GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Vibrational Spectra of a Mechanosensitive Channel.

We report the simulated vibrational spectra of a mechanosensitive membrane channel in different gating states. Our results show that while linear absorption is insensitive to structural differences, linear dichroism and sum-frequency generation spectroscopies are sensitive to the orientation of the transmembrane helices, which is changing during the opening process. Linear dichroism cannot distinguish an intermediate structure from the closed structure, but sum-frequency generation can. In addition, we find that two-dimensional infrared spectroscopy can be used to distinguish all three investigated gating states of the mechanosensitive membrane channel.

Structural investigation of MscL gating using experimental data and coarse grained MD simulations.

The mechanosensitive channel of large conductance (MscL) has become a model system in which to understand mechanosensation, a process involved in osmoregulation and many other physiological functions. While a high resolution closed state structure is available, details of the open structure and the gating mechanism remain unknown. In this study we combine coarse grained simulations with restraints from EPR and FRET experiments to study the structural changes involved in gating with much greater level of conformational sampling than has previously been possible. We generated a set of plausible open pore structures that agree well with existing open pore structures and gating models. Most interestingly, we found that membrane thinning induces a kink in the upper part of TM1 that causes an outward motion of the periplasmic loop away from the pore centre. This previously unobserved structural change might present a new mechanism of tension sensing and might be related to a functional role in osmoregulation.

Hybrid simulations: combining atomistic and coarse-grained force fields using virtual sites.

Hybrid simulations, in which part of the system is represented at atomic resolution and the remaining part at a reduced, coarse-grained, level offer a powerful way to combine the accuracy associated with the atomistic force fields to the sampling speed obtained with coarse-grained (CG) potentials. In this work we introduce a straightforward scheme to perform hybrid simulations, making use of virtual sites to couple the two levels of resolution. With the help of these virtual sites interactions between molecules at different levels of resolution, i.e. between CG and atomistic molecules, are treated the same way as the pure CG-CG interactions. To test our method, we combine the Gromos atomistic force field with a number of coarse-grained potentials, obtained through several approaches that are designed to obtain CG potentials based on an existing atomistic model, namely iterative Boltzmann inversion, force matching, and a potential of mean force subtraction procedure (SB). We also explore the use of the MARTINI force field for the CG potential. A simple system, consisting of atomistic butane molecules dissolved in CG butane, is used to study the performance of our hybrid scheme. Based on the potentials of mean force for atomistic butane in CG solvent, and the properties of 1:1 mixtures of atomistic and CG butane which should exhibit ideal mixing behavior, we conclude that the MARTINI and SB potentials are particularly suited to be combined with the atomistic force field. The MARTINI potential is subsequently used to perform hybrid simulations of atomistic dialanine peptides in both CG butane and water. Compared to a fully atomistic description of the system, the hybrid description gives similar results provided that the dielectric screening of water is accounted for. Within the field of biomolecules, our method appears ideally suited to study e.g. protein-ligand binding, where the active site and ligand are modeled in atomistic detail and the rest of the protein, together with the solvent, is coarse-grained.

Protein shape change has a major effect on the gating energy of a mechanosensitive channel.

Increasing experimental evidence has shown that membrane protein functionality depends on molecular composition of cell membranes. However, the origin of this dependence is not fully understood. It is reasonable to assume that specific lipid-protein interactions are important, yet more generic effects due to mechanical properties of lipid bilayers likely play a significant role too. Previously it has been demonstrated using models for elastic properties of membranes and lateral pressure profiles of lipid bilayers that the mechanical properties of a lipid bilayer can contribute as much as ∼10 k(B)T to the free energy difference associated with a change in protein conformational state. Here, we extend those previous approaches to a more realistic model for a large mechanosensitive channel (MscL). We use molecular dynamics together with the MARTINI model to simulate the open and closed states of MscL embedded in a DOPC bilayer. We introduce a procedure to calculate the mechanical energy change in the channel gating using a three-dimensional pressure distribution inside a membrane, computed from the molecular dynamics simulations. We decompose the mechanical energy to terms associated with area dilation and shape contribution. Our results highlight that the lateral pressure profile of a lipid bilayer together with the shape change in gating can induce a contribution of ∼30 k(B)T on the gating energy of MscL. This contribution arises largely from the interfacial tension between hydrophobic and hydrophilic regions in a lipid bilayer.

Release of content through mechano-sensitive gates in pressurized liposomes.

