Conserve Water: A Method for the Analysis of Solvent in Molecular Dynamics

Tutorial on Molecular Latent Space Simulators (LSSs): Spatially and Temporally Continuous Data-Driven Surrogate Dynamical Models of Molecular Systems

The inherently serial nature and requirement for short integration time steps in the numerical integration of molecular dynamics (MD) calculations place strong limitations on the accessible simulation time scales and statistical uncertainties in sampling slowly relaxing dynamical modes and rare events. Molecular latent space simulators (LSSs) are a data-driven approach to learning a surrogate dynamical model of the molecular system from modest MD training trajectories that can generate synthetic trajectories at a fraction of the computational cost. The training data may comprise single long trajectories or multiple short, discontinuous trajectories collected over, for example, distributed computing resources. Provided the training data provide sufficient sampling of the relevant thermodynamic states and dynamical transitions to robustly learn the underlying microscopic propagator, an LSS furnishes a global model of the dynamics capable of producing temporally and spatially continuous molecular trajectories. Trained LSS models have produced simulation trajectories at up to 6 orders of magnitude lower cost than standard MD to enable dense sampling of molecular phase space and large reduction of the statistical errors in structural, thermodynamic, and kinetic observables. The LSS employs three deep learning architectures to solve three independent learning problems over the training data: (i) an encoding of the high-dimensional MD into a low-dimensional slow latent space using state-free reversible VAMPnets (SRVs), (ii) a propagator of the microscopic dynamics within the low-dimensional latent space using mixture density networks (MDNs), and (iii) a generative decoding of the low-dimensional latent coordinates back to the original high-dimensional molecular configuration space using conditional Wasserstein generative adversarial networks (cWGANs) or denoising diffusion probability models (DDPMs). In this software tutorial, we introduce the mathematical and numerical background and theory of LSS and present example applications of a user-friendly Python package software implementation to alanine dipeptide and a 28-residue beta-beta-alpha (BBA) protein within simple Google Colab notebooks.

Reducing the assemblies of amyloid-beta multimers by sodium dodecyl sulfate surfactant at concentrations lower than critical micelle concentration: molecular dynamics simulation exploration

Amyloid-β peptide, the predominant proteinaceous component of senile plaques, is responsible for the incidence of Alzheimer's disease (AD), an age-associated neurodegenerative disorder. Specifically, the amyloid-β(1-42) (Aβ1-42) isoform, known for its high toxicity, is the predominant biomarker for the preliminary diagnosis of AD. The aggregation of the Aβ1-42 peptides can be affected by the components of the cellular medium through changing their structures and molecular interactions. In this study, we investigated the effect of sodium dodecyl sulfate (SDS) at much lower concentrations than the critical micelle concentration (CMC) on Aβ1-42 aggregation. For this purpose, we studied mono-, di-, tri- and tetramers of Aβ1-42 peptide in two different concentrations of SDS molecules (10 and 40 molecules) using a 300 ns molecular dynamics simulation for each system. The distance between the center of mass (COM) of Aβ1-42 peptides confirms that an increase in the number of SDS molecules decreases their aggregation probability due to greater interaction with SDS molecules. Besides, the less compactness parameter reveals the reduced aggregation probability of Aβ1-42 peptides. Based on the energetic FEL landscapes, SDS molecules with the concentration closer to the CMC are an effective inhibitory agent to prevent the formation of Aβ1-42 fibrils. Also, the aggregation direction of the peptide pairs can be predicted by determining the direction of the accumulation-deterrent forces.Communicated by Ramaswamy H. Sarma.

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

Markov State Model of Solvent Features Reveals Water Dynamics in Protein-Peptide Binding

In this work, we investigate the role of solvent in the binding reaction of the p53 transactivation domain (TAD) peptide to its receptor MDM2. Previously, our group generated 831 μs of explicit-solvent aggregate molecular simulation trajectory data for the MDM2-p53 peptide binding reaction using large-scale distributed computing and subsequently built a Markov State Model (MSM) of the binding reaction (Zhou et al. 2017). Here, we perform a tICA analysis and construct an MSM with similar hyperparameters while using only solvent-based structural features. We find a remarkably similar landscape but accelerated implied timescales for the slowest motions. The solvent shells contributing most to the first tICA eigenvector are those centered on Lys24 and Thr18 of the p53 TAD peptide in the range of 3-6 Å. Important solvent shells were visualized to reveal solvation and desolvation transitions along the peptide-protein binding trajectories. Our results provide a solvent-centric view of the hydrophobic effect in action for a realistic peptide-protein binding scenario.

