DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB)

QM/MM analysis suggests that Alkaline Phosphatase (AP) and nucleotide pyrophosphatase/phosphodiesterase slightly tighten the transition state for phosphate diester hydrolysis relative to solution: implication for catalytic promiscuity in the AP superfamily

Several members of the Alkaline Phosphatase (AP) superfamily exhibit a high level of catalytic proffciency and promiscuity in structurally similar active sites. A thorough characterization of the nature of transition state for different substrates in these enzymes is crucial for understanding the molecular mechanisms that govern those remarkable catalytic properties. In this work, we study the hydrolysis of a phosphate diester, MpNPP(-), in solution, two experimentally well-characterized variants of AP (R166S AP, R166S/E322Y AP) and wild type Nucleotide pyrophosphatase/phosphodiesterase (NPP) by QM/MM calculations in which the QM method is an approximate density functional theory previously parametrized for phosphate hydrolysis (SCC-DFTBPR). The general agreements found between these calculations and available experimental data for both solution and enzymes support the use of SCC-DFTBPR/MM for a semiquantitative analysis of the catalytic mechanism and nature of transition state in AP and NPP. Although phosphate diesters are cognate substrates for NPP but promiscuous substrates for AP, the calculations suggest that their hydrolysis reactions catalyzed by AP and NPP feature similar synchronous transition states that are slightly tighter in nature compared to that in solution, due in part to the geometry of the bimetallic zinc motif. Therefore, this study provides the first direct computational support to the hypothesis that enzymes in the AP superfamily catalyze cognate and promiscuous substrates via similar transition states to those in solution. Our calculations do not support the finding of recent QM/MM studies by López-Canut and co-workers, who suggested that the same diester substrate goes through a much looser transition state in NPP/AP than in solution, a result likely biased by the large structural distortion of the bimetallic zinc site in their simulations. Finally, our calculations for different phosphate diester orientations and phosphorothioate diesters highlight that the interpretation of thio-substitution experiments is not always straightforward.

Insights into the mechanistic dichotomy of the protein farnesyltransferase peptide substrates CVIM and CVLS

Protein farnesyltransferase (FTase) catalyzes farnesylation of a variety of peptide substrates. (3)H α-secondary kinetic isotope effect (α-SKIE) measurements of two peptide substrates, CVIM and CVLS, are significantly different and have been proposed to reflect a rate-limiting S(N)2-like transition state with dissociative characteristics for CVIM, while, due to the absence of an isotope effect, CVLS was proposed to have a rate-limiting peptide conformational change. Potential of mean force quantum mechanical/molecular mechanical studies coupled with umbrella sampling techniques were performed to further probe this mechanistic dichotomy. We observe the experimentally proposed transition state (TS) for CVIM but find that CVLS has a symmetric S(N)2 TS, which is also consistent with the absence of a (3)H α-SKIE. These calculations demonstrate facile substrate-dependent alterations in the transition state structure catalyzed by FTase.

Glu-286 rotation and water wire reorientation are unlikely the gating elements for proton pumping in cytochrome C oxidase

One of the key unresolved issues regarding proton pumping in cytochrome c oxidase (CcO) is the identity of the gating element that prevents the backflow of protons. In this study, we analyze two popular proposals for this element: isomerization of the key branching residue (Glu-286) and (re)orientation of water molecules in the hydrophobic cavity. Using a multifaceted set of computational analyses that involve CcO embedded in either an implicit or explicit treatment of lipid membrane, we show that neither Glu-286 nor active-site water likely constitutes the gating element. Detailed energetic and structural analyses of the simulation results indicate that the gating-relevant properties of these structural motifs observed in previous work are likely a result of the simplified computational models employed in those studies.

