A methodology of quantifying membrane permeability based on returning probability theory and molecular dynamics simulation.

We propose a theoretical approach to estimate the permeability coefficients of substrates (permeants) for crossing membranes from donor (D) phase to acceptor (A) phase by means of molecular dynamics (MD) simulation. A fundamental aspect of our approach involves reformulating the returning probability (RP) theory, a rigorous bimolecular reaction theory, to describe permeation phenomena. This reformulation relies on the parallelism between permeation and bimolecular reaction processes. In the present method, the permeability coefficient is represented in terms of the thermodynamic and kinetic quantities for the reactive (R) phase that exists within the inner region of a membrane. One can evaluate these quantities using multiple MD trajectories starting from phase R. We apply the RP theory to the permeation of ethanol and methylamine at different concentrations (infinitely dilute and 1 mol % conditions of permeants). Under the 1 mol% condition, the present method yields a larger permeability coefficient for ethanol (0.12 ± 0.01 cm s-1) than for methylamine (0.069 ± 0.006 cm s-1), while the values of the permeability coefficient are satisfactorily close to those obtained from the brute-force MD simulations (0.18 ± 0.03 and 0.052 ± 0.005 cm s-1 for ethanol and methylamine, respectively). Moreover, upon analyzing the thermodynamic and kinetic contributions to the permeability, we clarify that a higher concentration dependency of permeability for ethanol, as compared to methylamine, arises from the sensitive nature of ethanol's free-energy barrier within the inner region of the membrane against ethanol concentration.

Influence of cholesterol on hydrogen-bond dynamics of water molecules in lipid-bilayer systems at varying temperatures.

Cholesterol (Chol) plays a crucial role in shaping the intricate physicochemical attributes of biomembranes, exerting a considerable influence on water molecules proximal to the membrane interface. In this study, we conducted molecular dynamics simulations on the bilayers of two lipid species, dipalmitoylphosphatidylcholine (DPPC) and palmitoyl sphingomyelin; they are distinct with respect to the structures of the hydrogen-bond (H-bond) acceptors. Our investigation focuses on the dynamic properties and H-bonds of water molecules in the lipid-membrane systems, with a particular emphasis on the influence of Chol at varying temperatures. Notably, in the gel phase at 303 K, the presence of Chol extends the lifetimes of H-bonds of the oxygen atoms acting as H-bond acceptors within DPPC with water molecules by a factor of 1.5-2.5. In the liquid-crystalline phase at 323 K, on the other hand, H-bonding dynamics with lipid membranes remain largely unaffected by Chol. This observed shift in H-bonding states serves as a crucial key to unraveling the subtle control mechanisms governing water dynamics in lipid-membrane systems.

High Antifouling Performance of Weakly Hydrophilic Polymer Brushes: A Molecular Dynamics Study.

The antifouling performance of polymer brushes usually improves with increasing hydrophilicity of the grafted polymer. However, in some cases, less hydrophilic polymers show comparable or better antifouling performance than do more hydrophilic polymers. We investigate the mechanism of this anomalous behavior using molecular dynamics (MD) simulations of coarse-grained (CG) models of weakly and strongly hydrophilic polymers. The antifouling performance is evaluated from the potential of mean force of a model protein. The strongly hydrophilic polymer exhibits a better antifouling performance than the weakly hydrophilic polymer when the substrate of the polymer brush is repulsive. However, when the substrate is sufficiently attractive, the weakly hydrophilic polymer brush becomes more effective than the strongly hydrophilic brush in a certain range of grafting density. This is because the weakly hydrophilic polymer chains form a tightly packed layer that prevents the adsorbate molecule from contacting the substrate. We also perform all-atom (AA) MD simulations for several standard polymers to examine the correspondence with the CG polymer models. The weakly hydrophilic CG polymer is found to be similar to poly[N-(2-hydroxypropyl)methacrylamide] and poly(2-hydroxyethyl methacrylate), both of which have a hydroxyl group in a monomer unit. The strongly hydrophilic CG polymer resembles zwitterionic poly(carboxybetaine methacrylate). A discussion referring to the adsorption free energies of proteins on surfaces calculated in previous AA MD studies suggests that the higher antifouling performance of less hydrophilic polymer brushes can be realized for various combinations of protein and surface.

