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The microscopic effects of each substituent of the Hf catalyst and the growing polymer on the monomer insertion process were investigated for Hf-pyridyl amido-catalyzed coordinative chain transfer polymerization using the Red Moon method. Since the Hf catalyst has two reaction sites, cis - and trans -sites, we separately applied the appropriate analysis methods to each one, revealing that the naphthalene ring influenced monomer insertion at the cis -one, while the i -Pr group and the hexyl group of the adjacent 1-octene unit did the trans -one. It was interesting to find that the hexyl group of the 1-octene-inserted catalyst (oHfCat) pushes the naphthalene ring toward the cis -site and narrows the space at the cis -site, thus indirectly creating a steric hindrance to cis -insertions. Further, the relative position of the Hf catalyst and the growing polymer was found to be strongly influenced by the patterns of insertion reactions, i.e., cis - or trans -insertions. In particular, it was clarified that, after trans -insertions, the growing polymer on the Hf atom covers the cis -site, making cis -insertion less likely to occur. These studies reveal the microscopic effects of the catalyst substituents and the growing polymer on the catalyst during the polymerization reaction process; these microscopic analyses using the RM method should provide atomistic insights that are not easy to obtain experimentally for advanced catalyst design and polymerization control.

The objective of our work is to investigate the impact of pH on the structural changes of hemoglobin that affect its O 2 affinity, known as the Bohr effect. We conducted molecular dynamics (MD) simulations to explore the transition between various hemoglobin states based on the protonation states (PSs) of two histidine residues (βHis143 and βHis146). We conducted the MD simulations from the R and R2 states with three sets of PSs assuming pH values of 7.0, 6.5, and 5.5, aiming to investigate the influence of pH on hemoglobin behavior. Our results demonstrated that the protonated His residues promote the state transition from the R state to the R2 state and encourage elongation of the distance between the β1-β2 subunits by weakening the inter-subunit interactions in the R state. These observations, aligning with the experimental evidence, indicate that the R2 state typically crystallizes under low pH conditions. Our findings suggest that the relationship between the PSs and the structural stability of the R state plays a role in the acid and alkaline Bohr effect.

The Hf-pyridyl amido complex ((pyridylamido)Hf(IV)) is a cationic catalyst activated by ion-pairing with auxiliary catalyst B(C 6 F 5 ) 4 to show high activity for α-olefin polymerization. Previously, it was experimentally observed that the consumption rate of 1-octene in the 1-octene/ethene copolymerization is 3-fold compared to the 1-octene homopolymerization in coordinative chain transfer polymerization using the catalyst HfCat + -B(C 6 F 5 ) 4 - ion pair (IP) and the chain transfer agent (CTA) ZnEt 2 . In the present study, we have performed atomistic chemical simulations of the IP-catalyzed homopolymerization of 1-octene and copolymerization of 1-octene and ethene on the basis of the Red Moon (RM) methodology. Using the analysis by polymer propagation diagrams (PPDs), in the 1-octene homopolymerization and the 1-octene/ethene copolymerization with the 1-octene-inserted catalyst (oHfCat), it is theoretically shown that the propagation reactions intermittently pause due to the steric hindrance of two hexyl groups of the oHfCat and the 1-octene inserted adjacent to the Hf atom. On the other hand, in the polymerizations with the ethene-inserted catalyst (eHfCat), it is reasonably recognized that the propagation reactions occur smoothly at a constant rate, and the polymerization continuously proceeds due to the relatively smaller steric hindrance. In conclusion, it was shown, for the first time, that the RM method can be used to reveal the microscopic effects of monomers and substituents in the polymerization reaction processes. Therefore, our current work using PPDs demonstrates the promising potential of the RM methodology in studying catalytic olefin polymerizations and complex chemical reaction systems in general.

