Efficient Conformational Search Based on Structural Dissimilarity Sampling: Applications for Reproducing Structural Transitions of Proteins

Structural Dissimilarity Sampling (SDS) is proposed as an efficient conformational search method to promote structural transitions essential for the biological functions of proteins. In SDS, initial structures are selected based on structural dissimilarity, and conformational resampling is repeated. Conformational resampling is performed as follows: (I) arrangement of initial structures for a diverse distribution at the edge of a conformational subspace and (II) promotion of the structural transitions with multiple short-time molecular dynamics (MD) simulations restarting from the diversely distributed initial structures. Cycles of (I) and (II) are repeated to intensively promote structural transitions because conformational resampling from the initial structures would quickly expand conformational distributions toward unvisited conformational subspaces. As a demonstration, SDS was first applied to maltodextrin binding protein (MBP) in explicit water to reproduce structural transitions between the open and closed states of MBP. Structural transitions of MBP were successfully reproduced with SDS in nanosecond-order simulation times. Starting from both the open and closed forms, SDS successfully reproduced the structural transitions within 25 cycles (a total of 250 ns of simulation time). For reference, a conventional long-time (500 ns) MD simulation under <i>NPT</i> (300 K and 1 bar) starting from the open form failed to reproduce the structural transition. In addition to the open–closed motions of MBP, SDS was applied to folding processes of the fast-folding proteins (chignolin, Trp-cage, and villin) and successfully sampled their native states. To confirm how the selections of initial structures affected conformational sampling efficiency, numbers of base sets for characterizing structural dissimilarity of initial structures were addressed in distinct trials of SDS. The parameter searches showed that the conformational sampling efficiency was relatively insensitive with respect to the numbers of base sets, indicating the robustness of SDS for actual applications

Temperature-Shuffled Structural Dissimilarity Sampling Based on a Root-Mean-Square Deviation

Structural dissimilarity sampling (SDS) has been proposed as an enhanced conformational sampling method for finding neighboring metastable states of a given reactant or generating transition pathways starting from the reactant. SDS repeats a cycle of two steps: (1) selections of initial structures based on structural dissimilarities by referring to a measure and (2) conformational resampling by restarting short-time molecular dynamics (MD) simulations from the initial structures. In the present study, the measure was defined as the root-mean-square deviation (RMSD) among the resampled snapshots to characterize their structural dissimilarities. Additionally, the temperatures in restarting the short-time MD simulations were randomly shuffled at the beginning of each cycle to further promote the conformational transitions. We call this approach temperature-shuffled SDS (TSF-SDS). As a demonstration, TSF-SDS was applied to promote the open–closed transition of T4 lysozyme (T4L) in explicit water. TSF-SDS successfully reproduced the relevant domain motion with nanosecond-order simulation time, whereas conventional SDS without shuffling of the temperatures failed to promote the transition of T4L, indicating the high conformational sampling efficiency of TSF-SDS for promoting essential conformational transitions of proteins. Furthermore, as a wide-range application, TSF-SDS efficiently identified the native state of trp-cage and a dissociation process of ubiquitin dimer in explicit water

Self-Avoiding Conformational Sampling Based on Histories of Past Conformational Searches

Self-avoiding conformational sampling (SACS) is proposed as an enhanced conformational sampling method for proteins. In SACS, the following conformational resampling is repeated for a given protein: (1) identification of newly visited states in a subspace and (2) conformational resampling by restarting short-time molecular dynamics (MD) simulations from the newly visited states. To identify the newly visited states, a set of history-dependent histograms projected onto the subspace is used. One is constructed from the trajectories sampled at the current (<i>i</i>th) cycle, and the other is constructed from all of the trajectories accumulated up through the previous ((<i>i</i> – 1)­th) cycle. By reference to the history-dependent histograms, the newly visited states appearing at the current (<i>i</i>th) cycle are defined as a difference set between them. By repeating the cycle of conformational resampling, SACS prevents the system from revisiting states that have already been visited for previous cycles, promoting structural transitions via resampling from the newly visited states. To verify the conformational sampling efficiency of SACS, the present method was applied to reveal underlying mechanisms of biologically important domain motions of maltodextrin binding protein in explicit water and successfully reproduced the open–closed transition with a reasonable (nanosecond-order) computational cost