Synergistic Solvation as the Enhancement of Local Mixing.

Mixing two solvents can sometimes make a much better solvent than expected from their weighted mean. This phenomenon, called synergistic solvation, has commonly been explained via the Hildebrand and Hansen solubility parameters, yet their inability in other solubilization phenomena, most notably hydrotropy, necessitates an alternative route to elucidating solubilization. While, recently, the universal theory of solubilization was founded on the statistical thermodynamic fluctuation theory (as a generalization of the Kirkwood-Buff theory), its demand for experimental data processing has been a hindrance for its wider application. This can be overcome by the solubility isotherm theory, which is founded on the fluctuation theory yet reduces experimental data processing significantly to the level of isotherm analysis in sorption. The isotherm analysis identifies the driving force of synergistic solvation as the enhancement of solvent mixing around the solute, opposite in behavior to hydrotropy (characterized by the enhancement of demixing or self-association around the solute). Thus, the fluctuation theory, including its solubility isotherms, provides a universal language for solubilization across the historic subcategorization of solubilizers, for which different (and often contradictory) mechanistic models have been proposed.

Sorption Hysteresis: A Statistical Thermodynamic Fluctuation Theory.

Hysteresis is observed commonly in sorption isotherms of porous materials. Still, there has so far been no unified approach that can both model hysteresis and assess its underlying energetics. Standard approaches, such as capillary condensation and isotherms based on interfacial equations of state, have not proved to be up to the task. Here, we show that a statistical thermodynamic approach can achieve the following needs simultaneously: (i) showing why adsorption and desorption transitions may be sharp yet continuous; (ii) providing a simple (analytic) isotherm equation for hysteresis branches; (iii) clarifying the energetics underlying sorption hysteresis; and (iv) providing macroscopic and nanoscopic perspectives to understanding hysteresis. This approach identifies the two pairs of parameters (determinable by fitting experimental data) that are required to describe the hysteresis: the free energy per molecule within the pore clusters and the cluster size in the pores. The present paper focuses on providing mechanistic insights to IUPAC hysteresis types H1, H2(a), and H2(b) and can also be applied to the isotherm types IV and V.

Unveiling interatomic distances influencing the reaction coordinates in alanine dipeptide isomerization: An explainable deep learning approach.

The present work shows that the free energy landscape associated with alanine dipeptide isomerization can be effectively represented by specific interatomic distances without explicit reference to dihedral angles. Conventionally, two stable states of alanine dipeptide in vacuum, i.e., C7eq (ß-sheet structure) and C7ax (left handed α-helix structure), have been primarily characterized using the main chain dihedral angles, φ (C-N-Cα-C) and ψ (N-Cα-C-N). However, our recent deep learning combined with the "Explainable AI" (XAI) framework has shown that the transition state can be adequately captured by a free energy landscape using φ and θ (O-C-N-Cα) [Kikutsuji et al., J. Chem. Phys. 156, 154108 (2022)]. In the perspective of extending these insights to other collective variables, a more detailed characterization of the transition state is required. In this work, we employ interatomic distances and bond angles as input variables for deep learning rather than the conventional and more elaborate dihedral angles. Our approach utilizes deep learning to investigate whether changes in the main chain dihedral angle can be expressed in terms of interatomic distances and bond angles. Furthermore, by incorporating XAI into our predictive analysis, we quantified the importance of each input variable and succeeded in clarifying the specific interatomic distance that affects the transition state. The results indicate that constructing a free energy landscape based on the identified interatomic distance can clearly distinguish between the two stable states and provide a comprehensive explanation for the energy barrier crossing.

