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.

Lipid dynamics studied by calculation of 31P solid-state NMR spectra using ensembles from molecular dynamics simulations.

We present a method to calculate (31)P solid-state NMR spectra based on the dynamic input from extended molecular dynamics (MD) simulations. The dynamic information confered by MD simulations is much more comprehensive than the information provided by traditional NMR dynamics models based on, for example, order parameters. Therefore, valuable insight into the dynamics of biomolecules may be achieved by the present method. We have applied this method to study the dynamics of lipid bilayers containing the antimicrobial peptide alamethicin, and we show that the calculated (31)P spectra obtained with input from MD simulations are in agreement with experiments under a large range of different sample conditions, including vesicles and oriented samples with and without peptides. We find that the changes in the (31)P spectra upon addition of peptide stem from lipids with reduced diffusion due to peptide-lipid interactions.

Conformational flexibility of the leucine binding protein examined by protein domain coarse-grained molecular dynamics.

Periplasmic binding proteins are the initial receptors for the transport of various substrates over the inner membrane of gram-negative bacteria. The binding proteins are composed of two domains, and the substrate is entrapped between these domains. For several of the binding proteins it has been established that a closed-up conformation exists even without substrate present, suggesting a highly flexible apo-structure which would compete with the ligand-bound protein for the transporter interaction. For the leucine binding protein (LBP), structures of both open and closed conformations are known, but no closed-up structure without substrate has been reported. Here we present molecular dynamics simulations exploring the conformational flexibility of LBP. Coarse grained models based on the MARTINI force field are used to access the microsecond timescale. We show that a standard MARTINI model cannot maintain the structural stability of the protein whereas the ELNEDIN extension to MARTINI enables simulations showing a stable protein structure and nanosecond dynamics comparable to atomistic simulations, but does not allow the simulation of conformational flexibility. A modification to the MARTINI-ELNEDIN setup, referred to as domELNEDIN, is therefore presented. The domELNEDIN setup allows the protein domains to move independently and thus allows for the simulation of conformational changes. Microsecond domELNEDIN simulations starting from either the open or the closed conformations consistently show that also for LBP, the apo-structure is flexible and can exist in a closed form.

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.

Modeling the Self-Assembly and Stability of DHPC Micelles Using Atomic Resolution and Coarse Grained MD Simulations.

Membrane mimics such as micelles and bicelles are widely used in experiments involving membrane proteins. With the aim of being able to carry out molecular dynamics simulations in environments comparable to experimental conditions, we set out to test the ability of both coarse grained and atomistic resolution force fields to model the experimentally observed behavior of the lipid 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC), which is a widely used lipid for biophysical characterization of membrane proteins. It becomes clear from our results that a satisfactory modeling of DHPC aggregates in solution poses different demands to the force field than do the modeling of bilayers. First, the representation of the short tailed lipid DHPC in the coarse grained force field MARTINI is assessed with the intend of successfully self-assemble micelles with structural characteristics comparable to experimental data. Then, the use of the recently presented polarizable water model in MARTINI is shown to be essential for producing micelles that are structurally in accordance with experiments. For the atomistic representations of DHPC micelles in solution the GROMOS96 force field with lipid parameters by A. Kukol fails to maintain stable micelles, whereas the most recent CHARMM36 lipid parameters and GROMOS96 with the so-called Berger lipid parameters both succeed in this regard.

Protonation states of important acidic residues in the central Ca²âº ion binding sites of the Ca²âº-ATPase: a molecular modeling study.

The P-type ATPases are responsible for the transport of cations across cell membranes. The sarco(endo)plasmic reticulum Ca²âº-ATPase (SERCA) transports two Ca²âº 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 Ca²âº 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 Ca²âº-free conformation of SERCA. Such knowledge will be important for an improved understanding of atomistic details of the transport mechanism of protons and Ca²âº 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 Ca²âº binding sites during the simulation in which Ca²âº ions are absent. Furthermore, a hypothesis for the exchange of protons from the central binding cavity is proposed.

Mutual adaptation of a membrane protein and its lipid bilayer during conformational changes.

The structural elucidation of membrane proteins continues to gather pace, but we know little about their molecular interactions with the lipid environment or how they interact with the surrounding bilayer. Here, with the aid of low-resolution X-ray crystallography, we present direct structural information on membrane interfaces as delineated by lipid phosphate groups surrounding the sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA) in its phosphorylated and dephosphorylated Ca(2+)-free forms. The protein-lipid interactions are further analysed using molecular dynamics simulations. We find that SERCA adapts to membranes of different hydrophobic thicknesses by inducing local deformations in the lipid bilayers and by undergoing small rearrangements of the amino-acid side chains and helix tilts. These mutually adaptive interactions allow smooth transitions through large conformational changes associated with the transport cycle of SERCA, a strategy that may be of general nature for many membrane proteins.

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.