Assessment of Methodology and Chemical Group Dependences in the Calculation of the p<i>K</i>_a for Several Chemical Groups

We have investigated the dependencies of various computational methods in the calculation of acid dissociation constants (p<i>K</i>_a values) of certain chemical groups found in protonatable amino acids based on our previous scheme [Matsui; Phys. Chem. Chem. Phys. 2012, 14, 4181−4187]. By changing the quantum chemical (QC) method (Hartree–Fock (HF) and perturbation theory, and composite methods, or exchange–correlation functionals in density functional theory (DFT)), basis sets, solvation models, and the cavities used in the solvent models, we have exhaustively tested about 2,200 combinations to find the best combination for p<i>K</i>_a estimation among them. Of the tested parameters, the choice of the basis set and cavity is the most crucial to reproduce experimental values compared to other factors. Concerning the basis set, the inclusion of diffuse functions is quite important for carboxyl, thiol, and phenol groups judging from the mean absolute errors (MAEs) measured from the experimental values. Of the cavity models, between the Pauling, Klamt, and the universal force field (UFF) definitions, the UFF defined cavity is the best choice, resulting in the smallest MAEs. Concerning the QC methods, hybrid DFTs and range-separated DFTs always provide better results than pure DFTs and HF. As a result, we found that LC-ϖPBE/6-31+G­(d) with PCM-SMD/UFF provides the best p<i>K</i>_a estimation with a MAE within 0.15 p<i>K</i>_a units

Ion-Pairing Crystal Polymorphs of Interlocked [2 + 1]-Type Receptor–Anion Complexes

The formation of a solid-state totally charge-segregated assembly (polymorph <b>A</b>) of negatively charged layers comprising [2 + 1]-type Cl^– complexes of an arylethynyl-substituted dipyrrolyldiketone boron complex and positively charged layers of tetrabutylammonium (TBA) cations has already been reported. The formation of two new crystalline polymorphs (polymorphs <b>B</b> and <b>C</b>), in addition to polymorph <b>A</b>, is reported in this study. Both polymorphs <b>B</b> and <b>C</b> formed charge-by-charge assemblies, and the dihedral angles between two receptor units in the interlocked complexes depended on the geometries of TBA cations and the resulting packing structures. Two nonorthogonally arranged planes induced <i>P</i>- and <i>M</i>-form chiral geometries, providing diverse arrangements of chiral species according to crystal polymorphs. Furthermore, the stabilities of the three polymorphs were examined by interfragment interaction energies, which were calculated by <i>ab initio</i> electronic structure calculations using the fragment molecular orbital (FMO) method

Theoretical Insight into Stereoselective Reaction Mechanisms of 2,4-Pentanediol-Tethered Ketene-Olefin [2 + 2] Cycloaddition

We report ab initio molecular dynamics calculations based on density functional theory performed on an intramolecular [2 + 2] cycloaddition between ketene and olefin linked with a 2,4-pentanediol (PD) tether. We find that the encounter of the ketene and olefin moieties could be prearranged in the thermal equilibrated state before the cycloaddition. The reaction mechanism is found to be stepwise, similar to that of intermolecular ketene [2 + 2] cycloadditions with ordinary alkenes. A distinct feature of the reaction pathway for a major diastereoisomer is a differential activation free energy of about 1.5 kcal/mol, including 2.8 kcal/mol as the differential activation entropy, with a transition state consisting of a flexible nine-membered ring in the olefin-PD-ketene moiety. This theoretical study provides a reasonable explanation for the strict stereocontrollability of the PD-tethered ketene-olefin cycloaddition, irrespective of reaction types or conditions

Protein Structure Validation Derives a Smart Conformational Search in a Physically Relevant Configurational Subspace

