Exploiting Coordinate Scaling Relations To Accelerate Exact Exchange Calculations

Exact exchange is an important constituent in many state-of-the-art approximations to the exchange-correlation (xc) functional of Kohn–Sham DFT. However, its evaluation can be computationally intensive, which can be particularly prohibitive in DFT-based molecular dynamics (MD) simulations, often restricted to semilocal functionals. We derive a scheme based on the formal coordinate scaling properties of the exact xc functional that allows for a substantial reduction of the cost of the evaluation of both the exact exchange energy and potential. We show that within a plane-wave/pseudopotential framework, excellent accuracy is retained, while speed ups from up to ∼6 can be reached. The coordinate scaling thus accelerates hybrid-functional-based first-principles MD simulations by nearly one order of magnitude

Influence on speed and fuel consumption of changed speed limits (110 to 90 km/h)

G proteins are part of the G-protein-coupled receptor (GPCR) signal transduction cascade in which they transfer a signal from the membrane-embedded GPCR to other proteins in the cell. In the case of the inhibitory G-protein heterotrimer, permanent N-terminal myristoylation can transiently localize the Gα_<i>i</i> subunit at the membrane as well as crucially influence Gα_<i>i</i>’s function in the GTP-bound conformation. The attachment of lipids to proteins is known to be essential for membrane trafficking; however, our results suggest that lipidation is also important for protein–protein interactions during signal transduction. Here we investigate the effect of myristoylation on the structure and dynamics of soluble Gα_<i>i</i>1 and its possible implication for signal transduction. A 2 μs classical molecular dynamics simulation of a myristoylated Gα_<i>i</i>1–GTP complex suggests that the myristoyl-induced conformational changes of the switch II and alpha helical domains create new possibilities for protein–protein interactions and emphasize the importance of permanent lipid attachment for the conformation and functional tunability of signaling proteins

Rearrangements of AC5’s active site differ between the Gα_i1^myr:AC5 complex and free AC5 system.

<p>(A) Graph of the distances between the Cα atom of Gly518 (red dot in image <i>B</i>) and the Cα atoms of Asn1202 (green dot in image <i>B</i>) and Asn1205 (yellow dot in image <i>B</i>). The respective distances in the Gα_s:AC(ATPαS) X-ray structure (PDB code 1CJK) of Gly518-Asn1202 (Gly439-Asn1022 in PDB 1CJK) and Gly518-Asn1205 (Gly439-Asn1025 in PDB 1CJK) are 11 Å and 8.5 Å. (B) Detail of AC’s active site of the free AC5 system (purple), the Gα_i1^myr:AC5 complex (cyan) and the Gα_s:AC(ATPαS) X-ray structure (PDB code 1CJK) in orange. The location of the residues used in image <i>A</i> are assigned according to the Gα_i1^myr:AC5 structure. In the active site the location of the Mg²⁺ ion is shown for all three structures as well as the position of ATPαS from the fully activated AC structure (PDB code 1CJK).</p

Differences and similarities of Gα:AC complexes and activated Gα subunit structures.

<p>(A) Structural alignment of GTP-analog-bound Gα_i1 (PDB code 1AZT) in cyan and GTP-analog-bound Gα_s (PDB code 1AS0) in grey. (B) View of the Gα_s:AC complex (PDB code 1AZS) from the cytosolic side. The Gα_s subunit is depicted in grey, while the C1 domain is represented in blue and the C2 domain is shown in red. The location of the Gα_i1 structure is described by the cyan star. (C) View of the docked Gα_i1^myr:AC5 complex from the cytosolic side. The Gα_i1^myr subunit is depicted in cyan with the myristoyl moiety shown in yellow and the GTP molecule in orange. The C1 domain is represented in blue and the C2 domain is shown in red. The location of the Gα_s structure is described by the grey star.</p

Conformational changes around the Gα_s binding site on C2 show distinct events of closure in Gα_i1^myr:AC5.

<p>(A) Graph of the distance between the α2 and the α3 helix of C2 including Cα atoms of Asn1091 and Phe1171, of free AC5 and Gα_i1^myr:AC5. A detailed representation of the Gα_s binding site is shown in image <i>C</i>. (B) the Gα_s binding site of the free AC5 system (purple), the Gα_i1^myr:AC5 complex (cyan) and PDB structure 1AZS (yellow) in which the Gα_s subunit is also shown. (C) Detail of the Gα_s binding site of Gα_i1^myr:AC5 in which residues that are involved in the closing of the binding site are shown.</p

Change of location of C2’s β7-β8 loop occurs in both Gα_i1^myr:AC5 and free AC5 systems and a significant difference is observed between RMSD values of free AC5 and Gα_i1^myr:AC5 for the C2 domain.

