Quantum Chemical Calculation of Molecular and Periodic Peptide and Protein Structures.

Special-purpose classical force fields (FFs) provide good accuracy at very low computational cost, but their application is limited to systems for which potential energy functions are available. This excludes most metal-containing proteins or those containing cofactors. In contrast, the GFN2-xTB semiempirical quantum chemical method is parametrized for almost the entire periodic table. The accuracy of GFN2-xTB is assessed for protein structures with respect to experimental X-ray data. Furthermore, the results are compared with those of two special-purpose FFs, HF-3c, PM6-D3H4X, and PM7. The test sets include proteins without any prosthetic groups as well as metalloproteins. Crystal packing effects are examined for a set of smaller proteins to validate the molecular approach. For the proteins without prosthetic groups, the special purpose FF OPLS-2005 yields the smallest overall RMSD to the X-ray data but GFN2-xTB provides similarly good structures with even better bond-length distributions. For the metalloproteins with up to 5000 atoms, a good overall structural agreement is obtained with GFN2-xTB. The full geometry optimizations of protein structures with on average 1000 atoms in wall-times below 1 day establishes the GFN2-xTB method as a versatile tool for the computational treatment of various biomolecules with a good accuracy/computational cost ratio.

Global Dynamics of Yeast Hsp90 Middle and C-Terminal Dimer Studied by Advanced Sampling Simulations.

The Hsp90 protein complex is one of the most abundant molecular chaperone proteins that assists in folding of a variety of client proteins. During its functional cycle it undergoes large domain rearrangements coupled to the hydrolysis of ATP and association or dissociation of domain interfaces. In order to better understand the domain dynamics comparative Molecular Dynamics (MD) simulations of a sub-structure of Hsp90, the dimer formed by the middle (M) and C-terminal domain (C), were performed. Since this MC dimer lacks the ATP-binding N-domain it allows studying global motions decoupled from ATP binding and hydrolysis. Conventional (c)MD simulations starting from several different closed and open conformations resulted in only limited sampling of global motions. However, the application of a Hamiltonian Replica exchange (H-REMD) method based on the addition of a biasing potential extracted from a coarse-grained elastic network description of the system allowed much broader sampling of domain motions than the cMD simulations. With this multiscale approach it was possible to extract the main directions of global motions and to obtain insight into the molecular mechanism of the global structural transitions of the MC dimer.

Accelerated flexible protein-ligand docking using Hamiltonian replica exchange with a repulsive biasing potential.

A molecular dynamics replica exchange based method has been developed that allows rapid identification of putative ligand binding sites on the surface of biomolecules. The approach employs a set of ambiguity restraints in replica simulations between receptor and ligand that allow close contacts in the reference replica but promotes transient dissociation in higher replicas. This avoids long-lived trapping of the ligand or partner proteins at nonspecific, sticky, sites on the receptor molecule and results in accelerated exploration of the possible binding regions. In contrast to common docking methods that require knowledge of the binding site, exclude solvent and often keep parts of receptor and ligand rigid the approach allows for full flexibility of binding partners. Application to peptide-protein, protein-protein and a drug-receptor system indicate rapid sampling of near-native binding regions even in case of starting far away from the native binding site outperforming continuous MD simulations. An application on a DNA minor groove binding ligand in complex with DNA demonstrates that it can also be used in explicit solvent simulations.

Exploring biomolecular dynamics and interactions using advanced sampling methods.

Molecular dynamics (MD) and Monte Carlo (MC) simulations have emerged as a valuable tool to investigate statistical mechanics and kinetics of biomolecules and synthetic soft matter materials. However, major limitations for routine applications are due to the accuracy of the molecular mechanics force field and due to the maximum simulation time that can be achieved in current simulations studies. For improving the sampling a number of advanced sampling approaches have been designed in recent years. In particular, variants of the parallel tempering replica-exchange methodology are widely used in many simulation studies. Recent methodological advancements and a discussion of specific aims and advantages are given. This includes improved free energy simulation approaches and conformational search applications.

Rapid alchemical free energy calculation employing a generalized born implicit solvent model.

Generalized Born (GB) implicit solvent models are typically used in postprocessing of molecular dynamics trajectories obtained from explicit solvent simulations to estimate binding free energies or effects of mutations in proteins. The possibility to employ a GB implicit solvent model for the calculation of rigorous free energy changes associated with alchemical transformations has been explored. During free energy perturbation (FEP) simulations, Lennard-Jones, Coulomb, and Born radii parameters are transformed gradually in a single-topology series. The FEP calculations are embedded in a replica exchange scheme allowing rapid convergence. The method was tested on the calculation of relative hydration free energies, relative binding free energies of a ligand-receptor system, and in silico alanine scanning of a peptide-protein complex. In all cases, good agreement with available experimental data was obtained. On medium sized protein-ligand systems and using a cluster of graphical processing units, the approach allows the calculation of relative free energy changes associated with a chemical modification of a binding partner within a few minutes of computer time and opens the possibility for systematic in silico studies.

Coupling between side chain interactions and binding pocket flexibility in HLA-B*44:02 molecules investigated by molecular dynamics simulations.

