A role for both conformational selection and induced fit in ligand binding by the LAO protein

Incorporating Prior Knowledge in the Seeds of Adaptive Sampling Molecular Dynamics Simulations of Ligand Transport in Enzymes with Buried Active Sites

Because most proteins have buried active sites, protein tunnels or channels play a crucial role in the transport of small molecules into buried cavities for enzymatic catalysis. Tunnels can critically modulate the biological process of protein-ligand recognition. Various molecular dynamics methods have been developed for exploring and exploiting the protein-ligand conformational space to extract high-resolution details of the binding processes, a recent example being energetically unbiased high-throughput adaptive sampling simulations. The current study systematically contrasted the role of integrating prior knowledge while generating useful initial protein-ligand configurations, called seeds, for these simulations. Using a nontrivial system of a haloalkane dehalogenase mutant with multiple transport tunnels leading to a deeply buried active site, simulations were employed to derive kinetic models describing the process of association and dissociation of the substrate molecule. The most knowledge-based seed generation enabled high-throughput simulations that could more consistently capture the entire transport process, explore the complex network of transport tunnels, and predict equilibrium dissociation constants, koff/kon, on the same order of magnitude as experimental measurements. Overall, the infusion of more knowledge into the initial seeds of adaptive sampling simulations could render analyses of transport mechanisms in enzymes more consistent even for very complex biomolecular systems, thereby promoting drug development efforts and the rational design of enzymes with buried active sites.

Molecular dynamics in multidimensional space explains how mutations affect the association path of neomycin to a riboswitch

Riboswitches are messenger RNA (mRNA) fragments binding specific small molecules to regulate gene expression. A synthetic N1 riboswitch, inserted into yeast mRNA controls the translation of a reporter gene in response to neomycin. However, its regulatory activity is sensitive to single-point RNA mutations, even those distant from the neomycin binding site. While the association paths of neomycin to N1 and its variants remain unknown, recent fluorescence kinetic experiments indicate a two-step process driven by conformational selection. This raises the question of which step is affected by mutations. To address this, we performed all-atom two-dimensional replica-exchange molecular dynamics simulations for N1 and U14C, U14C[Formula: see text], U15A, and A17G mutants, ensuring extensive conformational sampling of both RNA and neomycin. The obtained neomycin association and binding paths, along with multidimensional free-energy profiles, revealed a two-step binding mechanism, consisting of conformational selection and induced fit. Neomycin binds to a preformed N1 conformation upon identifying a stable upper stem and U-turn motif in the riboswitch hairpin. However, the positioning of neomycin in the binding site occurs at different RNA-neomycin distances for each mutant, which may explain their different regulatory activities. The subsequent induced fit arises from the interactions of the neomycin's N3 amino group with RNA, causing the G9 backbone to rearrange. In the A17G mutant, the critical C6-A17/G17 stacking forms at a closer RNA-neomycin distance compared to N1. These findings together with estimated binding free energies coincide with experiments and elucidate why the A17G mutation decreases and U15A enhances N1 activity in response to neomycin.

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.

Revealing the conformational dynamics of UDP-GlcNAc recognition by O-GlcNAc transferase via Markov state model

The O-linked N-acetylglucosamine (O-GlcNAc) glycosylation is a critical post-translational modification and closely linked to various physiological and pathological conditions. The O-GlcNAc transferase (OGT) functions as the only glycosyltransferase of O-GlcNAc glycosylation by transferring GlcNAc from UDP-GlcNAc to serine or threonine residues on protein substrates. The interaction mode of UDP-GlcNAc against OGT has been preliminarily revealed by the crystal structures, yet an atomic-level comprehension for the conformational dynamics of the recognition process remains elusive. Here, we construct the Markov state model based on extensive all-atom molecular dynamics (MD) simulations with an aggregated simulation time of ∼9 μs, and reveal that the UDP-GlcNAc recognition process by OGT encompasses four key metastable states, occurring within an estimated timescale of ∼10 μs. During UDP-GlcNAc recognition process, we find the pyrophosphate moiety (P2O52-) initially anchors to the active pocket via salt bridge and hydrogen bonds, facilitating subsequent binding of the uridine and GlcNAc moieties. Furthermore, the functional roles of K842 involved in the salt bridge with P2O52- were evaluated through extra mutant MD simulations. Overall, our study provides valuable insights into the UDP-GlcNAc recognition mechanism by OGT, which could further aid in mechanistic studies of O-GlcNAc glycosylation and drug development targeting on OGT.

