Similarity scores of vibrational spectra reveal the atomistic structure of pentapeptides in multiple basins.

Vibrational spectroscopy combined with theoretical calculations is a powerful tool for analyzing the interaction and conformation of peptides at the atomistic level. Nonetheless, identifying the structure becomes increasingly difficult as the peptide size grows large. One example is acetyl-SIVSF-N-methylamide, a capped pentapeptide, whose atomistic structure has remained unknown since its first observation [T. Sekiguchi, M. Tamura, H. Oba, P. Çarçarbal, R. R. Lozada-Garcia, A. Zehnacker-Rentien, G. Grégoire, S. Ishiuchi and M. Fujii, Angew. Chem., Int. Ed., 2018, 57, 5626-5629]. Here, we propose a novel conformational search method, which exploits the structure-spectrum correlation using a similarity score that measures the agreement of theoretical and experimental spectra. Surprisingly, the two conformers have distinctly different energy and geometry. The second conformer is 25 kJ mol-1 higher in energy than the other, lowest-energy conformer. The result implies that there are multiple pathways in the early stage of the folding process: one to the global minimum and the other to a different basin. Once such a structure is established, the second conformer is unlikely to overcome the barrier to produce the most stable structure due to a vastly different hydrogen bond network of the backbone. Our proposed method can characterize the lowest-energy conformer and kinetically trapped, high-energy conformers of complex biomolecules.

Learning QM/MM potential using equivariant multiscale model.

The machine learning (ML) method emerges as an efficient and precise surrogate model for high-level electronic structure theory. Its application has been limited to closed chemical systems without considering external potentials from the surrounding environment. To address this limitation and incorporate the influence of external potentials, polarization effects, and long-range interactions between a chemical system and its environment, the first two terms of the Taylor expansion of an electrostatic operator have been used as extra input to the existing ML model to represent the electrostatic environments. However, high-order electrostatic interaction is often essential to account for external potentials from the environment. The existing models based only on invariant features cannot capture significant distribution patterns of the external potentials. Here, we propose a novel ML model that includes high-order terms of the Taylor expansion of an electrostatic operator and uses an equivariant model, which can generate a high-order tensor covariant with rotations as a base model. Therefore, we can use the multipole-expansion equation to derive a useful representation by accounting for polarization and intermolecular interaction. Moreover, to deal with long-range interactions, we follow the same strategy adopted to derive long-range interactions between a target system and its environment media. Our model achieves higher prediction accuracy and transferability among various environment media with these modifications.

Allosteric regulation of ß-reaction stage I in tryptophan synthase upon the α-ligand binding.

Tryptophan synthase (TRPS) is a bifunctional enzyme consisting of α- and ß-subunits that catalyzes the last two steps of L-tryptophan (L-Trp) biosynthesis. The first stage of the reaction at the ß-subunit is called ß-reaction stage I, which converts the ß-ligand from an internal aldimine [E(Ain)] to an α-aminoacrylate [E(A-A)] intermediate. The activity is known to increase 3-10-fold upon the binding of 3-indole-D-glycerol-3'-phosphate (IGP) at the α-subunit. The effect of α-ligand binding on ß-reaction stage I at the distal ß-active site is not well understood despite the abundant structural information available for TRPS. Here, we investigate the ß-reaction stage I by carrying out minimum-energy pathway searches based on a hybrid quantum mechanics/molecular mechanics (QM/MM) model. The free-energy differences along the pathway are also examined using QM/MM umbrella sampling simulations with QM calculations at the B3LYP-D3/aug-cc-pVDZ level of theory. Our simulations suggest that the sidechain orientation of ßD305 near the ß-ligand likely plays an essential role in the allosteric regulation: a hydrogen bond is formed between ßD305 and the ß-ligand in the absence of the α-ligand, prohibiting a smooth rotation of the hydroxyl group in the quinonoid intermediate, whereas the dihedral angle rotates smoothly after the hydrogen bond is switched from ßD305-ß-ligand to ßD305-ßR141. This switch could occur upon the IGP-binding at the α-subunit, as evidenced by the existing TRPS crystal structures.

General Design Strategy to Precisely Control the Emission of Fluorophores via a Twisted Intramolecular Charge Transfer (TICT) Process.

