3-site Models Research Articles

2-Site versus 3-site models of ATP hydrolysis by F1-ATPase: definitive mathematical proof using combinatorics and conservation equations.

The F1-ATPase enzyme is the smallest-known molecular motor that rotates in 120° steps, driven by the hydrolysis of ATP. It is a multi-subunit enzyme that contains three catalytic sites. A central question is how the elementary chemical reactions that occur in the three sites are coupled to mechanical rotation. Various models and coupling schemes have been formulated in an attempt to answer this question. They can be classified as 2-site (bi-site) models, exemplified by Boyer's binding change mechanism first proposed 50years ago, and 3-site (tri-site) models such as Nath's torsional mechanism, first postulated 25years ago and embellished 1year back. Experimental data collated using diverse approaches have conclusively shown that steady-state ATP hydrolysis by F1-ATPase occurs in tri-site mode. Hence older models have been continually modified to make them conform to the new facts. Here, we have developed a pure mathematical approach based on combinatorics and conservation laws to test if proposed models are 2-site or 3-site. Based on this novel combinatorial approach, we have proved that older and modified models are effectively bi‒site models in that catalysis and rotation in F1-ATPase occurs in these models with only two catalytic sites occupied by bound nucleotide. Hence these models contradict consensus experimental data. The recent 2023 model of ATP hydrolysis by F1-ATPase has been proved to be a true tri-site model based on our novel mathematical approach. Such pure mathematical proofs constitute an important step forward for ATP mechanism. However, in what must be considered an aspect with great scientific potential, the power of such mathematical proofs has not been fully exploited to solve molecular biological problems, in our opinion. We believe that the creative application of pure mathematical proofs (for another example see Nath in Theory Biosci 141:249-260, 2022) can help resolve with finality various longstanding molecular-level issues that arise as a matter of course in the analysis of fundamental biological problems. Such issues have proved extraordinarily difficult to resolve by standard experimental, theoretical, or computational approaches.

Molecular Dynamics Simulation of Diffusion and O2 Dissolution in Water Using Four Water Molecular Models

This work evaluates four popular 3-site water models, TIP3P, SPC/E, SPC, and F3C, in predicting temperature-dependent O2 diffusion and dissolution and self-diffusion in liquid water for electrochemical devices, such as fuel cells, electrolyzers and metal-air batteries, using molecular dynamics simulations. We report that the TIP3P and SPC models overestimate O2 diffusivity, though qualitatively describe its temperature dependence, while the SPC/E and F3C models show a good prediction of O2 diffusivity with the former accurately predicting its activation energy. The TIP3P, SPC, and F3C models overestimate the O2 solubility with the TIP3P even incorrectly predicting its temperature dependence. The SPC/E model shows the best performance in predicting both the O2 diffusivity (<15% error) and solubility (<16% error) in the temperature range. The radial distribution functions of O atoms are present and show that lower peaks, i.e. more intermolecular space among water molecules for the random walks, leads to higher prediction of diffusivities. Comparison with literature experimental data is summarized.

PSO-Assisted Development of New Transferable Coarse-Grained Water Models.

We have employed two-to-one mapping scheme to develop three coarse-grained (CG) water models, namely, 1-, 2-, and 3-site CG models. Here, for the first time, particle swarm optimization (PSO) and gradient descent methods were coupled to optimize the force-field parameters of the CG models to reproduce the density, self-diffusion coefficient, and dielectric constant of real water at 300 K. The CG MD simulations of these new models conducted with various timesteps, for different system sizes, and at a range of different temperatures are able to predict the density, self-diffusion coefficient, dielectric constant, surface tension, heat of vaporization, hydration free energy, and isothermal compressibility of real water with excellent accuracy. The 1-site model is ∼3 and ∼4.5 times computationally more efficient than 2- and 3-site models, respectively. To utilize the speed of 1-site model and electrostatic interactions offered by 2- and 3-site models, CG MD simulations of 1:1 combination of 1- and 2-/3-site models were performed at 300 K. These mixture simulations could also predict the properties of real water with good accuracy. Two new CG models of benzene, consisting of beads with and without partial charges, were developed. All three water models showed good capacity to solvate these benzene models.