How ATP suppresses the fibrillation of amyloid peptides: analysis of the free-energy contributions.

Recent experiments have revealed that adenosine triphosphate (ATP) suppresses the fibrillation of amyloid peptides - a process closely linked to neurodegenerative diseases such as Alzheimer's and Parkinson's. Apart from the adsorption of ATP onto amyloid peptides, the molecular understanding is still limited, leaving the underlying mechanism for the fibrillation suppression by ATP largely unclear, especially in regards to the molecular energetics. Here we provide an explanation at the molecular scale by quantifying the free energies using all-atom molecular dynamics simulations. We found that the changes of the free energies due to the addition of ATP lead to a significant equilibrium shift towards monomeric peptides in agreement with experiments. Despite ATP being a highly charged species, the decomposition of the free energies reveals that the van der Waals interactions with the peptide are decisive in determining the relative stabilization of the monomeric state. While the phosphate moiety exhibits strong electrostatic interactions, the compensation by the water solvent results in a minor, overall Coulomb contribution. Our quantitative analysis of the free energies identifies which intermolecular interactions are responsible for the suppression of the amyloid fibril formation by ATP and offers a promising method to analyze the roles of similarly complex cosolvents in aggregation processes.

Solvation dynamics on the diffusion timescale elucidated using energy-represented dynamics theory.

Photoexcitation of a solute alters the solute-solvent interaction, resulting in the nonequilibrium relaxation of the solvation structure, often called a dynamic Stokes shift or solvation dynamics. Thanks to the local nature of the solute-solvent interaction, the characteristics of the local solvent environment dissolving the solute can be captured by the observation of this process. Recently, we derived the energy-represented Smoluchowski-Vlasov (ERSV) equation, a diffusion equation for molecular liquids, which can be used to analyze the solvation dynamics on the diffusion timescale. This equation expresses the time development for the solvent distribution on the solute-solvent pair interaction energy (energy coordinate). Since the energy coordinate can effectively treat the solvent flexibility in addition to the position and orientation, the ERSV equation can be utilized in various solvent systems. Here, we apply the ERSV equation to the solvation dynamics of 6-propionyl-2-dimethylamino naphthalene (Prodan) in water and different alcohol solvents (methanol, ethanol, and 1-propanol) for clarifying the differences of the relaxation processes among these solvents. Prodan is a solvent-sensitive fluorescent probe and is thus widely utilized for investigating heterogeneous environments. On the long timescale, the ERSV equation satisfactorily reproduces the relaxation time correlation functions obtained from the molecular dynamics (MD) simulations for these solvents. We reveal that the relaxation time coefficient on the diffusion timescale linearly correlates with the inverse of the translational diffusion coefficients for the alcohol solvents because of the Prodan-solvent energy distributions among the alcohols. In the case of water, the time coefficient deviates from the linear relationship for the alcohols due to the difference in the extent of importance of the collective motion between the water and alcohol solvents.

Replacing the Langmuir Isotherm with the Statistical Thermodynamic Fluctuation Theory.

In the age of all-atom simulations, primitive isotherm models, such as Langmuir, BET, and GAB, are still used widely for analyzing experimental data. However, their routine applications to complex materials are not in line with their underlying assumptions (i.e., statistically independent adsorption sites with no interfacial structural changes), which manifests as the temperature dependence of the monolayer capacity. Our proposal is to replace these models with the statistical thermodynamic fluctuation theory because the ABC isotherm derived from it (i) contains these primitive models as its special cases, (ii) is applicable to any interfacial geometry, and (iii) is linked to molecular distribution functions, sharing the same language as simulations. Rectifying the inability of the primitive isotherm models to handle attractive and repulsive interactions consistently leads to a reconsideration of how physical interpretations should be attributed to the isotherms of empirical origin (e.g., Freundlich).

Biased Bowl-Direction of Monofluorosumanene in the Solid State.