A Kinetic Transition Network Model Reveals the Diversity of Protein Dimer Formation Mechanisms

Protein homodimers have been classified as three-state or two-state dimers depending on whether a folded monomer forms before association, but the details of the folding-binding mechanisms are poorly understood. Kinetic transition networks of conformational states have provided insight into the folding mechanisms of monomeric proteins, but extending such a network to two protein chains is challenging as all the relative positions and orientations of the chains need to be included, greatly increasing the number of degrees of freedom. Here, we present a simplification of the problem by grouping all states of the two chains into two layers: a dissociated and an associated layer. We combined our two-layer approach with the Wako-Saito-Muñoz-Eaton method and used Transition Path Theory to investigate the dimer formation kinetics of eight homodimers. The analysis reveals a remarkable diversity of dimer formation mechanisms. Induced folding, conformational selection, and rigid docking are often simultaneously at work, and their contribution depends on the protein concentration. Pre-folded structural elements are always present at the moment of association, and asymmetric binding mechanisms are common. Our two-layer network approach can be combined with various methods that generate discrete states, yielding new insights into the kinetics and pathways of flexible binding processes.

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.

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

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

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

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

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

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

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

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

Markov field models: Scaling molecular kinetics approaches to large molecular machines

With recent advances in structural biology, including experimental techniques and deep learning-enabled high-precision structure predictions, molecular dynamics methods that scale up to large biomolecular systems are required. Current state-of-the-art approaches in molecular dynamics modeling focus on encoding global configurations of molecular systems as distinct states. This paradigm commands us to map out all possible structures and sample transitions between them, a task that becomes impossible for large-scale systems such as biomolecular complexes. To arrive at scalable molecular models, we suggest moving away from global state descriptions to a set of coupled models that each describe the dynamics of local domains or sites of the molecular system. We describe limitations in the current state-of-the-art global-state Markovian modeling approaches and then introduce Markov field models as an umbrella term that includes models from various scientific communities, including Independent Markov decomposition, Ising and Potts models, and (dynamic) graphical models, and evaluate their use for computational molecular biology. Finally, we give a few examples of early adoptions of these ideas for modeling molecular kinetics and thermodynamics.

Computer simulation of molecular recognition in biomolecular system: from in silico screening to generalized ensembles

Prediction of ligand-receptor complex structure is important in both the basic science and the industry such as drug discovery. We report various computation molecular docking methods: fundamental in silico (virtual) screening, ensemble docking, enhanced sampling (generalized ensemble) methods, and other methods to improve the accuracy of the complex structure. We explain not only the merits of these methods but also their limits of application and discuss some interaction terms which are not considered in the in silico methods. In silico screening and ensemble docking are useful when one focuses on obtaining the native complex structure (the most thermodynamically stable complex). Generalized ensemble method provides a free-energy landscape, which shows the distribution of the most stable complex structure and semi-stable ones in a conformational space. Also, barriers separating those stable structures are identified. A researcher should select one of the methods according to the research aim and depending on complexity of the molecular system to be studied.

Deep learning to decompose macromolecules into independent Markovian domains

The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the molecular system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large molecular systems the number of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decomposition (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decomposition of the molecular system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decomposition into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large molecular complexes from simulation data.

A litmus test for classifying recognition mechanisms of transiently binding proteins

Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin’s paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks.

The authors provide a litmus test for the recognition mechanism of transiently binding proteins based on nuclear magnetic resonance and find a conformational selection binding mechanism through concentration-dependent kinetics of ubiquitin and SH3.

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

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

Practical Protocols for Efficient Sampling of Kinase-Inhibitor Binding Pathways Using Two-Dimensional Replica-Exchange Molecular Dynamics

Molecular dynamics (MD) simulations are increasingly used to study various biological processes such as protein folding, conformational changes, and ligand binding. These processes generally involve slow dynamics that occur on the millisecond or longer timescale, which are difficult to simulate by conventional atomistic MD. Recently, we applied a two-dimensional (2D) replica-exchange MD (REMD) method, which combines the generalized replica exchange with solute tempering (gREST) with the replica-exchange umbrella sampling (REUS) in kinase-inhibitor binding simulations, and successfully observed multiple ligand binding/unbinding events. To efficiently apply the gREST/REUS method to other kinase-inhibitor systems, we establish modified, practical protocols with non-trivial simulation parameter tuning. The current gREST/REUS simulation protocols are tested for three kinase-inhibitor systems: c-Src kinase with PP1, c-Src kinase with Dasatinib, and c-Abl kinase with Imatinib. We optimized the definition of kinase-ligand distance as a collective variable (CV), the solute temperatures in gREST, and replica distributions and umbrella forces in the REUS simulations. Also, the initial structures of each replica in the 2D replica space were prepared carefully by pulling each ligand from and toward the protein binding sites for keeping stable kinase conformations. These optimizations were carried out individually in multiple short MD simulations. The current gREST/REUS simulation protocol ensures good random walks in 2D replica spaces, which are required for enhanced sampling of inhibitor dynamics around a target kinase.