Mechano-sensitive channels are ubiquitous membrane proteins that activate in response to increasing tension in the lipid membrane. They facilitate a sudden, nonselective release of solutes and water that safeguards the integrity of the cell in hypo- or hyper-osmotic shock conditions. We have simulated the rapid release of content from a pressurized liposome through a particular mechano-sensitive protein channel, MscL, embedded in the liposomal membrane. We show that a single channel is able to relax the liposome, stressed to the point of bursting, in a matter of microseconds. We map the full activation-deactivation cycle of MscL in near-atomic detail and are able to quantify the rapid decrease in liposomal stress as a result of channel activation. This provides a computational tool that opens the way to contribute to the rational design of functional nano-containers.

3D pressure field in lipid membranes and membrane-protein complexes.

We calculate full 3D pressure fields for inhomogeneous nanoscale systems using molecular dynamics simulation data. The fields represent systems with increasing level of complexity, ranging from semivesicles and vesicles to membranes characterized by coexistence of two phases, including also a protein-membrane complex. We show that the 3D pressure field is distinctly different for curved and planar bilayers, the pressure field depends strongly on the phase of the membrane, and that an integral protein modulates the tension and elastic properties of the membrane.

Evidence of molecular alignment fluctuations in aqueous dilute liquid crystalline media.

Protein dynamics can be studied by NMR measurements of aqueous dilute liquid crystalline samples. However, the measured residual dipolar couplings are sensitive not only to internal fluctuations but to all changes in internuclear vectors relative to the laboratory frame. We show that side-chain fluctuations and bond librations in the ps-ns time scale perturb the molecular shape and charge distribution of a small globular protein sufficiently to cause a noticeable variation in the molecular alignment. The alignment variation disperses the bond vectors of a conformational ensemble even further from the dispersion already caused by internal fluctuations of a protein. Consequently RDC-probed order parameters are lower than those obtained by laboratory frame relaxation measurements.

Conformational fluctuations affect protein alignment in dilute liquid crystal media.

The discovery of dilute liquid crystalline media to align biological macromolecules has opened many new possibilities to study protein and nucleic acid structures by NMR spectroscopy. We inspect the basic alignment phenomenon for an ensemble of protein conformations to deduce relative contributions of each member to the residual dipolar coupling signals. We find that molecular fluctuations can affect the alignment and discover a resulting emphasis of certain conformations. However, the internal fluctuations are largely uncorrelated with those of the alignment, implying that proteins have liquidlike molecular surfaces. Furthermore, we consider the implications of a dynamic bias to structure determination using data from the weak alignment method.

On the interpretation of residual dipolar couplings as reporters of molecular dynamics.

The analysis of residual dipolar couplings from an ensemble of conformations to extract molecular dynamics is intricate. The very mechanism that is necessary to perturb overall molecular tumbling to generate nonvanishing residual dipolar couplings gives rise to convoluted data. The measured values are essentially weighted averages over conformations. However, the weights are not simply the populations of conformations. Consequently, the observed order parameter is not exactly the true measure of motion. In the case of paramagnetic alignment, the apparent order parameter is expected to depend on the number of torsions that separate the locus of interest from the paramagnetic site. In the case of alignment due to steric obstruction, the uneven selection of conformations by their differing Saupe order matrices leads to a bias in the residual dipolar couplings-probed molecular dynamics.

Alignment of chain-like molecules.

The steric obstruction model, that describes the enhanced alignment of folded proteins by anisotropic medium, is extended to account for the residual dipolar couplings of chain-like polypeptides. The average alignment of each chain segment is calculated from an ensemble of conformations represented by a spatial probability distribution. The segmental alignment depends on chain length, flexibility and segment's position in the chain. Residual dipolar couplings in turn depend on internuclear vector directions within each fragment. The results of calculations and simulations explain salient features of the experimental data. With this insight residual dipolar couplings can be interpreted to assess the degree of denaturation, local structures and spatial organization of weakly structured proteins.

On the origin of residual dipolar couplings from denatured proteins.

Effects of steric obstruction on random flight chains are examined. Spatial probability distributions are elaborated to calculate residual dipolar couplings and residual chemical shift anisotropy, parameters that are acquired by NMR spectroscopy from solutes dissolved in dilute liquid crystals. Calculations yield chain length and residue position-dependent values in good agreement with simulations to provide understanding of recently acquired data from denatured proteins.