A new curved π-conjugated molecule 1-fluorosumanene (1) was designed and synthesized that possesses one fluorine atom on the benzylic carbon of sumanene. This compound can exhibit bowl inversion in solution, leading to the formation of two diastereomers, 1endo and 1exo, with different dipole moments. Experimental and theoretical investigation revealed an energetical relationship among 1exo, 1endo, and solvent to realize the various endo:exo ratios in the single crystals of 1 depending on the crystallization solvent. Significantly, the molecular dynamics (MD) simulations revealed that 1exo positively worked for the elongation of the stacking structure and the final endo:exo ratio was affected by the relative stability difference between 1endo and 1exo derived by solvation. Such an arrangeable endo:exo ratio of 1 realized the preparation of unique materials showing a different dielectric response from the same molecule 1 just by changing the crystallization solvent.

Actual Amount Adsorbed as Estimated from the Surface Excess Isotherm.

The amount of adsorption at equilibrium is commonly used for reporting solid/solution isotherms, despite the admonishment by the International Union of Pure and Applied Chemistry (IUPAC) against equating the surface excess (i.e., the measurable quantity for sorption, signifying the competitive sorption of adsorbate and solvent) with the actual amount adsorbed. The consensus, more generally stated, is that the surface excess cannot be divided into individual isotherms for sorbate and solvent unless simplifying model assumptions are introduced. Here we show, contrary to the IUPAC report, that there exists a simple method for assigning the total isotherm to the sorbate's actual amount adsorbed and to the individual solute isotherm. This requires a combination of isotherm and volumetric measurements. For dilute sorbates, we establish criteria to show if the total isotherm is dominated by the amount of sorption at the interface, in agreement with the common assumption in the practical literature. In the absence of the volume data, we propose an approximate yet more versatile method based on the specific surface area to carry out order-of-magnitude analysis to examine whether the actual amount adsorbed dominates surface excess. Application of our methods to the adsorption of sodium decyl sulfate on polystyrene latex, malachite green on activated carbons, and thiophenes on a metal-organic framework all demonstrated the dominance of the actual amount adsorbed, significantly simplifying isotherm analysis in terms of the underlying interactions (i.e., surface-sorbate and net self-interactions at the interface), eliminating the need for excess surface quantities. Analysis of fully miscible solvent-sorbate isotherms (e.g., the mixtures of organic solvents adsorbed on mesoporous silica and carbonaceous adsorbents) indicates the contributions from both sorbate and solvent isotherms.

Free-energy decomposition of salt effects on the solubilities of small molecules and the role of excluded-volume effects.

The roles of cations and anions are different in the perturbation on solvation, and thus, the analyses of the separated contributions from cations and anions are useful to establish molecular pictures of ion-specific effects. In this work, we investigate the effects of cations, anions, and water separately in the solvation of n-alcohols and n-alkanes by free-energy decomposition. By utilising energy-representation theory of solvation, we address the contributions arising from the direct solute-solvent interactions and the excluded-volume effects. It is found that the change in solvation of n-alcohols and n-alkanes upon addition of salt depends primarily on the anion species. The direct interaction between the anion and solute is in agreement with the Setschenow coefficient in terms of the ranking of salting-in and salting-out for n-alkanes, which corresponds to the extent of accumulation of the anion on the solute surface. For each of the n-alcohols and n-alkanes examined, the excluded-volume component in the Setschenow coefficient is well correlated to the (total) Setschenow coefficient when the salt effects are concerned. The ranking of the excluded-volume component in the variation of the salt species is parallel to the water contribution, which is correlated further to the change in the water density upon the addition of the salt.

Unraveling the Glass-like Dynamic Heterogeneity in Ring Polymer Melts: From Semiflexible to Stiff Chain.

