The Trp-cage: optimizing the stability of a globular miniprotein

NPEX: Never give up protein exploration with deep reinforcement learning

Elucidating unknown structures of proteins, such as metastable states, is critical in designing therapeutic agents. Protein structure exploration has been performed using advanced computational methods, especially molecular dynamics and Markov chain Monte Carlo simulations, which require untenably long calculation times and prior structural knowledge. Here, we developed an innovative method for protein structure determination called never give up protein exploration (NPEX) with deep reinforcement learning. The NPEX method leverages the soft actor-critic algorithm and the intrinsic reward system, effectively adding a bias potential without the need for prior knowledge. To demonstrate the method's effectiveness, we applied it to four models: a double well, a triple well, the alanine dipeptide, and the tryptophan cage. Compared with Markov chain Monte Carlo simulations, NPEX had markedly greater sampling efficiency. The significantly enhanced computational efficiency and lack of prior domain knowledge requirements of the NPEX method will revolutionize protein structure exploration.

Quantifying Disorder in a Protein by Mapping its Locally Correlated Structure and Kinetics

Proteins under physiological conditions are inherently mobile and sample a vast array of structures. Consequently, the need arises, on the one hand, at a local level to determine the independent moving parts and their associated conformations and kinetics, and on the other hand, at a global level, to quantify the disorder in the full protein molecule. We present an approach that provides these quantities in the form of local kinetic network models, which are constructed by analyzing the molecular dynamics (MD) trajectories of the protein molecule. Entropies of independent parts of the molecule are quantified. The method outlined here, using the Trp-cage miniprotein prototype, offers a new tool to understand the dynamic structural changes that ultimately govern the functioning of a protein. The method is particularly suited to problems where there are subtle changes in the structure or dynamics at local levels, for example, due to ligand binding.

Acceleration of Molecular Simulations by Parametric Time-Lagged tSNE Metadynamics

The potential of molecular simulations is limited by their computational costs. There is often a need to accelerate simulations using some of the enhanced sampling methods. Metadynamics applies a history-dependent bias potential that disfavors previously visited states. To apply metadynamics, it is necessary to select a few properties of the system─collective variables (CVs) that can be used to define the bias potential. Over the past few years, there have been emerging opportunities for machine learning and, in particular, artificial neural networks within this domain. In this broad context, a specific unsupervised machine learning method was utilized, namely, parametric time-lagged t-distributed stochastic neighbor embedding (ptltSNE) to design CVs. The approach was tested on a Trp-cage trajectory (tryptophan cage) from the literature. The trajectory was used to generate a map of conformations, distinguish fast conformational changes from slow ones, and design CVs. Then, metadynamic simulations were performed. To accelerate the formation of the α-helix, we added the α-RMSD collective variable. This simulation led to one folding event in a 350 ns metadynamics simulation. To accelerate degrees of freedom not addressed by CVs, we performed parallel tempering metadynamics. This simulation led to 10 folding events in a 200 ns simulation with 32 replicas.

Enhanced Coarse-Grained Molecular Dynamics Simulation with a Smoothed Hybrid Potential Using a Neural Network Model

In all-atom (AA) molecular dynamics (MD) simulations, the rugged energy profile of the force field makes it challenging to reproduce spontaneous structural changes in biomolecules within a reasonable calculation time. Existing coarse-grained (CG) models, in which the energy profile is set to a global minimum around the initial structure, are unsuitable to explore the structural dynamics between metastable states far away from the initial structure without any bias. In this study, we developed a new hybrid potential composed of an artificial intelligence (AI) potential and minimal CG potential related to the statistical bond length and excluded volume interactions to accelerate the transition dynamics while maintaining the protein character. The AI potential is trained by energy matching using a diverse structural ensemble sampled via multicanonical (Mc) MD simulation and the corresponding AA force field energy, profile of which is smoothed by energy minimization. By applying the new methodology to chignolin and TrpCage, we showed that the AI potential can predict the AA energy with significantly high accuracy, as indicated by a correlation coefficient (R-value) between the true and predicted energies exceeding 0.89. In addition, we successfully demonstrated that CGMD simulation based on the smoothed hybrid potential can significantly enhance the transition dynamics between various metastable states while preserving protein properties compared to those obtained with conventional CGMD and AAMD.

Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein

Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method. The mechanism by which the Trp-cage is stabilized during the folding process was examined by calculating the total energy, which is the sum of the conformational energy and SFE. The folding process of the Trp-cage resulted in a stable native state, with a total energy that was 62.4 kcal/mol lower than that of the unfolded state. The solvation entropy, which is considered to be responsible for the hydrophobic effect, contributed 31.3 kcal/mol to structural stabilization. In other words, the contribution of the solvation entropy accounted for approximately half of the total contribution to Trp-cage folding. The hydrophobic core centered on Trp6 contributed 15.6 kcal/mol to the total energy, whereas the solvation entropy contribution was 6.3 kcal/mol. The salt bridge formed by the hydrophilic side chains of Asp9 and Arg16 contributed 10.9 and 5.0 kcal/mol, respectively. This indicates that not only the hydrophobic core but also the salt bridge of the hydrophilic side chains gain solvation entropy and contribute to stabilizing the native structure of the Trp-cage.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Improving Estimation of the Koopman Operator with Kolmogorov-Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. We apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

Neural potentials of proteins extrapolate beyond training data

We evaluate neural network (NN) coarse-grained (CG) force fields compared to traditional CG molecular mechanics force fields. We conclude that NN force fields are able to extrapolate and sample from unseen regions of the free energy surface when trained with limited data. Our results come from 88 NN force fields trained on different combinations of clustered free energy surfaces from four protein mapped trajectories. We used a statistical measure named total variation similarity to assess the agreement between reference free energy surfaces from mapped atomistic simulations and CG simulations from trained NN force fields. Our conclusions support the hypothesis that NN CG force fields trained with samples from one region of the proteins' free energy surface can, indeed, extrapolate to unseen regions. Additionally, the force matching error was found to only be weakly correlated with a force field's ability to reconstruct the correct free energy surface.