<p>(A) Graph of the distances between the Cα atom of Gly1246 (green dot in image <i>B</i>) and the Cα atoms of Ala483 (red dot in image <i>B</i>) and Asn630 (orange dot in image <i>B</i>). (B) β7-β8 loop’s relocation in the free AC5 system (purple), the Gα_i1^myr:AC5 complex (cyan) and PDB structure 1AZS (yellow). The location of the residues used in image <i>A</i> are assigned according to the Gα_i1^myr:AC5 structure. (C) Root-mean-square deviations of the backbone of the C1 and the C2 domain. In the RMSD calculation the residues between 463 to 644 were taken into account for the C1 domain and the residues between 1065 to 1135 and 1145 to 1257 were used for the C2 domain.</p

Graphical representation of proposed AC5 inhibition mechanism by Gα_i1^myr with the upper row showing the cytosolic side of AC5 and the bottom row depicting AC5 from the membrane side.

<p>The myristoyl moiety bound to Gα_i1 is shown via a purple line on the subunit. The change that takes place in step (1) compared to the initially stimulated AC5 conformation, is the relocation of the C2 β7-β8 loop away from its active position. This alteration takes place near AC5’s active site (red star), which is also affected by this event. Conformational change (2) involves the loss of interaction between C1’s α2 and the C2 β4-β5 loop, weakening the active site. The final rearrangement (3) includes the closer packing of C2’s Gα_s interaction site, which appears to result in a less favourable C2 conformation for the interaction with Gα_s.</p

Conformational changes on membrane side of AC5 show C2’s loop dissociation, which only occurs in Gα_i1^myr:AC5.

<p>(A) Graph of the distances between the α2 helix of C1 and the β4-β5 loop of C2 in the Gα_i1^myr:AC5 structure (see image <i>B</i>). (B) AC5’s membrane side of the free AC5 system (purple), the Gα_i1^myr:AC5 complex (cyan) and PDB structure 1AZS (yellow) in which the α2 helix of C1 and the β4-β5 loop of C2 are highlighted. In the Gα_i1^myr:AC5 complex the location of the residues used in the angle calculation of image <i>D</i> are represented by a green (Ala488), pink (Leu495) and orange (Phe499) dot. (C) Graph of the distances between the α2 helix of C1 and the β4-β5 loop in the AC5 system (see image <i>B</i>). (D) Angle between three helical turns, including Cα atoms of Ala488, Leu495 and Phe499, in which the kinking of the α2 helix of C1 takes place (see image <i>B</i>).</p

A Versatile Multiple Time Step Scheme for Efficient <i>ab Initio</i> Molecular Dynamics Simulations

We present here our implementation of a time-reversible, multiple time step (MTS) method for full QM and hybrid QM/MM Born–Oppenheimer molecular dynamics simulations. The method relies on a fully flexible combination of electronic structure methods, from density functional theory to wave function-based quantum chemistry methods, to evaluate the nuclear forces in the reference and in the correction steps. The possibility of combining different electronic structure methods is based on the observation that exchange and correlation terms only contribute to low frequency modes of nuclear forces. We show how a pair of low/high level electronic structure methods that individually would lead to very different system properties can be efficiently combined in the reference and correction steps of this MTS scheme. The current MTS implementation makes it possible to perform highly accurate <i>ab initio</i> molecular dynamics simulations at reduced computational cost. Stable and accurate trajectories were obtained with time steps of several femtoseconds, similar to and even exceeding the ones usually adopted in classical molecular dynamics, in particular when using a generalized Langevin stochastic thermostat. Compared to the standard Velocity Verlet integration, the present MTS scheme allows for a 5- to 6-fold overall speedup, at an unaltered level of accuracy

Role of Environment for Catalysis of the DNA Repair Enzyme MutY

Control of the N-glycosylase reaction by the DNA repair enzyme, MutY, entails the organization of solvent molecules. Classical molecular dynamics and QM/MM simulations were used to investigate the solvent and environment effects contributing to catalysis. Our findings suggest that the entire reaction is an energetically neutral process, in which the first step is rate determining, requiring protonation of adenine (N₇) to initiate cleavage, and the second step is strongly exothermic, involving hydrolysis of an oxacarbenium ion intermediate. Although water molecules are catalytically active in both steps, the first step requires an entirely different level of solvent organization compared to the second. Needed to secure protonation at N₇, a long-term solvation pattern is established which facilitates the involvement of three out of the five structured water molecules in the active site. This persistent arrangement coordinates the catalytically active water molecules into prime positions to assist the proton transfer: (i) a water molecule frequently bridges the catalytic residues and (ii) the bridging water molecule is assisted by 1–2 other ‘supporting’ water molecules. To maintain this configuration, MutY, surprisingly, uses hydrophobic residues in combination with hydrophilic residues to tune the microenvironment into a ‘water trap’. Hydrophilic residues prolong solvent residence times by maintaining hydrogen-bonding networks, whereas the hydrophobic residues constrain the positioning of the catalytic water molecules that assist the proton-transfer event. In this way, the enzyme uses both entropic and enthalpic considerations to guide the water-assisted reaction