Surface structure of ferrihydrite: Insights from modeling surface charge

Ferrihydrite (FH) plays an important role in controlling the fate and transport of many compounds in nature due to its large surface area and high reactivity. This study is the first attempt to build a surface complexation model using the recently proposed surface structure that incorporates tetrahedrally coordinated Fe atoms (Hiemstra, 2013). The ability of the model to describe the surface charge curves of FH with different preparation methods and Points of Zero Net Proton Charge (PZNPC) is tested. In general, FH particles that have been subject to aging are larger and have lower specific surface area (SSA) and higher PZNPCs. The structural model includes 2 types of singly coordinated (SC) oxygens that are present only on the (1-11) and (1-10) faces and 5 types of triply coordinated (TC) oxygens that are also present on the basal planes (001) and (00-1), for a total of 11 sites. The 11 - site model was able to simulate fresh FH datasets with PZNPC lower than 8.5, but could only simulate higher PZNPCs when the contribution of the more acidic basal planes was minimized. The available microscopic observations do not support this condition, which suggests TC groups on the basal planes likely have log K values higher than the macroscopic PZNPC. We attempted to test this hypothesis through three versions of simplified 3-site models, using SC and one TC on (1-10) and (1-11), with log K 8.0 (equal to fresh FH PZNPC) and one TC group on the basal planes with log K 9.5. This enables fitting of the PZNPC of aged FH datasets by adjusting the face contributions. An unresolved issue is whether this model accurately describes the relative contribution of SC and TC sites to the overall charge, which has implications for accurate description of specific ion adsorption.

Sensitivity of Protein Glass Transition to the Choice of Water Model.

The sensitivity of protein glass transition temperature and dynamics of Trp-cage miniprotein to the choice of water models have been investigated by performing molecular dynamics simulations at different temperatures between 130 and 300 K using mTIP3P, TIP4P, and TIP4P-Ew water models with the CHARMM22 force field. Analysis of the structure of the protein and the ordering of the hydration shell water molecules revealed correlated dynamic crossovers of the protein and its hydration water. It is demonstrated that the parametrization of different water models is robust enough to probe the onset temperatures for the two dynamic crossovers of the peptide: the first one around 150 K which is attributed to active methyl group rotations and the second one around 200-230 K specifically pertaining to glass transition of the protein. The behavior of the protein has been found to be qualitatively similar to the three water models employed, while the structural ordering and number of hydration shell waters vary significantly among the 3-site and 4-site water models. The changes in the probability density map of methyl hydrogens of the protein with temperature also show sensitivity to the choice of water model.

Bottom-up coarse-grained models that accurately describe the structure, pressure, and compressibility of molecular liquids.

The present work investigates the capability of bottom-up coarse-graining (CG) methods for accurately modeling both structural and thermodynamic properties of all-atom (AA) models for molecular liquids. In particular, we consider 1, 2, and 3-site CG models for heptane, as well as 1 and 3-site CG models for toluene. For each model, we employ the multiscale coarse-graining method to determine interaction potentials that optimally approximate the configuration dependence of the many-body potential of mean force (PMF). We employ a previously developed "pressure-matching" variational principle to determine a volume-dependent contribution to the potential, UV(V), that approximates the volume-dependence of the PMF. We demonstrate that the resulting CG models describe AA density fluctuations with qualitative, but not quantitative, accuracy. Accordingly, we develop a self-consistent approach for further optimizing UV, such that the CG models accurately reproduce the equilibrium density, compressibility, and average pressure of the AA models, although the CG models still significantly underestimate the atomic pressure fluctuations. Additionally, by comparing this array of models that accurately describe the structure and thermodynamic pressure of heptane and toluene at a range of different resolutions, we investigate the impact of bottom-up coarse-graining upon thermodynamic properties. In particular, we demonstrate that UV accounts for the reduced cohesion in the CG models. Finally, we observe that bottom-up coarse-graining introduces subtle correlations between the resolution, the cohesive energy density, and the "simplicity" of the model.

