Designing a 20-residue protein

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.

The Peptide Bond: Resonance Increases Bond Order and Complicates Fragmentation

The enhancement of the peptide bond order by a resonance in the lone pair of N and the π-bond of CO is analyzed. A decomposition of the bond order in terms of localized molecular orbitals is developed and applied to the peptide bond. A combination of two rotations of hybrid orbitals is proposed to improve the boundary treatment in the fragment molecular orbital method. The developed approach is applied to peptide bonds, and it is found crucial to retain the π orbital in the variational space of both fragments across the boundary. The interaction energies between conventional amino acid residues in Trp-cage (1L2Y) are discussed.

PSPI: A deep learning approach for prokaryotic small protein identification

Small Proteins (SPs) are pivotal in various cellular functions such as immunity, defense, and communication. Despite their significance, identifying them is still in its infancy. Existing computational tools are tailored to specific eukaryotic species, leaving only a few options for SP identification in prokaryotes. In addition, these existing tools still have suboptimal performance in SP identification. To fill this gap, we introduce PSPI, a deep learning-based approach designed specifically for predicting prokaryotic SPs. We showed that PSPI had a high accuracy in predicting generalized sets of prokaryotic SPs and sets specific to the human metagenome. Compared with three existing tools, PSPI was faster and showed greater precision, sensitivity, and specificity not only for prokaryotic SPs but also for eukaryotic ones. We also observed that the incorporation of (n, k)-mers greatly enhances the performance of PSPI, suggesting that many SPs may contain short linear motifs. The PSPI tool, which is freely available at https://www.cs.ucf.edu/∼xiaoman/tools/PSPI/, will be useful for studying SPs as a tool for identifying prokaryotic SPs and it can be trained to identify other types of SPs as well.

Exact Analytical Algorithm for the Solvent-Accessible Surface Area and Derivatives in Implicit Solvent Molecular Simulations on GPUs

In this paper, we present differentiable solvent-accessible surface area (dSASA), an exact geometric method to calculate SASA analytically along with atomic derivatives on GPUs. The atoms in a molecule are first assigned to tetrahedra in groups of four atoms by Delaunay tetrahedralization adapted for efficient GPU implementation, and the SASA values for atoms and molecules are calculated based on the tetrahedralization information and inclusion-exclusion method. The SASA values from the numerical icosahedral-based method can be reproduced with >98% accuracy for both proteins and RNAs. Having been implemented on GPUs and incorporated into AMBER, we can apply dSASA to implicit solvent molecular dynamics simulations with the inclusion of this nonpolar term. The current GPU version of GB/SA simulations has been accelerated up to nearly 20-fold compared to the CPU version, outperforming LCPO, a commonly used, fast algorithm for calculating SASA, as the system size increases. While we focus on the accuracy of the SASA calculations for proteins and nucleic acids, we also demonstrate stable GB/SA MD mini-protein simulations.

A survey of experimental and computational identification of small proteins

Small proteins (SPs) are typically characterized as eukaryotic proteins shorter than 100 amino acids and prokaryotic proteins shorter than 50 amino acids. Historically, they were disregarded because of the arbitrary size thresholds to define proteins. However, recent research has revealed the existence of many SPs and their crucial roles. Despite this, the identification of SPs and the elucidation of their functions are still in their infancy. To pave the way for future SP studies, we briefly introduce the limitations and advancements in experimental techniques for SP identification. We then provide an overview of available computational tools for SP identification, their constraints, and their evaluation. Additionally, we highlight existing resources for SP research. This survey aims to initiate further exploration into SPs and encourage the development of more sophisticated computational tools for SP identification in prokaryotes and microbiomes.

Enhancement of energy decomposition analysis in fragment molecular orbital calculations

Energy decomposition analysis is one of the most attractive features of fragment molecular orbital (FMO) calculations from the point of view of practical applications. Here we report some enhancements for PIEDA in the ABINIT-MP program. One is a separation of the dispersion-type stabilization from the electron correlation energy, traditionally referred to as the "dispersion interaction" (DI). Another is an alternative evaluation of the electrostatic (ES) interaction using the restrained electrostatic potential (RESP) charges. The GA:CT stacked base pair and the Trp-Cage miniprotein were used as illustrative examples.