Dissecting the Protein Dynamics Coupled Ligand Binding with Kinetic Models and Single-Molecule FRET

Protein-ligand interactions are crucial to many biological processes. Ligand binding and dissociation are the basic steps that allow proteins to function. Protein conformational dynamics have been shown to play important roles in ligand binding and dissociation. However, it is challenging to determine the ligand binding kinetics of dynamic proteins. Here, we undertook comprehensive single-molecule FRET (smFRET) measurements and kinetic model analysis to characterize the conformational dynamics coupled ligand binding of glutamine-binding protein (GlnBP). We showed that hinge and T118A mutations of GlnBP affect its conformational dynamics as well as the ligand binding affinity. Based on smFRET measurements, the kinetic model of ligand-GlnBP interactions was constructed. Using experimentally measured parameters, we solved the rate equations of the model and obtained the undetectable parameters of the model which allowed us to understand the ligand binding kinetics fully. Our results demonstrate that modulation of the conformational dynamics of GlnBP affects the ligand binding and dissociation rates. This study provides insights into the binding kinetics of ligands, which are related to the protein function itself.

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.

Progress in deep Markov state modeling: Coarse graining and experimental data restraints

Recent advances in deep learning frameworks have established valuable tools for analyzing the long-timescale behavior of complex systems, such as proteins. In particular, the inclusion of physical constraints, e.g., time-reversibility, was a crucial step to make the methods applicable to biophysical systems. Furthermore, we advance the method by incorporating experimental observables into the model estimation showing that biases in simulation data can be compensated for. We further develop a new neural network layer in order to build a hierarchical model allowing for different levels of details to be studied. Finally, we propose an attention mechanism, which highlights important residues for the classification into different states. We demonstrate the new methodology on an ultralong molecular dynamics simulation of the Villin headpiece miniprotein.

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.

Multiscale Approach for Computing Gated Ligand Binding from Molecular Dynamics and Brownian Dynamics Simulations

We develop an approach to characterize the effects of gating by a multiconformation protein consisting of macrostate conformations that are either accessible or inaccessible to ligand binding. We first construct a Markov state model of the apo-protein from atomistic molecular dynamics simulations from which we identify macrostates and their conformations, compute their relative macrostate populations and interchange kinetics, and structurally characterize them in terms of ligand accessibility. We insert the calculated first-order rate constants for conformational transitions into a multistate gating theory from which we derive a gating factor γ that quantifies the degree of conformational gating. Applied to HIV-1 protease, our approach yields a kinetic network of three accessible (semi-open, open, and wide-open) and two inaccessible (closed and a newly identified, "parted") macrostate conformations. The parted conformation sterically partitions the active site, suggesting a possible role in product release. We find that the binding kinetics of drugs and drug-like inhibitors to HIV-1 protease falls in the slow gating regime. However, because γ = 0.75, conformational gating only modestly slows ligand binding. Brownian dynamics simulations of the diffusional association of eight inhibitors to the protease─having a wide range of experimental association constants (∼10⁴-10¹⁰ M^-1 s^-1)─yields gated rate constants in the range of ∼0.5-5.7 × 10⁸ M^-1 s^-1. This indicates that, whereas the association rate of some inhibitors could be described by the model, for many inhibitors either subsequent conformational transitions or alternate binding mechanisms may be rate-limiting. For systems known to be modulated by conformational gating, the approach could be scaled computationally efficiently to screen association kinetics for a large number of ligands.