Fluorogenic probes for bioimaging have become essential tools for life science and medicine, and the key to their development is a precise understanding of the mechanisms available for fluorescence off/on control, such as photoinduced electron transfer (PeT) and Förster resonance energy transfer (FRET). Here we establish a new molecular design strategy to rationally develop activatable fluorescent probes, which exhibit a fluorescence off/on change in response to target biomolecules, by controlling the twisted intramolecular charge transfer (TICT) process. This approach was developed on the basis of a thorough investigation of the fluorescence quenching mechanism of N-phenyl rhodamine dyes (commercially available as the QSY series) by means of time-dependent density functional theory (TD-DFT) calculations and photophysical evaluation of their derivatives. To illustrate and validate this TICT-based design strategy, we employed it to develop practical fluorogenic probes for HaloTag and SNAP-tag. We further show that the TICT-controlled fluorescence off/on mechanism is generalizable by synthesizing a Si-rhodamine-based fluorogenic probe for HaloTag, thus providing a palette of chemical dyes that spans the visible and near-infrared range.

Dynamics of nitric oxide controlled by protein complex in bacterial system.

Nitric oxide (NO) plays diverse and significant roles in biological processes despite its cytotoxicity, raising the question of how biological systems control the action of NO to minimize its cytotoxicity in cells. As a great example of such a system, we found a possibility that NO-generating nitrite reductase (NiR) forms a complex with NO-decomposing membrane-integrated NO reductase (NOR) to efficiently capture NO immediately after its production by NiR in anaerobic nitrate respiration called denitrification. The 3.2-Å resolution structure of the complex of one NiR functional homodimer and two NOR molecules provides an idea of how these enzymes interact in cells, while the structure may not reflect the one in cells due to the membrane topology. Subsequent all-atom molecular dynamics (MD) simulations of the enzyme complex model in a membrane and structure-guided mutagenesis suggested that a few interenzyme salt bridges and coulombic interactions of NiR with the membrane could stabilize the complex of one NiR homodimer and one NOR molecule and contribute to rapid NO decomposition in cells. The MD trajectories of the NO diffusion in the NiR:NOR complex with the membrane showed that, as a plausible NO transfer mechanism, NO released from NiR rapidly migrates into the membrane, then binds to NOR. These results help us understand the mechanism of the cellular control of the action of cytotoxic NO.

Fundamental peak disappears upon binding of a noble gas: a case of the vibrational spectrum of PtCO in an argon matrix.

Anharmonic vibrational state calculations were performed for PtCO and Ar-PtCO via the direct vibrational configuration interaction (VCI) method based on CCSD(T) energies and CCSD dipole moments at tens of thousands of grids, to get insights into the anomalous effect of a solid argon matrix on the vibrational spectra of PtCO. It was shown that, through the binding of Ar to PtCO via a strong van der Waals interaction, the Pt-C-O bending fundamental level drastically loses the infrared intensity although the corresponding overtone band shows a relatively large intensity. The origin of this phenomenon was analyzed based on the dipole moment surfaces and electron densities around the equilibrium structure. The present computations have solved the inconsistency between the gas-phase and the matrix-isolation experiments for PtCO.

Infrared Spectra of Protonated Water Clusters, H+(H2O)4, in Eigen and Zundel Forms Studied by Vibrational Quasi-Degenerate Perturbation Theory.

The infrared spectrum of H+(H2O)4 recently observed in a wide spectral range has shown a series of bands in a range of 1700-2500 cm-1, which can not be understood by the standard harmonic normal mode analysis. Here, we theoretically investigate the origin of these bands with a focus on (1) the possibility of coexistence of multiple isomers in the Eigen [H3O+(H2O)3] and Zundel [H5O2+(H2O)2] forms and (2) the effect of anharmonic coupling that gives rise to nonzero intensities for overtones and combination bands. Anharmonic vibrational calculations are carried out for the Eigen and Zundel clusters by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) based on optimized coordinates. The anharmonic potential energy surface and the dipole moment surfaces are generated by a multiresolution approach combining one-dimensional (1D) grid potential functions derived from CCSD(T)-F12, 2D and 3D grid potential functions derived from B3LYP for important coupling terms, and a quartic force field derived from B3LYP for less important terms. The spectrum calculated for the Eigen cluster is in excellent agreement with the experiment, assigning the bands in the range of 1700-2500 cm-1 to overtones and combination bands of a H3O+ moiety in line with recent reports [ J. Phys. Chem. A 2015 , 119 , 9425 ; Science 2016 , 354 , 1131 ]. On the other hand, characteristic OH stretching bands of the Zundel cluster is found to be absent in the experimental spectrum. We therefore conclude that the experimental spectrum originates solely from the Eigen cluster. Nonetheless, the present calculation for the Eigen cluster poorly reproduces a band observed at 1765 cm-1. A possible nature of this band is discussed.