Incorporation of antimicrobial peptides into membranes: a combined liquid-state NMR and molecular dynamics study of alamethicin in DMPC/DHPC bicelles.

Detailed insight into the interplay between antimicrobial peptides and biological membranes is fundamental to our understanding of the mechanism of bacterial ion channels and the action of these in biological host-defense systems. To explore this interplay, we have studied the incorporation, membrane-bound structure, and conformation of the antimicrobial peptide alamethicin in lipid bilayers using a combination of 1H liquid-state NMR spectroscopy and molecular dynamics (MD) simulations. On the basis of experimental NMR data, we evaluate simple in-plane and transmembrane incorporation models as well as pore formation for alamethicin in DMPC/DHPC (1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine/1,2-dihexanoyl-sn-glycero-3-phosphatidylcholine) bicelles. Peptide-lipid nuclear Overhauser effect (NOE) and paramagnetic relaxation enhancement (PRE) data support a transmembrane configuration of the peptide in the bilayers, but they also reveal that the system cannot be described by a single simple conformational model because there is a very high degree of dynamics and heterogeneity in the three-component system. To explore the origin of this heterogeneity and dynamics, we have compared the NOE and PRE data with MD simulations of an ensemble of alamethicin peptides in a DMPC bilayer. From all-atom MD simulations, the contacts between peptide, lipid, and water protons are quantified over a time interval up to 95 ns. The MD simulations provide a statistical base that reflects our NMR data and even can explain some initially surprising NMR results concerning specific interactions between alamethicin and the lipids.

The augmented Roothaan-Hall method for optimizing Hartree-Fock and Kohn-Sham density matrices.

We present a novel method for the optimization of Hartree-Fock and Kohn-Sham energies that does not suffer from the flaws of the conventionally used two-step Roothaan-Hall (RH) with direct inversion in iterative subspace (DIIS) acceleration scheme, improving the reliability of the optimization while reducing its cost. The key to its success is the replacement of the two separate steps of each RH/DIIS iteration by a single concerted step that fully exploits the Hessian information available from the previous iterations. It is a trust-region based method and therefore by design converges to an energy minimum. Numerical examples are given to illustrate that the algorithm is robust and cost efficient, converging smoothly to a minimum also in cases when the RH/DIIS algorithm fails to converge or when it converges to a saddle point rather than to a minimum. The algorithm is based on matrix multiplications and becomes linearly scaling for sufficiently large systems.

Peptide aggregation and pore formation in a lipid bilayer: a combined coarse-grained and all atom molecular dynamics study.

We present a simulation study where different resolutions, namely coarse-grained (CG) and all-atom (AA) molecular dynamics simulations, are used sequentially to combine the long timescale reachable by CG simulations with the high resolution of AA simulations, to describe the complete processes of peptide aggregation and pore formation by alamethicin peptides in a hydrated lipid bilayer. In the 1-micros CG simulations the peptides spontaneously aggregate in the lipid bilayer and exhibit occasional transitions between the membrane-spanning and the surface-bound configurations. One of the CG systems at t = 1 micros is reverted to an AA representation and subjected to AA simulation for 50 ns, during which water molecules penetrate the lipid bilayer through interactions with the peptide aggregates, and the membrane starts leaking water. During the AA simulation significant deviations from the alpha-helical structure of the peptides are observed, however, the size and arrangement of the clusters are not affected within the studied time frame. Solid-state NMR experiments designed to match closely the setup used in the molecular dynamics simulations provide strong support for our finding that alamethicin peptides adopt a diverse set of configurations in a lipid bilayer, which is in sharp contrast to the prevailing view of alamethicin oligomers formed by perfectly aligned helical alamethicin peptides in a lipid bilayer.

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 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.

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.

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.

Stability, metastability, and unstability of three-electron-bonded radical anions. A model ab initio theoretical study.

The stability of O therefore O, N therefore N, S therefore S, P therefore P, and Si therefore Si three-electron bonds in anionic radicals isoelectronic to dihalogen radical anions is studied by means of ab initio calculations on model systems. The difficulty of generating the dissociation energy profiles of such anions and their rearrangement to neutral species is solved by a practical method which consists of calculating the neutral and anionic energy profiles separately and shifting the curves with respect to each other to match the experimental energy gap between the asymptotes. Here the neutral and anionic reaction profiles are calculated at the CASPT2 and MP2 levels, respectively. The calculations predict that the O therefore O bond is likely to be observed in anions of the type [RO therefore OR](*-), where R is any alkyl substituent or carbon chain. The anion Si(2)H(6)(*-) is found to be a metastable species, with a fair barrier to electron detachment. The barrier is much smaller for N(2)H(4)(*-) and P(2)H(4)(*-), thus precluding experimental observation. However, these species can be stabilized by electron-attractor substituents, the effect of which can be quantitatively estimated by means of the parent anion's diagrams and some fast complementary calculations. An example is given with the [CF(3)HN therefore NHCF(3)](*-) anionic complex.