Opposing roles of organic salts on mini-protein structure

We investigated the effects of 1-ethyl-3-methylimidazolium chloride ([EMIM][Cl]) and choline chloride ([Chol][Cl]) on the local environment and conformational landscapes of Trp-cage and Trpzip4 mini-proteins using experimental and computational approaches. Fluorescence experiments and computational simulations revealed distinct behaviors of the mini-proteins in the presence of these organic salts. [EMIM][Cl] showed a strong interaction with Trp-cage, leading to fluorescence quenching and destabilization of its native structural interactions. Conversely, [Chol][Cl] had a negligible impact on Trp-cage fluorescence at low concentrations but increased it at high concentrations, indicating a stabilizing role. Computational simulations elucidated that [EMIM][Cl] disrupted the hydrophobic core packing and decreased proline-aromatic residue contacts in Trp-cage, resulting in a more exposed environment for Trp residues. In contrast, [Chol][Cl] subtly influenced the hydrophobic core packing, creating a hydrophobic environment near the tryptophan residues. Circular dichroism experiments revealed that [Chol][Cl] stabilized the secondary structure of both mini-proteins, although computational simulations did not show significant changes in secondary content at the explored concentrations. The simulations also demonstrated a more rugged free energy landscape for Trp-cage and Trpzip4 in [EMIM][Cl], suggesting destabilization of the tertiary structure for Trp-cage and secondary structure for Trpzip4. Similar fluorescence trends were observed for Trpzip4, with [EMIM][Cl] quenching fluorescence and exhibiting stronger interaction, while [Chol][Cl] increased the fluorescence at high concentrations. These findings highlight the interplay between [EMIM][Cl] and [Chol][Cl] with the mini-proteins and provide a detailed molecular-level understanding of how these organic salts impact the nearby surroundings and structural variations. Understanding such interactions is valuable for diverse applications, from biochemistry to materials science.

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.

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.

Einstein Model of a Graph to Characterize Protein Folded/Unfolded States

The folded structures of proteins can be accurately predicted by deep learning algorithms from their amino-acid sequences. By contrast, in spite of decades of research studies, the prediction of folding pathways and the unfolded and misfolded states of proteins, which are intimately related to diseases, remains challenging. A two-state (folded/unfolded) description of protein folding dynamics hides the complexity of the unfolded and misfolded microstates. Here, we focus on the development of simplified order parameters to decipher the complexity of disordered protein structures. First, we show that any connected, undirected, and simple graph can be associated with a linear chain of atoms in thermal equilibrium. This analogy provides an interpretation of the usual topological descriptors of a graph, namely the Kirchhoff index and Randić resistance, in terms of effective force constants of a linear chain. We derive an exact relation between the Kirchhoff index and the average shortest path length for a linear graph and define the free energies of a graph using an Einstein model. Second, we represent the three-dimensional protein structures by connected, undirected, and simple graphs. As a proof of concept, we compute the topological descriptors and the graph free energies for an all-atom molecular dynamics trajectory of folding/unfolding events of the proteins Trp-cage and HP-36 and for the ensemble of experimental NMR models of Trp-cage. The present work shows that the local, nonlocal, and global force constants and free energies of a graph are promising tools to quantify unfolded/disordered protein states and folding/unfolding dynamics. In particular, they allow the detection of transient misfolded rigid states.

Frequency-Selective Anharmonic Mode Analysis of Thermally Excited Vibrations in Proteins

Low-frequency molecular vibrations at far-infrared frequencies are thermally excited at room temperature. As a consequence, thermal fluctuations are not limited to the immediate vicinity of local minima on the potential energy surface, and anharmonic properties cannot be ignored. The latter is particularly relevant in molecules with multiple conformations, such as proteins and other biomolecules. However, existing theoretical and computational frameworks for the analysis of molecular vibrations have so far been limited by harmonic or quasi-harmonic approximations, which are ill-suited to describe anharmonic low-frequency vibrations. Here, we introduce a fully anharmonic analysis of molecular vibrations based on a time correlation formalism that eliminates the need for harmonic or quasi-harmonic approximations. We use molecular dynamics simulations of a small protein to demonstrate that this new approach, in contrast to harmonic and quasi-harmonic normal modes, correctly identifies the collective degrees of freedom associated with molecular vibrations at any given frequency. This allows us to unambiguously characterize the anharmonic character of low-frequency vibrations in the far-infrared spectrum.

The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water

Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in water.