Detection of Sphingomyelin Clusters by Raman Spectroscopy.

Sphingomyelin (SM) is a major sphingolipid in mammalian cells that forms specific lipid domains in combination with cholesterol (Chol). Using molecular-dynamics simulation and density functional theory calculation, we identified a characteristic Raman band of SM at ∼1643 cm(-1) as amide I of the SM cluster. Experimental results indicate that this band is sensitive to the hydration of SM and the presence of Chol. We showed that this amide I Raman band can be utilized to examine the membrane distribution of SM. Similarly to SM, ceramide phosphoethanolamine (CerPE) exhibited an amide I Raman band in almost the same region, although CerPE lacks three methyl groups in the phosphocholine moiety of SM. In contrast to SM, the amide I band of CerPE was not affected by Chol, suggesting the importance of the methyl groups of SM in the SM-Chol interaction.

A weight averaged approach for predicting amide vibrational bands of a sphingomyelin bilayer.

Infrared (IR) and Raman spectra of a sphingomyelin (SM) bilayer have been calculated for the amide I, II and A modes and the double-bonded CC stretching mode by a weight averaged approach, based on an all-atom molecular dynamics (MD) simulation and a vibrational structure calculation. Representative structures and statistical weights of SM clusters connected by hydrogen bonds (HBs) are observed in MD trajectories. After constructing smaller fragments from the SM clusters, the vibrational spectra of the target modes were calculated by normal mode analysis with a correction for anharmonicity, using density functional theory. The final IR and Raman spectra of a SM bilayer were obtained as the weight averages over all SM clusters. The calculated Raman spectrum is in excellent agreement with a recent measurement, providing a clear assignment of the peak in question observed at 1643 cm(-1) to the amide I modes of a SM bilayer. The analysis of the IR spectrum has also revealed that the amide bands are sensitive to the water content inside the membrane, since their band positions are strongly modulated by the HB between SM and water molecules. The present study suggests that the amide I band serves as a marker to identify the formation of SM clusters, and opens a new way to detect lipid rafts in the biological membrane.

Vibrational quasi-degenerate perturbation theory with optimized coordinates: applications to ethylene and trans-1,3-butadiene.

A perturbative extension to optimized coordinate vibrational self-consistent field (oc-VSCF) is proposed based on the quasi-degenerate perturbation theory (QDPT). A scheme to construct the degenerate space (P space) is developed, which incorporates degenerate configurations and alleviates the divergence of perturbative expansion due to localized coordinates in oc-VSCF (e.g., local O-H stretching modes of water). An efficient configuration selection scheme is also implemented, which screens out the Hamiltonian matrix element between the P space configuration (p) and the complementary Q space configuration (q) based on a difference in their quantum numbers (λpq = ∑s|ps - qs|). It is demonstrated that the second-order vibrational QDPT based on optimized coordinates (oc-VQDPT2) smoothly converges with respect to the order of the mode coupling, and outperforms the conventional one based on normal coordinates. Furthermore, an improved, fast algorithm is developed for optimizing the coordinates. First, the minimization of the VSCF energy is conducted in a restricted parameter space, in which only a portion of pairs of coordinates is selectively transformed. A rational index is devised for this purpose, which identifies the important coordinate pairs to mix from others that may remain unchanged based on the magnitude of harmonic coupling induced by the transformation. Second, a cubic force field (CFF) is employed in place of a quartic force field, which bypasses intensive procedures that arise due to the presence of the fourth-order force constants. It is found that oc-VSCF based on CFF together with the pair selection scheme yields the coordinates similar in character to the conventional ones such that the final vibrational energy is affected very little while gaining an order of magnitude acceleration. The proposed method is applied to ethylene and trans-1,3-butadiene. An accurate, multi-resolution potential, which combines the MP2 and coupled-cluster with singles, doubles, and perturbative triples level of electronic structure theory, is generated and employed in the oc-VQDPT2 calculation to obtain the fundamental tones as well as selected overtones/combination tones coupled to the fundamentals through the Fermi resonance. The calculated frequencies of ethylene and trans-1,3-butadiene are found to be in excellent agreement with the experimental values with a mean absolute error of 8 and 9 cm(-1), respectively.