Molecular Mechanism of Methanol Inhibition in CALB-Catalyzed Alcoholysis: Analyzing Molecular Dynamics Simulations by a Markov State Model

Lipases are widely used enzymes that catalyze hydrolysis and alcoholysis of fatty acid esters. At high concentrations of small alcohols such as methanol or ethanol, many lipases are inhibited by the substrate. The molecular basis of the inhibition of Candida antarctica lipase B (CALB) by methanol was investigated by unbiased molecular dynamics (MD) simulations, and the substrate binding kinetics was analyzed by Markov state models (MSMs). The modeled fluxes of productive methanol binding at concentrations between 50 mM and 5.5 M were in good agreement with the experimental activity profile of CALB, with a peak at 300 mM. The kinetic and structural analysis uncovered the molecular basis of CALB inhibition. Beyond 300 mM, the kinetic bottleneck results from crowding of methanol in the substrate access channel, which is caused by the gradual formation of methanol patches close to Leu140 (helix α5), Leu278, and Ile285 (helix α10) at a distance of 4-5 Å from the active site. Our findings demonstrate the usefulness of unbiased MD simulations to study enzyme-substrate interactions at realistic substrate concentrations and the feasibility of scale-bridging by an MSM analysis to derive kinetic information.

Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics

A novel approach to simulate simple protein-ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein-protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein-protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package.

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.

Interplay of substrate polymorphism and conformational plasticity of Plasmodium tyrosyl-tRNA synthetase

Aminoacyl-tRNA synthetases are an indispensable component of ribosomal protein translational machinery and Plasmodium Tyrosyl-tRNA synthetase (PfTyrRS) is a validated drug target. This manuscript illustrates the dynamic conformational landscape of PfTyrRS in the context of substrate binding. Molecular dynamics simulations of PfTyrRS in the presence and absence of ligand show conformational heterogeneity for both the protein and the bound ligand. Diverse conformations for the evolutionarily conserved ATP binding motif (KMSKS) have been observed in both apo- and holo PfTyrRS. Further, the presented attributes of the tyrosyl-adenylate conformational sub-states in situ along with their implications on the strength of intermolecular interactions would be a pertinent benchmark for molecular design studies. In addition, an analysis of the ligand hydration pattern foregrounds the structurally conserved water-mediated inter-molecular interactions. The quantitative assessment of the conformational landscape, based on the fluctuations of the distance between the ligand binding pockets, of apo-PfTyrRS and holo-PfTyrRS highlights the nature of diversity in conformational sampling for the two cases. Evidently, the holo-PfTyrRS adopts a rather compact conformation compared to the apo-PfTyrRS. An intriguing asymmetry in the dynamics of the two monomers is contextualized with the functional asymmetry of the symmetrically dimeric PfTyrRS. Importantly, the network of non-bonded contacts in the apo- and holo- simulated ensembles has been analyzed. The graph-theoretic analysis-based novel insights concerning the nature of information flow as a function of ligation state would prove valuable in understanding PfTyrRS functions. The results presented here contend that understanding allostery in PfTyrRS is essential to astutely design structure-based inhibitors.

Unsupervised Learning Methods for Molecular Simulation Data

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

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

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

Independent Markov decomposition: Toward modeling kinetics of biomolecular complexes

To advance the mission of in silico cell biology, modeling the interactions of large and complex biological systems becomes increasingly relevant. The combination of molecular dynamics (MD) simulations and Markov state models (MSMs) has enabled the construction of simplified models of molecular kinetics on long timescales. Despite its success, this approach is inherently limited by the size of the molecular system. With increasing size of macromolecular complexes, the number of independent or weakly coupled subsystems increases, and the number of global system states increases exponentially, making the sampling of all distinct global states unfeasible. In this work, we present a technique called independent Markov decomposition (IMD) that leverages weak coupling between subsystems to compute a global kinetic model without requiring the sampling of all combinatorial states of subsystems. We give a theoretical basis for IMD and propose an approach for finding and validating such a decomposition. Using empirical few-state MSMs of ion channel models that are well established in electrophysiology, we demonstrate that IMD models can reproduce experimental conductance measurements with a major reduction in sampling compared with a standard MSM approach. We further show how to find the optimal partition of all-atom protein simulations into weakly coupled subunits.

Hydrogen/Deuterium Exchange and Nuclear Magnetic Resonance Spectroscopy Reveal Dynamic Allostery on Multiple Time Scales in the Serine Protease Thrombin

A deeper understanding of how hydrogen/deuterium exchange mass spectrometry (HDX-MS) reveals allostery is important because HDX-MS can reveal allostery in systems that are not amenable to nuclear magnetic resonance (NMR) spectroscopy. We were able to study thrombin and its complex with thrombomodulin, an allosteric regulator, by both HDX-MS and NMR. In this Perspective, we compare and contrast the results from both experiments and from molecular dynamics simulations. NMR detects changes in the chemical environment around the protein backbone N-H bond vectors, providing residue-level information about the conformational exchange between distinct states. HDX-MS detects changes in amide proton solvent accessibility and H-bonding. Taking advantage of NMR relaxation dispersion measurements of the time scale of motions, we draw conclusions about the motions reflected in HDX-MS experiments. Both experiments detect allostery, but they reveal different components of the allosteric transition. The insights gained from integrating NMR and HDX-MS into thrombin dynamics enable a clearer interpretation of the evidence for allostery revealed by HDX-MS in larger protein complexes and assemblies that are not amenable to NMR.