Polymorphic amyloid nanostructures of hormone peptides involved in glucose homeostasis display reversible amyloid formation

A large group of hormones are stored as amyloid fibrils in acidic secretion vesicles before they are released into the bloodstream and readopt their functional state. Here, we identify an evolutionarily conserved hexapeptide sequence as the major aggregation-prone region (APR) of gastrointestinal peptides of the glucagon family: xFxxWL. We determine nine polymorphic crystal structures of the APR segments of glucagon-like peptides 1 and 2, and exendin and its derivatives. We follow amyloid formation by CD, FTIR, ThT assays, and AFM. We propose that the pH-dependent changes of the protonation states of glutamate/aspartate residues of APRs initiate switching between the amyloid and the folded, monomeric forms of the hormones. We find that pH sensitivity diminishes in the absence of acidic gatekeepers and amyloid formation progresses over a broad pH range. Our results highlight the dual role of short aggregation core motifs in reversible amyloid formation and receptor binding.

Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.

Folding-unfolding asymmetry and a RetroFold computational algorithm

We treat protein folding as molecular self-assembly, while unfolding is viewed as disassembly. Fracture is typically a much faster process than self-assembly. Self-assembly is often an exponentially decaying process, since energy relaxes due to dissipation, while fracture is a constant-rate process as the driving force is opposed by damping. Protein folding takes two orders of magnitude longer than unfolding. We suggest a mathematical transformation of variables, which makes it possible to view self-assembly as time-reversed disassembly, thus folding can be studied as reversed unfolding. We investigate the molecular dynamics modelling of folding and unfolding of the short Trp-cage protein. Folding time constitutes about 800 ns, while unfolding (denaturation) takes only about 5.0 ns and, therefore, fewer computational resources are needed for its simulation. This RetroFold approach can be used for the design of a novel computation algorithm, which, while approximate, is less time-consuming than traditional folding algorithms.

Visualizing the Residue Interaction Landscape of Proteins by Temporal Network Embedding

Characterizing the structural dynamics of proteins with heterogeneous conformational landscapes is crucial to understanding complex biomolecular processes. To this end, dimensionality reduction algorithms are used to produce low-dimensional embeddings of the high-dimensional conformational phase space. However, identifying a compact and informative set of input features for the embedding remains an ongoing challenge. Here, we propose to harness the power of Residue Interaction Networks (RINs) and their centrality measures, established tools to provide a graph theoretical view on molecular structure. Specifically, we combine the closeness centrality, which captures global features of the protein conformation at residue-wise resolution, with EncoderMap, a hybrid neural-network autoencoder/multidimensional-scaling like dimensionality reduction algorithm. We find that the resulting low-dimensional embedding is a meaningful visualization of the residue interaction landscape that resolves structural details of the protein behavior while retaining global interpretability. This feature-based graph embedding of temporal protein graphs makes it possible to apply the general descriptive power of RIN formalisms to the analysis of protein simulations of complex processes such as protein folding and multidomain interactions requiring no protein-specific input. We demonstrate this on simulations of the fast folding protein Trp-Cage and the multidomain signaling protein FAT10. Due to its generality and modularity, the presented approach can easily be transferred to other protein systems.

Rehydration Post-orientation: Investigating Field-Induced Structural Changes via Computational Rehydration

Proteins can be oriented in the gas phase using strong electric fields, which brings advantages for structure determination using X-ray free electron lasers. Both the vacuum conditions and the electric-field exposure risk damaging the protein structures. Here, we employ molecular dynamics simulations to rehydrate and relax vacuum and electric-field exposed proteins in aqueous solution, which simulates a refinement of structure models derived from oriented gas-phase proteins. We find that the impact of the strong electric fields on the protein structures is of minor importance after rehydration, compared to that of vacuum exposure and ionization in electrospraying. The structures did not fully relax back to their native structure in solution on the simulated timescales of 200 ns, but they recover several features, including native-like intra-protein contacts, which suggests that the structures remain in a state from which the fully native structure is accessible. Our findings imply that the electric fields used in native mass spectrometry are well below a destructive level, and suggest that structures inferred from X-ray diffraction from gas-phase proteins are relevant for solution and in vivo conditions, at least after in silico rehydration.

Exploring the Transferability of Replica Exchange Structure Reservoirs to Accelerate Generation of Ensembles for Alternate Hamiltonians or Protein Mutations

Generating precise ensembles is commonly a prerequisite to understand the energetics of biological processes using Molecular Dynamics (MD) simulations. Previously, we have shown how unweighted reservoirs built from high temperature MD simulations can accelerate convergence of Boltzmann-weighted ensembles by at least 10× with the Reservoir Replica Exchange MD (RREMD) method. Therefore, in this work, we explore whether an unweighted structure reservoir generated with one Hamiltonian (solute force field plus solvent model) can be reused to quickly generate accurately weighted ensembles for Hamiltonians other than the one that was used to generate the reservoir. We also extended this methodology to rapidly estimate the effects of mutations on peptide stability by using a reservoir of diverse structures obtained from wild-type simulations. These results suggest that structures generated via fast methods such as coarse-grained models or structures predicted by Rosetta or deep learning approaches could be integrated into a reservoir to accelerate generation of ensembles using more accurate representations.