We performed the atomistic simulation of 1-octene polymerization reaction catalyzed by the ionic pair (IP) consisting of the cationic active species of (pyridylamido)Hf(IV) catalyst, HfCat P n + , and different counteranions (CAs), B(C 6 F 5 ) 4 - and MeB(C 6 F 5 ) 3 - , at different monomer concentrations. Using a hybrid Monte Carlo/molecular dynamics method, that is, the Red Moon (RM) method, the reaction progress measured by the "RM cycle" was transformed into effective real time using the time transformation theory. Then, the degree of polymerization was found to be consistent with that in the chemical kinetics, a macroscopic theory, and experimental ones. Remarkably, the current simulation has revealed the different dynamical features in the polymerization behavior originating from the CA. Namely, the HfCat P n + -B(C 6 F 5 ) 4 - IP mainly forms an outer-sphere IP (OSIP) throughout the polymerization. The HfCat P n + -MeB(C 6 F 5 ) 3 - IP, on the other hand, forms an inner-sphere IP (ISIP) in the initial stage of polymerization, and the ratio of ISIP steeply drops after the first monomer insertion because the IP interaction is reduced by the steric hindrance between the inserted monomers and the CA. In conclusion, we have shown that the microscopic IP dynamics interwoven with the polymerization reaction can be computationally observed in the real-time domain by using the RM method. Therefore, our current work demonstrates the promising potential of the RM method in studying catalytic olefin polymerization and complex chemical reaction systems.

Radical polymerization is an economic and practical polymerization method over ionic and coordination polymerizations and is widely used for polymer production. Although many efforts have been made to improve the convenience and controllability of radical polymerization, it is still a challenge to directly observe the microbehaviors of propagation, which may provide inspiration for the development of polymerization processes. In this study, we focused on the tacticity of polystyrene produced by bulk radical polymerization since there is a debate over the temperature dependence. The propagation process is simulated via Red Moon methodology, which is a cost-effective method for handling complex chemical reaction systems. By the multiple pathway analysis for the propagation reaction model composed of the dimer radical and the monomer using density functional theory, we obtained the relative energies in multiple transition states, whose energy differences are partly explained by the π-π stacking interactions. Via performing Red Moon simulations from 30 to 190 °C, we confirmed that meso contents moderately increase as the temperature increases, which is explained by the influence of temperature on the probability density of the reaction conformations of each pathway. The successful prediction and explanation for tacticity demonstrate the potential of Red Moon methodology in unveiling the microbehaviors of propagation.

In the context of a molecular-level understanding of the allostery mechanisms, human adult hemoglobin (HbA) has been extensively studied for over half a century. Chloride ions (Cl - ) have been known as one of HbA allosteric effectors, which stabilizes the T-state preferable to release oxygen molecules. The functional mechanisms were individually proposed by Ueno and Perutz several decades ago. Ueno considered that the site-specific Cl - binding is essential, while Perutz proposed the non-site-specific interaction between HbA and Cl - . Each speculation explains the mechanism plausibly since each was tightly associated with its reasonable experimental observation. However, both mechanisms themselves still seem to make their speculations controversial. In the present study, we have theoretically reconsidered these apart from their approaches. Our atomistic molecular dynamics simulations then showed that the increase of Cl - concentration suppresses the conformational conversion from the T-state. Interestingly, chloride ions loosely interact with the amino acid residues inside the HbA central cavity, suggesting that both Perutz's and Ueno's speculations are involved in understanding the microscopic roles of Cl - . In conclusion, we theoretically certified that the effect of Cl - competes against that of solvated O 2 , i.e., the destabilization of T-state through the non-site-specific interaction, implying the concerted regulation of HbA under physiological conditions.

Atomistic simulation of the 1-octene polymerization reaction by a (pyridylamido)Hf(IV) catalyst was conducted on the basis of Red Moon (RM) methodology, focusing on the effect of the counteranions (CAs), MeB(C 6 F 5 ) 3 - , and B(C 6 F 5 ) 4 - , on the catalyst activity and chain termination reaction. We show that RM simulation reasonably reproduces the faster reaction rate with B(C 6 F 5 ) 4 - than with MeB(C 6 F 5 ) 3 - . Notably, the initiation of the polymerization reaction with MeB(C 6 F 5 ) 3 - is comparatively slow due to the difficulty of the first insertion. Then, we investigated the free energy map of the ion pair (IP) structures consisting of each CA and the cationic (pyridylamido)Hf(IV) catalyst with the growing polymer chain (HfCat P n + ), which determines the polymerization reaction rates, and found that HfCat P n + -MeB(C 6 F 5 ) 3 - can keep forming "inner-sphere" IPs even after the polymer chain becomes sufficiently bulky, while HfCat P n + -B(C 6 F 5 ) 4 - forms mostly "outer-sphere" IPs. Finally, we further tried to elucidate the origin of the broader molecular weight distribution (MWD) of the polymer experimentally produced with B(C 6 F 5 ) 4 - than that with MeB(C 6 F 5 ) 3 - . Then, through the trajectory analysis of the RM simulations, it was revealed that the chain termination reaction would be more sensitive to the IP structures than the monomer insertion reaction because the former involves a more constrained structure than the latter, which is likely to be a possible origin of the MWDs dependent on the CAs.

