Standard Molecular Dynamics Simulations Research Articles

What Is the Protonation State of Proteins in Crystals? Insights from Constant pH Molecular Dynamics Simulations.

X-ray crystallography is an important technique to determine the positions of atoms in a protein crystal. However, because the native environment in which proteins function, is not a crystal, but a solution, it is not a priori clear if the crystal structure represents the functional form of the protein. Because the protein structure and function often depend critically on the pH, the question arises whether proton affinities are affected by crystallization. X-ray diffraction usually does not reveal protons, which makes it difficult to experimentally measure pKa shifts in crystals. Here, we investigate whether this challenge can be addressed by performing in silico titration with constant pH molecular dynamics (MD) simulations. We compare the computed pKa values of proteins between solution and crystal environment and analyze these differences in the context of molecular interactions. For the proteins considered in this work, pKa shifts were mostly found for residues at the crystal interfaces, where the environment is more apolar in the crystal than in water. Although convergence was an obstacle, our simulations suggest that in principle it is possible to apply constant pH MD to protein crystals routinely and assess the effect of crystallization on protein function more systematically than with standard MD simulations. We also highlight technical challenges that need to be addressed to make MD simulations of crystals more reliable.

Structure and Energetics of PET-Hydrolyzing Enzyme Complexes: A Systematic Comparison from Molecular Dynamics Simulations.

Discovered in 2016, the enzyme PETase, secreted by bacterial Ideonella Sakaiensis 201-F6, has an excellent hydrolytic activity toward poly(ethylene terephthalate) (PET) at room temperature, while it decreases at higher temperatures due to the low thermostability. Many variants have been engineered to overcome this limitation, which hinders industrial application. In this work, we systematically compare PETase wild-type (WT) and four mutants (DuraPETase, ThermoPETase, FastPETase, and HotPETase) using standard molecular dynamics (MD) simulations and unbinding free energy calculations. In particular, we analyze the enzymes' structural characteristics and binding to a tetrameric PET chain (PET4) under two temperature conditions: T1─300 K and T2─350 K. Our results indicate that (i) PET4 forms stable complexes with the five enzymes at room temperature (∼300 K) and (ii) most of the interactions are localized close to the active site of the protein, where the W185 and Y87 residues interact with the aromatic rings of the substrate. Specifically, (iii) the W185 side-chain explores different conformations in each variant (a phenomenon known in the literature as "W185 wobbling"). This suggests that the binding pocket retains structural plasticity and flexibility among the variants, facilitating substrate recognition and localization events at moderate temperatures. Moreover, (iv) PET4 establishes aromatic interactions with the catalytic H237 residue, stabilizing the catalytic triad composed of residues S160-H237-D206, and helping the system achieve an effective configuration for the hydrolysis reaction. Conversely, (v) the binding affinity decreases at a higher temperature (∼350 K), retaining moderate interactions only for HotPETase. Finally, (vi) MD simulations of complexes formed with poly(ethylene-2,5-furan dicarboxylate) (PEF) show no persistent interactions, suggesting that these enzymes are not yet optimized for binding this alternative semiaromatic plastic polymer. Our study offers valuable insights into the structural stability of these enzymes and the molecular determinants driving PET binding onto their surfaces, sheds light on the mechanistic steps that precede the onset of hydrolysis, and provides a foundation for future enzyme optimization.

Multistate Method to Efficiently Account for Tautomerism and Protonation in Alchemical Free-Energy Calculations.

The majority of drug-like molecules contain at least one ionizable group, and many common drug scaffolds are subject to tautomeric equilibria. Thus, these compounds are found in a mixture of protonation and/or tautomeric states at physiological pH. Intrinsically, standard classical molecular dynamics (MD) simulations cannot describe such equilibria between states, which negatively impacts the prediction of key molecular properties in silico. Following the formalism described by de Oliveira and co-workers (J. Chem. Theory Comput. 2019, 15, 424-435) to consider the influence of all states on the binding process based on alchemical free-energy calculations, we demonstrate in this work that the multistate method replica-exchange enveloping distribution sampling (RE-EDS) is well suited to describe molecules with multiple protonation and/or tautomeric states in a single simulation. We apply our methodology to a series of eight inhibitors of factor Xa with two protonation states and a series of eight inhibitors of glycogen synthase kinase 3β (GSK3β) with two tautomeric states. In particular, we show that given a sufficient phase-space overlap between the states, RE-EDS is computationally more efficient than standard pairwise free-energy methods.

