Free Energy Profile for the Complete Transport of Nonpolar Molecules through a Carbon Nanotube.

Gas molecules or weakly interacting molecules are commonly observed to diffuse through and fill space. Therefore, when the molecules initially confined in one compartment are allowed to move through a channel into another empty compartment, we expect that some molecules will be transported into the initially empty compartment. In this work, we thermodynamically analyze this transport process using a simple model consisting of graphene plates, a carbon nanotube (CNT), and nonpolar molecules that are weakly interacting with each other. Specifically, we calculate the free energy change, or the potential of mean force (PMF), as the molecules are transported from one compartment to another compartment. The PMF profile clearly exhibits a global minimum, or a free energy well, at the state wherein the molecules are evenly distributed over the two compartments. To better understand the thermodynamic origin of the well, we calculate the energetic and entropic contributions to the formation of the well, and we show that the entropic change is responsible for it and is the driving force for transport. Our work not only enables a fundamental understanding of the thermodynamic nature of the transport of weakly interacting molecules with molecular details, but also provides a method for calculating the free energy change during transport between two separate spaces connected by a nanochannel.

Free energy change in the complete transport of all water molecules through a carbon nanotube.

In this work, we investigated the free energy barrier for transporting water molecules from one place to another. To properly address this issue, we considered a simple model system in which two separate compartments were connected via a subnanometer channel; all water molecules were initially in one compartment, and the other compartment was empty. Using umbrella sampling in molecular dynamics simulations, we calculated the free energy change for transporting all water molecules to the initially empty compartment. The free energy profile clearly indicated the presence of a free energy barrier, and the magnitude and shape of the barrier were dependent on the number of water molecules to be transported. To better understand the nature of the profile, we performed additional analyses on the potential energy of the system and hydrogen bonding between water molecules. Our study sheds light on a method for calculating the free energy of a transport system as well as the fundamental aspects of water transport.

Virtual and biochemical screening to identify the inhibitors of binding between SARS-CoV-2 spike protein and human angiotensin-converting enzyme 2.

Severe acute respiratory syndrome coronavirus (SARS-CoV-2) appeared as a new viral pathogen and caused the COVID-19 pandemic worldwide. Since the antiviral medicines effective for the treatment of COVID-19 are rare, it is necessary to identify the new candidate molecules for chemotherapy. The glycosylated Spike protein (S-protein) of SARS-CoV-2 plays a critical role in entering into the host cell through a direct interaction with human angiotensin-converting enzyme 2 (ACE2). For this reason, S-protein has served as one of the most effective therapeutic targets for discovering the antiviral medicines for COVID-19. In this work, we report the new small-molecule inhibitors of the interaction between the S-protein of SARS-CoV-2 and human ACE2, which were discovered through the structure-based virtual screening and in vitro biochemical binding assays. As a consequence of combining the computational and experimental validations, three novel inhibitors against the binding of S-protein and ACE2 were found with the associated IC50 values ranging from 50 to 100 µM. Although the biochemical potencies are moderate, the newly found inhibitors are worth being considered for further investigation by structure-activity relationship analysis to maximize the antiviral activity because of the low molecular weights and good physicochemical properties as a drug candidate. The interaction patterns of the new inhibitors in the ACE2-binding region of S-protein are addressed in detail.

Osmosis-Driven Water Transport through a Nanochannel: A Molecular Dynamics Simulation Study.

In this work, we study a chemical method to transfer water molecules from a nanoscale compartment to another initially empty compartment through a nanochannel. Without any external force, water molecules do not spontaneously move to the empty compartment because of the energy barrier for breaking water hydrogen bonds in the transport process and the attraction between water molecules and the compartment walls. To overcome the energy barrier, we put osmolytes into the empty compartment, and to remove the attraction, we weaken the compartment-water interaction. This allows water molecules to spontaneously move to the empty compartment. We find that the initiation and time-transient behavior of water transport depend on the properties of the osmolytes specified by their number and the strength of their interaction with water. Interestingly, when osmolytes strongly interact with water molecules, transport immediately starts and continues until all water molecules are transferred to the initially empty compartment. However, when the osmolyte interaction strength is intermediate, transport initiates stochastically, depending on the number of osmolytes. Surprisingly, because of strong water-water interactions, osmosis-driven water transport through a nanochannel is similar to pulling a string at a constant speed. Our study helps us understand what minimal conditions are needed for complete transfer of water molecules to another compartment through a nanochannel, which may be of general concern in many fields involving molecular transfer.

Effects of the Size, the Number, and the Spatial Arrangement of Reactive Patches on a Sphere on Diffusion-limited Reaction Kinetics: A Comprehensive Study.