Transforaminal Full-Endoscopic Ventral Facetectomy: Midterm Results and Factors Associated with Poor Surgical Outcomes.

BACKGROUND: Full-endoscopic spine surgery (FESS) is a well-established procedure for herniated nucleus pulposus. It is a minimally invasive surgery that can be performed under local anesthesia through only an 8-mm skin incision. With improvements in surgical equipment such as high-speed drills, the indications for FESS have expanded to include lumbar spinal stenosis (LSS). We perform a transforaminal full-endoscopic ventral facetectomy (TF-FEVF) for unilateral nerve root-type lateral recess stenosis (LRS) using a transforaminal approach under local anesthesia.The aim of this study was to examine the postoperative results of TF-FEVF for LRS and to identify factors associated with poor surgical outcomes. 85 patients who underwent TF-FEVF for LRS under local anesthesia. Clinical outcomes were determined by visual analog scale (VAS) and the modified MacNab criteria. Evaluation was performed using magnetic resonance imaging (MRI), computed tomography (CT), and flexion-extension radiographs. METHODS: This study involved 85 patients (47 males and 38 females) who underwent TF-FEVF for LRS. The mean age was 70.5 years and the mean follow-up duration was 14.8 months. Data were collected on sex, age, level of operation, diagnosis, history of spine surgery at the same level, and duration of follow-up. The diagnosis was categorized as LSS with or without disk bulging. Clinical evaluation was performed using the VAS and modified MacNab criteria. MRI was used to evaluate the degree of disk degeneration, vertebral endplate degeneration, disk height, thickening of the ligamentum flavum, and stenosis. Bony stenosis was evaluated using CT. Sagittal translation and sagittal angulation were also measured by flexion-extension radiographs, and the Cobb angle was measured using a standing front view radiograph. All variables were compared between patients with excellent/good outcomes (E/G group) and those with fair/poor outcomes (F/P group) using the modified MacNab criteria. RESULTS: Postoperative VAS showed that leg pain decreased from 59.0 ± 28.6 preoperatively to 17.9 ± 27.2 at the final follow-up (p < 0.01) and that lower back pain also decreased from 60.7 ± 26.6 preoperatively to 27.3 ± 28.6 at final follow-up (p < 0.01). According to the modified MacNab criteria, the results during the final follow-up were excellent in 39 cases, good in 21 cases, fair in 13 cases, and poor in 12 cases. There were no significant differences in sex, age, diagnosis, history of spine surgery, and duration of follow-up periods between the 60 cases (70.6%) in the E/G group and the 25 cases (29.4%) in the F/P group. Imaging evaluation revealed statistically significant differences between the E/G group and the F/P group in intervertebral angle flexion (3.2 vs. 0.4 degrees; p < 0.05), sagittal angulation (4.3 vs. 8.1 degrees; p < 0.05), slip in flexion (0.9 vs. 2.8 mm; p < 0.05), sagittal translation (0.7 vs. 1.6 mm; p < 0.05), and Cobb angle (-0.5 vs. -1.9 degrees; p < 0.05). CONCLUSION: Midterm results of TF-FEVF were generally favorable; factors contributing to good or poor TF-FEVF outcomes were large sagittal angulation, large sagittal translation, and concave side.

Full-endoscopic spine surgery in oldest old patients aged over 90 years:A case report.

