Autoencoders for dimensionality reduction in molecular dynamics: Collective variable dimension, biasing, and transition states.

The heat shock protein 90 (Hsp90) is a molecular chaperone that controls the folding and activation of client proteins using the free energy of ATP hydrolysis. The Hsp90 active site is in its N-terminal domain (NTD). Our goal is to characterize the dynamics of NTD using an autoencoder-learned collective variable (CV) in conjunction with adaptive biasing force Langevin dynamics. Using dihedral analysis, we cluster all available experimental Hsp90 NTD structures into distinct native states. We then perform unbiased molecular dynamics (MD) simulations to construct a dataset that represents each state and use this dataset to train an autoencoder. Two autoencoder architectures are considered, with one and two hidden layers, respectively, and bottlenecks of dimension k ranging from 1 to 10. We demonstrate that the addition of an extra hidden layer does not significantly improve the performance, while it leads to complicated CVs that increase the computational cost of biased MD calculations. In addition, a two-dimensional (2D) bottleneck can provide enough information of the different states, while the optimal bottleneck dimension is five. For the 2D bottleneck, the 2D CV is directly used in biased MD simulations. For the five-dimensional (5D) bottleneck, we perform an analysis of the latent CV space and identify the pair of CV coordinates that best separates the states of Hsp90. Interestingly, selecting a 2D CV out of the 5D CV space leads to better results than directly learning a 2D CV and allows observation of transitions between native states when running free energy biased dynamics.

Chasing Collective Variables Using Autoencoders and Biased Trajectories.

Free energy biasing methods have proven to be powerful tools to accelerate the simulation of important conformational changes of molecules by modifying the sampling measure. However, most of these methods rely on the prior knowledge of low-dimensional slow degrees of freedom, i.e., collective variables (CVs). Alternatively, such CVs can be identified using machine learning (ML) and dimensionality reduction algorithms. In this context, approaches where the CVs are learned in an iterative way using adaptive biasing have been proposed: at each iteration, the learned CV is used to perform free energy adaptive biasing to generate new data and learn a new CV. In this paper, we introduce a new iterative method involving CV learning with autoencoders: Free Energy Biasing and Iterative Learning with AutoEncoders (FEBILAE). Our method includes a reweighting scheme to ensure that the learning model optimizes the same loss at each iteration and achieves CV convergence. Using the alanine dipeptide system and the solvated chignolin mini-protein system as examples, we present results of our algorithm using the extended adaptive biasing force as the free energy adaptive biasing method.

Contact Map Fingerprints of Protein-Ligand Unbinding Trajectories Reveal Mechanisms Determining Residence Times Computed from Scaled Molecular Dynamics.

The binding kinetic properties of potential drugs may significantly influence their subsequent clinical efficacy. Predictions of these properties based on computer simulations provide a useful alternative to their expensive and time-consuming experimental counterparts, even at an early drug discovery stage. Herein, we perform scaled molecular dynamics (ScaledMD) simulations on a set of 27 ligands of HSP90 belonging to more than seven chemical series to estimate their relative residence times. We introduce two new techniques for the analysis and the classification of the simulated unbinding trajectories. The first technique, which helps in estimating the limits of the free energy well around the bound state, and the second one, based on a new contact map fingerprint, allow the description and the comparison of the paths that lead to unbinding. Using these analyses, we find that ScaledMD's relative residence time generally enables the identification of the slowest unbinders. We propose an explanation for the underestimation of the residence times of a subset of compounds, and we investigate how the biasing in ScaledMD can affect the mechanistic insights that can be gained from the simulations.

Automated Design of Macrocycles for Therapeutic Applications: From Small Molecules to Peptides and Proteins.

Macrocycles and cyclic peptides are increasingly attractive therapeutic modalities as they often have improved affinity, are able to bind to extended protein surfaces, and otherwise have favorable properties. Macrocyclization of a known binder may stabilize its bioactive conformation and improve its metabolic stability, cell permeability, and in certain cases oral bioavailability. Herein, we present implementation and application of an approach that automatically generates, evaluates, and proposes cyclizations utilizing a library of well-established chemical reactions and reagents. Using the three-dimensional (3D) conformation of the linear molecule in complex with a target protein as the starting point, this approach identifies attachment points, generates linkers, evaluates their geometric compatibility, and ranks the resulting molecules with respect to their predicted conformational stability and interactions with the target protein. As we show here with prospective and retrospective case studies, this procedure can be applied for the macrocyclization of small molecules and peptides and even PROteolysis TArgeting Chimeras (PROTACs) and proteins.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems.