A theoretical study of the solvatochromic shifts of para-nitrophenol ( pNP) and para-nitrophenolate anion ( pNP - ) in aqueous solution is presented using a QM/MM methodology with molecular dynamics simulation. The optimized structures in aqueous solution are obtained using both the polarizable continuum and the free-energy gradient methods. For pNP, the calculated redshifts at the CASPT2 (12,10) level are, respectively, 0.71 and 0.94 eV, in good agreement with the experimental ones (0.80-0.83 eV), whereas for pNP - , they are small. The difference between the solvatochromic shifts of pNP and pNP - is calculated as 0.71 eV in good agreement with the experimental one (0.79-0.81 eV). Finally, these shifts are understood in terms of the solvent effect on the solute structure, accurately calculated by the present theoretical treatment.

Thrombin is a serine protease involved in the blood coagulation reaction, and it shows maximum enzymatic activity in the presence of Na + . It has been supposed that Na + binding promotes conversion from the inactive form, with a collapsed primary substrate pocket (S1 pocket), to the active form, with a properly formed S1 pocket. However, the evidence supporting this activation mechanism was derived from the X-ray crystallographic structures solved under nonphysiological conditions and using thrombin mutants; thus, it still remains elusive whether the activation mechanism is actually attributed to Na + binding. To address the problem, we employed all-atom molecular dynamics simulations for both active and inactive forms of thrombin in the presence and absence of Na + binding and examined the effect of Na + binding on S1-pocket formation. In contrast to the conventional supposition, we revealed that Na + binding does not prevent S1-pocket collapse virtually, but rather, the bound Na + can move to the S1 pocket, thus blocking substrate access directly. Additionally, it was clarified that Na + binding does not promote S1-pocket formation. According to these insights, we concluded that Na + binding is irrelevant to the interconversion between the inactive and active forms of thrombin.

Ring-opening polymerization of lactones initiated by cyclodextrins has been reported as a promising polymer synthetic method. To investigate the unknown molecular level mechanism of the initiation reaction, we executed molecular dynamics simulations of model systems composed of single or multiple β-cyclodextrin (β-CD) molecules in δ-valerolactone (VL) solvent and explored the reactant complex structures satisfying three conditions (VL inclusion in the β-CD cavity, hydrogen bonding, and nucleophilic attack) at the same time. As a result, we confirmed the formation of the reactant complex structure. Comparison between the single and multiple β-CD models revealed that the formation is more frequent and the distance for the nucleophilic attack is shorter in the multiple model. Therefore, we anticipate that the reaction proceeds more efficiently by the cooperation of multiple β-CDs. This finding will contribute to understanding the reaction mechanism from the atomistic point of view.

Thrombin has been studied as a paradigmatic protein of Na(+)-activated allosteric enzymes. Earlier structural studies suggest that Na(+)-binding promotes the thrombin-substrate association reaction. However, it is still elusive because (1) the structural change, driven by Na(+)-binding, is as small as the thermal fluctuation, and (2) the bound Na(+) is close to Asp189 in the primary substrate binding pocket (S1-pocket), possibly preventing substrate access via repulsive interaction. It still remains a matter of debate whether Na(+)-binding actually promotes the reaction. To solve this problem, we examined the effect of Na(+) on the reaction by employing molecular dynamics (MD) simulations. By executing independent 210 MD simulations of apo and holo systems, we obtained 80 and 26 trajectories undergoing substrate access to S1-pocket, respectively. Interestingly, Na(+)-binding results in a 3-fold reduction of the substrate access. Furthermore, we examined works for the substrate access and release, and found that Na(+)-binding is disadvantageous for the presence of the substrate in the S1-pocket. These observations provide the insight that the bound Na(+) is essentially a negative effecter in thrombin-substrate stereospecific complex formation. The insight rationalizes an enigmatic feature of thrombin, relatively low Na(+)-binding affinity. This is essential to reduce the disadvantage of Na(+)-binding in the substrate-binding.