Analysis of Protein Folding Simulation with Moving Root Mean Square Deviation

We apply moving root-mean-square deviation (mRMSD), which does not require a reference structure, as a method for analyzing protein dynamics. This method can be used to calculate the root-mean-square deviation (RMSD) of structure between two specified time points and to analyze protein dynamics behavior through time series analysis. We applied this method to the Trp-cage trajectory calculated by the Anton supercomputer and found that it shows regions of stable states as well as the conventional RMSD. In addition, we extracted a characteristic structure in which the side chains of Asp1 and Arg16 form hydrogen bonds near the most stable structure of the Trp-cage. We also determined that ≥20 ns is an appropriate time interval to investigate protein dynamics using mRMSD. Applying this method to NuG2 protein, we found that mRMSD can be used to detect regions of metastable states in addition to the stable state. This method can be applied to molecular dynamics simulations of proteins whose stable structures are unknown.

The Role of Transient Intermediate Structures in the Unfolding of the Trp-Cage Fast-Folding Protein: Generating Ensembles from Time-Resolved X-ray Solution Scattering with Genetic Algorithms

The Trp-cage miniprotein is one of the smallest systems to exhibit a stable secondary structure and fast-folding dynamics, serving as an apt model system to study transient intermediates with both experimental and computational analyses. Previous spectroscopic characterizations that have been done on Trp-cage have inferred a single stable intermediate on a pathway from folded to unfolded basins. We aim to bridge the understanding of Trp-cage structural folding dynamics on microsecond-time scales, by utilizing time-resolved X-ray solution scattering to probe the temperature-induced unfolding pathway. Our results indicate the formation of a conformationally extended intermediate on the time scale of 1 μs, which undergoes complete unfolding within 5 μs. We further investigated the atomistic structural details of the unfolding pathway using a genetic algorithm to generate ensemble model fits to the scattering profiles. This analysis paves the way for direct benchmarking of theoretical models of protein folding ensembles produced with molecular dynamics simulations.

Non-Aromatic Fluorescence in Biological Matter: The Exception or the Rule?

While in the vast majority of cases fluorescence in biological matter has been attributed to aromatic or conjugated groups, peptides associated with neurodegenerative diseases, such as Alzheimer's, Parkinson's, or Huntington's, have been recently shown to display an intrinsic visible fluorescence even in the absence of aromatic residues. This has called the attention of researchers from many different fields, trying to understand the origin of this peculiar behavior and, at the same time, motivating the search for novel strategies to control the optical properties of new biophotonic materials. Today, after nearly 15 years of its discovery, there is a growing consensus about the mechanism underlying this phenomenon, namely, that electronic interactions between non-optically active molecules can result in supramolecular assemblies that are fluorescent. Despite this progress, many aspects of this phenomenon remain uncharted territory. In this Perspective, we lay down the state-of-the-art in the field highlighting the open questions from both experimental and theoretical fronts in this fascinating emerging area of non-aromatic fluorescence.

Miniproteins in medicinal chemistry

Miniproteins exhibit great potential as scaffolds for drug candidates because of their well-defined structure and good synthetic availability. Because of recently described methodologies for their de novo design, the field of miniproteins is emerging and can provide molecules that effectively bind to problematic targets, i.e., those that have been previously considered to be undruggable. This review describes methodologies for the development of miniprotein scaffolds and for the construction of biologically active miniproteins.

Accurate Description of Solvent-Exposed Salt Bridges with a Non-polarizable Force Field Incorporating Solvent Effects

The strength of salt bridges resulting from the interaction of cations and anions is modulated by their environment. However, polarization of the solvent molecules by the charged moieties makes the accurate description of cation-anion interactions in an aqueous solution by means of a pairwise additive potential energy function and classical combination rules particularly challenging. In this contribution, aiming at improving the representation of solvent-exposed salt-bridge interactions with an all-atom non-polarizable force field, we put forth here a parametrization strategy. First, the interaction of a cation and an anion is characterized by hybrid quantum mechanical/molecular mechanics (QM/MM) potential of mean force (PMF) calculations, whereby constantly exchanging solvent molecules around the ions are treated at the quantum mechanical level. The Lennard-Jones (LJ) parameters describing the salt-bridge ion pairs are then optimized to match the reference QM/MM PMFs through the so-called nonbonded FIX, or NBFIX, feature of the CHARMM force field. We apply the new set of parameters, coined CHARMM36m-SBFIX, to the calculation of association constants for the ammonium-acetate and guanidinium-acetate complexes, the osmotic pressures for glycine zwitterions, guanidinium, and acetate ions, and to the simulation of both folded and intrinsically disordered proteins. Our findings indicate that CHARMM36m-SBFIX improves the description of solvent-exposed salt-bridge interactions, both structurally and thermodynamically. However, application of this force field to the standard binding free-energy calculation of a protein-ligand complex featuring solvent-excluded salt-bridge interactions leads to a poor reproduction of the experimental value, suggesting that the parameters optimized in an aqueous solution cannot be readily transferred to describe solvent-excluded salt-bridge interactions. Put together, owing to their sensitivity to the environment, modeling salt-bridge interactions by means of a single, universal set of LJ parameters remains a daunting theoretical challenge.