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

Allostery in Its Many Disguises: From Theory to Applications.

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

Phase Diagram of a Stratum Corneum Lipid Mixture.

Computational modeling of lipid ternary mixtures is challenging because of their complicated and segmented phase diagram, the long timescales required for mixing the system components, and the necessity to sufficiently sample the three-dimensional phase space. Here, we investigate a ternary system, which mimics the lipid matrix of the stratum corneum, the outermost layer of the epidermis and the primary barrier for transdermal drug absorption. Our system consists of ceramide, cholesterol, and lignoceric acid at 23 different composition ratios, which we study at two different temperatures using coarse-grained molecular dynamics (CG MD) simulations. As CG MD simulations heavily depend on the choice of parameters, first an improved set of ceramide CG parameters was developed that reproduces experimental and all-atom simulation data. Second, the performance of the recently updated MARTINI 2015 cholesterol force field was systematically evaluated and compared to the 2007 model. We provide a detailed analysis of the structural and dynamic properties of the ternary system, such as area per lipid, area compressibility modulus, lipid order parameters, bilayer thickness, lipid tail interdigitation, and lateral self-diffusion. Based on the analysis of these properties, we devise a phase diagram of the ternary system, where three different phases, namely, liquid-disordered, gel, and liquid-ordered, are observed. The individual occurrence of a certain phase not only depends on the component molar ratio and the temperature but also decisively on the employed cholesterol force field.

Exercise Training Attenuates the Development of Cardiac Autonomic Dysfunction in Diabetic Rats.

BACKGROUND/AIM: Exercise training usually complements pharmacological therapy of type 1 diabetes mellitus, however, little is known about its impact on cardiac autonomic neuropathy. Our aim was to evaluate the impact of exercise on electrocardiographic parameters and heart rate variability in diabetic rats. MATERIALS AND METHODS: Wistar rats were randomly assigned to four groups (n=12): Sedentary control (SC), sedentary diabetic (SD), exercise control (EC), and exercise diabetic (ED). Diabetes was induced by a single intraperitoneal injection of streptozotocin (45 mg/kg). Exercise groups underwent 8 weeks of training on a treadmill. At the end of the study, echocardiography was performed and continuous electrocardiographic recording was obtained by intra-abdominally implanted telemetric devices. Diabetes induction significantly reduced the heart rate and increased the blood glucose level (p<0.001) and R-wave amplitude (p<0.05). Frequency-domain spectral variables were also analyzed. The SD group had a significantly lower absolute high-frequency component (p<0.05) and higher normalized low-frequency component, as well as low-frequency power divided by the high-frequency power ratio when compared to the SC and EC groups (p<0.05). All these diabetes-related adverse changes in heart rate variability parameters were significantly reversed by exercise training (p<0.05). Overall, our study shows that early initiation of systemic exercise training prevents the development of cardiac autonomic neuropathy in rats with type 1 diabetes mellitus, by favorable change in the balance between parasympathetic and sympathetic activity.

Effect of 5-trans Isomer of Arachidonic Acid on Model Liposomal Membranes Studied by a Combined Simulation and Experimental Approach.

Unsaturated fatty acids are found in humans predominantly in the cis configuration. Fatty acids in the trans configuration are primarily the result of human processing (trans fats), but can also be formed endogenously by radical stress. The cis-trans isomerization of fatty acids by free radicals could be connected to several pathologies. Trans fats have been linked to an increased risk of coronary artery disease; however, the reasons for the resulting pathogenesis remain unclear. Here, we investigate the effect of a mono-trans isomer of arachidonic acid (C20:4-5trans, 8cis, 11cis, 14cis) produced by free radicals in physiological concentration on a model erythrocyte membrane using a combined experimental and theoretical approach. Molecular Dynamics (MD) simulations of two model lipid bilayers containing arachidonic acid and its 5-trans isomer in 3 mol% were carried out for this purpose. The 5-trans isomer formation in the phospholipids was catalyzed by HOCH2CH2S· radicals, generated from the corresponding thiol by γ-irradiation, in multilamellar vesicles of SAPC. Large unilamellar vesicles were made by the extrusion method (LUVET) as a biomimetic model for cis-trans isomerization. Atomic Force Microscopy and Dynamic Light Scattering were used to measure the average size, morphology, and the z-potential of the liposomes. Both results from MD simulations and experiments are in agreement and indicate that the two model membranes display different physicochemical properties in that the bilayers containing the trans fatty acids were more ordered and more rigid than those containing solely the cis arachidonic acid. Correspondingly, the average size of the liposomes containing trans isomers was smaller than the ones without.