In solution chemical reaction, we often need to consider a multidimensional free energy (FE) surface (FES) which is analogous to a Born-Oppenheimer potential energy surface. To survey the FES, an efficient computational research protocol is proposed within the QM/MM framework; (i) we first obtain some stable states (or transition states) involved by optimizing their structures on the FES, in a stepwise fashion, finally using the free energy gradient (FEG) method, and then (ii) we directly obtain the FE differences among any arbitrary states on the FES, efficiently by employing the QM/MM method with energy representation (ER), i.e., the QM/MM-ER method. To validate the calculation accuracy and efficiency, we applied the above FEG-ER methodology to a typical isomerization reaction of glycine in aqueous solution, and reproduced quite satisfactorily the experimental value of the reaction FE. Further, it was found that the structural relaxation of the solute in the QM/MM force field is not negligible to estimate correctly the FES. We believe that the present research protocol should become prevailing as one computational strategy and will play promising and important roles in solution chemistry toward solution reaction ergodography.

Upon protein-substrate association reaction, dewetting of the substrate-binding pocket is one of the rate-limiting processes. However, understanding the microscopic mechanism still remains challenging because of practical limitations of experimental methodologies. We have addressed the problem here by using molecular dynamics (MD) simulation of the thrombin-substrate association reaction. During the MD simulation, ArgP1 in a substrate accessed thrombin's substrate-binding pocket and formed specific hydrogen bonds (H-bonds) with Asp189 in thrombin, while the catalytic serine of thrombin was still away from the substrate's active site. It is assumed that the thrombin-substrate association reaction is regulated by a stepwise mechanism. Furthermore, in the earlier stage of ArgP1 access to the pocket, we observed that ArgP1 was spatially separated from Asp189 by two water molecules in the pocket. These water molecules transferred from the pocket, followed by the specific H-bond formation between thrombin and the substrate. Interestingly, they were not evacuated directly from the pocket to the bulk solvent, but moved to the water channel of thrombin. This observation indicates that the channel plays functional roles in dewetting upon the association reaction.

FT-30, a typical aromatic polyamide membrane, is formed by interfacial polycondensation (IP) reaction between m-phenylenediamine (MPD) and benzene 1,3,5-tricarboxylic acid chloride (TMC) monomers. To investigate its microscopic characteristics, we performed an atomistic molecular simulation using the hybrid MC/MD reaction method modified to allow intercellular chemical bonds stretching over the periodic boundaries. Starting with appropriate monomer model systems, we succeeded in making membrane models by simulating a succession of condensation reactions. Through an analysis comparing our calculation results for the degrees of polymer cross-linking (DPC) and the composition ratios to the experimental results, we clarified the MPD/TMC mixing ratios in the near-surface active (NSA) and interior active (IA) regions associated with the reaction mechanism of IP. Further, we executed water diffusion simulations using the membrane model of the IA region and showed the calculated values of the total mass density of the hydrated membrane and the partition coefficient K to be in good agreement with the experimental ones. In conclusion, the present computationally modeled polyamide membrane has sufficient fidelity to the actual membrane and should be considered a stable spatial structure in the local equilibrium state under a nonequilibrium stationary state of permeation.