Neptunium(V) sorption to goethite at attomolar to micromolar concentrations

Sorption of 10−18–10−5M neptunium (Np) to goethite was examined using liquid scintillation counting and gamma spectroscopy. A combination approach using 239Np and long lived 237Np was employed to span this wide concentration range. 239Np detection limits were determined to be 2×10−18M and 3×10−17M for liquid scintillation counting and gamma spectroscopy, respectively. Sorption was found to be linear below 10−11M, in contrast to the non-linear behavior observed at higher concentrations both here and in the literature. 2-site and 3-site Langmuir models were used to simulate sorption behavior over the entire 10−18–10−5M range. The 3-site model fit yielded Type I and II site densities of 3.56sites/nm2 (99.6%) and 0.014±0.007sites/nm2 (0.4±0.1%), consistent with typical “high affinity” and “low affinity” sites reported in the literature [21]. Modeling results for both models suggest that sorption below ∼10−11M is controlled by a third (Type III) site with a density on the order of ∼7×10−5sites/nm2 (∼0.002%). While the nature of this “site” cannot be determined from isotherm data alone, the sorption data at ultra-low Np concentrations indicate that Np(V) sorption to goethite at environmentally relevant concentrations will be (1) linear and (2) higher than previous (high concentration) laboratory experiments suggest.

Conditional reversible work method for molecular coarse graining applications

Systematically coarse grained models for complex fluids usually lack chemical and thermodynamic transferability. Efforts to improve transferability require the development of effective potentials with unequivocal physical significance. In this paper, we introduce conditional reversible work (CRW) potentials that describe nonbonded interactions in coarse grained models at the pair level. The method used to obtain these potentials is straightforward to implement, can be readily extended to compute hydration contributions in implicit-solvent potentials, and is easy to automize. As a first illustration of the method, we present CRW potentials for 3-site models of hexane and toluene. The temperature-transferability of the liquid phase density obtained with these potentials has been investigated, and a comparison has been made with effective potentials obtained by the iterative Boltzmann inversion method.

Are Skinfold-Based Models Accurate and Suitable for Assessing Changes in Body Composition in Highly Trained Athletes?

This study was designed to assess the usefulness of skinfold (SKF) equations developed by Jackson and Pollock (JP) and by Evans (Ev) in tracking body composition changes (relative fat mass [%FM], absolute fat mass [FM], and fat-free mass [FFM]) of elite male judo athletes before a competition using a 4-compartment (4C) model as the reference method. A total of 18 male, top-level (age: 22.6 +/- 2.9 yr) athletes were evaluated at baseline (weight: 73.4 +/- 7.9 kg; %FM4C: 7.0 +/- 3.3%; FM4C: 5.1 +/- 2.6 kg; and FFM4C: 68.3 +/- 7.3 kg) and before a competition (weight: 72.7 +/- 7.5 kg; %FM4C: 6.5 +/- 3.4%; FM4C: 4.8 +/- 2.6 kg; and FFM4C: 67.9 +/- 7.1 kg). Measures of body density assessed by air displacement plethysmography, bone mineral content by dual energy X-ray absorptiometry, and total-body water by bioelectrical impedance spectroscopy were used to estimate 4C model %FM, FM, and FFM. Seven SKF site models using both JP and Ev were used to estimate %FM, FM, and FFM along with the simplified Ev3SKF site. Changes in %FM, FM, and FFM were not significantly different from the 4C model. The regression model for the SKF in question and the reference method did not differ from the line of identity in estimating changes in %FM, FM, and FFM. The limits of agreement were similar, ranging from -3.4 to 3.6 for %FM, -2.7 to 2.5 kg for FM, and -2.5 to 2.7 kg for FFM. Considering the similar performance of both 7SKF- and 3SKF-based equations compared with the criterion method, these data indicate that either the 7- or 3-site SFK models are not valid to detect %FM, FM, and FFM changes of highly trained athletes. These results highlighted the inaccuracy of anthropometric models in tracking desired changes in body composition of elite male judo athletes before a competition.

Adsorption of carbon dioxide of 1-site and 3-site models in pillared clays: A Gibbs ensemble Monte Carlo simulation