BACKGROUND: Transforaminal full-endoscopic spine surgery (FESS) is the least invasive spinal surgery and can be performed under local anesthesia. In Japan, the population is rapidly aging and the number of spinal surgeries performed in the elderly is also increasing. OBJECT: In this report, we describe 3 patients aged 90 years or older in whom we performed FESS under local anesthesia. CASE: The first case was a 90-year-old man who presented with severe leg pain. He had multiple medical comorbidities and was unsuitable for general anesthesia. We performed FESS. After surgery, the leg pain resolved with full recovery of muscle strength. He was discharged with no perioperative complications. The second case was a 90-year-old man who presented with severe leg pain. MRI showed a herniated nucleus pulposus and foraminal stenosis at L4/5. We performed FESS. The leg pain improved immediately after surgery. The third case was a 91-year-old woman in whom we diagnosed left L5 radiculopathy due to foraminal stenosis at L5/S1. After surgery, her leg pain was relieved. CONCLUSION: FESS is a good surgical procedure for elderly patients who are in a poor general condition because it is minimally invasive and can be performed under local anesthesia with early mobilization. J. Med. Invest. 71 : 169-173, February, 2024.

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models.

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Extensivity of energy and electronic and vibrational structure methods for crystals.

A pedagogical proof is presented for the extensivity of energies of metallic and nonmetallic crystals that proceeds by elucidating the asymptotic distance dependence of the effective chemical interactions: kinetic, Coulomb, exchange, and correlation. On this basis, a guideline for the size-consistent design of electronic and vibrational methods is proposed. This guideline underscores the significance of the distinct use of the intermediate and standard normalization of wave functions for extensive and intensive quantities, includes the extensive and intensive diagram theorems as the unambiguous criteria for determining size consistency of a method for extensive and intensive quantities, and introduces the extensive-intensive consistency theorem, which stipulates the precise balance between the determinant spaces reached by extensive and intensive operators. Electronic and vibrational methods for crystals are reviewed that are inspired by these formal analyses or developed in accordance with the guideline.

Fermi resonance in solid CO2 under pressure.

The symmetric-stretching fundamental (ν1) and the bending first overtone (2ν2) of CO2, which are accidentally degenerate with the same symmetry, undergo a Fermi resonance and give rise to two Raman bands with a frequency difference of 107 cm(-1) and an intensity ratio of 2.1. Both the frequency difference and intensity ratio can be varied by pressure applied to CO2 in condensed phases, which has been utilized as a spectroscopic geobarometer for minerals with CO2 inclusion. This study calculates the pressure dependence of the Fermi dyad frequency difference and intensity ratio by combining the embedded-fragment second-order Mo̸ller-Plesset perturbation calculations of harmonic frequencies of solid CO2 under pressure and the coupled-cluster singles and doubles with noniterative triples and vibrational configuration-interaction calculations of anharmonic frequencies of molecular CO2. It reproduces frequency difference quantitatively and intensity ratio qualitatively up to 10 GPa. The analysis of the results is shown to render strong support for one particular order of unperturbed frequencies, ν1 > 2ν2, in both the gas and solid phases, which has been a matter of controversy for decades.

Advantages of Revision Transforaminal Full-Endoscopic Spine Surgery in Patients who have Previously Undergone Posterior Spine Surgery.