Developing a User-Friendly Code for the Fast Estimation of Well-Behaved Real-Space Partial Charges

The Quantum Theory of Atoms in Molecules (QTAIM) provides an intuitive, yet physically sound, strategy to determine the partial charges of any chemical system relying on the topology induced by the electron density ρ(r) . In a previous work [J. Chem. Phys. 2022, 156, 014112], we introduced a machine learning (ML) model for the computation of QTAIM charges of C, H, O, and N atoms at a fraction of the conventional computational cost. Unfortunately, the independent nature of the atomistic predictions implies that the raw atomic charges may not necessarily reconstruct the exact molecular charge, limiting the applicability of the latter in the chemistry realm. Trying to solve such an inconvenience, we introduce NNAIMGUI, a user-friendly code which combines the inferring abilities of ML with an equilibration strategy to afford adequately behaved partial charges. The performance of this approach is put to the test in a variety of scenarios including interpolation and extrapolation regimes (e.g chemical reactions) as well as large systems. The results of this work prove that the equilibrated charges retain the chemically accurate behavior reproduced by the ML models. Furthermore, NNAIMGUI is a fully flexible architecture allowing users to train and use tailor-made models targeted at any atomic property of choice. In this way, the GUI-interfaced code, equipped with visualization utilities, makes the computation of real-space atomic properties much more appealing and intuitive, paving the way toward the extension of QTAIM related descriptors beyond the theoretical chemistry community.

A Study of a Protein-Folding Machine: Transient Rotation of the Polypeptide Backbone Facilitates Rapid Folding of Protein Domains in All-Atom Molecular Dynamics Simulations

Molecular dynamics simulations of protein folding typically consider the polypeptide chain at equilibrium and in isolation from the cellular components. We argue that in order to understand protein folding as it occurs in vivo, it should be modeled as an active, energy-dependent process, in which the cellular protein-folding machine directly manipulates the polypeptide. We conducted all-atom molecular dynamics simulations of four protein domains, whose folding from the extended state was augmented by the application of rotational force to the C-terminal amino acid, while the movement of the N-terminal amino acid was restrained. We have shown earlier that such a simple manipulation of peptide backbone facilitated the formation of native structures in diverse α-helical peptides. In this study, the simulation protocol was modified, to apply the backbone rotation and movement restriction only for a short time at the start of simulation. This transient application of a mechanical force to the peptide is sufficient to accelerate, by at least an order of magnitude, the folding of four protein domains from different structural classes to their native or native-like conformations. Our in silico experiments show that a compact stable fold may be attained more readily when the motions of the polypeptide are biased by external forces and constraints.

Enhanced sampling in explicit solvent by deep learning module in FSATOOL

FSATOOL is an integrated molecular simulation and data analysis program. Its old molecular dynamics engine only supports simulations in vacuum or implicit solvent. In this work, we implement the well-known smooth particle mesh Ewald method for simulations in explicit solvent. The new developed engine is runnable on both CPU and GPU. All the existed analysis modules in the program are compatible with the new engine. Moreover, we also build a complete deep learning module in FSATOOL. Based on the module, we further implement two useful trajectory analysis methods: state-free reversible VAMPnets and time-lagged autoencoder. They are good at searching the collective variables related to the conformational transitions of biomolecules. In FSATOOL, these collective variables can be further used to construct a bias potential for the enhanced sampling purpose. We introduce the implementation details of the methods and present their actual performances in FSATOOL by a few enhanced sampling simulations.

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.

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.

A density fitting scheme for the fast evaluation of molecular electrostatic potential

Molecular electrostatic potential (MEP) is a significant and crucial physical quantity that can be applied to a large number of scenarios, such as the prediction of nucleophilic or electrophilic attacks, fitting atomic charges, σ-hole, and so forth. The computational cost for the MEP has an O(N² ) scaling with the increase of atoms, which is intractable and laborious for macromolecules. Herein, a density fitting molecular electrostatic potential (DF-MEP) is used to reduce the computational costs for the macromolecular MEP. It is found that the accuracy of DF-MEP is almost identical to the conventional molecular electrostatic potential (Conv-MEP), while the computational costs can be reduced to an O(N) scaling, for example, the computational time of 699,200 grids for the Trp-cage molecule (304 atoms) only takes 16.6 s at the B3LYP-D3(BJ)/def2-SVP level of theory with 16 CPU cores compared with 3060.2 s for the Conv-MEP method.

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.

Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

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.

Understanding the Role of Intramolecular Ion-Pair Interactions in Conformational Stability Using an Ab Initio Thermodynamic Cycle

Intramolecular ion-pair interactions yield shape and functionality to many molecules. With proper orientation, these interactions overcome steric factors and are responsible for the compact structures of several peptides. In this study, we present a thermodynamic cycle based on isoelectronic and alchemical mutation to estimate the intramolecular ion-pair interaction energy. We determine these energies for 26 benchmark molecules with common ion-pair combinations and compare them with results obtained using intramolecular symmetry-adapted perturbation theory. For systems with long linkers, the ion-pair energies evaluated using both approaches deviate by less than 2.5% in the vacuum phase. The thermodynamic cycle based on density functional theory facilitates calculations of salt-bridge interactions in model tripeptides with continuum/microsolvation modeling and four large peptides: 1EJG (crambin), 1BDK (bradykinin), 1L2Y (a mini-protein with a tryptophan cage), and 1SCO (a toxin from the scorpion venom).