Solution-State Preorganization of Cyclic β-Hairpin Ligands Determines Binding Mechanism and Affinities for MDM2

Understanding mechanisms of protein folding and binding is crucial to designing their molecular function. Molecular dynamics (MD) simulations and Markov state model (MSM) approaches provide a powerful way to understand complex conformational change that occurs over long time scales. Such dynamics are important for the design of therapeutic peptidomimetic ligands, whose affinity and binding mechanism are dictated by a combination of folding and binding. To examine the role of preorganization in peptide binding to protein targets, we performed massively parallel explicit-solvent MD simulations of cyclic β-hairpin ligands designed to mimic the p53 transactivation domain and competitively bind mouse double minute 2 homologue (MDM2). Disrupting the MDM2-p53 interaction is a therapeutic strategy to prevent degradation of the p53 tumor suppressor in cancer cells. MSM analysis of over 3 ms of aggregate trajectory data enabled us to build a detailed mechanistic model of coupled folding and binding of four cyclic peptides which we compare to experimental binding affinities and rates. The results show a striking relationship between the relative preorganization of each ligand in solution and its affinity for MDM2. Specifically, changes in peptide conformational populations predicted by the MSMs suggest that entropy loss upon binding is the main factor influencing affinity. The MSMs also enable detailed examination of non-native interactions which lead to misfolded states and comparison of structural ensembles with experimental NMR measurements. In contrast to an MSM study of p53 transactivation domain (TAD) binding to MDM2, MSMs of cyclic β-hairpin binding show a conformational selection mechanism. Finally, we make progress toward predicting accurate off rates of cyclic peptides using multiensemble Markov models (MEMMs) constructed from unbiased and biased simulated trajectories.

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

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

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

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

Unraveling the Coupling between Conformational Changes and Ligand Binding in Ribose Binding Protein Using Multiscale Molecular Dynamics and Free-Energy Calculations

Conformational changes of proteins upon ligand binding are usually explained in terms of several mechanisms including the induced fit, conformational selection, or their mixtures. Due to the slow time scales, conventional molecular dynamics (cMD) simulations based on the atomistic models cannot easily simulate the open-to-closed conformational transition in proteins. In our previous study, we have developed an enhanced sampling scheme (generalized replica exchange with solute tempering selected surface charged residues: gREST_SSCR) for multidomain proteins and applied it to ligand-mediated conformational changes in the G134R mutant of ribose-binding protein (RBPG134R) in solution. The free-energy landscape (FEL) of RBPG134R in the presence of a ribose at the binding site included the open and closed states and two intermediates, open-like and closed-like forms. Only the open and open-like forms existed in the FEL without a ribose. In the current study, the coupling between the conformational changes and ligand binding is further investigated using coarse-grained MD, multiple atomistic cMD, and free-energy calculations. The ribose is easily dissociated from the binding site of wild-type RBP and RBPG134R in the cMD simulations starting from the open and open-like forms. In contrast, it is stable at the binding site in the simulations from the closed and closed-like forms. The free-energy calculations provide the binding affinities of different structures, supporting the results of cMD simulations. Importantly, cMD simulations from the closed-like structures reveal transitions toward the closed one in the presence of a bound ribose. On the basis of the computational results, we propose a molecular mechanism in which conformational selection and induced fit happen in the first and second halves of the open-to-closed transition in RBP, respectively.

Atomic resolution of short-range sliding dynamics of thymine DNA glycosylase along DNA minor-groove for lesion recognition

Thymine DNA glycosylase (TDG), as a repair enzyme, plays essential roles in maintaining the genome integrity by correcting several mismatched/damaged nucleobases. TDG acquires an efficient strategy to search for the lesions among a vast number of cognate base pairs. Currently, atomic-level details of how TDG translocates along DNA as it approaches the lesion site and the molecular mechanisms of the interplay between TDG and DNA are still elusive. Here, by constructing the Markov state model based on hundreds of molecular dynamics simulations with an integrated simulation time of ∼25 μs, we reveal the rotation-coupled sliding dynamics of TDG along a 9 bp DNA segment containing one G·T mispair. We find that TDG translocates along DNA at a relatively faster rate when distant from the lesion site, but slows down as it approaches the target, accompanied by deeply penetrating into the minor-groove, opening up the mismatched base pair and significantly sculpturing the DNA shape. Moreover, the electrostatic interactions between TDG and DNA are found to be critical for mediating the TDG translocation. Notably, several uncharacterized TDG residues are identified to take part in regulating the conformational switches of TDG occurred in the site-transfer process, which warrants further experimental validations.