MHC class I molecules present antigenic peptides to cytotoxic T-cells at the cell surface. Peptide loading of class I molecules in the endoplasmatic reticulum can involve interaction with the tapasin chaperone protein. The human class I allotype HLA-B*44:02 with an Asp at position 116 at the floor of the F pocket (which binds the peptide C-terminal residues) depends on tapasin for efficient peptide loading. However, HLA-B*44:05 (identical to B*44:02 except for tyrosine 116) can efficiently load peptides in the absence of tapasin. Both allotypes adopt very similar structures in the presence of the same peptide. Molecular dynamics simulations indicate a significantly higher conformational flexibility of the F pocket in the absence of a peptide for B*44:02 compared to B*44:05. Free energy simulations to open the F pocket indicate a molecular side chain switch mechanism that underlies the global opening motion. This side chain switch involves the rearrangement of salt bridges and hydrogen bonding of the basic arginine 97 with three acidic aspartate residues 114, 116 and 156 near the F pocket. A replica exchange simulation to specifically accelerate side chain motions demonstrates that the same side chain rearrangements induce global opening motions of the F pocket. In case of B*44:05 the free energy barrier for F pocket opening was significantly higher compared to B*44:02 and no associated side chain rearrangement was observed. Such coupling of local side chain rearrangements with global conformational changes might be the basis for allosteric changes in other class I allotypes as well as for allosteric changes in other proteins.

Hamiltonian replica exchange combined with elastic network analysis to enhance global domain motions in atomistic molecular dynamics simulations.

Coarse-grained elastic network models (ENM) of proteins offer a low-resolution representation of protein dynamics and directions of global mobility. A Hamiltonian-replica exchange molecular dynamics (H-REMD) approach has been developed that combines information extracted from an ENM analysis with atomistic explicit solvent MD simulations. Based on a set of centers representing rigid segments (centroids) of a protein, a distance-dependent biasing potential is constructed by means of an ENM analysis to promote and guide centroid/domain rearrangements. The biasing potentials are added with different magnitude to the force field description of the MD simulation along the replicas with one reference replica under the control of the original force field. The magnitude and the form of the biasing potentials are adapted during the simulation based on the average sampled conformation to reach a near constant biasing in each replica after equilibration. This allows for canonical sampling of conformational states in each replica. The application of the methodology to a two-domain segment of the glycoprotein 130 and to the protein cyanovirin-N indicates significantly enhanced global domain motions and improved conformational sampling compared with conventional MD simulations.

Hamiltonian replica-exchange simulations with adaptive biasing of peptide backbone and side chain dihedral angles.

A Hamiltonian Replica-Exchange Molecular Dynamics (REMD) simulation method has been developed that employs a two-dimensional backbone and one-dimensional side chain biasing potential specifically to promote conformational transitions in peptides. To exploit the replica framework optimally, the level of the biasing potential in each replica was appropriately adapted during the simulations. This resulted in both high exchange rates between neighboring replicas and improved occupancy/flow of all conformers in each replica. The performance of the approach was tested on several peptide and protein systems and compared with regular MD simulations and previous REMD studies. Improved sampling of relevant conformational states was observed for unrestrained protein and peptide folding simulations as well as for refinement of a loop structure with restricted mobility of loop flanking protein regions.

Dipeptides promote folding and peptide binding of MHC class I molecules.

MHC class I molecules bind only those peptides with high affinity that conform to stringent length and sequence requirements. We have now investigated which peptides can aid the in vitro folding of class I molecules, and we find that the dipeptide glycyl-leucine efficiently supports the folding of HLA-A*02:01 and H-2K(b) into a peptide-receptive conformation that rapidly binds high-affinity peptides. Treatment of cells with glycyl-leucine induces accumulation of peptide-receptive H-2K(b) and HLA-A*02:01 at the surface of cells. Other dipeptides with a hydrophobic second amino acid show similar enhancement effects. Our data suggest that the dipeptides bind into the F pocket like the C-terminal amino acids of a high-affinity peptide.

Advanced replica-exchange sampling to study the flexibility and plasticity of peptides and proteins.

Molecular dynamics (MD) simulations are ideally suited to investigate protein and peptide plasticity and flexibility simultaneously at high spatial (atomic) and high time resolution. However, the applicability is still limited by the force field accuracy and by the maximum simulation time that can be routinely achieved in current MD simulations. In order to improve the sampling the replica-exchange (REMD) methodology has become popular and is now the most widely applied advanced sampling approach. Many variants of the REMD method have been designed to reduce the computational demand or to enhance sampling along specific sets of conformational variables. An overview on recent methodological advances and discussion of specific aims and advantages of the approaches will be given. Applications in the area of free energy simulations and advanced sampling of intrinsically disordered peptides and proteins will also be discussed. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Buckling of stiff polymer rings in weak spherical confinement.

Confinement is a versatile and well-established tool to study the properties of polymers either to understand biological processes or to develop new nanobiomaterials. We investigate the conformations of a semiflexible polymer ring in weak spherical confinement imposed by an impenetrable shell. We develop an analytic argument for the dominating polymer trajectory depending on polymer flexibility considering elastic and entropic contributions. Monte Carlo simulations are performed to assess polymer ring conformations in probability densities and by the shape measures asphericity and nature of asphericity. Comparison of the analytic argument with the mean asphericity and the mean nature of asphericity confirm our reasoning to explain polymer ring conformations in the stiff regime, where elastic response prevails.