Efficient and accurate density-based prediction of macromolecular polarizabilities

Accurately and efficiently predicting macromolecules' polarizabilities is an open problem. In this work, we employ a few simple density-based quantities from the information-theoretic approach (ITA) to predict polarizability of proteins. We first build quantitative structure/property relationships between molecular polarizabilities and ITA quantities. We then verify the broad applicability of ITA quantities for polarizability prediction for inorganic, organic, and biological systems with both localized and delocalized electronic structure. As a proof-of-concept application, we predict the molecular polarizabilities of complex proteins. Based on the linear regression equations for 20 natural amino acid residues, 400 dipeptides, and 8000 tripeptides, one then predicts the molecular polarizability of a larger peptide or even a protein once the molecular wavefunction is obtained. Because it is extremely costly to determine the wavefunction for a macromolecule like a protein, we propose to combine the ITA with the linear-scaling generalized energy-based fragmentation (GEBF) method to predict the macromolecular polarizability. In GEBF, the total molecular polarizability is obtained as a linear combination of the corresponding quantities from a series of small subsystems. We can predict them based on the subsystem wavefunction and linear regression equations rather than compute them from the nearly-intractable coupled-perturbed Hartree-Fock or Kohn-Sham equations for the whole macromolecule. Computational results showcase that the GEBF-ITA protocol should be an inexpensive yet accurate theoretical tool for predicting macromolecular polarizabilities.

Personal Precise Force Field for Intrinsically Disordered and Ordered Proteins Based on Deep Learning

Intrinsically disordered proteins (IDPs) are proteins without a fixed three-dimensional (3D) structure under physiological conditions and are associated with Parkinson's disease, Alzheimer's disease, cancer, cardiovascular disease, amyloidosis, diabetes, and other diseases. Experimental methods can hardly capture the ensemble of diverse conformations for IDPs. Molecular dynamics (MD) simulations can sample continuous conformations that might provide a valuable complement to experimental data. However, the accuracy of MD simulations depends on the quality of force field. In particular, the evolutionary conservation and coevolution of IDPs introduce that current force fields could not precisely reproduce the conformation of IDPs. In order to improve the performance of force field, deep learning and reweighting methods were used to automatically generate personal force field parameters for intrinsically disordered and ordered proteins. At first, the deep learning method predicted more accuracy φ/ψ dihedral of residue than the previous method. Then, reweighting optimized the personal force field parameters for each residue. Finally, typical representative systems such as IDPs, structure protein, and fast-folding protein were used to evaluate this force field. The results indicate that two personal force field parameters (named PPFF1 and PPFF1_af2) could better reproduce the experimental observables than ff03CMAP force field. In summary, this strategy will provide feasibility for the development of precise personal force fields.

Physiological models to study the effect of molecular crowding on multi-drug bound proteins: insights from SARS-CoV-2 main protease

Molecular Dynamics simulations are often used in drug design. However, such simulations do not account for the physiological environment of the receptor; hence overlook its impact on biomolecular interactions. To address this lacuna, we identified three objectives to pursue - develop models of physiological environment, study a drug-receptor complex in such environments, and identify methods to analyze these complicated simulations. Two novel physiological models were developed and studied. The first, called 'm10', comprises of 10 of the most abundant cytoplasmic metabolites at physiological concentrations. The second, called 'phy', supplements m10 with an additional crowder protein to elicit macromolecular crowding effect. The main protease (M^pro) of SARS-CoV-2, being essential for viral replication, is an attractive drug target for COVID-19. Hence, we chose M^pro docked with multiple drugs as our model drug-receptor system. With a plethora of compounds, physiological systems can be exceedingly large and complex. A novel Spark-based software (SparkTraj) was developed to rapidly analyze non-specific contacts and water interactions. Our study shows that crowding enhances the difference in the dynamics of apo- vs drug-bound complexes. Metabolites, at times as a cluster, were seen interacting with the protease, drugs, and binding sites in drug-free receptor. Except one that crawled to an adjacent pocket in phy, the drugs remained in their respective pockets in all simulations. Given these observations, we hope that the models and approach presented here would help the optimization, evaluation, and selection of potential drugs. Generic biomolecular dynamics could also benefit from such models and tools.Communicated by Ramaswamy H. Sarma.