Since proteins perform biological functions through their dynamic properties, molecular dynamics (MD) simulation is a sophisticated strategy for investigating their functions. Analyses of trajectories provide statistical information about a specific protein as a free-energy landscape (FEL). However, the timescale of normal MD is shorter than that of biological functions, resulting in statistically insufficient conformational sampling, finally leading to unreliable FEL calculation. To search for a broad configurational subspace, an external bias is imposed on a target protein as biased sampling. However, its regulation is challenging because the optimal strength of the perturbation is unknown. Furthermore, a physically irrelevant configurational subspace was searched when imposing an inappropriate external bias. To address this issue, we newly proposed an external biased regulation scheme known as the G-factor external bias limiter (GERBIL). In GERBIL, protein configurations generated by external bias are structurally validated by an indicator (G-factor), enabling the search for a physically relevant subspace. In addition to biased sampling, nonbiased sampling might search for a physically irrelevant configurational subspace because repeating multiple MD simulations from several initial structures tends to search for an overly broad configurational subspace. For this issue, the structural qualities of configurations generated by nonbiased sampling have not been investigated. Therefore, we confirmed whether the G-factor screened the collapsed (low-quality) configurations generated by nonbiased sampling. To address this issue, the outlier flooding method (OFLOOD) was adopted in GERBIL as a nonbiased sampling method, which is referred to as OFLOOD-GERBIL. OFLOOD rapidly expands a configurational subspace by resampling the rarely occurring states of a given protein and tends to search an overly broad subspace. Thus, we considered that GERBIL might improve the excessive conformational search of OFLOOD for a physically irrelevant configurational subspace. As a demonstration, OFLOOD and OFLOOD-GERBIL were applied to a globular protein (T4 lysozyme) and their conformational search qualities were assessed. Based on our assessment, normal OFLOOD without the outlier validation frequently sampled low-quality configurations, whereas OFLOOD-GERBIL with the outlier validation intensively sampled high-quality configurations. In conclusion, OFLOOD-GERBIL derives a smart conformational search in a physically relevant configurational subspace, indicating that protein structure validation works in both nonbiased and biased sampling methods

A Density Functional Theory Based Protocol to Compute the Redox Potential of Transition Metal Complex with the Correction of Pseudo-Counterion: General Theory and Applications

We propose an accurate scheme to evaluate the redox potential of a wide variety of transition metal complexes by adding a charge-dependent correction term for a counterion around the charged complexes, which is based on Generalized Born theory, to the solvation energy. The mean absolute error (MAE) toward experimental redox potentials of charged complexes is considerably reduced from 0.81 V (maximum error 1.22 V) to 0.22 V (maximum error 0.50 V). We found a remarkable exchange-correlation functional dependence on the results rather than the basis set ones. The combination of Wachters+f (for metal) and 6-31++G­(d,p) (for other atoms) with the B3LYP functional gives the least MAE 0.15 V for the test complexes. This scheme is applicable to other solvents, and heavier transition metal complexes such as M₁(CO)₅(pycn) (M₁ = Cr, Mo, W), M₂(mnt)₂ (M₂ = Ni, Pd, Pt), and M₃(bpy)₃ (M₃ = Fe, Ru, Os) with the same quality

Photochromic Switching of Diradical Character: Design of Efficient Nonlinear Optical Switches

Open-shell singlet diradical molecules have been widely investigated because they are key to understanding the nature of chemical bonds. We propose a new concept for reversible switching of diradical characteran index of the instability of chemical bondsof a molecule by photochromic reaction. Photochromic diarylethene derivatives with various open-shell singlet diradical characters are theoretically designed, and their photochromic diradical character switching behaviors are clarified. These results contribute to designing highly efficient third-order nonlinear optical switching substances based on the correlation between the diradical character and second hyperpolarizability

Origin of the Enhancement of the Second Hyperpolarizabilities in Open-Shell Singlet Transition-Metal Systems with Metal–Metal Multiple Bonds

Using the spin-unrestricted coupled-cluster method, we explore the origin of the second hyperpolarizabilities (γ) of singlet dichromium(II) and dimolybdenum(II) model systems with various bond lengths as a function of the diradical characters of the dσ, dπ, and dδ orbitals. Both systems exhibit enhanced γ values in the intermediate diradical character region, but by using a partitioning scheme, the dσ electrons are shown to play the essential role in contrast with the π-electrons of conventional organic π-conjugated systems. Then, in the equilibrium bond length region, the γ values are still governed by dσ electrons in the dichromium(II) system, although by dδ/dπ electrons in the dimolybdenum(II) system