high densities of transition-metal atoms with sufficient spacing between the metal atoms to avoid aggregation. A significant increase in activity in electrochemical CO2 reduction (used as a representative reaction) was demonstrated on a Ni single-atom catalyst with increased Ni loading.