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.

Fundamental Redesign of the TIGER2hs Kernel to Address Severe Parameter Sensitivity

Replica exchange molecular dynamics simulations are one of the most popular approaches to enhance conformational sampling of molecular systems. Applications range from protein folding to protein-protein or other host-guest interactions, as well as binding free energy calculations. While these methods are computationally expensive, highly accurate results can be obtained. We recently developed TIGER2hs, an improved version of the temperature intervals with global exchange of replicas (TIGER2) algorithm. This method combines the replica-based enhanced sampling in an explicit solvent with a hybrid solvent energy evaluation. During the exchange attempts, bulk water is replaced by an implicit solvent model, allowing sampling with significantly less replicas than parallel tempering (REMD). This enables accurate enhanced sampling calculations with only a fraction of computational resources compared to REMD. Our latest results highlight several issues with sampling imbalance and parameter sensitivity within the original TIGER2 exchange algorithms that affect the overall state populations. A high sensitivity on replica number and maximum temperature is eliminated by changing to a pairwise exchange kernel (PE) without additional sorting. Simulations are controlled by adjusting the average temperature change per exchange ⟨ΔT/χ⟩ to below 30 K to mimic a controlled temperature mixing of replicas similar to REMD. Thus, this parameter provides an applicable property for selecting combinations of replica number and maximum temperature to adjust simulations for best accuracy, with flexible resource investment. This increases the robustness of the method and ensures results in excellent agreement with REMD, as demonstrated for three different peptides.

Extending machine learning beyond interatomic potentials for predicting molecular properties

Machine learning (ML) is becoming a method of choice for modelling complex chemical processes and materials. ML provides a surrogate model trained on a reference dataset that can be used to establish a relationship between a molecular structure and its chemical properties. This Review highlights developments in the use of ML to evaluate chemical properties such as partial atomic charges, dipole moments, spin and electron densities, and chemical bonding, as well as to obtain a reduced quantum-mechanical description. We overview several modern neural network architectures, their predictive capabilities, generality and transferability, and illustrate their applicability to various chemical properties. We emphasize that learned molecular representations resemble quantum-mechanical analogues, demonstrating the ability of the models to capture the underlying physics. We also discuss how ML models can describe non-local quantum effects. Finally, we conclude by compiling a list of available ML toolboxes, summarizing the unresolved challenges and presenting an outlook for future development. The observed trends demonstrate that this field is evolving towards physics-based models augmented by ML, which is accompanied by the development of new methods and the rapid growth of user-friendly ML frameworks for chemistry.

A New Transfer Free Energy Based Implicit Solvation Model for the Description of Disordered and Folded Proteins

Most biological events occur on time scales that are difficult to access using conventional all-atom molecular dynamics simulations in explicit solvent. Implicit solvent techniques offer a promising solution to this problem, alleviating the computational cost associated with the simulation of large systems and accelerating the sampling compared to explicit solvent models. The substitution of water molecules by a mean field, however, introduces simplifications that may penalize accuracy and impede the prediction of certain physical properties. We demonstrate that existing implicit solvent models developed using a transfer free energy approach, while satisfactory at reproducing the folding behavior of globular proteins, fare less well in characterizing the conformational properties of intrinsically disordered proteins. We develop a new implicit solvent model that maximizes the degree of accuracy for both disordered and folded proteins. We show, by comparing the simulation outputs to experimental data, that in combination with the a99SB-disp force field, the implicit solvent model can describe both disordered (aβ40, PaaA2, and drkN SH3) and folded ((AAQAA)₃, CLN025, Trp-cage, and GTT) peptides. Our implicit solvent model permits a computationally efficient investigation of proteins containing both ordered and disordered regions, as well as the study of the transition between ordered and disordered protein states.

Molecular Mechanism of Antimicrobial Excipient-Induced Aggregation in Parenteral Formulations of Peptide Therapeutics