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.

The Role of Calcium in Regulating the Conformational Dynamics of d-Galactose/d-Glucose-Binding Protein Revealed by Markov State Model Analysis

The d-glucose/d-galactose-binding protein (GGBP) from Escherichia coli is a substrate-binding protein (SBP) associated with sugar transport and chemotaxis. It is also a calcium-binding protein, which makes it unique in the SBP family. However, the functional importance of Ca²⁺ binding is not fully understood. Here, the calcium-dependent properties of GGBP were explored by all-atom molecular dynamics simulations and Markov state model (MSM) analysis as well as single-molecule Förster resonance energy transfer (smFRET) measurements. In agreement with previous experimental studies, we observed the structure stabilization effect of Ca²⁺ binding on the C-terminal domain of GGBP, especially the Ca²⁺-binding site. Interestingly, the MSMs of calcium-depleted GGBP and calcium-bound GGBP (GGBP/Ca²⁺) demonstrate that Ca²⁺ greatly stabilizes the open conformation, and smFRET measurements confirmed this result. Further analysis reveals that Ca²⁺ binding disturbs the local hydrogen bonding interactions and the conformational dynamics of the hinge region, thereby weakening the long-range interdomain correlations to favor the open conformation. These results suggest an active regulatory role of Ca²⁺ binding in GGBP, which finely tunes the conformational distribution. The work sheds new light on the study of calcium-binding proteins in prokaryotes.

A comprehensive binding study illustrates ligand recognition in the periplasmic binding protein PotF

Periplasmic binding proteins (PBPs) are ubiquitous receptors in gram-negative bacteria. They sense solutes and play key roles in nutrient uptake. Escherichia coli's putrescine receptor PotF has been reported to bind putrescine and spermidine. We reveal that several similar biogenic polyamines are recognized by PotF. Using isothermal titration calorimetry paired with X-ray crystallography of the different complexes, we unveil PotF's binding modes in detail. The binding site for PBPs is located between two lobes that undergo a large conformational change upon ligand recognition. Hence, analyzing the influence of ligands on complex formation is crucial. Therefore, we solved crystal structures of an open and closed apo state and used them as a basis for molecular dynamics simulations. In addition, we accessed structural behavior in solution for all complexes by ¹H-¹⁵N HSQC NMR spectroscopy. This combined analysis provides a robust framework for understanding ligand binding for future developments in drug design and protein engineering.

Markov State Models to Elucidate Ligand Binding Mechanism

Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.

Conformational ordering of intrinsically disordered peptides for targeting translation initiation

BACKGROUND

Intrinsically disordered regions (IDRs) in proteins can regulate their activity by facilitating protein-protein interactions (PPIs) as exemplified in the recruitment of the eukaryotic translation initiation factor 4E (eIF4E) protein by the protein eIF4G. Deregulation of this PPI module is central to a broad spectrum of cancer related malignancies and its targeted inhibition through bioactive peptides is a promising strategy for therapeutic intervention.

METHODS

We employed molecular dynamics simulations coupled with biophysical assays to rationally develop peptide derivatives from the intrinsically disordered eIF4G scaffold by incorporating non-natural amino acids that facilitates disorder-to-order transition.

RESULTS

The conformational heterogeneity of these peptides and the degree of structural reorganization required to adopt the optimum mode of interaction with eIF4E underscores their differential binding affinities. The presence of a pre-structured local helical element in the ensemble of structures was instrumental in the efficient docking of the peptides on to the protein surface. The formation of Y4: P38 hydrogen-bond interaction between the peptide and eIF4E is a rate limiting event in the efficient recognition of the protein since it occurs through the disordered region of the peptide.

CONCLUSIONS

These insights were exploited to further design features into the peptide to propagate bound-state conformations in solution which resulted in the generation of a potent eIF4E binder.

GENERAL SIGNIFICANCE

The study illustrates the molecular basis of eIF4E recognition by a disordered epitope from eIF4G and its modulation to generate peptides that can potentially attenuate translation initiation in oncology.