Topological bio-scaling analysis as a universal measure of protein folding

Scaling relationships for polymeric molecules establish power law dependencies between the number of molecular segments and linear dimensions, such as the radius of gyration. They also establish spatial topological properties of the chains, such as their dimensionality. In the spatial domain, power exponents α = 1 (linear stretched molecule), α = 0.5 (the ideal chain) and α = 0.333 (compact globule) are significant. During folding, the molecule undergoes the transition from the one-dimensional linear to the three-dimensional globular state within a very short time. However, intermediate states with fractional dimensions can be stabilized by modifying the solubility (e.g. by changing the solution temperature). Topological properties, such as dimension, correlate with the interaction energy, and thus by tuning the solubility one can control molecular interaction. We investigate these correlations using the example of a well-studied short model of Trp-cage protein. The radius of gyration is used to estimate the fractal dimension of the chain at different stages of folding. It is expected that the same principle is applicable to much larger molecules and that topological (dimensional) characteristics can provide insights into molecular folding and interactions.

Physiological, Structural, and Functional Insights Into the Cryoprotection of Membranes by the Dehydrins

Plants can be exposed to cold temperatures and have therefore evolved several mechanisms to prevent damage caused by freezing. One of the most important targets are membranes, which are particularly susceptible to cold damage. To protect against such abiotic stresses, plants express a family of proteins known as late embryogenesis abundant (LEA) proteins. Many LEA proteins are intrinsically disordered, that is, they do not contain stable secondary or tertiary structures alone in solution. These proteins have been shown in a number of studies to protect plants from damage caused by cold, drought, salinity, and osmotic stress. In this family, the most studied proteins are the type II LEA proteins, better known as dehydrins (dehydration-induced proteins). Many physiological studies have shown that dehydrins are often located near the membrane during abiotic stress and that the expression of dehydrins helps to prevent the formation of oxidation-modified lipids and reduce the amount of electrolyte leakage, two hallmarks of damaged membranes. One of the earliest biophysical clues that dehydrins are involved in membrane cryoprotection came from in vitro studies that demonstrated a binding interaction between the protein and membranes. Subsequent work has shown that one conserved motif, known as K-segments, is involved in binding, while recent studies have used NMR to explore the residue specific structure of dehydrins when bound to membranes. The biophysical techniques also provide insight into the mechanism by which dehydrins protect the membrane from cold stress, which appears to mainly involve the lowering of the transition temperature.

Computational Modeling of the Thermodynamics of the Mesophilic and Thermophilic Mutants of Trp-Cage Miniprotein

We characterize the folding-unfolding thermodynamics of two mutants of the miniprotein Trp-cage by combining extended molecular dynamics simulations and an advanced statistical-mechanical-based approach. From a set of molecular dynamics simulations in an explicit solvent performed along a reference isobar, we evaluated the structural and thermodynamic behaviors of a mesophilic and a thermophilic mutant of the Trp-cage and their temperature dependence. In the case of the thermophilic mutant, computational data confirm that our theoretical-computational approach is able to reproduce the available experimental estimate with rather good accuracy. On the other hand, the mesophilic mutant does not show a clear two-state (folded and unfolded) behavior, preventing us from reconstructing its thermodynamics; thus, an analysis of its structural behavior along a reference isobar is presented. Our results show that an extended sampling of these kinds of systems coupled to an advanced statistical-mechanical-based treatment of the data can provide an accurate description of the folding-unfolding thermodynamics along a reference isobar, rationalizing the discrepancies between the simulated and experimental systems.

GraphVAMPNet, using graph neural networks and variational approach to Markov processes for dynamical modeling of biomolecules

Finding low dimensional representation of data from long-timescale trajectories of biomolecular processes such as protein-folding or ligand-receptor binding is of fundamental importance and kinetic models such as Markov modeling have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and linear dynamical model in an end-to-end manner. VAMPNet is based on variational approach to Markov processes (VAMP) and relies on neural networks to learn the coarse-grained dynamics. In this contribution, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint which is used in the VAMPNet to generate a coarse-grained representation. This type of molecular representation results in a higher resolution and more interpretable Markov model than the standard VAMPNet enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.

The Halophyte Dehydrin Sequence Landscape

Dehydrins (DHNs) belong to the LEA (late embryogenesis abundant) family group II, that comprise four conserved motifs (the Y-, S-, F-, and K-segments) and are known to play a multifunctional role in plant stress tolerance. Based on the presence and order of these segments, dehydrins are divided into six subclasses: YnSKn, FnSKn, YnKn, SKn, Kn, and KnS. DHNs are rarely studied in halophytes, and their contribution to the mechanisms developed by these plants to survive in extreme conditions remains unknown. In this work, we carried out multiple genomic analyses of the conservation of halophytic DHN sequences to discover new segments, and examine their architectures, while comparing them with their orthologs in glycophytic plants. We performed an in silico analysis on 86 DHN sequences from 10 halophytic genomes. The phylogenetic tree showed that there are different distributions of the architectures among the different species, and that FSKn is the only architecture present in every plant studied. It was found that K-, F-, Y-, and S-segments are highly conserved in halophytes and glycophytes with a few modifications, mainly involving charged amino acids. Finally, expression data collected for three halophytic species (Puccinillia tenuiflora, Eutrema salsugenium, and Hordeum marinum) revealed that many DHNs are upregulated by salt stress, and the intensity of this upregulation depends on the DHN architecture.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Residue Folding Degree-Relationship to Secondary Structure Categories and Use as Collective Variable

Recently, we have shown that the residue folding degree, a network-based measure of folded content in proteins, is able to capture backbone conformational transitions related to the formation of secondary structures in molecular dynamics (MD) simulations. In this work, we focus primarily on developing a collective variable (CV) for MD based on this residue-bound parameter to be able to trace the evolution of secondary structure in segments of the protein. We show that this CV can do just that and that the related energy profiles (potentials of mean force, PMF) and transition barriers are comparable to those found by others for particular events in the folding process of the model mini protein Trp-cage. Hence, we conclude that the relative segment folding degree (the newly proposed CV) is a computationally viable option to gain insight into the formation of secondary structures in protein dynamics. We also show that this CV can be directly used as a measure of the amount of α-helical content in a selected segment.