Antimicrobial preservatives are used as functional excipients in multidose formulations of biological therapeutics to destroy or inhibit the growth of microbial contaminants, which may be introduced by repeatedly administering doses. Antimicrobial agents can also induce the biophysical instability of proteins and peptides, which presents a challenge in optimizing the drug product formulation. Elucidating the structural basis for aggregation aids in understanding the underlying mechanism and can offer valuable knowledge and rationale for designing drug substances and drug products; however, this remains largely unexplored due to the lack of high-resolution characterization. In this work, we utilize solution nuclear magnetic resonance (NMR) as an advanced biophysical tool to study an acylated 31-residue peptide, acyl-peptide A, and its interaction with commonly used antimicrobial agents, benzyl alcohol and m-cresol. Our results suggest that acyl-peptide A forms soluble octamers in the aqueous solution, which tumble slowly due to an increased molecular weight as measured by diffusion ordered spectroscopy and ¹H relaxation measurement. The addition of benzyl alcohol does not induce aggregation of acyl-peptide A and has no chemical shift perturbation in ¹H-¹H NOESY spectra, suggesting no detectable interaction with the peptide. In contrast, the addition of 1% (w/v) m-cresol results in insoluble aggregates composed of 25% (w/w) peptides after a 24-hour incubation at room temperature as quantified by ¹H NMR. Interestingly, ¹H-¹³C heteronuclear single-quantum coherence and ¹H-¹H total correlation experiment spectroscopy have identified m-cresol and peptide interactions at specific residues, including Met, Lys, Glu, and Gln, suggesting that there may be a combination of hydrophobic, hydrogen bonding, and electrostatic interactions with m-cresol driving this phenomenon. These site-specific interactions have promoted the formation of higher-order oligomerization such as dimers and trimers of octamers, eventually resulting in insoluble aggregates. Our study has elucidated a structural basis of m-cresol-induced self-association that can inform the optimized design of drug substances and products. Moreover, it has demonstrated solution NMR as a high-resolution tool to investigate the structure and dynamics of biological drug products and provide an understanding of excipient-induced peptide and protein aggregation.

Resolution exchange with tunneling for enhanced sampling of protein landscapes

Simulations of protein folding and protein association happen on timescales that are orders of magnitude larger than what can typically be covered in all-atom molecular dynamics simulations. Use of low-resolution models alleviates this problem but may reduce the accuracy of the simulations. We introduce a replica-exchange-based multiscale sampling technique that combines the faster sampling in coarse-grained simulations with the potentially higher accuracy of all-atom simulations. After testing the efficiency of our Resolution Exchange with Tunneling (ResET) in simulations of the Trp-cage protein, an often used model to evaluate sampling techniques in protein simulations, we use our approach to compare the landscape of wild-type and A2T mutant Aβ_{1-42} peptides. Our results suggest a mechanism by that the mutation of a small hydrophobic alanine (A) into a bulky polar threonine (T) may interfere with the self-assembly of Aβ fibrils.

A Transfer Free Energy Based Implicit Solvent Model for Protein Simulations in Solvent Mixtures: Urea-Induced Denaturation as a Case Study

We developed a method for implicit solvent molecular dynamics simulations of proteins in solvent mixtures (model with implicit solvation thermodynamics, MIST). The MIST method introduces experimental group transfer free energies to the generalized Born formulation for generating molecular trajectories without the need for developing rigorous explicit-solvent force fields for multicomponent solutions. As a test case, we studied the urea-induced denaturation of the Trp-cage miniprotein in water. We demonstrate that our method allows efficient exploration of the conformational space of the protein in only a few hundreds of nanoseconds of all-atom unbiased simulations. Furthermore, selective implementation of the transfer free energies of specific peptide groups, backbone, and side chains enables us to decouple their specific energetic contributions to the conformational changes of the protein. The approach herein developed can readily be extended to the investigation of complex matrices as well as to the characterization of protein aggregation. The MIST method is implemented in Plumed (ver. 2.8) as a separate module called SASA.

A fast-slow method to treat solute dynamics in explicit solvent

Aiming to reduce the computational cost in the current explicit solvent molecular dynamics (MD) simulation, this paper proposes a fast-slow method for the fast MD simulation of biomolecules in explicit solvent. This fast-slow method divides the entire system into two parts: a core layer (typically solute or biomolecule) and a peripheral layer (typically solvent molecules). The core layer is treated using standard MD method but the peripheral layer is treated by a slower dynamics method to reduce the computational cost. We compared four different simulation models in testing calculations for several small proteins. These include gas-phase, implicit solvent, fast-slow explicit solvent and standard explicit solvent MD simulations. Our study shows that gas-phase and implicit solvent models do not provide a realistic solvent environment and fail to correctly produce reliable dynamic structures of proteins. On the other hand, the fast-slow method can essentially reproduce the same solvent effect as the standard explicit solvent model while gaining an order of magnitude in efficiency. This fast-slow method thus provides an efficient approach for accelerating the MD simulation of biomolecules in explicit solvent.

