Bicelles and Other Membrane Mimics: Comparison of Structure, Properties, and Dynamics from MD Simulations

The increased interest in studying membrane proteins has led to the development of new membrane mimics such as bicelles and nanodiscs. However, only limited knowledge is available of how these membrane mimics are affected by embedded proteins and how well they mimic a lipid bilayer. Herein, we present molecular dynamics simulations to elucidate structural and dynamic properties of small bicelles and compare them to a large alignable bicelle, a small nanodisc, and a lipid bilayer. Properties such as lipid packing and properties related to embedding both an α-helical peptide and a transmembrane protein are investigated. The small bicelles are found to be very dynamic and mainly assume a prolate shape substantiating that small bicelles cannot be regarded as well-defined disclike structures. However, addition of a peptide results in an increased tendency to form disc-shaped bicelles. The small bicelles and the nanodiscs show increased peptide solvation and difference in peptide orientation compared to embedding in a bilayer. The large bicelle imitated a bilayer well with respect to both curvature and peptide solvation, although peripheral binding of short tailed lipids to the embedded proteins is observed, which could hinder ligand binding or multimer formation.

Regulation of the Ca(2+)-ATPase by cholesterol: a specific or non-specific effect?

Like other integral membrane proteins, the activity of the Sarco/Endoplasmic Reticulum Ca(2+)-ATPase (SERCA) is regulated by the membrane environment. Cholesterol is present in the endoplasmic reticulum membrane at low levels, and it has the potential to affect SERCA activity both through direct, specific interaction with the protein or through indirect interaction through changes of the overall membrane properties. There are experimental data arguing for both modes of action for a cholesterol-mediated regulation of SERCA. In the current study, coarse-grained molecular dynamics simulations are used to address how a mixed lipid-cholesterol membrane interacts with SERCA. Candidates for direct regulatory sites with specific cholesterol binding modes are extracted from the simulations. The binding pocket for thapsigargin, a nanomolar inhibitor of SERCA, has been suggested as a cholesterol binding site. However, the thapsigargin binding pocket displayed very little cholesterol occupation in the simulations. Neither did atomistic simulations of cholesterol in the thapsigargin binding pocket support any specific interaction. The current study points to a non-specific effect of cholesterol on SERCA activity, and offers an alternative interpretation of the experimental results used to argue for a specific effect.

The Dalton quantum chemistry program system

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Ion pathways in the sarcoplasmic reticulum Ca2+-ATPase

The sarco/endoplasmic reticulum Ca(2+)-ATPase (SERCA) is a transmembrane ion transporter belonging to the P(II)-type ATPase family. It performs the vital task of re-sequestering cytoplasmic Ca(2+) to the sarco/endoplasmic reticulum store, thereby also terminating Ca(2+)-induced signaling such as in muscle contraction. This minireview focuses on the transport pathways of Ca(2+) and H(+) ions across the lipid bilayer through SERCA. The ion-binding sites of SERCA are accessible from either the cytoplasm or the sarco/endoplasmic reticulum lumen, and the Ca(2+) entry and exit channels are both formed mainly by rearrangements of four N-terminal transmembrane α-helices. Recent improvements in the resolution of the crystal structures of rabbit SERCA1a have revealed a hydrated pathway in the C-terminal transmembrane region leading from the ion-binding sites to the cytosol. A comparison of different SERCA conformations reveals that this C-terminal pathway is exclusive to Ca(2+)-free E2 states, suggesting that it may play a functional role in proton release from the ion-binding sites. This is in agreement with molecular dynamics simulations and mutational studies and is in striking analogy to a similar pathway recently described for the related sodium pump. We therefore suggest a model for the ion exchange mechanism in P(II)-ATPases including not one, but two cytoplasmic pathways working in concert.

Flexible P-type ATPases interacting with the membrane

Cation pumps and lipid flippases of the P-type ATPase family maintain electrochemical gradients and asymmetric lipid distributions across membranes, and offer significant insight of protein:membrane interactions. The sarcoplasmic reticulum Ca(2+)-ATPase features flexible and adaptive interactions with the surrounding membrane, while the Na(+),K(+)-ATPase complex is modulated by membrane components and a role for the γ-subunit as a stabilizer of a specific lipid interaction with the α-subunit has been proposed. The first crystal structure of a heavy-metal transporting ATPase shows a markedly amphipathic helix at the cytoplasmic membrane surface, highlighting this structure as a general motif of all P-type ATPases although with specialization to different membranes. Residues of central importance for the lipid flippase activity of the P4-type ATPase subfamily have been pinpointed by mutational studies, but the transport pathway and mechanism remain unknown.

Tracing cytoplasmic Ca(2+) ion and water access points in the Ca(2+)-ATPase

Sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA) transports two Ca(2+) ions across the membrane of the sarco(endo)plasmic reticulum against the concentration gradient, harvesting the required energy by hydrolyzing one ATP molecule during each transport cycle. Although SERCA is one of the best structurally characterized membrane transporters, it is still largely unknown how the transported Ca(2+) ions reach their transmembrane binding sites in SERCA from the cytoplasmic side. Here, we performed extended all-atom molecular dynamics simulations of SERCA. The calculated electrostatic potential of the protein reveals a putative mechanism by which cations may be attracted to and bind to the Ca(2+)-free state of the transporter. Additional molecular dynamics simulations performed on a Ca(2+)-bound state of SERCA reveal a water-filled pathway that may be used by the Ca(2+) ions to reach their buried binding sites from the cytoplasm. Finally, several residues that are involved in attracting and guiding the cations toward the possible entry channel are identified. The results point to a single Ca(2+) entry site close to the kinked part of the first transmembrane helix, in a region loaded with negatively charged residues. From this point, a water pathway outlines a putative Ca(2+) translocation pathway toward the transmembrane ion-binding sites.