Molecular Docking Improved with Human Spatial Perception Using Virtual Reality.

Adaptive steered molecular dynamics (ASMD) is a computational biophysics method in which an external force is applied to a selected set of atoms or a specific reaction coordinate to induce a particular molecular motion. Virtual reality (VR) based methods for protein-ligand docking are beneficial for visualizing on-the-fly interactive molecular dynamics and performing promising docking trajectories. In this paper, we propose a novel method to guide ASMD with optimal trajectories collected from human experiences using interactive molecular dynamics in virtual reality (iMD-VR). We also explain the benefits of using VR as a tool for expediting the process of ligand binding, outlining an experimental protocol that enables iMD-VR users to guide Amprenavir into and out of the binding pockets of HIV-1 protease and recreate their respective crystallographic binding poses within 5 minutes. Later, we discuss our analysis of the results from iMD-VR-assisted ASMD simulation and assess its performance compared to a standard ASMD simulation. From the accuracy point of view, our proposed method calculates higher Potential Mean Force (PMF) values consistently relative to a standard ASMD simulation with an almost twofold increase in all the experiments. Finally, we describe the novelty of the research and discuss results showcasing a faster and more effective convergence of the ligand to the protein's binding site as compared to a standard molecular dynamics simulation, proving the effectiveness of VR in the field of drug discovery. Future work includes the development of an artificial intelligence algorithm capable of predicting optimal binding trajectories for many protein-ligand pairs, as well as the required force needed to steer the ligand to follow the said trajectory.

Mechanical Stability and Unfolding Pathways of Parallel Tetrameric G-Quadruplexes Probed by Pulling Simulations.

Guanine quadruplex (GQ) is a noncanonical nucleic acid structure formed by guanine-rich DNA and RNA sequences. Folding of GQs is a complex process, where several aspects remain elusive, despite being important for understanding structure formation and biological functions of GQs. Pulling experiments are a common tool for acquiring insights into the folding landscape of GQs. Herein, we applied a computational pulling strategy─steered molecular dynamics (SMD) simulations─in combination with standard molecular dynamics (MD) simulations to explore the unfolding landscapes of tetrameric parallel GQs. We identified anisotropic properties of elastic conformational changes, unfolding transitions, and GQ mechanical stabilities. Using a special set of structural parameters, we found that the vertical component of pulling force (perpendicular to the average G-quartet plane) plays a significant role in disrupting GQ structures and weakening their mechanical stabilities. We demonstrated that the magnitude of the vertical force component depends on the pulling anchor positions and the number of G-quartets. Typical unfolding transitions for tetrameric parallel GQs involve base unzipping, opening of the G-stem, strand slippage, and rotation to cross-like structures. The unzipping was detected as the first and dominant unfolding event, and it usually started at the 3'-end. Furthermore, results from both SMD and standard MD simulations indicate that partial spiral conformations serve as a transient ensemble during the (un)folding of GQs.

Refinement of Docked Protein-Protein Complexes Using Repulsive Scaling Replica Exchange Simulations.