Ring polymers are an intriguing class of polymers with unique physical properties, and understanding their behavior is important for developing accurate theoretical models. In this study, we investigate the effect of chain stiffness and monomer density on the static and dynamic behaviors of ring polymer melts using molecular dynamics simulations. Our first focus is on the non-Gaussian parameter of center-of-mass displacement as a measure of dynamic heterogeneity, which is commonly observed in glass-forming liquids. We find that the non-Gaussianity in the displacement distribution increases with the monomer density and stiffness of the polymer chains, suggesting that excluded volume interactions between centers of mass have a strong effect on the dynamics of ring polymers. We then analyze the relationship between the radius of gyration and monomer density for semiflexible and stiff ring polymers. Our results indicate that the relationship between the two varies with chain stiffness, which can be attributed to the competition between repulsive forces inside the ring and from adjacent rings. Finally, we study the dynamics of bond-breakage virtually connected between the centers of mass of rings to analyze the exchanges of intermolecular networks of bonds. Our results demonstrate that the dynamic heterogeneity of bond-breakage is coupled with the non-Gaussianity in ring polymer melts, highlighting the importance of the bond-breaking method in determining the intermolecular dynamics of ring polymer melts. Overall, our study sheds light on the factors that govern the dynamic behaviors of ring polymers.

Elucidating protein-ligand binding kinetics based on returning probability theory.

The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host-guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein-ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT.

Sorption from Solution: A Statistical Thermodynamic Fluctuation Theory.

Given an experimental solid/solution sorption isotherm, how can we gain insight into the underlying sorption mechanism on a molecular basis? Classifying sorption isotherms, for both completely and partially miscible solvent/sorbate systems, has been useful, yet the molecular foundation of these classifications remains speculative. Isotherm models, developed predominantly for solid/gas sorption, have been adapted to solid/solution isotherms, yet how their parameters should be interpreted physically has long remained ambiguous. To overcome the inconclusiveness, we establish in this paper a universal theory that can be used for interpreting and modeling solid/solution sorption. This novel theory shares the same theoretical foundation (i.e., the statistical thermodynamic fluctuation theory) not only with solid/gas sorption but also with solvation in liquid solutions and solution nonidealities. The key is the Kirkwood-Buff χ parameter, which quantifies the net self-interaction (i.e., solvent-solvent and sorbate-sorbate interactions minus solvent-sorbate interaction) via the Kirkwood-Buff integral in the same manner as the solvation theory and, unlike the Flory χ, is not limited to the lattice model. We will demonstrate that the Kirkwood-Buff χ is the key not only to isotherm classification but also to generalizing our recent statistical thermodynamic gas (vapor) isotherm, which is capable of fitting most of the solid/solution isotherm types.

Molecular Dynamics Study of the Antifouling Mechanism of Hydrophilic Polymer Brushes.

We perform all-atom molecular dynamics simulations of the adsorption of amino acid side-chain analogues on polymer brushes. The analogues examined are nonpolar isobutane, polar propionamide, negatively charged propionate ion, and positively charged butylammonium ion. The polymer brushes consist of a sheet of graphene and strongly hydrophilic poly(carboxybetaine methacrylate) (PCBMA) or weakly hydrophilic poly(2-hydroxyethyl methacrylate) (PHEMA). The effective interactions between isobutane and polymer chains are repulsive for PCBMA and attractive for PHEMA. Gibbs energy decomposition analysis shows that this is due to the abundance of water in the PCBMA brush, which increases the steric repulsion and decreases the Lennard-Jones attraction. The affinity of the hydrophilic analogues is low for both PCBMA and PHEMA chains, but the balance between the components of the Gibbs energy is different for the two polymers. The simulations are performed at several θ, where θ is the degree of overlap of polymer chains. The antifouling performance against the neutral analogues is better for PCBMA than for PHEMA in the low and high θ regimes. However, in the middle θ regime, the antifouling performance of PHEMA is close to or better than that of PCBMA. This is attributed to the formation of a dense layer of PHEMA on the graphene surface that inhibits direct adsorption of analogue molecules on graphene. The charged analogues do not bind to either the PHEMA or PCBMA brush irrespective of θ.