Structure dictates the mechanism of ligand recognition in the histidine and maltose binding proteins

Two mechanisms, induced fit (IF) and conformational selection (CS), have been proposed to explain ligand recognition coupled conformational changes. The histidine binding protein (HisJ) adopts the CS mechanism, in which a pre-equilibrium is established between the open and the closed states with the ligand binding to the closed state. Despite being structurally similar to HisJ, the maltose binding protein (MBP) adopts the IF mechanism, in which the ligand binds the open state and induces a transition to the closed state. To understand the molecular determinants of this difference, we performed molecular dynamics (MD) simulations of coarse-grained dual structure based models. We find that intra-protein contacts unique to the closed state are sufficient to promote the conformational transition in HisJ, indicating a CS-like mechanism. In contrast, additional ligand-mimicking contacts are required to “induce” the conformational transition in MBP suggesting an IF-like mechanism. In agreement with experiments, destabilizing modifications to two structural features, the spine helix (SH) and the balancing interface (BI), present in MBP but absent in HisJ, reduce the need for ligand-mimicking contacts indicating that SH and BI act as structural restraints that keep MBP in the open state. We introduce an SH like element into HisJ and observe that this can impede the conformational transition increasing the importance of ligand-mimicking contacts. Similarly, simultaneous mutations to BI and SH in MBP reduce the barrier to conformational transitions significantly and promote a CS-like mechanism. Together, our results show that structural restraints present in the protein structure can determine the mechanism of conformational transitions and even simple models that correctly capture such structural features can predict their positions. MD simulations of such models can thus be used, in conjunction with mutational experiments, to regulate protein ligand interactions, and modulate ligand binding affinities.

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MBP operates by induced fit, HisJ by the conformational selection mechanism.

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Dual structure based models (dSBMs) encode two structures of a protein.

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MD simulations of dSBMs can identify the mechanism of conformational transitions.

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Locks, absent in HisJ, hold MBP open with ligand contacts required for closing.

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Binding mechanisms can be modified by altering such structural locks.

Ligand-bound glutamine binding protein assumes multiple metastable binding sites with different binding affinities

Protein dynamics plays key roles in ligand binding. However, the microscopic description of conformational dynamics-coupled ligand binding remains a challenge. In this study, we integrate molecular dynamics simulations, Markov state model (MSM) analysis and experimental methods to characterize the conformational dynamics of ligand-bound glutamine binding protein (GlnBP). We show that ligand-bound GlnBP has high conformational flexibility and additional metastable binding sites, presenting a more complex energy landscape than the scenario in the absence of ligand. The diverse conformations of GlnBP demonstrate different binding affinities and entail complex transition kinetics, implicating a concerted ligand binding mechanism. Single molecule fluorescence resonance energy transfer measurements and mutagenesis experiments are performed to validate our MSM-derived structure ensemble as well as the binding mechanism. Collectively, our study provides deeper insights into the protein dynamics-coupled ligand binding, revealing an intricate regulatory network underlying the apparent binding affinity.

Zhang, Wu, Feng et al. show that ligand-bound glutamine binding protein assumes multiple metastable binding sites, presenting a more dynamic energy landscape than its ligand-free form. This study provides insights into the ligand-binding mechanisms coupled with protein dynamics that underly the apparent binding affinity.

Markov State Model Analysis of Haloperidol Binding to the D3 Dopamine Receptor

We have developed Markov state models (MSMs) and hidden Markov models (HMMs) that describe the binding of haloperidol to the D₃ dopamine receptor. Haloperidol is an antipsychotic drug that binds with nanomolar affinity to the D₃ dopamine receptor, where it functions as an inverse agonist. The models were constructed using an adaptive sampling approach from 519 individual molecular dynamics simulations totaling 122 μs of simulated time and encompass the entire drug binding process. They reveal short-lived metastable bound states and two distinct long-lived bound conformations that cannot be separated in affinity using our current methodology. This work extends the use of MSMs and HMMs to study ligand binding, which thus far has been limited to simpler systems.

The physical basis and practical consequences of biological promiscuity

Proteins interact with metabolites, nucleic acids, and other proteins to orchestrate the myriad catalytic, structural and regulatory functions that support life from the simplest microbes to the most complex multicellular organisms. These molecular interactions are often exquisitely specific, but never perfectly so. Adventitious "promiscuous" interactions are ubiquitous due to the thousands of macromolecules and small molecules crowded together in cells. Such interactions may perturb protein function at the molecular level, but as long as they do not compromise organismal fitness, they will not be removed by natural selection. Although promiscuous interactions are physiologically irrelevant, they are important because they can provide a vast reservoir of potential functions that can provide the starting point for evolution of new functions, both in nature and in the laboratory.