Collective Variable for Metadynamics Derived From AlphaFold Output

AlphaFold is a neural network–based tool for the prediction of 3D structures of proteins. In CASP14, a blind structure prediction challenge, it performed significantly better than other competitors, making it the best available structure prediction tool. One of the outputs of AlphaFold is the probability profile of residue–residue distances. This makes it possible to score any conformation of the studied protein to express its compliance with the AlphaFold model. Here, we show how this score can be used to drive protein folding simulation by metadynamics and parallel tempering metadynamics. Using parallel tempering metadynamics, we simulated the folding of a mini-protein Trp-cage and β hairpin and predicted their folding equilibria. We observe the potential of the AlphaFold-based collective variable in applications beyond structure prediction, such as in structure refinement or prediction of the outcome of a mutation.

Modulation of free energy landscapes as a strategy for the design of antimicrobial peptides

Computational design of antimicrobial peptides (AMPs) is a promising area of research for developing novel agents against drug-resistant bacteria. AMPs are present naturally in many organisms, from bacteria to humans, a time-tested mechanism that makes them attractive as effective antibiotics. Depending on the environment, AMPs can exhibit α-helical or β-sheet conformations, a mix of both, or lack secondary structure; they can be linear or cyclic. Prediction of their structures is challenging but critical for rational design. Promising AMP leads can be developed using essentially two approaches: traditional modeling of the physicochemical mechanisms that determine peptide behavior in aqueous and membrane environments and knowledge-based, e.g., machine learning (ML) techniques, that exploit ever-growing AMP databases. Here, we explore the conformational landscapes of two recently ML-designed AMPs, characterize the dependence of these landscapes on the medium conditions, and identify features in peptide and membrane landscapes that mediate protein-membrane association. For both peptides, we observe greater conformational diversity in an aqueous solvent than in a less polar solvent, and one peptide is seen to alter its conformation more dramatically than the other upon the change of solvent. Our results support the view that structural rearrangement in response to environmental changes is central to the mechanism of membrane-structure disruption by linear peptides. We expect that the design of AMPs by ML will benefit from the incorporation of peptide conformational substates as quantified here with molecular simulations.

Development of a Hybrid-Resolution Force Field for Peptide Self-Assembly Simulations: Optimizing Peptide-Peptide and Peptide-Solvent Interactions

Atomic descriptions of peptide self-assembly are crucial to an understanding of disease-related peptide aggregation and the design of peptide-assembled materials. Obtaining these descriptions through computer simulation is challenging because current force fields, which were not designed for this process and are often unable to describe correctly peptide self-assembly behavior and the sequence dependence. Here, we developed a framework using dipeptide aggregation as a model system to improve force fields for simulations of self-assembly. Aggregation-related structural properties were designed and used to guide the optimization of peptide-peptide and peptide-solvent interactions. With this framework, we developed a self-assembly force field, termed PACE-ASM, by reoptimizing a hybrid-resolution force field that was originally developed for folding simulation. With its applicability in folding simulations, the new PACE was used to simulate the self-assembly of two disease-related short peptides, Aβ_16-21 and PHF6, into β-sheet-rich cross-β amyloids. These simulations reproduced the crystal structures of Aβ_16-21 and PHF6 amyloids at near-atomic resolution and captured the difference in packing orientations between the two sequences, a task which is challenging even with all-atom force fields. Apart from cross-β amyloids, the self-assembly of emerging helix-rich cross-α amyloids by another peptide PSMα3 can also be correctly described with the new PACE, manifesting the versatility of the force field. We demonstrated that the ability of the PACE-ASM to model peptide self-assembly is based largely on its improved description of peptide-peptide and peptide-solvent interactions. This was achieved with our optimization framework that can readily identify and address the deficiency in describing these interactions.

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.

An open-source framework for fast-yet-accurate calculation of quantum mechanical features

We present the open-source framework kallisto that enables the efficient and robust calculation of quantum mechanical features for atoms and molecules. For a benchmark set of 49 experimental molecular polarizabilities,...

Protein nanofibrils and their use as building blocks of sustainable materials

The development towards a sustainable society requires a radical change of many of the materials we currently use. Besides the replacement of plastics, derived from petrochemical sources, with renewable alternatives, we will also need functional materials for applications in areas ranging from green energy and environmental remediation to smart foods. Proteins could, with their intriguing ability of self-assembly into various forms, play important roles in all these fields. To achieve that, the code for how to assemble hierarchically ordered structures similar to the protein materials found in nature must be cracked. During the last decade it has been demonstrated that amyloid-like protein nanofibrils (PNFs) could be a steppingstone for this task. PNFs are formed by self-assembly in water from a range of proteins, including plant resources and industrial side streams. The nanofibrils display distinct functional features and can be further assembled into larger structures. PNFs thus provide a framework for creating ordered, functional structures from the atomic level up to the macroscale. This review address how industrial scale protein resources could be transformed into PNFs and further assembled into materials with specific mechanical and functional properties. We describe what is required from a protein to form PNFs and how the structural properties at different length scales determine the material properties. We also discuss potential chemical routes to modify the properties of the fibrils and to assemble them into macroscopic structures.