A comprehensive computer simulation insight into inhibitory mechanisms of EGCG and NQTrp ligands on amyloid-beta assemblies as the Alzheimer's disease insignia

Amyloid-β peptide with predominant presence in the senile plaques is the most common agent for Alzheimer's disease (AD) incidence. Assembly of the amyloid-β(1-42) (Aβ1-42) isoform is known as the main reason for the AD appearance. Epigallocatechin gallate (EGCG) and 1,4-naphthoquinone-2-yl-L-tryptophan (NQTrp) are two small molecules that inhibit the formation of the Aβ1-42 fibrils. The present study provides molecular insight to clarify the inhibitory mechanisms of the EGCG and NQTrp ligands on the Aβ1-42 assemblies by using molecular dynamics (MD) simulation. Hence, nine different Aβ1-42-containing systems including the monomer, dimer, and hexamer of Aβ1-42 considering each of them in a media with no ligands, in the presence of one EGCG ligand, and in the presence of one EGCG ligand were studied with a simulation time of 1 µs for each system. The precise investigation of the peptide-ligand distance, conformational factor (Pi), solvent accessible surface area (SASA), dictionary of secondary structure (DSSP), and Lys28-Ala42 salt bridge analyses confirmed that the hydroxyl-rich structure of the EGCG ligand applied its inhibitory effect on the aggregation of the peptides indirectly by involving water molecules. While the hydroxyl-free structure of the NQTrp ligand exposed its inhibitory effect through a direct interaction with the Aβ1-42 peptides. Besides, reduced density gradient (RDG) analysis clarified the hydrogen bonding interactions as the dominant ones for the peptide-EGCG systems, and also, steric and van der Waals interactions for the peptide-NQTrp systems.Communicated by Ramaswamy H. Sarma.

Protein Design: From the Aspect of Water Solubility and Stability

Water solubility and structural stability are key merits for proteins defined by the primary sequence and 3D-conformation. Their manipulation represents important aspects of the protein design field that relies on the accurate placement of amino acids and molecular interactions, guided by underlying physiochemical principles. Emulated designer proteins with well-defined properties both fuel the knowledge-base for more precise computational design models and are used in various biomedical and nanotechnological applications. The continuous developments in protein science, increasing computing power, new algorithms, and characterization techniques provide sophisticated toolkits for solubility design beyond guess work. In this review, we summarize recent advances in the protein design field with respect to water solubility and structural stability. After introducing fundamental design rules, we discuss the transmembrane protein solubilization and de novo transmembrane protein design. Traditional strategies to enhance protein solubility and structural stability are introduced. The designs of stable protein complexes and high-order assemblies are covered. Computational methodologies behind these endeavors, including structure prediction programs, machine learning algorithms, and specialty software dedicated to the evaluation of protein solubility and aggregation, are discussed. The findings and opportunities for Cryo-EM are presented. This review provides an overview of significant progress and prospects in accurate protein design for solubility and stability.

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.

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.

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.

Molecular dynamics simulations reveal ligand-controlled positioning of a peripheral protein complex in membranes

Bryostatin is in clinical trials for Alzheimer’s disease, cancer, and HIV/AIDS eradication. It binds to protein kinase C competitively with diacylglycerol, the endogenous protein kinase C regulator, and plant-derived phorbol esters, but each ligand induces different activities. Determination of the structural origin for these differing activities by X-ray analysis has not succeeded due to difficulties in co-crystallizing protein kinase C with relevant ligands. More importantly, static, crystal-lattice bound complexes do not address the influence of the membrane on the structure and dynamics of membrane-associated proteins. To address this general problem, we performed long-timescale (400–500 µs aggregate) all-atom molecular dynamics simulations of protein kinase C–ligand–membrane complexes and observed that different protein kinase C activators differentially position the complex in the membrane due in part to their differing interactions with waters at the membrane inner leaf. These new findings enable new strategies for the design of simpler, more effective protein kinase C analogs and could also prove relevant to other peripheral protein complexes.

Natural supplies of bryostatin, a compound in clinical trials for Alzheimer’s disease, cancer, and HIV, are scarce. Here, the authors perform molecular dynamics simulations to understand how bryostatin interacts with membrane-bound protein kinase C, offering insights for the design of bryostatin analogs.

