Lea Thøgersen

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.

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.

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.

Ion Pathways in the Sarcoplasmic Reticulum Ca2+-ATPase

The sarco/endoplasmic reticulum Ca2+-ATPase (SERCA) is a transmembrane ion transporter belonging to the PII-type ATPase family. It performs the vital task of re-sequestering cytoplasmic Ca2+ to the sarco/endoplasmic reticulum store, thereby also terminating Ca2+-induced signaling such as in muscle contraction. This minireview focuses on the transport pathways of Ca2+ 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 Ca2+ 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 Ca2+-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 PII-ATPases including not one, but two cytoplasmic pathways working in concert.

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.

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.

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 from1H-15N and2H 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.

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.