Accurate prediction and evaluation of protein-protein complex structures is of major importance to understand the cellular interactome. Predicted complex structures based on deep learning approaches or traditional docking methods require often structural refinement and rescoring for realistic evaluation. Standard molecular dynamics (MD) simulations are time-consuming and often do not structurally improve docking solutions. Better refinement can be achieved with our recently developed replica-exchange-based scheme employing different levels of repulsive biasing between proteins in each replica simulation (RS-REMD). The bias acts specifically on the intermolecular interactions based on an increase in effective pairwise van der Waals radii without changing interactions within each protein or with the solvent. It allows for an improvement of the predicted protein-protein complex structure and simultaneous realistic free energy scoring of protein-protein complexes. The setup of RS-REMD simulations is described in detail including the application on two examples (all necessary scripts and input files can be obtained from https://gitlab.com/TillCyrill/mmib ).

Dealing with Induced Fit, Conformational Selection, and Secondary Poses in Molecular Dynamics Simulations for Reliable Free Energy Predictions.

In this study, we have tested the performance of standard molecular dynamics (MD) simulations, replicates of shorter standard MD simulations, and Hamiltonian Replica Exchange (HREM) simulations for the sampling of two macrocyclic hosts for guest delivery, characterized by induced fit (phenyl-based host) and conformation selection (naphthyl-based host) and of the ODR-BRD4(I) drug-receptor system where the ligand can assume two main poses. For the optimization of the HREM simulation, we have proposed and tested an on-the-fly iterative scheme for equalizing the acceptance ratio along the replica progression at a constant replica number resulting in a moderate impact of the sampling efficiency. Concerning standard MD, we have found that, while splitting the total allocated simulation time in short MD replicates can reproduce the sampling efficiency of HREM in the phenyl-based host and in the ODR-BRD4(I) complex, in the naphthyl-based macrocycle, characterized by long-lived metastable states, enhanced sampling techniques are the only viable alternative for a reliable canonical sampling of the rugged conformational landscape.

Atomistic Picture of Opening-Closing Dynamics of DNA Holliday Junction Obtained by Molecular Simulations.

Holliday junction (HJ) is a noncanonical four-way DNA structure with a prominent role in DNA repair, recombination, and DNA nanotechnology. By rearranging its four arms, HJ can adopt either closed or open state. With enzymes typically recognizing only a single state, acquiring detailed knowledge of the rearrangement process is an important step toward fully understanding the biological function of HJs. Here, we carried out standard all-atom molecular dynamics (MD) simulations of the spontaneous opening-closing transitions, which revealed complex conformational transitions of HJs with an involvement of previously unconsidered "half-closed" intermediates. Detailed free-energy landscapes of the transitions were obtained by sophisticated enhanced sampling simulations. Because the force field overstabilizes the closed conformation of HJs, we developed a system-specific modification which for the first time allows the observation of spontaneous opening-closing HJ transitions in unbiased MD simulations and opens the possibilities for more accurate HJ computational studies of biological processes and nanomaterials.

Hypersound-perturbed molecular dynamics simulation for accelerating slow biomolecular interaction processes.

Capturing the dynamic processes of biomolecular systems in atomistic detail remains difficult despite recent experimental advances. Although molecular dynamics (MD) techniques enable atomic-level observations, simulations of “slow” biomolecular processes (with timescales longer than submilliseconds) are challenging because of current computer speed limitations. Therefore, we developed a method to accelerate MD simulations by high-frequency ultrasound (hypersound) perturbation. The binding events between the protein CDK2 and its small-molecule inhibitors were nearly undetectable in 100-ns standard MD simulations, but the method successfully accelerated their slow binding rates by up to 10-20 times. Hypersound-accelerated MD simulations revealed a variety of microscopic kinetic features of the inhibitors on the protein surface, such as the existence of different binding pathways to the active site. Moreover, the simulations allowed the estimation of the corresponding kinetic parameters and exploring other druggable pockets. This method can thus provide deeper insight into the microscopic interactions controlling biomolecular processes.

A Bayesian inference approach to determining structural ensembles using cryo-EM and molecular dynamics.