We investigate how the size, the number, and the spatial arrangement of identical nonoverlapping reactive patches on a sphere influence the overall reaction kinetics of bimolecular diffusion-limited (or diffusion-controlled) reactions that occur between the patches and the reactants diffusing around the sphere. First, in the arrangement of two patches, it is known that the overall rate constant increases as the two patches become more separated from each other but decreases when they become closer to each other. In this work, we further study the dependence of the patch arrangement on the kinetics with three and four patches using the finite element method (FEM). In addition to the patch arrangement, the kinetics is also dependent on the number and size of the patches. Therefore, we study such dependences by calculating the overall rate constants using the FEM for various cases, especially for large-sized patches, and this study is complementary to the kinetic studies that were performed by Brownian dynamics (BD) simulation methods for small-sized patches. The numerical FEM and BD simulation results are compared with the results from various kinetic theories to evaluate the accuracies of the theories. Remarkably, this comparison indicates that our theory, which was recently developed based on the curvature-dependent kinetic theory, shows good agreement with the FEM and BD numerical results. From this validation, we use our theory to further study the variation of the overall rate constant when the patches are arbitrarily arranged on a sphere. Our theory also confirms that to maximize the overall rate constant, we need to break large-sized patches into smaller-sized patches and arrange them to be maximally separated to reduce their competition.

Equilibration of molecules between two compartments through a nanochannel in the presence of osmolytes: a molecular dynamics simulation study.

Using molecular dynamics simulations, we study the equilibration of a system consisting of two nanoscale compartments connected by a carbon nanotube through which small mobile molecules can pass. The system is initially in a state where only one compartment is filled with molecules and the other is empty. When the molecules are allowed to move from the filled compartment to the empty one, the system starts equilibrating and finally reaches an equilibrium state where the molecules are distributed between the two compartments. In the absence of osmolytes, the equilibrium distribution of molecules is simply determined by the relative volumes of the compartments, but in the presence of osmolytes, the distribution is dependent on not only the relative compartment volumes but also the osmolyte properties. To systematically study the effect of osmolytes, we investigate how the number of osmolytes and the strength of the interaction between molecules and osmolytes affect the equilibrium state. Interestingly, we find that osmolytes strongly interacting with molecules can drain the initially filled compartment and induce the complete transfer of molecules to the initially empty compartment. We also study the kinetic and thermodynamic aspects of the equilibration processes.

Theory of curvature-dependent kinetics of diffusion-limited reactions and its application to ligand binding to a sphere with multiple receptors.

We present a simple theory that explains how surface curvature affects the reaction kinetics of diffusion-limited reactions on spherically curved surfaces. In this theory, we derive a quadratic equation under the conditions that the rate constant satisfies the Hill and Smoluchowski rate constants at the lowest and highest curvatures, respectively, and that at a certain intermediate curvature, there should be a maximum value of the rate constant, which was recently found in our previous work. We find that the result obtained from our theory is in good agreement with the corresponding one obtained from numerical calculation. In addition, we show that our theory can be directly applied to the Solc-Stockmayer model of axially symmetric reactants, which can be considered as a spherical reactant with a single reaction site. Furthermore, we discuss using our theory to improve the formula for the rate constant in the Berg-Purcell ligand-binding model of a cell membrane covered by multiple receptors. Our simple theory yields insight into the effect of curvature on diffusion-influenced reactions and provides a useful formula for easily and quantitatively evaluating the curvature effect.

Effect of surface curvature on diffusion-limited reactions on a curved surface.

To investigate how the curvature of a reactive surface can affect reaction kinetics, we use a simple model in which a diffusion-limited bimolecular reaction occurs on a curved surface that is hollowed inward, flat, or extended outward while keeping the reactive area on the surface constant. By numerically solving the diffusion equation for this model using the finite element method, we find that the rate constant is a non-linear function of the surface curvature and that there is an optimal curvature providing the maximum value of the rate constant, which indicates that a spherical reactant whose entire surface is reactive (a uniformly reactive sphere) is not the most reactive species for a given reactive surface area. We discuss how this result arises from the interplay between two opposing effects: the exposedness of the reactive area to its partner reactants, which causes the rate constant to increase as the curvature increases, and the competition occurring on the reactive surface, which decreases the rate constant. This study helps us to understand the role of curvature in surface reactions and allows us to rationally design reactants that provide a high reaction rate.

Enzyme localization, crowding, and buffers collectively modulate diffusion-influenced signal transduction: Insights from continuum diffusion modeling.