Dynamical matrix propagator scheme for large-scale proton dynamics simulations

We derive a matrix formalism for the simulation of long range proton dynamics for extended systems and timescales. On the basis of an ab initio molecular dynamics simulation, we construct a Markov chain, which allows us to store the entire proton dynamics in an M × M transition matrix (where M is the number of oxygen atoms). In this article, we start from common topology features of the hydrogen bond network of good proton conductors and utilize them as constituent constraints of our dynamic model. We present a thorough mathematical derivation of our approach and verify its uniqueness and correct asymptotic behavior. We propagate the proton distribution by means of transition matrices, which contain kinetic data from both ultra-short (sub-ps) and intermediate (ps) timescales. This concept allows us to keep the most relevant features from the microscopic level while effectively reaching larger time and length scales. We demonstrate the applicability of the transition matrices for the description of proton conduction trends in proton exchange membrane materials.

Investigating Cryptic Binding Sites by Molecular Dynamics Simulations

This Account highlights recent advances and discusses major challenges in investigations of cryptic (hidden) binding sites by molecular simulations. Cryptic binding sites are not visible in protein targets crystallized without a ligand and only become visible crystallographically upon binding events. These sites have been shown to be druggable and might provide a rare opportunity to target difficult proteins. However, due to their hidden nature, they are difficult to find through experimental screening. Computational methods based on atomistic molecular simulations remain one of the best approaches to identify and characterize cryptic binding sites. However, not all methods are equally efficient. Some are more apt at quickly probing protein dynamics but do not provide thermodynamic or druggability information, while others that are able to provide such data are demanding in terms of time and resources. Here, we review the recent contributions of mixed-solvent simulations, metadynamics, Markov state models, and other enhanced sampling methods to the field of cryptic site identification and characterization. We discuss how these methods were able to provide precious information on the nature of the site opening mechanisms, to predict previously unknown sites which were used to design new ligands, and to compute the free energy landscapes and kinetics associated with the opening of the sites and the binding of the ligands. We highlight the potential and the importance of such predictions in drug discovery, especially for difficult ("undruggable") targets. We also discuss the major challenges in the field and their possible solutions.

To probe the binding pathway of a selective compound (D089-0563) to c-MYC Pu24 G-quadruplex using free ligand binding simulations and Markov state model analysis

D089-0563 is a highly promising anti-cancer compound that selectively binds the transcription-silencing G-quadruplex element (Pu27) at the promoter region of the human c-MYC oncogene; however, its binding mechanism remains elusive.

Disclosing the Mechanism of Spontaneous Aggregation and Template-Induced Misfolding of the Key Hexapeptide (PHF6) of Tau Protein Based on Molecular Dynamics Simulation

The microtubule-associated protein tau is critical for the development and maintenance of the nervous system. Tau dysfunction is associated with a variety of neurodegenerative diseases called tauopathies, which are characterized by neurofibrillary tangles formed by abnormally aggregated tau protein. Studying the aggregation mechanism of tau protein is of great significance for elucidating the etiology of tauopathies. The hexapeptide ³⁰⁶VQIVYK³¹¹ (PHF6) of R3 has been shown to play a vital role in promoting tau aggregation. In this study, long-term all-atom molecular dynamics simulations in explicit solvent were performed to investigate the mechanisms of spontaneous aggregation and template-induced misfolding of PHF6, and the dimerization at the early stage of nucleation was further specifically analyzed by the Markov state model (MSM). Our results show that PHF6 can spontaneously aggregate to form multimers enriched with β-sheet structure and the β-sheets in multimers prefer to exist in a parallel way. It is observed that PHF6 monomer can be induced to form a β-sheet structure on either side of the template but in a different way. In detail, the β-sheet structure is easier to form on the left side but does not extend well, but on the right side, the monomer can form the extended β-sheet structure. Furthermore, MSM analysis shows that the formation of dimer mainly occurs in three steps. First, the separated monomers collide with each other at random orientations, and then a dimer with short β-sheet structure at the N-terminal forms; finally, β-sheets elongate to form an extended parallel β-sheet dimer. During these processes, multiple intermediate states are identified and multiple paths can form a parallel β-sheet dimer from the disordered coil structure. Moreover, the residues I308, V309, and Y310 play an essential role in the dimerization. In a word, our results uncover the aggregation and misfolding mechanism of PHF6 from the atomic level, which can provide useful theoretical guidance for rational design of effective therapeutic drugs against tauopathies.