Advances in cryo-EM have led to an enormous increase in the number of high-resolution structures solved and deposited within the Protein Data Bank. However, the way protein models are represented has not kept pace as static single structure models continue to be widely accepted as accurate depictions of proteins despite their underlying conformational heterogeneity and dynamics. While advances in image processing allows for the construction of multiple distinct conformational states directly from raw 2D images, functionally important highly dynamic regions of proteins, including highly-dynamic side chains, are often averaged out resulting in low resolution and an inability to accurately determine local structures. Here we present ‘EMMIVox’, a Bayesian inference approach to determining structural ensembles of biological entities by combining cryo-EM data with molecular dynamics (MD) simulations. EMMIVox, which is able to automatically detect and downweigh noisy experimental data, calculates accurate structural ensembles of proteins and protein complexes including any lipids, small-molecules and ordered water present in experimental maps. Using EMMIVox, we generated single structure models for a variety of high-resolution cryo-EM maps (1.9 Å - 3.5 Å), including membrane proteins and ligand-protein complexes. EMMIVox models outperformed deposited structures in terms of stereochemical descriptors (MolProbity and Clashcore) as well as metrics that quantify how well the model fits the density map (map-model cross correlation and EMRinger). Finally, we determined the structural ensembles of the type 1a tau filament (1.9 Å) and the SPP1 bacteriophage (4 Å) in detail, demonstrating the accuracy of our structural ensemble compared to standard MD simulations. Inference of structural ensembles and their representative populations will have wide ranging applications in structural biology and drug discovery. EMMIVox is available in the Integrative Structural and Dynamical Biology module of the open-source, freely-available PLUMED library (www.plumed.org).

Allosteric Boost by TAB1 on the TAK1 Kinase Favorably Sculpts the Thermodynamic Landscape of Activation.

The intricate mechanisms of allosteric regulation in kinases are of general interest to the scientific community for potential therapeutic implications. However, the diversity among kinases and their regulatory routes requires a case-by-case study to widen the repertoire of known mechanisms. The present study achieves this by understanding TAK1 kinase activation by TAB1 as a model phenomenon for the first time. Despite the known capacity of TAK1 to switch between its inactive ("DFG-out") and active-like ("DFG-in") conformations, the questionable role of TAB1 in offering an energetic favor to this has been addressed here using sequential combination of enhanced sampling methods like targeted molecular dynamics (TMD) and Gaussian accelerated molecular dynamics (GaMD). It reveals how a minimal domain of TAB1 sufficiently acts like a "catalytic gear" by favorably sculpting TAK1's thermodynamic landscape (potential of mean force in 2D) that accelerates "in"-"out" conformational switching of the conserved DFG motif. Standard molecular dynamics simulations (∼5 μs) reveal that TAB1 fascinatingly exploits the "lever-like" αF helix of TAK1 kinase domain to remotely propel the DFG motif via subtle helical "unfolding-folding" modifications within the kinase activation loop. The presence of two charged residues on terminal poles of αF helix imparts it, with this unique "lever-like" utility, and this turns out to be one important signature of co-evolution between TAK1 and TAB1. The entire mechanism of TAB1's impact transduction, which is found to be analogous to the moves in the popular "Chinese checker" game, gives a clear proof of the "dynamics-driven allostery" concept in kinases. The findings further benchmark TAK1's known autophosphorylation capacity. A novel insight into kinase allostery is thus provided, which potentiates investigation of similar capacities in other kinases.

Molecular-based analysis of nanoparticle solvation: Classical density functional approach

Proper statistical mechanics understanding of nanoparticle solvation processes requires an accurate description of the molecular structure of the solvent. Achieving this goal with standard molecular dynamics (MD) simulation methods is challenging due to large length scales. An alternative approach to this problem can be formulated using classical density functional theory (cDFT), where a full configurational description of the positions of all the atoms is replaced by collective atomic site densities in the molecule. Using an example of the negatively charged silica-like system in an aqueous polar environment represented by a two-site water model, we demonstrate that cDFT can reproduce MD data at a fraction of the computational cost. An important implication of this result is the ability to understand how the solvent molecular features may affect the system's properties at the macroscopic scale. A concrete example highlighted in this work is the analysis of nanoparticle interactions with sizes of up to 100nm in diameter.