We shed light on important roles of unbound Na(+) molecules in enzymatic activation of thrombin. Molecular mechanism of Na(+)-activation of thrombin has been discussed in the context of allostery. However, the recent challenge to redesign K(+)-activated thrombin revealed that the allosteric interaction is insufficient to explain the mechanism. Under these circumstances, we have examined the roles of unbound Na(+) molecule in maximization of thrombin-substrate association reaction rate. We performed all-atomic molecular dynamics (MD) simulations of thrombin in the presence of three different cations; Li(+), Na(+), and Cs(+). Although these cations are commonly observed in the vicinity of the S1-pocket of thrombin, smaller cations are distributed more densely and extensively than larger ones. This suggests the two observation rules: (i) thrombin surrounded by Na(+) is at an advantage in the initial step of association reaction, namely, the formation of an encounter complex ensemble, and (ii) the presence of Na(+) molecules does not necessarily have an advantage in the final step of association reaction, namely, the formation of the stereospecific complex. In conclusion, we propose a conjecture that unbound Na(+) molecules also affect the maximization of rate constant of thrombin-substrate association reaction through optimally forming an encounter complex ensemble.

The heme oxygen (O2) binding site of human hemoglobin (HbA) is buried in the interior of the protein, and there is a debate over the O2 entry pathways from solvent to the binding site. As a first step to understand HbA O2 binding process at the atomic level, we detected all significant multiple O2 entry pathways from solvent to the binding site in the α and β subunits of the T-state tetramer HbA by utilizing ensemble molecular dynamics (MD) simulation. By executing 128 independent 8 ns MD trajectories in O2-rich aqueous solvent, we simulated the O2 entry processes and obtained 141 and 425 O2 entry events in the α and β subunits of HbA, respectively. We developed the intrinsic pathway identification by clustering method to achieve a persuasive visualization of the multiple entry pathways including both the shapes and relative importance of each pathway. The rate constants of O2 entry estimated from the MD simulations correspond to the experimentally observed values, suggesting that O2 ligands enter the binding site through multiple pathways. The obtained multiple pathway map can be utilized for future detailed analysis of HbA O2 binding process.

A mixture of ferrous ions and hydrogen peroxide, known as Fenton's reagent, is an effective oxidant and has been widely used in various industrial applications; however, there is still controversy about what the oxidizing agents are and how they are produced. In this study, we have determined minimum free-energy paths (MFEPs) from Fenton's reagent to possible oxidizing agents such as hydroxyl radicals and ferryl-oxo species by combining ab initio molecular dynamics simulations and an MFEP search method. Along the MFEPs, representative free-energy profiles of the Fenton reaction were elucidated. On the basis of the free-energy profiles, we revealed that the reaction producing ferryl-oxo species from Fenton's reagent is more energetically favorable than that yielding a free hydroxyl radical, by 24.4 kcal mol(-1), which indicates that the ferryl-oxo species is the primary oxidizing agent in reactions of Fenton's reagent. Moreover, we clarified that the ferryl-oxo species is favorably formed via a two-step reaction pathway, which reaches the product through a dihydroxyiron(IV) intermediate. The energetics charting the free-energy profiles provided valuable information for a comprehensive understanding of Fenton reactions. We concluded that a ferryl-oxo species produced from Fenton's reagent serves as the primary oxidizing agent in the Fenton reaction.

The transfer free energy (TFE) of apomyoglobin (AMb) from pure water into aqueous solution with trimethylamine N-oxide (TMAO) was investigated by all-atom molecular dynamics (MD) simulation combined with the Kirkwood-Buff (KB) integral method. The simulated TFE and the preferential interaction parameter correlated favorably with experimental values. In addition, the time-resolved KB integral revealed that a significant fluctuation in the TFE arose from the alteration in TMAO solvation around AMb. Furthermore, spatial decomposition of the KB integrals revealed how the local elements of the TFE are spatially distributed around AMb. These results revealed the spatio-temporal characteristics of the protein TFE into the molecular crowding condition with TMAO.

The influence of hydrostatic pressure on the partial molar volume (PMV) of the protein apomyoglobin (AMb) was investigated by all-atom molecular dynamics (MD) simulations. Using the time-resolved Kirkwood-Buff (KB) approach, the dynamic behavior of the PMV was identified. The simulated time average value of the PMV and its reduction by 3000 bar pressurization correlated with experimental data. In addition, with the aid of the surficial KB integral method, we obtained the spatial distributions of the components of PMV to elucidate the detailed mechanism of the PMV reduction. New R-dependent PMV profiles identified the regions that increase or decrease the PMV under the high pressure condition. The results indicate that besides the hydration in the vicinity of the protein surface, the outer space of the first hydration layer also significantly influences the total PMV change. These results provide a direct and detailed picture of pressure induced PMV reduction.