Variational embedding of protein folding simulations using Gaussian mixture variational autoencoders

Conformational sampling of biomolecules using molecular dynamics simulations often produces a large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here, we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE), that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscape of protein folding with highly separated clusters that correspond to the metastable states during folding. Since GMVAE uses a mixture of Gaussians as its prior, it can directly acknowledge the multi-basin nature of the protein folding free energy landscape. To make the model end-to-end differentiable, we use a Gumbel-softmax distribution. We test the model on three long-timescale protein folding trajectories and show that GMVAE embedding resembles the folding funnel with folded states down the funnel and unfolded states outside the funnel path. Additionally, we show that the latent space of GMVAE can be used for kinetic analysis and Markov state models built on this embedding produce folding and unfolding timescales that are in close agreement with other rigorous dynamical embeddings such as time independent component analysis.

Designed Trp-Cage Proteins with Antimicrobial Activity and Enhanced Stability

α-Helical antimicrobial peptides (αAMPs) are among the potential candidates for new anti-infectives to tackle the global crisis in antibiotic resistance, but they suffer from low bioavailability due to high susceptibility to enzymatic degradation. Here, we describe a strategy to increase the resistance of αAMPs against proteases. Fusing the 12-residue αAMP KR-12 with a Trp-cage domain induces an α-helical structure in the otherwise unfolded KR-12 moiety in solution. The resulting antimicrobial Trp-cage exhibits higher proteolytic resistance due to its stable fold as evidenced by correlating sequence-resolved digest data with structural analyses. In addition, the antimicrobial Trp-cage displays increased activity against bacteria in the presence of physiologically relevant concentrations of NaCl, while the hemolytic activity remains negligible. In contrast to previous strategies, the presented approach is not reliant on artificial amino acids and is therefore applicable to biosynthetic procedures. Our study aims to improve the pharmacokinetics of αAMPs to facilitate their use as therapeutics.

Advances in Application of Azobenzene as a Trigger in Biomedicine: Molecular Design and Spontaneous Assembly

Azobenzene is a well-known derivative of stimulus-responsive molecular switches and has shown superior performance as a functional material in biomedical applications. The results of multiple studies have led to the development of light/hypoxia-responsive azobenzene for biomedical use. In recent years, long-wavelength-responsive azobenzene has been developed. Matching the longer wavelength absorption and hypoxia-response characteristics of the azobenzene switch unit to the bio-optical window results in a large and effective stimulus response. In addition, azobenzene has been used as a hypoxia-sensitive connector via biological cleavage under appropriate stimulus conditions. This has resulted in on/off state switching of properties such as pharmacology and fluorescence activity. Herein, recent advances in the design and fabrication of azobenzene as a trigger in biomedicine are summarized.

The order of PDZ3 and TrpCage in fusion chimeras determines their properties-a biophysical characterization

Most of the structural proteins known today are composed of domains that carry their own functions while keeping their structural properties. It is supposed that such domains, when taken out of the context of the whole protein, can retain their original structure and function to a certain extent. Information on the specific functional and structural characteristics of individual domains in a new context of artificial fusion proteins may help to reveal the rules of internal and external domain communication. Moreover, this could also help explain the mechanism of such communication and address how the mutual allosteric effect plays a role in a such multi-domain protein system. The simple model system of the two-domain fusion protein investigated in this work consisted of a well-folded PDZ3 domain and an artificially designed small protein domain called Tryptophan Cage (TrpCage). Two fusion proteins with swapped domain order were designed to study their structural and functional features as well as their biophysical properties. The proteins composed of PDZ3 and TrpCage, both identical in amino acid sequence but different in composition (PDZ3-TrpCage, TrpCage-PDZ3), were studied using circualr dichroism (CD) spectrometry, analytical ultracentrifugation, and molecular dynamic simulations. The biophysical analysis uncovered different structural and denaturation properties of both studied proteins, revealing their different unfolding pathways and dynamics.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Applications of KBFF20

Here, we perform structural, thermodynamic, and kinetics tests of the Kirkwood-Buff-derived force field, KBFF20, for peptides and proteins developed in the previous article. The physical/structural tests measure the ability of KBFF20 to capture the experimental J-couplings for small peptides, to keep globular monomeric and oligomeric proteins folded, and to produce the experimentally relevant expanded conformational ensembles of intrinsically disordered proteins. The thermodynamic-based tests probe KBFF20's ability to quantify the preferential interactions of sodium chloride around native β-lactoglobulin and urea around native lysozyme, to reproduce the melting curves for small helix- and sheet-based peptides, and to fold the small proteins Trp-cage and Villin. The kinetics-based tests quantify how well KBFF20 can match the experimental contact formation rates of small, repeat-sequence peptides of variable lengths and the rotational diffusion coefficients of globular proteins. The results suggest that KBFF20 is naturally able to reproduce properties of both folded and disordered proteins, which we attribute to the use of the Kirkwood-Buff theory as the foundation of the force field's development. However, we show that KBFF20 tends to lose some well-defined secondary structural elements and increases the percentage of coil regions, indicating that the perfect balance of all interactions remains elusive. Nevertheless, we argue that KBFF20 is an improvement over recently modified force fields that require ad hoc interventions to prevent the collapse of intrinsically disordered proteins.