Charged Small Molecule Binding to Membranes in MD Simulations Evaluated against NMR Experiments.

Interactions of charged molecules with biomembranes regulate many of their biological activities, but their binding affinities to lipid bilayers are difficult to measure experimentally and model theoretically. Classical molecular dynamics (MD) simulations have the potential to capture the complex interactions determining how charged biomolecules interact with membranes, but systematic overbinding of sodium and calcium cations in standard MD simulations raises the question of how accurately force fields capture the interactions between lipid membranes and charged biomolecules. Here, we evaluate the binding of positively charged small molecules, etidocaine, and tetraphenylphosphonium to a phosphatidylcholine (POPC) lipid bilayer using the changes in lipid head-group order parameters. We observed that these molecules behave oppositely to calcium and sodium ions when binding to membranes: (i) their binding affinities are not overestimated by standard force field parameters, (ii) implicit inclusion of electronic polarizability increases their binding affinity, and (iii) they penetrate into the hydrophobic membrane core. Our results can be explained by distinct binding mechanisms of charged small molecules with hydrophobic moieties and monoatomic ions. The binding of the former is driven by hydrophobic effects, while the latter has direct electrostatic interactions with lipids. In addition to elucidating how different kinds of charged biomolecules bind to membranes, we deliver tools for further development of MD simulation parameters and methodology.

Using Metadynamics To Explore the Free Energy of Dewetting in Biologically Relevant Nanopores.

Water confined within hydrophobic spaces can undergo cooperative dewetting transitions due to slight changes in water density and pressure that push water toward the vapor phase. Many transmembrane protein ion channels contain nanoscale hydrophobic pores that could undergo dewetting transitions, sometimes blocking the flow of ions without physical blockages. Standard molecular dynamics simulations have been extensively applied to study the behavior of water in nanoscale pores, but the large free energy barriers of dewetting often prevent direct sampling of both wet and dry states and quantitative studies of the hydration thermodynamics of biologically relevant pores. Here, we describe a metadynamics protocol that uses the number of waters within the pore as the collective variable to drive many reversible transitions between relevant hydration states and calculate well-converged free energy profiles of pore hydration. By creating model nanopore systems and changing their radius and morphology and including various cosolvents, we quantify how these pore properties and cosolvents affect the dewetting transition. The results reveal that the dewetting free energy of nanoscale pores is determined by two key thermodynamic parameters, namely, the effective surface tension coefficients of water-air and water-pore interfaces. Importantly, while the effect of salt can be fully captured in the water activity dependence, amphipathic cosolvents such as alcohols modify both dry and wet states of the pore and dramatically shift the wet-dry equilibrium. The metadynamics approach could be applied to studies of dewetting transitions within nanoscale pores of proteins and provide new insights into why different pore properties evolved in biological systems.

Slip-Spring Hybrid Particle-Field Molecular Dynamics for Coarse-Graining Branched Polymer Melts: Polystyrene Melts as an Example.

The topology of chains significantly modifies the dynamical properties of polymer melts. Here, we extend a recently developed efficient simulation method, namely the slip-spring hybrid particle-field (SS-hPF) model, to study the structural and dynamical properties of branched polymer melts over large spatial-temporal scales. In the coarse-grained SS-hPF simulation of polymers, the bonded potentials are derived by iterative Boltzmann inversion from the underlying fine-grained model. The nonbonded potentials are computed from a density functional field instead of pairwise interactions used in standard molecular dynamics simulations, which increases the computational efficiency by a factor of 10-20. The entangled dynamics is lost due to the soft-core nature of density functional field interactions. It is recovered by a multichain slip-spring model that is rigorously parametrized from existing experimental or simulation data. To quantitatively predict the relaxation and diffusion of branched polymers, which are dominated by arm retraction rather than chain reptation, the slip-spring algorithm is augmented to improve the polymer dynamics near the branch point. Multiple dynamical observables, e.g., diffusion coefficients, arm relaxations, and tube survival probabilities, are characterized in an example coarse-grained model of symmetric and asymmetric star-shaped polystyrene melts. Consistent dynamical behaviors are identified and compared with theoretical predictions. With a single rescaling factor, the prediction of diffusion coefficients agrees well with the available experimental measurements. In this work, an efficient approach is provided to build chemistry-specific coarse-grained models for predicting the dynamics of branched polymers.