The structural dynamics of the clamshell rotation of photodissociated carbonmonoxy myoglobin, which is expected to be important for hemoglobin allostery, is investigated by the perturbation ensemble method. In this method, many pairs of perturbed and unperturbed molecular dynamics trajectories are ensemble-averaged to cancel out thermal noises and to detect subtle changes. The number of MD trajectory pairs, in this work 2000 pairs, should be determined to obtain physical properties of interest with statistically meaningful precisions. The calculated structural changes after 20 ps of the photodissociation are consistent with those by time-resolved X-ray diffraction at 100 ps delay time. In the heme proximal side region including the F and H helices, both helices displaced in the proximal direction. Meanwhile, in the heme distal side region including E and A helices, both helices moved toward the heme group after photodissociation. These proximal and distal side displacements occur on a fast time scale (almost complete within 3 ps) and are consistent with the clamshell rotation. Moreover, it was found that the ensemble-averaged structural dynamics of the photodissociated MbCO is independent of the amount of initial excess vibrational energy of the heme, or the difference of excitation photon wavelength. These results provide atomistic details on the functionally important dynamics of the clamshell rotation. Application of the present methodology to Hb will give new insight into the incipient stereochemical mechanism of hemoglobin allostery.

The partial molar volume (PMV) of the protein chymotrypsin inhibitor 2 (CI2) was calculated by all-atom MD simulation. Denatured CI2 showed almost the same average PMV value as that of native CI2. This is consistent with the phenomenological question of the protein volume paradox. Furthermore, using the surficial Kirkwood-Buff approach, spatial distributions of PMV were analyzed as a function of the distance from the CI2 surface. The profiles of the new R-dependent PMV indicate that, in denatured CI2, the reduction in the solvent electrostatic interaction volume is canceled out mainly by an increment in thermal volume in the vicinity of its surface. In addition, the PMV of the denatured CI2 was found to increase in the region in which the number density of water atoms is minimum. These results provide a direct and detailed picture of the mechanism of the protein volume paradox suggested by Chalikian et al.

Ectoine, a zwitterionic compatible solute (CS), acts as an effective stabilizer of protein function. Using molecular dynamics simulation, solvent spatial distributions around both met-enkephalin (M-Enk) and chymotrypsin inhibitor 2 (CI2) were investigated at the molecular level in ectoine aqueous solution. An unexpected finding was that ectoine exhibits preferential binding, as an overall tendency, around both peptides. However, with the aid of the surficial Kirkwood-Buff parameter, it was clearly shown that the preferential exclusion of ectoine from the peptide surface was weaker in the smaller M-Enk than in the larger CI2. It is concluded that a denser and more structured hydration layer, such as that developed on the surface of CI2, is an important factor in the exclusion of ectoine.

The effectiveness of the ensemble perturbation method, in which many pairs of perturbed and unperturbed molecular dynamics simulations are executed for the ensemble average, has been demonstrated by calculating the subtle anisotropic structural change of carbonmonoxy myoglobin (MbCO) triggered by ligand photolysis. The results show that Mb largely expands in the direction perpendicular to the heme plane and slightly contracts in the horizontal one. This agrees well with the report in the transient grating experiment. In addition, it is suggested that the expansion contributes strongly to the fast energy-transfer process to the water solvent because it is undergone almost within several picoseconds. The mechanical work done on the solvent by the expansion within 1 ps was thermodynamically estimated to be 4.8 kcal/mol.

The methyllithium tetramer (CH3Li)4 structure in the bcc crystal has been theoretically optimized with the use of density functional theory calculations under the periodic boundary condition. The X-ray structure shows that the methyl-group conformation in tetramer in crystal takes the staggered form rather than the eclipsed form that is taken in the isolated tetramer, i.e., the crystal packing effect, and this has been reproduced for the first time. It is concluded that the staggered form is advantageous in crystal, as a whole, due to the larger electrostatic stabilization via the induced intratetramer multipolarization, although it should cause, simultaneously, smaller destabilization in intratetramer electronic energy.