Proton storage site in bacteriorhodopsin: new insights from quantum mechanics/molecular mechanics simulations of microscopic pK(a) and infrared spectra

Identifying the group that acts as the proton storage/loading site is a challenging but important problem for understanding the mechanism of proton pumping in biomolecular proton pumps, such as bacteriorhodopsin (bR) and cytochrome c oxidase. Recent experimental studies of bR propelled the idea that the proton storage/release group (PRG) in bR is not an amino acid but a water cluster embedded in the protein. We argue that this idea is at odds with our knowledge of protein electrostatics, since invoking the water cluster as the PRG would require the protein to raise the pK(a) of a hydronium by almost 11 pK(a) units, which is difficult considering known cases of pK(a) shifts in proteins. Our recent quantum mechanics/molecular mechanics (QM/MM) simulations suggested an alternative "intermolecular proton bond" model in which the stored proton is shared between two conserved Glu residues (194 and 204). Here we show that this model leads to microscopic pK(a) values consistent with available experimental data and the functional requirement of a PRG. Extensive QM/MM simulations also show that, independent of a number of technical issues, such as the influence of QM region size, starting X-ray structure, and nuclear quantum effects, the "intermolecular proton bond" model is qualitatively consistent with available spectroscopic data. Potential of mean force calculations show explicitly that the stored proton strongly prefers the pair of Glu residues over the water cluster. The results and analyses help highlight the importance of considering protein electrostatics and provide arguments for why the "intermolecular proton bond" model is likely applicable to the PRG in biomolecular proton pumps in general.

Lagrangian formulation with dissipation of Born-Oppenheimer molecular dynamics using the density-functional tight-binding method

An important element determining the time requirements of Born-Oppenheimer molecular dynamics (BOMD) is the convergence rate of the self-consistent solution of Roothaan equations (SCF). We show here that improved convergence and dynamics stability can be achieved by use of a Lagrangian formalism of BOMD with dissipation (DXL-BOMD). In the DXL-BOMD algorithm, an auxiliary electronic variable (e.g., the electron density or Fock matrix) is propagated and a dissipative force is added in the propagation to maintain the stability of the dynamics. Implementation of the approach in the self-consistent charge density functional tight-binding method makes possible simulations that are several hundred picoseconds in lengths, in contrast to earlier DFT-based BOMD calculations, which have been limited to tens of picoseconds or less. The increase in the simulation time results in a more meaningful evaluation of the DXL-BOMD method. A comparison is made of the number of iterations (and time) required for convergence of the SCF with DXL-BOMD and a standard method (starting with a zero charge guess for all atoms at each step), which gives accurate propagation with reasonable SCF convergence criteria. From tests using NVE simulations of C(2)F(4) and 20 neutral amino acid molecules in the gas phase, it is found that DXL-BOMD can improve SCF convergence by up to a factor of two over the standard method. Corresponding results are obtained in simulations of 32 water molecules in a periodic box. Linear response theory is used to analyze the relationship between the energy drift and the correlation of geometry propagation errors.

Density-functional expansion methods: generalization of the auxiliary basis

The formulation of density-functional expansion methods is extended to treat the second and higher-order terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the self-consistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis.

Application of the SCC-DFTB method to neutral and protonated water clusters and bulk water

The self-consistent charge density functional tight-binding (SCC-DFTB) method has been actively employed to study proton-transfer processes in biological systems. Recent studies in the literature employing SCC-DFTB reported that the method favors the Zundel form of the hydrated proton over the Eigen form, both in gas-phase water clusters and in bulk water, in disagreement with both higher-level calculations and experimental data. In this work, we explore the performance of SCC-DFTB for protonated gas-phase water clusters and bulk water (the latter both with and without an excess proton) with a modified O-H repulsive potential reported in our earlier work and with on-site third-order expansion of the DFT energy. Our results show that, with the proper set of published parameters, SCC-DFTB does correctly favor the Eigen form of the hydrated proton as compared to the Zundel form, both in gas-phase clusters and in the bulk; the amphiphilic character of the hydrated proton discussed in the literature has also been observed. The analyses do, however, bring forth remaining limitations in terms of the solvation structure around the hydrated proton as well as the structure of bulk water, which can guide future improvements of the method.