Recognition and Binding of RsmE to an AGGAC Motif of RsmZ: Insights from Molecular Dynamics Simulations.

CsrA/RsmE is a post-transcriptional regulator protein widely distributed in bacteria. It impedes the expression of target mRNAs by attaching their 5' untranslated region. The translation is restored by small, noncoding RNAs that sequester CsrA/RsmE acting as sponges. In both cases, the protein recognizes and attaches to specific AGGAX and AXGGAX motifs, where X refers to any nucleotide. RsmZ of Pseudomonas protegens is one of these small RNAs. The structures of some of its complexes with RsmE were disclosed a few years ago. We have used umbrella sampling simulations to force the unbinding of RsmE from the AGGAC motif located in the single-stranded region sited between stem loops 2 and 3 of RsmZ. The calculations unveiled the identity of the main residues and nucleotides involved in the process. They also showed that the region adopts a hairpin-like conformation during the initial stages of the binding. The ability to acquire this conformation requires that the region has a length of at least nine nucleotides. Besides, we performed standard molecular dynamics simulations of the isolated fragments, analyzed their typical conformations, and characterized their movements. This analysis revealed that the free molecules oscillate along specific collective coordinates that facilitate the initial stages of the binding. The results strongly suggest that the flexibility of the single-stranded region of RsmZ crucially affects the ability of its binding motif to catch RsmE.

Gmxapi: A GROMACS-native Python interface for molecular dynamics with ensemble and plugin support.

Gmxapi provides an integrated, native Python API for both standard and advanced molecular dynamics simulations in GROMACS. The Python interface permits multiple levels of integration with the core GROMACS libraries, and legacy support is provided via an interface that mimics the command-line syntax, so that all GROMACS commands are fully available. Gmxapi has been officially supported since the GROMACS 2019 release and is enabled by default in current versions of the software. Here we describe gmxapi 0.3 and later. Beyond simply wrapping GROMACS library operations, the API permits several advanced operations that are not feasible using the prior command-line interface. First, the API allows custom user plugin code within the molecular dynamics force calculations, so users can execute custom algorithms without modifying the GROMACS source. Second, the Python interface allows tasks to be dynamically defined, so high-level algorithms for molecular dynamics simulation and analysis can be coordinated with loop and conditional operations. Gmxapi makes GROMACS more accessible to custom Python scripting while also providing support for high-level data-flow simulation algorithms that were previously feasible only in external packages.

Exploring the conformational space of a receptor for drug design: An ERα case study

Protein flexibility is challenging for both experimentalists and modellers, especially in the field of drug design. Estrogen Receptor alpha (ERα) is an extensively studied Nuclear Receptor (NR) and a well-known therapeutic target with an important role in development and physiology. It is also a frequent off-target in standard toxicity tests for endocrine disruption. Here, we aim to evaluate the degree to which the conformational space and macromolecular flexibility of this well-characterized drug target can be described. Our approach exploits hundreds of crystallographic structures by means of molecular dynamics simulations and of virtual screening. The analysis of hundreds of crystal structures confirms the presence of two main conformational states, known as ’agonist’ and ’antagonist’, that mainly differ by the orientation of the C-terminal helix H12 which serves to close the binding pocket. ERα also shows some loop flexibility, as well as variable side-chain orientations in its active site. We scrutinized the extent to which standard molecular dynamics simulations or crystallographic refinement as ensemble recapitulate most of the variability features seen by the array of available crystal structures. In parallel, we investigated on the kind and extent of flexibility that are required to achieve convincing docking for all high-affinity ERα ligands present in BindingDB. Using either only one conformation with a few side-chains set flexible, or static structure ensembles in parallel during docking led to good quality and similar pose predictions. These results suggest that the several hundreds of crystal structures already known can properly describe the whole conformational universe of ERα′s ligand binding domain. This opens the road for better drug design and affinity computation.