Adaptively Iterative Multiscale Switching Simulation Strategy and Applications to Protein Folding and Structure Prediction

Structure prediction is an important means to quickly understand new protein functions. However, the prediction of effects of proteins that have no detectable templates is still to be improved. Molecular dynamics simulation is supposed to be the primary research tool for structure predictions, but it still has limitations of huge computational cost in all-atom (AA) models and rough accuracy in coarse-grained (CG) models. We propose a universal multiscale simulation strategy named AIMS in which simulations can iteratively switch among multiple resolutions in order to adaptively trade off AA accuracy and CG high-efficiency. AIMS follows the idea of CG-guided enhanced sampling so that final results always keep AA accuracy. We successfully achieve four ab initio and four data-assisted protein structure predictions using AIMS. The prediction result is an ensemble rather than a structure and provides special insights on folding metastable states. AIMS is estimated to achieve a computational speed about 40 times faster than that of conventional AA simulations.

On the vibrational free energy of hydrated proteins

When the hydration shell of a protein is filled with at least 0.6 gram of water per gram of protein, a significant anti-correlation between the vibrational free energy and the potential energy of energy-minimized conformers is observed. This means that low potential energy, well-hydrated, protein conformers tend to be more rigid than high-energy ones. On the other hand, in the case of CASP target 624, when its hydration shell is filled, a significant energy gap is observed between the crystal structure and the best conformers proposed during the prediction experiment, strongly suggesting that including explicit water molecules may help identifying unlikely conformers among good-looking ones.

The Uniqueness of Tryptophan in Biology: Properties, Metabolism, Interactions and Localization in Proteins

Tryptophan (Trp) holds a unique place in biology for a multitude of reasons. It is the largest of all twenty amino acids in the translational toolbox. Its side chain is indole, which is aromatic with a binuclear ring structure, whereas those of Phe, Tyr, and His are single-ring aromatics. In part due to these elaborate structural features, the biosynthetic pathway of Trp is the most complex and the most energy-consuming among all amino acids. Essential in the animal diet, Trp is also the least abundant amino acid in the cell, and one of the rarest in the proteome. In most eukaryotes, Trp is the only amino acid besides Met, which is coded for by a single codon, namely UGG. Due to the large and hydrophobic π-electron surface area, its aromatic side chain interacts with multiple other side chains in the protein, befitting its strategic locations in the protein structure. Finally, several Trp derivatives, namely tryptophylquinone, oxitriptan, serotonin, melatonin, and tryptophol, have specialized functions. Overall, Trp is a scarce and precious amino acid in the cell, such that nature uses it parsimoniously, for multiple but selective functions. Here, the various aspects of the uniqueness of Trp are presented in molecular terms.

Sampling of the conformational landscape of small proteins with Monte Carlo methods

Computer simulation provides an increasingly realistic picture of large-scale conformational change of proteins, but investigations remain fundamentally constrained by the femtosecond timestep of molecular dynamics simulations. For this reason, many biologically interesting questions cannot be addressed using accessible state-of-the-art computational resources. Here, we report the development of an all-atom Monte Carlo approach that permits the modelling of the large-scale conformational change of proteins using standard off-the-shelf computational hardware and standard all-atom force fields. We demonstrate extensive thermodynamic characterization of the folding process of the α-helical Trp-cage, the Villin headpiece and the β-sheet WW-domain. We fully characterize the free energy landscape, transition states, energy barriers between different states, and the per-residue stability of individual amino acids over a wide temperature range. We demonstrate that a state-of-the-art intramolecular force field can be combined with an implicit solvent model to obtain a high quality of the folded structures and also discuss limitations that still remain.

Simple Model of Protein Energetics To Identify Ab Initio Folding Transitions from All-Atom MD Simulations of Proteins

A fundamental requirement to predict the native conformation, address questions of sequence design and optimization, and gain insights into the folding mechanisms of proteins lies in the definition of an unbiased reaction coordinate that reports on the folding state without the need to compare it to reference values, which might be unavailable for new (designed) sequences. Here, we introduce such a reaction coordinate, which does not depend on previous structural knowledge of the native state but relies solely on the energy partition within the protein: the spectral gap of the pair nonbonded energy matrix (ENergy Gap, ENG). This quantity can be simply calculated along unbiased MD trajectories. We show that upon folding the gap increases significantly, while its fluctuations are reduced to a minimum. This is consistently observed for a diverse set of systems and trajectories. Our approach allows one to promptly identify residues that belong to the folding core as well as residues involved in non-native contacts that need to be disrupted to guide polypeptides to the folded state. The energy gap and fluctuations criteria are then used to develop an automatic detection system which allows us to extract and analyze folding transitions from a generic MD trajectory. We speculate that our method can be used to detect conformational ensembles in dynamic and intrinsically disordered proteins, revealing potential preorganization for binding.