Self-assembly of anionic, ligand-coated nanoparticles in lipid membranes.

Ligand-functionalized nanoparticles (NPs) are a promising platform for imaging and drug delivery applications. A number of recent molecular simulation and theoretical studies explored how these NPs interact with model lipid membranes. However, interactions between ligand-coated NPs leading to possible cooperative effects and association have not been investigated. In this coarse-grained molecular dynamics study, we focus on a specific case of several anionic, ligand-coated NPs embedded in a lipid membrane. Several new effects are observed. Specifically, in the presence of cholesterol in the membrane, NPs tend to form linear clusters, or chains. Analysis of the driving forces for this association reveals an important role of the recently discovered orderphobic effect, although we acknowledge that a combination of factors must be at play. At the same time, we argue that the specific linear shape of the clusters is a result of a subtle balance between the forces that stabilize a NP in the membrane and the forces that drive the NP-NP association processes. These effects, observed for the first time in the NP-membrane systems, have also direct correspondence to similar effects in protein-membrane systems and these links between the two realms should be explored further.

DPPC-cholesterol phase diagram using coarse-grained Molecular Dynamics simulations.

Cholesterol-phospholipid bilayers continue to be the current state of the art in membrane models and serve as representative systems for studying the effect of cholesterol on the cell membrane. As the mixing of different lipid species requires long spatio-temporal scales, coarse-grained models have gained increasing popularity in modeling such membrane systems. In this paper, a systematic study of the MARTINI coarse-grained model for the DPPC-cholesterol binary system has been performed. We construct the phase diagram of DPPC lipid bilayers in the presence of different cholesterol concentrations and at different temperatures using coarse-grained Molecular Dynamics (MD) simulations with the MARTINI force field. The phase diagram based on the condensation effect is directly comparable to available experimental data and demonstrates qualitative agreement over all cholesterol concentrations. Self-assembled bilayers quantitatively reproduce experimental observables, such as lateral diffusion of lipids, electron density, area per lipid and lipid order parameters. The phase diagram of the DPPC-cholesterol binary system also reveals the profound effect of cholesterol on the physical properties of phospholipid bilayers such lipid order, diffusion, and fluidity. Cholesterol induces the liquid-ordered phase, which increases the fluidity of the phospholipid hydrocarbon chains above the gel to liquid-crystalline phase transition temperature and decreases it below the phase transition. The present study suggests that the MARTINI force field can be successfully used to obtain molecular level insights into cholesterol-DPPC model membranes.

Alchemical Free Energy Calculations and Isothermal Titration Calorimetry Measurements of Aminoadamantanes Bound to the Closed State of Influenza A/M2TM.

Adamantane derivatives, such as amantadine and rimantadine, have been reported to block the transmembrane domain (TM) of the M2 protein of influenza A virus (A/M2) but their clinical use has been discontinued due to evolved resistance in humans. Although experiments and simulations have provided adequate information about the binding interaction of amantadine or rimantadine to the M2 protein, methods for predicting binding affinities of whole series of M2 inhibitors have so far been scarcely applied. Such methods could assist in the development of novel potent inhibitors that overcome A/M2 resistance. Here we show that alchemical free energy calculations of ligand binding using the Bennett acceptance ratio (BAR) method are valuable for determining the relative binding potency of A/M2 inhibitors of the aminoadamantane type covering a binding affinity range of only ∼2 kcal mol(-1). Their binding affinities measured by isothermal titration calorimetry (ITC) against the A/M2TM tetramer from the Udorn strain in its closed form at pH 8 were used as experimental probes. The binding constants of rimantadine enantiomers against M2TMUdorn were measured for the first time and found to be equal. Two series of alchemical free energy calculations were performed using 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipids to mimic the membrane environment. A fair correlation was found for DPPC that was significantly improved using DMPC, which resembles more closely the DPC lipids used in the ITC experiments. This demonstrates that binding free energy calculations by the BAR approach can be used to predict relative binding affinities of aminoadamantane derivatives toward M2TM with good accuracy.