BACKGROUND: Revision lumbar spine surgery via a posterior approach is more challenging than primary surgery because of epidural or perineural scar tissue. It demands more extensive removal of the posterior structures to confirm intact bony landmarks and could cause iatrogenic instability; therefore, fusion surgery is often added. However, adjacent segment disease after fusion surgery could be a problem, and further exposure of the posterior muscles could result in multiple operated back syndrome. To address these problems, we now perform transforaminal full-endoscopic spine surgery (TF-FES) as revision surgery in patients who have previously undergone posterior lumbar surgery. There have been several reports on the advantages of TF-FES, which include feasibility of local anesthesia, minimal invasiveness to posterior structures, and less scar tissue with fewer adhesions. In this study, we aim to assess the clinical outcomes of revision TF-FES and its advantages. METHODS: We evaluated 48 consecutive patients with a history of posterior lumbar spine surgery who underwent revision TF-FES (at 60 levels) under local anesthesia. Intraoperative blood loss, operating time, and complication rate were evaluated. Postoperative outcomes were assessed using the modified Macnab criteria and visual analog scale (VAS) scores for leg pain, back pain, and leg numbness. We also compared the outcome of revision FES with that of primary FES. RESULTS: Mean operating time was 70.5 ± 14.4 (52-106) minutes. Blood loss was unmeasurable. The clinical outcomes were rated as excellent at 16 levels (26.7%), good at 28 (46.7%), fair at 10 (16.7%), and poor at 6 (10.0%). The mean preoperative VAS score was 6.0 ± 2.6 for back pain, 6.8 ± 2.4 for leg pain, and 6.3 ± 2.8 for leg numbness. At the final follow-up, the mean postoperative VAS scores for leg pain, back pain, and leg numbness were 4.3 ± 2.5, 3.8 ± 2.6, and 4.6 ± 3.2, respectively. VAS scores for all three parameters were significantly improved (p < 0.05). There was no significant difference in operating time, intraoperative blood loss, or the complication rate between revision FES and primary FES. CONCLUSIONS: Clinical outcomes of revision TF-FES in patients with a history of posterior lumbar spine surgery were acceptable (excellent and good in 73.4% of cases). TF-FES can preserve the posterior structures and avoid scar tissue and adhesions. Therefore, TF-FES could be an effective procedure for patients who have previously undergone posterior lumbar spine surgery.

Transforming Growth Factor-ß Induces Interleukin-6 Secretion from Human Ligamentum Flavum-Derived Cells through Partial Activation of p38 and p44/42 Mitogen-Activated Protein Kinases.

STUDY DESIGN: This experimental study was performed using human ligamentum flavum-derived cells (HFCs). PURPOSE: To investigate the intracellular signaling mechanism of interleukin-6 (IL-6) secretion in transforming growth factor-ß (TGF- ß)-stimulated HFCs. OVERVIEW OF LITERATURE: Lumbar spinal stenosis (LSS) is a prevalent disease among the elderly, characterized by debilitating pain in the lower extremities. Although the number of patients with LSS has increased in recent years, the underlying pathomechanism remains unclear. Clinical examinations typically rely on magnetic resonance imaging to diagnose patients, revealing ligamentum flavum hypertrophy. Some studies have suggested an association between ligamentum flavum hypertrophy and inflammation/fibrosis, and expression of TGF-ß and IL-6 has been observed in surgically obtained ligamentum flavum samples. However, direct evidence linking TGF-ß and IL-6 expression in HFCs is lacking. METHODS: HFCs were obtained from patients with LSS who had undergone decompression surgery. The cells were stimulated with TGF-ß and pretreated with either the p38 mitogen-activated protein (MAP) kinase inhibitor SB203580 or the p44/42 MAP kinase inhibitor FR180204. IL-6 secretion in the cell culture medium and IL-6 messenger RNA (mRNA) expression levels were analyzed using an enzyme-linked immunoassay and real-time polymerase chain reaction, respectively. RESULTS: TGF-ß administration resulted in a dose- and time-dependent stimulation of IL-6 release. Treatment with SB203580 and FR180204 markedly suppressed TGF-ß-induced IL-6 secretion from HFCs. Moreover, these inhibitors suppressed IL-6 mRNA expression in response to TGF-ß stimulation. CONCLUSIONS: Our findings indicate that TGF-ß induces IL-6 protein secretion and gene expression in HFCs through the activation of p38 or p44/42 MAP kinases. These results suggest a potential association between IL-6-mediated inflammatory response and tissue hypertrophy in LSS, and we provide insights into molecular targets for therapeutic interventions targeting LSS-related inflammation through our analysis of the MAP kinase pathway using HFCs.

Optimized coordinates for anharmonic vibrational structure theories.