Visible-light-driven photocontrol of the Trp-cage protein fold by a diazocine cross-linker

Diazocines are characterized by extraordinary photochemical properties rendering them of particular interest for switching the conformation of biomolecules with visible light. Current developments afford synthetic access to unprecedented diazocine derivatives promising particular opportunities in photocontrol of proteins and biological systems. In this work, the well-established approach of photocontrolling the secondary structure of α-helices was exploited using a diazocine to reversibly fold and unfold the tertiary structure of a small protein. The protein of choice was the globulary folded Trp-cage, a widely used model system for the elucidation of protein folding pathways. A specifically designed, short and rigid dicarboxy-functionalized diazocine-based cross-linker was attached to two solvent-exposed side chains at the α-helix of the miniprotein through the use of a primary amine-selective active ester. This cross-linking strategy is orthogonal to the common cysteine-based chemistry. The cross-linked Trp-cage was successfully photoisomerized and exhibited a strong correlation between protein fold and diazocine isomeric state. As determined by NMR spectroscopy, the cis-isomer stabilized the fold, while the trans-isomer led to complete protein unfolding. The successful switching of the protein fold in principle demonstrates the ability to control protein function, as the activity depends on their structural integrity.

Development of a Force Field for the Simulation of Single-Chain Proteins and Protein-Protein Complexes

The accuracy of atomistic physics-based force fields for the simulation of biological macromolecules has typically been benchmarked experimentally using biophysical data from simple, often single-chain systems. In the case of proteins, the careful refinement of force field parameters associated with torsion-angle potentials and the use of improved water models have enabled a great deal of progress toward the highly accurate simulation of such monomeric systems in both folded and, more recently, disordered states. In living organisms, however, proteins constantly interact with other macromolecules, such as proteins and nucleic acids, and these interactions are often essential for proper biological function. Here, we show that state-of-the-art force fields tuned to provide an accurate description of both ordered and disordered proteins can be limited in their ability to accurately describe protein-protein complexes. This observation prompted us to perform an extensive reparameterization of one variant of the Amber protein force field. Our objective involved refitting not only the parameters associated with torsion-angle potentials but also the parameters used to model nonbonded interactions, the specification of which is expected to be central to the accurate description of multicomponent systems. The resulting force field, which we call DES-Amber, allows for more accurate simulations of protein-protein complexes, while still providing a state-of-the-art description of both ordered and disordered single-chain proteins. Despite the improvements, calculated protein-protein association free energies still appear to deviate substantially from experiment, a result suggesting that more fundamental changes to the force field, such as the explicit treatment of polarization effects, may simultaneously further improve the modeling of single-chain proteins and protein-protein complexes.

Unperturbed Detection of the Dynamic Structure in the Hydrophobic Core of Trp-Cage via Two-Dimensional Infrared Spectroscopy

The tyrosine ring mode is an intrinsic non-perturbing site-specific infrared reporter for conformational dynamics within protein systems. This transition is influenced by direct and indirect interactions associated with the electron-donating ability and the hydrophobicity of the surrounding molecules. Utilizing an intrinsic tyrosine moiety, two-dimensional infrared spectra of Trp-cage, often called the "hydrogen atom" of protein folding, were measured in the folded and denatured states to uncover the dynamics of the hydrophobic core. The vibrational lifetimes and the correlation decays of the tyrosine ring mode showed significant changes upon both temperature and chemical denaturation of the Trp-cage miniprotein, indicating important structural features of the hydrophobic core and its dynamics. The observed Trp6-Tyr3 interactions are in good agreement with the prior studies of the folded state, but they reach beyond the static structure. These stacking interactions and orientations fluctuate on the picosecond time scale as measured through the spectral dephasing within a dehydrated environment.

Compactness of Protein Folds Alters Disulfide-Bond Reducibility by Three Orders of Magnitude: A Comprehensive Kinetic Case Study on the Reduction of Differently Sized Tryptophan Cage Model Proteins

A new approach to monitor disulfide-bond reduction in the vicinity of aromatic cluster(s) has been derived by using the near-UV range (λ=266-293 nm) of electronic circular dichroism (ECD) spectra. By combining the results from NMR and ECD spectroscopy, the 3D fold characteristics and associated reduction rate constants (k) of E19_SS, which is a highly thermostable, disulfide-bond reinforced 39-amino acid long exenatide mimetic, and its N-terminally truncated derivatives have been determined under different experimental conditions. Single disulfide bond reduction of the E19_SS model (with an 18-fold excess of tris(2-carboxyethyl)phosphine, pH 7, 37 °C) takes hours, which is 20-30 times longer than that expected, and thus, would not reach completion by applying commonly used reduction protocols. It is found that structural, steric, and electrostatic factors influence the reduction rate, resulting in orders of magnitude differences in reduction half-lives (900>t_1/2 >1 min) even for structurally similar, well-folded derivatives of a small model protein.

Approximating dynamic proximity with a hybrid geometry energy-based kernel for diffusion maps

The diffusion map is a dimensionality reduction method. The reduction coordinates are associated with the leading eigenfunctions of the backward Fokker-Planck operator, providing a dynamic meaning for these coordinates. One of the key factors that affect the accuracy of diffusion map embedding is the dynamic measure implemented in the Gaussian kernel. A common practice in diffusion map study of molecular systems is to approximate dynamic proximity with RMSD (root-mean-square deviation). In this paper, we present a hybrid geometry-energy based kernel. Since high energy-barriers may exist between geometrically similar conformations, taking both RMSD and energy difference into account in the kernel can better describe conformational transitions between neighboring conformations and lead to accurate embedding. We applied our diffusion map method to the β-hairpin of the B1 domain of streptococcal protein G and to Trp-cage. Our results in β-hairpin show that the diffusion map embedding achieves better results with the hybrid kernel than that with the RMSD-based kernel in terms of free energy landscape characterization and a new correlation measure between the cluster center Euclidean distances in the reduced-dimension space and the reciprocals of the total net flow between these clusters. In addition, our diffusion map analysis of the ultralong molecular dynamics trajectory of Trp-cage has provided a unified view of its folding mechanism. These promising results demonstrate the effectiveness of our diffusion map approach in the analysis of the dynamics and thermodynamics of molecular systems. The hybrid geometry-energy criterion could be also useful as a general dynamic measure for other purposes.