Stochastic steps in secondary active sugar transport

Secondary active transporters, such as those that adopt the leucine-transporter fold, are found in all domains of life, and they have the unique capability of harnessing the energy stored in ion gradients to accumulate small molecules essential for life as well as expel toxic and harmful compounds. How these proteins couple ion binding and transport to the concomitant flow of substrates is a fundamental structural and biophysical question that is beginning to be answered at the atomistic level with the advent of high-resolution structures of transporters in different structural states. Nonetheless, the dynamic character of the transporters, such as ion/substrate binding order and how binding triggers conformational change, is not revealed from static structures, yet it is critical to understanding their function. Here, we report a series of molecular simulations carried out on the sugar transporter vSGLT that lend insight into how substrate and ions are released from the inward-facing state of the transporter. Our simulations reveal that the order of release is stochastic. Functional experiments were designed to test this prediction on the human homolog, hSGLT1, and we also found that cytoplasmic release is not ordered, but we confirmed that substrate and ion binding from the extracellular space is ordered. Our findings unify conflicting published results concerning cytoplasmic release of ions and substrate and hint at the possibility that other transporters in the superfamily may lack coordination between ions and substrate in the inward-facing state.

HTMD: High-Throughput Molecular Dynamics for Molecular Discovery

Recent advances in molecular simulations have allowed scientists to investigate slower biological processes than ever before. Together with these advances came an explosion of data that has transformed a traditionally computing-bound into a data-bound problem. Here, we present HTMD, a programmable, extensible platform written in Python that aims to solve the data generation and analysis problem as well as increase reproducibility by providing a complete workspace for simulation-based discovery. So far, HTMD includes system building for CHARMM and AMBER force fields, projection methods, clustering, molecular simulation production, adaptive sampling, an Amazon cloud interface, Markov state models, and visualization. As a result, a single, short HTMD script can lead from a PDB structure to useful quantities such as relaxation time scales, equilibrium populations, metastable conformations, and kinetic rates. In this paper, we focus on the adaptive sampling and Markov state modeling features.

The pathway of ligand entry from the membrane bilayer to a lipid G protein-coupled receptor

The binding process through the membrane bilayer of lipid-like ligands to a protein target is an important but poorly explored recognition process at the atomic level. In this work we succeeded in resolving the binding of the lipid inhibitor ML056 to the sphingosine-1-phosphate receptor 1 (S1P1R) using unbiased molecular dynamics simulations with an aggregate sampling of over 800 μs. The binding pathway is a multi-stage process consisting of the ligand diffusing in the bilayer leaflet to contact a "membrane vestibule" at the top of TM 7, subsequently moving from this lipid-facing vestibule to the orthosteric binding cavity through a channel formed by TMs 1 and 7 and the N-terminal of the receptor. Unfolding of the N-terminal alpha-helix increases the volume of the channel upon ligand entry, helping to reach the crystallographic pose that also corresponds to the predicted favorable pose. The relaxation timescales of the binding process show that the binding of the ligand to the "membrane vestibule" is the rate-limiting step in the multi microseconds timescale. We comment on the significance and parallels of the binding process in the context of other binding studies.

PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models

Markov (state) models (MSMs) and related models of molecular kinetics have recently received a surge of interest as they can systematically reconcile simulation data from either a few long or many short simulations and allow us to analyze the essential metastable structures, thermodynamics, and kinetics of the molecular system under investigation. However, the estimation, validation, and analysis of such models is far from trivial and involves sophisticated and often numerically sensitive methods. In this work we present the open-source Python package PyEMMA ( http://pyemma.org ) that provides accurate and efficient algorithms for kinetic model construction. PyEMMA can read all common molecular dynamics data formats, helps in the selection of input features, provides easy access to dimension reduction algorithms such as principal component analysis (PCA) and time-lagged independent component analysis (TICA) and clustering algorithms such as k-means, and contains estimators for MSMs, hidden Markov models, and several other models. Systematic model validation and error calculation methods are provided. PyEMMA offers a wealth of analysis functions such that the user can conveniently compute molecular observables of interest. We have derived a systematic and accurate way to coarse-grain MSMs to few states and to illustrate the structures of the metastable states of the system. Plotting functions to produce a manuscript-ready presentation of the results are available. In this work, we demonstrate the features of the software and show new methodological concepts and results produced by PyEMMA.