A procedure to determine optimal vibrational coordinates is developed on the basis of an earlier idea of Thompson and Truhlar [J. Chem. Phys. 77, 3031 (1982)]. For a given molecule, these coordinates are defined as the unitary transform of the normal coordinates that minimizes the energy of the vibrational self-consistent-field (VSCF) method for the ground state. They are justified by the fact that VSCF in these coordinates becomes exact in two limiting cases: harmonic oscillators, where the optimized coordinates are normal, and noninteracting anharmonic oscillators, in which the optimized coordinates are localized on individual oscillators. A robust and general optimization algorithm is developed, which decomposes the transformation matrix into a product of Jacobi matrices, determines the rotation angle of each Jacobi matrix that minimizes the energy, and iterates the process until a minimum in the whole high dimension is reached. It is shown that the optimized coordinates are neither entirely localized nor entirely delocalized (or normal) in any of the molecules (the water, water dimer, and ethylene molecules) examined (apart from the aforementioned limiting cases). Rather, high-frequency stretching modes tend to be localized, whereas low-frequency skeletal vibrations remain normal. On the basis of these coordinates, we introduce two new vibrational structure methods: optimized-coordinate VSCF (oc-VSCF) and optimized-coordinate vibrational configuration interaction (oc-VCI). For the modes that become localized, oc-VSCF is found to outperform VSCF, whereas, for both classes of modes, oc-VCI exhibits much more rapid convergence than VCI with respect to the rank of excitations. We propose a rational configuration selection for oc-VCI when the optimized coordinates are localized. The use of the optimized coordinates in VCI with this configuration selection scheme reduces the mean absolute errors in the frequencies of the fundamentals and the first overtones/combination tones from 104.7 (VCI) to 10.7 (oc-VCI) and from 132.4 (VCI) to 8.2 (oc-VCI) cm(-1) for the water molecule and the water dimer, respectively. It is also shown that the degree of coupling in the potential for ethylene is reduced effectively from four modes to three modes by the transformation from the normal to optimized coordinates, which enhances the accuracy of oc-VCI with low-rank excitations.

Computational Analysis on the Allostery of Tryptophan Synthase: Relationship between α/ß-Ligand Binding and Distal Domain Closure.

Tryptophan synthase (TRPS) is a bifunctional enzyme consisting of α and ß-subunits and catalyzes the last two steps of l-tryptophan (L-Trp) biosynthesis, namely, cleavage of 3-indole-d-glycerol-3'-phosphate (IGP) into indole and glyceraldehyde-3-phosphate (G3P) in the α-subunit, and a pyridoxal phosphate (PLP)-dependent reaction of indole and l-serine (L-Ser) to produce L-Trp in the ß-subunit. Importantly, the IGP binding at the α-subunit affects the ß-subunit conformation and its ligand-binding affinity, which, in turn, enhances the enzymatic reaction at the α-subunit. The intersubunit communications in TRPS have been investigated extensively for decades because of the fundamental and pharmaceutical importance, while it is still difficult to answer how TRPS allostery is regulated at the atomic detail. Here, we investigate the allosteric regulation of TRPS by all-atom classical molecular dynamics (MD) simulations and analyze the potential of mean-force (PMF) along conformational changes of the α- and ß-subunits. The present simulation has revealed a widely opened conformation of the ß-subunit, which provides a pathway for L-Ser to enter into the ß-active site. The IGP binding closes the α-subunit and induces a wide opening of the ß-subunit, thereby enhancing the binding affinity of L-Ser to the ß-subunit. Structural analyses have identified critical hydrogen bonds (HBs) at the interface of the two subunits (αG181-ßS178, αP57-ßR175, etc.) and HBs between the ß-subunit (ßT110 - ßH115) and a complex of PLP and L-Ser (an α-aminoacrylate intermediate). The former HBs regulate the allosteric, ß-subunit opening, whereas the latter HBs are essential for closing the ß-subunit in a later step. The proposed mechanism for how the interdomain communication in TRPS is realized with ligand bindings is consistent with the previous experimental data, giving a general idea to interpret the allosteric regulations in multidomain proteins.

Weight average approaches for predicting dynamical properties of biomolecules.

Recent advances in atomistic molecular dynamics (MD) simulations of biomolecules allow us to explore their conformational spaces widely, observing large-scale conformational fluctuations or transitions between distinct structures. To reproduce or refine experimental data using MD simulations, structure ensembles, which are characterized by multiple structures and their statistical weights on the rugged free-energy landscapes, are often used. Here, we summarize weight average approaches for various experimental measurements. Weight average approaches are now applied to hybrid quantum mechanics/molecular mechanics MD simulations to predict fast vibrational motions in a protein with a high accuracy for better understanding of molecular functions from atomic structures.