Cooperativity in Sorption Isotherms.

We present a general theory of cooperativity in sorption isotherms that can be applied to sorbent/gas and sorbent/solution isotherms and is valid even when sorbates dissolve into or penetrate the sorbent. Our universal foundation, based on the principles of statistical thermodynamics, is the excess number of sorbates (around a probe sorbate), which can capture the cooperativities of sigmoidal and divergent isotherms alike via the ln-ln gradient of an isotherm (the excess number relationship). The excess number relationship plays a central role in deriving isotherm equations. Its combination with the characteristic relationship (i.e., a succinct summary of the sorption mechanism via the dependence of excess number on interfacial coverage or sorbate activity) yields a differential equation whose solution is an isotherm equation. The cooperative isotherm equations for convergent and divergent cooperativities derived from this novel method can be applied to fit experimental data traditionally fitted via various isotherm models, with a clear statistical thermodynamic interpretation of their parameters..

Revealing the hidden dynamics of confined water in acrylate polymers: Insights from hydrogen-bond lifetime analysis.

Polymers contain functional groups that participate in hydrogen bond (H-bond) with water molecules, establishing a robust H-bond network that influences bulk properties. This study utilized molecular dynamics (MD) simulations to examine the H-bonding dynamics of water molecules confined within three poly(meth)acrylates: poly(2-methoxyethyl acrylate) (PMEA), poly(2-hydroxyethyl methacrylate) (PHEMA), and poly(1-methoxymethyl acrylate) (PMC1A). Results showed that H-bonding dynamics significantly slowed as the water content decreased. Additionally, the diffusion of water molecules and its correlation with H-bond breakage were analyzed. Our findings suggest that when the H-bonds between water molecules and the methoxy oxygen of PMEA are disrupted, those water molecules persist in close proximity and do not diffuse on a picosecond time scale. In contrast, the water molecules H-bonded with the hydroxy oxygen of PHEMA and the methoxy oxygen of PMC1A diffuse concomitantly with the breakage of H-bonds. These results provide an in-depth understanding of the impact of polymer functional groups on H-bonding dynamics.

Understanding Sorption Mechanisms Directly from Isotherms.

Currently, more than 100 isotherm models coexist for the six IUPAC isotherm types. However, no mechanistic insights can be reached when several models, each claiming a different mechanism, fit an experimental isotherm equally well. More frequently, popular isotherm models [such as the site-specific models like Langmuir, Brunauer-Emmett-Teller (BET), and Guggenheim-Anderson-de Boer (GAB)] have been applied to real and complex systems that break their basic assumptions. To overcome such conundrums, we establish a universal approach to model all isotherm types, attributing the difference to the sorbate-sorbate and sorbate-surface interactions in a systematic manner. We have generalized the language of the traditional sorption models (such as the monolayer capacity and the BET constant) to the model-free concepts of partitioning and association coefficients that can be applied across the isotherm types. Through such a generalization, the apparent contradictions, caused by applying the site-specific models alongside with cross-sectional area of sorbates for the purpose of surface area determination, can be eliminated straightforwardly.

Arylazopyrazole-Based Photoswitchable Inhibitors Selective for Escherichia coli Dihydrofolate Reductase.

Selective inhibitors of Escherichia coli dihydrofolate reductase (eDHFR) are crucial chemical biology tools that have widespread clinical applications. We developed a set of eDHFR-selective photoswitchable inhibitors by derivatizing the structure of our previously reported methotrexate (MTX) azolog, azoMTX. Substitution of the skeletal p-phenylene group of azoMTX with bulky bis-alkylated arylazopyrazole moieties significantly increased its selectivity toward eDHFR over human DHFR. Owing to the physical properties of arylazopyrazoles, the new ligands exhibited nearly complete Z-to-E photoconversion and high thermostability of Z-isomers. In addition, real-time photoreversible control of eDHFR activity was achieved by alternatively switching the illumination light wavelengths.