(Invited) Computational Simulations of Selective Interactions between ssDNA and SWCNTs

Structure-specific interactions between single-stranded DNA oligos and SWCNTs form the basis of important selective sorting methods yet remain poorly understood. Among these interactions is the differential affinity of (ATT)4 for one of the two (7,5) enantiomers. To understand the nature of the affinity difference, we have performed molecular dynamics (MD) simulations followed by free energy (replica exchange) calculations over the temperature range of 290 to 727 K. Comparisons between the conformational free energy landscapes of (ATT)4 structure on right-handed and left-handed (7,5) SWCNTs (respectively known as M and P in stereochemical convention) suggest that (ATT)4 has more contact area with M than with the P enantiomer. However, the corresponding end-to-end distances of (ATT)4 fall nearly in the same region on the landscape. Our standard MD simulations for (ATTT)3 interactions with SWCNTs also suggest that this DNA sequence covers (8,4) SWCNT more effectively than (7,6) and (8,3) SWCNTs, which is consistent with our recent dye-quenching experiments.Other experiments have revealed that when guanines in ssDNA oligos are covalently functionalized to SWCNT sidewalls, the extent of functionalization can depend on the position of the guanine within the oligo. Central positions within long oligos (e.g. T15GT15) lead to greater functionalization than end guanine positions (e.g. T30G). We have performed both standard MD and free energy calculations to investigate the source of this effect. For efficient guanine functionalization of SWCNTs, guanine needs to remain adsorbed on the SWCNT surface. Our computational observations suggest that the central guanine within T15GT15 oligo remains adsorbed on the (6,5) SWCNT surface even when the DNA interacts with other neighboring DNA strands. Under these conditions, the end guanine in T30G is destabilized and tends to desorb from (6,5) SWCNT surface due to inter-strand interactions. Our free energy calculations also suggest that oligos with a central guanine assume more elongated DNA conformations at the surface of a (6,5) SWCNT than do oligos with end guanines. We suggest that DNA elongation is associated with more stable adsorption on the SWCNT surface, supporting efficient covalent functionalization of central guanines. Figure 1

Energy-dependent protein folding: modeling how a protein folding machine may work

Background: Proteins fold robustly and reproducibly in vivo, but many cannot fold in vitro in isolation from cellular components. Despite the remarkable progress that has been achieved by the artificial intelligence approaches in predicting the protein native conformations, the pathways that lead to such conformations, either in vitro or in vivo, remain largely unknown. The slow progress in recapitulating protein folding pathways in silico may be an indication of the fundamental deficiencies in our understanding of folding as it occurs in nature. Here we consider the possibility that protein folding in living cells may not be driven solely by the decrease in Gibbs free energy and propose that protein folding in vivo should be modeled as an active energy-dependent process. The mechanism of action of such a protein folding machine might include direct manipulation of the peptide backbone. Methods: To show the feasibility of a protein folding machine, we conducted molecular dynamics simulations that were augmented by the application of mechanical force to rotate the C-terminal amino acid while simultaneously limiting the N-terminal amino acid movements. Results: Remarkably, the addition of this simple manipulation of peptide backbones to the standard molecular dynamics simulation indeed facilitated the formation of native structures in five diverse alpha-helical peptides. Steric clashes that arise in the peptides due to the forced directional rotation resulted in the behavior of the peptide backbone no longer resembling a freely jointed chain. Conclusions: These simulations show the feasibility of a protein folding machine operating under the conditions when the movements of the polypeptide backbone are restricted by applying external forces and constraints. Further investigation is needed to see whether such an effect may play a role during co-translational protein folding in vivo and how it can be utilized to facilitate folding of proteins in artificial environments.