Protonation states of important acidic residues in the central Ca²⁺ ion binding sites of the Ca²⁺-ATPase: a molecular modeling study

The P-type ATPases are responsible for the transport of cations across cell membranes. The sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) transports two Ca²⁺ ions from the cytoplasm to the lumen of the sarco(endo)plasmic reticulum and countertransports two or three protons per catalytic cycle. Two binding sites for Ca²⁺ ions have been located via protein crystallography, including four acidic amino acid residues that are essential to the ion coordination. In this study, we present molecular dynamics (MD) simulations examining the protonation states of these amino acid residues in a Ca²⁺-free conformation of SERCA. Such knowledge will be important for an improved understanding of atomistic details of the transport mechanism of protons and Ca²⁺ ions. Eight combinations of the protonation of four central acidic residues, Glu309, Glu771, Asp800, and Glu908, are tested from 10 ns MD simulations with respect to protein stability and ability to maintain a structure similar to the crystal structure. The trajectories for the most prospective combinations of protonation states were elongated to 50 ns and subjected to more detailed analysis, including prediction of pK(a) values of the four acidic residues over the trajectories. From the simulations we find that the combination leaving only Asp800 as charged is most likely. The results are compared to available experimental data and explain the observed destabilization upon full deprotonation, resulting in the entry of cytoplasmic K⁺ ions into the Ca²⁺ binding sites during the simulation in which Ca²⁺ ions are absent. Furthermore, a hypothesis for the exchange of protons from the central binding cavity is proposed.

Residue-specific information about the dynamics of antimicrobial peptides from (1)H-(15)N and (2)H solid-state NMR spectroscopy

We present a new method to obtain information about the conformational dynamics of membrane-proteins using solid-state NMR experiments of oriented samples. By measuring the orientation-dependent (1)H-(15)N dipole-dipole coupling, (15)N anisotropic chemical shift, and (2)H quadrupole coupling parameters for a single residue, it is possible to obtain information about the local dynamics of each residue in the protein. This may be interpreted on an individual basis or through models extended to study conformational motion of membrane-protein segments. The method is demonstrated for the antimicrobial peptaibol alamethicin for which combined analysis of anisotropic interactions for the Aib(8) residue provides detailed information about helix-tilt angle, wobbling, and oscillatory rotation around the helix axis in the membrane bound state. This information is in very good agreement with coarse-grained MD simulations of the peptide in lipid bilayers.

Resolution enhancement in solid-state NMR of oriented membrane proteins by anisotropic differential linebroadening

We demonstrate that a significant improvement in the spectral resolution may be achieved in solid-state NMR experiments of proteins in inhomogeneously disordered oriented lipid bilayers. Using 1H homonuclear decoupling instead of standard 1H heteronuclear decoupling, the 15N line widths may be reduced by up to seven times for such samples. For large oriented membrane proteins, such resolution enhancements may be crucial for assignment and structural interpretation.

Linear-scaling implementation of molecular electronic self-consistent field theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.

Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field theories for the calculation of frequency-dependent molecular response properties and excitation energies is presented, based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis, avoiding the use of canonical orbitals. The response equations are solved iteratively, by an atomic-orbital subspace method equivalent to that of molecular-orbital theory. Important features of the subspace method are the use of paired trial vectors (to preserve the algebraic structure of the response equations), a nondiagonal preconditioner (for rapid convergence), and the generation of good initial guesses (for robust solution). As a result, the performance of the iterative method is the same as in canonical molecular-orbital theory, with five to ten iterations needed for convergence. As in traditional direct Hartree-Fock and Kohn-Sham theories, the calculations are dominated by the construction of the effective Fock/Kohn-Sham matrix, once in each iteration. Linear complexity is achieved by using sparse-matrix algebra, as illustrated in calculations of excitation energies and frequency-dependent polarizabilities of polyalanine peptides containing up to 1400 atoms.

The trust-region self-consistent field method in Kohn–Sham density-functional theory

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.

The trust-region self-consistent field method: Towards a black-box optimization in Hartree–Fock and Kohn–Sham theories

The trust-region self-consistent field (TRSCF) method is presented for optimizing the total energy E(SCF) of Hartree-Fock theory and Kohn-Sham density-functional theory. In the TRSCF method, both the Fock/Kohn-Sham matrix diagonalization step to obtain a new density matrix and the step to determine the optimal density matrix in the subspace of the density matrices of the preceding diagonalization steps have been improved. The improvements follow from the recognition that local models to E(SCF) may be introduced by carrying out a Taylor expansion of the energy about the current density matrix. At the point of expansion, the local models have the same gradient as E(SCF) but only an approximate Hessian. The local models are therefore valid only in a restricted region-the trust region-and steps can only be taken with confidence within this region. By restricting the steps of the TRSCF model to be inside the trust region, a monotonic and significant reduction of the total energy is ensured in each iteration of the TRSCF method. Examples are given where the TRSCF method converges monotonically and smoothly, but where the standard DIIS method diverges.