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.

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.

Computationally Designed ACE2 Decoy Receptor Binds SARS-CoV-2 Spike (S) Protein with Tight Nanomolar Affinity

Even with the availability of vaccines, therapeutic options for COVID-19 still remain highly desirable, especially in hospitalized patients with moderate or severe disease. Soluble ACE2 (sACE2) is a promising therapeutic candidate that neutralizes SARS CoV-2 infection by acting as a decoy. Using computational mutagenesis, we designed a number of sACE2 derivatives carrying three to four mutations. The top-predicted sACE2 decoy based on the in silico mutagenesis scan was subjected to molecular dynamics and free-energy calculations for further validation. After illuminating the mechanism of increased binding for our designed sACE2 derivative, the design was verified experimentally by flow cytometry and BLI-binding experiments. The computationally designed sACE2 decoy (ACE2-FFWF) bound the receptor-binding domain of SARS-CoV-2 tightly with low nanomolar affinity and ninefold affinity enhancement over the wild type. Furthermore, cell surface expression was slightly greater than wild-type ACE2, suggesting that the design is well-folded and stable. Having an arsenal of high-affinity sACE2 derivatives will help to buffer against the emergence of SARS CoV-2 variants. Here, we show that computational methods have become sufficiently accurate for the design of therapeutics for current and future viral pandemics.

CORE-MD II: A fast, adaptive, and accurate enhanced sampling method

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

A Conserved Hydrophobic Moiety and Helix-Helix Interactions Drive the Self-Assembly of the Incretin Analog Exendin-4

Exendin-4 is a pharmaceutical peptide used in the control of insulin secretion. Structural information on exendin-4 and related peptides especially on the level of quaternary structure is scarce. We present the first published association equilibria of exendin-4 directly measured by static and dynamic light scattering. We show that exendin-4 oligomerization is pH dependent and that these oligomers are of low compactness. We relate our experimental results to a structural hypothesis to describe molecular details of exendin-4 oligomers. Discussion of the validity of this hypothesis is based on NMR, circular dichroism and fluorescence spectroscopy, and light scattering data on exendin-4 and a set of exendin-4 derived peptides. The essential forces driving oligomerization of exendin-4 are helix–helix interactions and interactions of a conserved hydrophobic moiety. Our structural hypothesis suggests that key interactions of exendin-4 monomers in the experimentally supported trimer take place between a defined helical segment and a hydrophobic triangle constituted by the Phe22 residues of the three monomeric subunits. Our data rationalize that Val19 might function as an anchor in the N-terminus of the interacting helix-region and that Trp25 is partially shielded in the oligomer by C-terminal amino acids of the same monomer. Our structural hypothesis suggests that the Trp25 residues do not interact with each other, but with C-terminal Pro residues of their own monomers.

Pressure Unfolding of Proteins: New Insights into the Role of Bound Water

High pressures can be detrimental for protein stability, resulting in unfolding and loss of function. This phenomenon occurs because the unfolding transition is accompanied by a decrease in volume, which is typically attributed to the elimination of cavities that are present within the native state as a result of packing defects. We present a novel computational approach that enables the study of pressure unfolding in atomistically detailed protein models in implicit solvent. We include the effect of pressure using a transfer free energy term that allows us to decouple the effect of protein residues and bound water molecules on the volume change upon unfolding. We discuss molecular dynamics simulations results using this protocol for two model proteins, Trp-cage and staphylococcal nuclease (SNase). We find that the volume reduction of bound water is the key energetic term that drives protein denaturation under the effect of pressure, for both Trp-cage and SNase. However, we note differences in unfolding mechanisms between the smaller Trp-cage and the larger SNase protein. Indeed, the unfolding of SNase, but not Trp-cage, is seen to be further accompanied by a reduction in the volume of internal cavities. Our results indicate that, for small peptides, like Trp-cage, pressure denaturation is driven by the increase in solvent accessibility upon unfolding, and the subsequent increase in the number of bound water molecules. For larger proteins, like SNase, the cavities within the native fold act as weak spots, determining the overall resistance to pressure denaturation. Our simulations display a striking agreement with the pressure-unfolding profile experimentally obtained for SNase and represent a promising approach for a computationally efficient and accurate exploration of pressure-induced denaturation of proteins.