Adsorption behavior of carbon dioxide confined in pillared clays is analyzed by using constant pressure Gibbs ensemble Monte Carlo (GEMC) method. In our simulation, 1-site and 3-site models are used to represent carbon dioxide. At the 1-site model, carbon dioxide is described as a Lennard–Jones (LJ) sphere, while at the 3-site model, carbon dioxide is modeled as a three-sites linear chain represented by EPM2 potential considering the quadrapolar effect. The potential model from Yi et al. for pillared clays is used to emphasize its quasi two-dimensional structure. Comparing the calculated results from the 1-site and the 3-site models at T = 228.15 and 258.15 K, we observe that the adsorption amount from the two models is the same basically. However, the local density presents a significant difference, because the shoulder in the main peak near the wall from 3-site model can reflect the orientation of carbon dioxide. Accordingly, in the systematical investigation to explore the effect of porosity and pore width on the adsorption of carbon dioxide in pillared clays, the 3-site model was only used. We observe that for a narrow pore of H = 1.02 nm , each isotherm shape displays type I curve, suggesting that it is not inflected by the porosity. However, for the larger pores of H = 1.70 and H = 2.38 nm , the increase of the porosity alters the shape of adsorption isotherms from a simple linear relation to the first order jump, indicating that the porosity is of very important factor to affect adsorption and phase behavior of fluids confined in pillared clays. The excess adsorptions of carbon dioxide at supercritical temperatures of T = 323.15 and 348.15 K are also investigated. We find that the maximum exists for each excess isotherm, and the optimal pressure corresponding to the maximum increases with the pore width. However, the porosity has no significant effect on the optimal pressure.

The Structure of Liquid Methanol: A Molecular Dynamics Study Using Three-Site Models

The structure of liquid methanol at 298.15 K is investigated by performing molecular dynamics (MD) simulations in NVE ensemble using two 3-site force field models. The simulated structural results are compared with the recent neutron diffraction (ND) results obtained at the partial pair distribution function (pdf) level by employing H/D substitution on the hydroxyl hydrogen, Ho. Overall agreement is found between the simulated and experimental total intermolecular radial distribution functions (rdfs). The ability of the 3-site model simulations to satisfactorily reproduce experimental X—X (X = C, O or H- a methyl hydrogen) intermolecular partial distribution function, dominated by contributions from the methyl group. demonstrates that the methyl group does not participate in any bonding in the liquid. However, a comparison between the simulated and experimental Ho—Ho and X—Ho functions reveals that discrepancies still exist at a quantitative level.

Molecular dynamics studies of NaCl solutions in methanol–water mixtures.: An effect of NaCl on hydrogen bonded network

Hydrogen bonds of methanol and water molecules in binary solvents and in ternary solutions containing NaCl have been investigated by molecular dynamics simulation. Methanol and water molecules have been described using 3-site flexible models. Average numbers of the H-bonds were computed using geometric and energetic definitions. Special attention has been paid to the influence of the mixture composition and addition of NaCl on H-bond statistics and energies. Increase of the methanol concentration causes a decrease of the average H-bond numbers and an increase of the H-bond strength. The influence of NaCl on the H-bonded network is limited. An NaCl effect is evident only on the molecules in the solvation shells of ions.

Flexible molecular models for molecular dynamics study of near and supercritical water

Four flexible water models based on the harmonic and a modified anharmonic form of Toukan and Rahman intramolecular potential models grafted onto 3-site and 4-site intermolecular models were proposed, and the influence of their flexibility and intermolecular potential on the phase behavior were examined. A global optimization of the potential parameters was performed according to the physical properties and IR spectra of water at the ambient state. The critical properties of the four models were estimated by using direct molecular dynamics (MD) simulation of liquid–vapor coexisting phases and fitting the coexisting densities to the law of rectilinear diameter and the scaling law for density with a scaling exponent of β c=0.325. Based on a similar intermolecular model (the simple point charge model, SPC) we found that the anharmonic model gave a critical point ( T c=370.3±3.6°C; ρ c=0.32±0.006 g/cm 3) which agreed well with the experimental properties ( T c=374.0°C; ρ c=0.322 g/cm 3), while the harmonic model gave low values ( T c=337.3±8.5°C; ρ c=0.290±0.007 g/cm 3). On the other hand, for anharmonic flexible water models adopting the experimental value, the model grafted onto a 3-site TIPS model (the transferable intermolecular potential functions, TIP3P) did not provide satisfactory reproduction of the critical point ( T c=320.1±5.2°C; ρ c=0.288±0.005 g/cm 3), while the model grafted onto a 4-site TIPS model (modified TIP4P model with M-site on the center of mass, referred to as cm4P) provided good representation of critical properties ( T c=368.4±6.2°C; ρ c=0.307±0.005 g/cm 3). The flexible models with anharmonic form of flexibility grafted the SPC or cm4P model are suitable model for study of water and aqueous solutions in state points ranging from liquid to near- and supercritical region.