Membrane Protein Structure, Function, and Dynamics: a Perspective from Experiments and Theory.

Membrane proteins mediate processes that are fundamental for the flourishing of biological cells. Membrane-embedded transporters move ions and larger solutes across membranes; receptors mediate communication between the cell and its environment and membrane-embedded enzymes catalyze chemical reactions. Understanding these mechanisms of action requires knowledge of how the proteins couple to their fluid, hydrated lipid membrane environment. We present here current studies in computational and experimental membrane protein biophysics, and show how they address outstanding challenges in understanding the complex environmental effects on the structure, function, and dynamics of membrane proteins.

Exploring a non-ATP pocket for potential allosteric modulation of PI3Kα.

Allosteric modulators offer a novel approach for kinase inhibition because they target less conserved binding sites compared to the active site; thus, higher selectivity may be obtained. PIK-108, a known pan phosphoinositide 3-kinase (PI3K) inhibitor, was recently detected to occupy a non-ATP binding site in the PI3Kα C-lobe. This newly identified pocket is located close to residue 1047, which is frequently mutated in human cancers (H1047R). In order to assess the interactions, stability, and any possible allosteric effects of this inhibitor on PI3Kα, extensive molecular dynamics (MD) simulations in aqueous solution were performed for the wild type (WT) human, WT murine, and H1047R human mutant PI3Kα proteins with PIK-108 placed in both catalytic and non-ATP sites. We verify the existence of the second binding site in the vicinity of the hotspot H1047R PI3Kα mutation through binding site identification and MD simulations. PIK-108 remains stable in both sites in all three variants throughout the course of the simulations. We demonstrate that the pose and interactions of PIK-108 in the catalytic site are similar in the murine WT and human mutant forms, while they are significantly different in the case of human WT PI3Kα protein. PIK-108 binding in the non-ATP pocket also differs significantly among the three variants. Finally, we examine whether the non-ATP binding site is implicated in PI3Kα allostery in terms of its communication with the active site using principal component analysis and perform in vitro experiments to verify our hypotheses.

Membrane partitioning of anionic, ligand-coated nanoparticles is accompanied by ligand snorkeling, local disordering, and cholesterol depletion.

Intracellular uptake of nanoparticles (NPs) may induce phase transitions, restructuring, stretching, or even complete disruption of the cell membrane. Therefore, NP cytotoxicity assessment requires a thorough understanding of the mechanisms by which these engineered nanostructures interact with the cell membrane. In this study, extensive Coarse-Grained Molecular Dynamics (MD) simulations are performed to investigate the partitioning of an anionic, ligand-decorated NP in model membranes containing dipalmitoylphosphatidylcholine (DPPC) phospholipids and different concentrations of cholesterol. Spontaneous fusion and translocation of the anionic NP is not observed in any of the 10-µs unbiased MD simulations, indicating that longer timescales may be required for such phenomena to occur. This picture is supported by the free energy analysis, revealing a considerable free energy barrier for NP translocation across the lipid bilayer. 5-µs unbiased MD simulations with the NP inserted in the bilayer core reveal that the hydrophobic and hydrophilic ligands of the NP surface rearrange to form optimal contacts with the lipid bilayer, leading to the so-called snorkeling effect. Inside cholesterol-containing bilayers, the NP induces rearrangement of the structure of the lipid bilayer in its vicinity from the liquid-ordered to the liquid phase spanning a distance almost twice its core radius (8-10 nm). Based on the physical insights obtained in this study, we propose a mechanism of cellular anionic NP partitioning, which requires structural rearrangements of both the NP and the bilayer, and conclude that the translocation of anionic NPs through cholesterol-rich membranes must be accompanied by formation of cholesterol-lean regions in the proximity of NPs.

Investigating the structure and dynamics of the PIK3CA wild-type and H1047R oncogenic mutant.