Optimizing the fold stability of the circularly permuted Trp-cage motif

Through optimization of the linker region and key stabilizing mutations, it has been possible to improve the stability of the circularly permuted (cp) Trp-cage miniprotein. However, even the most stable Trp-cage circular permutants are still less stable than the analogous standard topology (std) Trp-cages. Extending mutational studies of Trp-cage fold stability to cp-species, including analogs lacking chain terminal charges, has uncovered and quantitated some additional stabilizing and destabilizing interactions. Upon protonation, the circular permutants are destabilized to a much greater extent than the standard topology series. End effects, particularly Coulombic interactions, appear to be more important for the cp-series while the Y10/P4 interaction in the cp-series is not as significant a stabilizing feature as the corresponding Y3/P19 in the standard topology series.

Directed C(sp3)-H arylation of tryptophan: transformation of the directing group into an activated amide

The aminoquinoline-directed C–H activation was used to synthezise unnatural tryptophans for solid phase peptide synthesis for the first time.

The 8-aminoquinoline (8AQ) directed C(sp³)–H functionalization was applied in the synthesis of β-arylated tryptophan derivatives. The laborious protecting group reorganization towards α-amino acids compatible for solid phase peptide synthesis (SPPS) was cut short by the transformation of the directing group into an activated amide, which was either used directly in peptide coupling or in the gram scale synthesis of storable Fmoc-protected amino acids for SPPS. In this work, directed C–H activation and nonplanar amide chemistry complement each other for the synthesis of hybrids between phenylalanine and tryptophan with restricted side chain mobility.

Sequence Tolerance of a Single-Domain Antibody with a High Thermal Stability: Comparison of Computational and Experimental Fitness Profiles

The sequence fitness of a llama single-domain antibody with an unusually high thermal stability is explored by a combined computational and experimental study. Starting with the X-ray crystallographic structure, RosettaBackrub simulations were applied to model sequence-structure tolerance profiles and identify key substitution sites. From the model calculations, an experimental site-directed mutagenesis was used to produce a panel of mutants, and their melting temperatures were determined by thermal denaturation. The results reveal a sequence fitness of an excess stability of approximately 12 °C, a value taken from a decrease in the melting temperature of an electrostatic charge-reversal substitution in the CRD3 without a deleterious effect on the binding affinity to the antigen. The tolerance for the disruption of antigen recognition without loss in the thermal stability was demonstrated by the introduction of a proline in place of a tyrosine in the CDR2, producing a mutant that eliminated binding. To further assist the sequence design and the selection of engineered single-domain antibodies, an assessment of different computational strategies is provided of their accuracy in the detection of substitution "hot spots" in the sequence tolerance landscape.

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. III. Determination of scale-consistent backbone-local and correlation potentials in the UNRES force field and force-field calibration and validation

The general theory of the construction of scale-consistent energy terms in the coarse-grained force fields presented in Paper I of this series has been applied to the revision of the UNRES force field for physics-based simulations of proteins. The potentials of mean force corresponding to backbone-local and backbone-correlation energy terms were calculated from the ab initio energy surfaces of terminally blocked glycine, alanine, and proline, and the respective analytical expressions, derived by using the scale-consistent formalism, were fitted to them. The parameters of all these potentials depend on single-residue types, thus reducing their number and preventing over-fitting. The UNRES force field with the revised backbone-local and backbone-correlation terms was calibrated with a set of four small proteins with basic folds: tryptophan cage variant (TRP1; α), Full Sequence Design (FSD; α + β), villin headpiece (villin; α), and a truncated FBP-28 WW-domain variant (2MWD; β) (the NEWCT-4P force field) and, subsequently, with an enhanced set of 9 proteins composed of TRP1, FSD, villin, 1BDC (α), 2I18 (α), 1QHK (α + β), 2N9L (α + β), 1E0L (β), and 2LX7 (β) (the NEWCT-9P force field). The NEWCT-9P force field performed better than NEWCT-4P in a blind-prediction-like test with a set of 26 proteins not used in calibration and outperformed, in a test with 76 proteins, the most advanced OPT-WTFSA-2 version of UNRES with former backbone-local and backbone-correlation terms that contained more energy terms and more optimizable parameters. The NEWCT-9P force field reproduced the bimodal distribution of backbone-virtual-bond angles in the simulated structures, as observed in experimental protein structures.

Reversing the typical pH stability profile of the Trp-cage

The Trp-cage, an 18-20 residue miniprotein, has emerged as a primary test system for evaluating computational fold prediction and folding rate determination efforts. As it turns out, a number of stabilizing interactions in the Trp-cage folded state have a strong pH dependence; all prior Trp-cage mutants have been destabilized under carboxylate-protonating conditions. Notable among the pH dependent stabilizing interactions within the Trp-cage are: (1) an Asp as the helix N-cap, (2) an H-bonded Asp9/Arg16 salt bridge, (3) an interaction between the chain termini which are in close spatial proximity, and (4) additional side chain interactions with Asp9. In the present study, we have prepared Trp-cage species that are significantly more stable at pH 2.5 (rather than 7) and quantitated the contribution of each interaction listed above. The Trp-cage structure remains constant with the pH change. The study has also provided measures of the stabilizing contribution of indole ring shielding from surface exposure and the destabilizing effects of an ionized Asp at the C-terminus of an α-helix.