The PIK3CA gene is one of the most frequently mutated oncogenes in human cancers. It encodes p110α, the catalytic subunit of phosphatidylinositol 3-kinase alpha (PI3Kα), which activates signaling cascades leading to cell proliferation, survival, and cell growth. The most frequent mutation in PIK3CA is H1047R, which results in enzymatic overactivation. Understanding how the H1047R mutation causes the enhanced activity of the protein in atomic detail is central to developing mutant-specific therapeutics for cancer. To this end, Surface Plasmon Resonance (SPR) experiments and Molecular Dynamics (MD) simulations were carried out for both wild-type (WT) and H1047R mutant proteins. An expanded positive charge distribution on the membrane binding regions of the mutant with respect to the WT protein is observed through MD simulations, which justifies the increased ability of the mutated protein variant to bind to membranes rich in anionic lipids in our SPR experiments. Our results further support an auto-inhibitory role of the C-terminal tail in the WT protein, which is abolished in the mutant protein due to loss of crucial intermolecular interactions. Moreover, Functional Mode Analysis reveals that the H1047R mutation alters the twisting motion of the N-lobe of the kinase domain with respect to the C-lobe and shifts the position of the conserved P-loop residues in the vicinity of the active site. These findings demonstrate the dynamical and structural differences of the two proteins in atomic detail and propose a mechanism of overactivation for the mutant protein. The results may be further utilized for the design of mutant-specific PI3Kα inhibitors that exploit the altered mutant conformation.

Homogeneous Hydrophobic-Hydrophilic Surface Patterns Enhance Permeation of Nanoparticles through Lipid Membranes.

We employ coarse-grained molecular dynamics simulations to understand why certain interaction patterns on the surface of a nanoparticle promote its translocation through a lipid membrane. We demonstrate that switching from a random, heterogeneous distribution of hydrophobic and hydrophilic areas on the surface of a nanoparticle to even, homogeneous patterns substantially flattens the translocation free-energy profile and dramatically enhances permeation. We then proceed to construct a more detailed coarse-grained model of a nanoparticle with flexible hydrophobic and hydrophilic ligands arranged into striped domains. Molecular dynamics simulations of these nanoparticles show that the terminal groups of the ligands tend to arrange themselves into homogeneous patterns, despite the underlying striped domains. These observations are linked to recent experimental studies.

Free Energy Calculations Reveal the Origin of Binding Preference for Aminoadamantane Blockers of Influenza A/M2TM Pore.

Aminoadamantane derivatives, such as amantadine and rimantadine, have been reported to block the M2 membrane protein of influenza A virus (A/M2TM), but their use has been discontinued due to reported resistance in humans. Understanding the mechanism of action of amantadine derivatives could assist the development of novel potent inhibitors that overcome A/M2TM resistance. Here, we use Free Energy Perturbation calculations coupled with Molecular Dynamics simulations (FEP/MD) to rationalize the thermodynamic origin of binding preference of several aminoadamantane derivatives inside the A/M2TM pore. Our results demonstrate that apart from crucial protein-ligand intermolecular interactions, the flexibility of the protein, the water network around the ligand, and the desolvation free energy penalty to transfer the ligand from the aqueous environment to the transmembrane region are key elements for the binding preference of these compounds and thus for lead optimization. The high correlation of the FEP/MD results with available experimental data (R(2) = 0.85) demonstrates that this methodology holds predictive value and can be used to guide the optimization of drug candidates binding to membrane proteins.

Interactions of phospholipid bilayers with several classes of amphiphilic alpha-helical peptides: insights from coarse-grained molecular dynamics simulations.

In this article, we focus on several types of interactions between lipid membranes and alpha-helical peptides, based on the distribution of hydrophobic and hydrophilic residues along the helix. We employ a recently proposed coarse-grained model MARTINI and test its ability to capture diverse types of behavior. MARTINI provides useful insights on the formation of barrel-stave and toroidal pores and on the relation between these two mechanisms. Amphipathic nonspanning peptides are also described with sufficient accuracy. The picture is not as clear for fusion and transmembrane peptides. For each class of peptides, we calculate the potential of mean force (PMF) for peptide translocation across the lipid bilayer and demonstrate that each class has a distinct shape of PMF. The reliability of these calculations, as well as wider implications of the results, is discussed.