Biochemical reaction networks consisting of coupled enzymes connect substrate signaling events with biological function. Substrates involved in these reactions can be strongly influenced by diffusion "barriers" arising from impenetrable cellular structures and macromolecules, as well as interactions with biomolecules, especially within crowded environments. For diffusion-influenced reactions, the spatial organization of diffusion barriers arising from intracellular structures, non-specific crowders, and specific-binders (buffers) strongly controls the temporal and spatial reaction kinetics. In this study, we use two prototypical biochemical reactions, a Goodwin oscillator, and a reaction with a periodic source/sink term to examine how a diffusion barrier that partitions substrates controls reaction behavior. Namely, we examine how conditions representative of a densely packed cytosol, including reduced accessible volume fraction, non-specific interactions, and buffers, impede diffusion over nanometer length-scales. We find that diffusion barriers can modulate the frequencies and amplitudes of coupled diffusion-influenced reaction networks, as well as give rise to "compartments" of decoupled reactant populations. These effects appear to be intensified in the presence of buffers localized to the diffusion barrier. These findings have strong implications for the role of the cellular environment in tuning the dynamics of signaling pathways.

Accelerated molecular dynamics simulations of protein folding.

Folding of four fast-folding proteins, including chignolin, Trp-cage, villin headpiece and WW domain, was simulated via accelerated molecular dynamics (aMD). In comparison with hundred-of-microsecond timescale conventional molecular dynamics (cMD) simulations performed on the Anton supercomputer, aMD captured complete folding of the four proteins in significantly shorter simulation time. The folded protein conformations were found within 0.2-2.1 Å of the native NMR or X-ray crystal structures. Free energy profiles calculated through improved reweighting of the aMD simulations using cumulant expansion to the second-order are in good agreement with those obtained from cMD simulations. This allows us to identify distinct conformational states (e.g., unfolded and intermediate) other than the native structure and the protein folding energy barriers. Detailed analysis of protein secondary structures and local key residue interactions provided important insights into the protein folding pathways. Furthermore, the selections of force fields and aMD simulation parameters are discussed in detail. Our work shows usefulness and accuracy of aMD in studying protein folding, providing basic references in using aMD in future protein-folding studies.

Electrostatic channeling in P. falciparum DHFR-TS: Brownian dynamics and Smoluchowski modeling.

We perform Brownian dynamics simulations and Smoluchowski continuum modeling of the bifunctional Plasmodium falciparum dihydrofolate reductase-thymidylate synthase (P. falciparum DHFR-TS) with the objective of understanding the electrostatic channeling of dihydrofolate generated at the TS active site to the DHFR active site. The results of Brownian dynamics simulations and Smoluchowski continuum modeling suggest that compared to Leishmania major DHFR-TS, P. falciparum DHFR-TS has a lower but significant electrostatic-mediated channeling efficiency (?15-25%) at physiological pH (7.0) and ionic strength (150 mM). We also find that removing the electric charges from key basic residues located between the DHFR and TS active sites significantly reduces the channeling efficiency of P. falciparum DHFR-TS. Although several protozoan DHFR-TS enzymes are known to have similar tertiary and quaternary structure, subtle differences in structure, active-site geometry, and charge distribution appear to influence both electrostatic-mediated and proximity-based substrate channeling.

Molecular dynamics simulation study of conformational changes of transcription factor TFIIS during RNA polymerase II transcriptional arrest and reactivation.

Transcription factor IIS (TFIIS) is a protein known for catalyzing the cleavage reaction of the 3'-end of backtracked RNA transcript, allowing RNA polymerase II (Pol II) to reactivate the transcription process from the arrested state. Recent structural studies have provided a molecular basis of protein-protein interaction between TFIIS and Pol II. However, the detailed dynamic conformational changes of TFIIS upon binding to Pol II and the related thermodynamic information are largely unknown. Here we use computational approaches to investigate the conformational space of TFIIS in the Pol II-bound and Pol II-free (unbound) states. Our results reveal two distinct conformations of TFIIS: the closed and the open forms. The closed form is dominant in the Pol II-free (unbound) state of TFIIS, whereas the open form is favorable in the Pol II-bound state. Furthermore, we discuss the free energy difference involved in the conformational changes between the two forms in the presence or absence of Pol II. Additionally, our analysis indicates that hydrophobic interactions and the protein-protein interactions between TFIIS and Pol II are crucial for inducing the conformational changes of TFIIS. Our results provide novel insights into the functional interplay between Pol II and TFIIS as well as mechanism of reactivation of Pol II transcription by TFIIS.

A model study of sequential enzyme reactions and electrostatic channeling.

We study models of two sequential enzyme-catalyzed reactions as a basic functional building block for coupled biochemical networks. We investigate the influence of enzyme distributions and long-range molecular interactions on reaction kinetics, which have been exploited in biological systems to maximize metabolic efficiency and signaling effects. Specifically, we examine how the maximal rate of product generation in a series of sequential reactions is dependent on the enzyme distribution and the electrostatic composition of its participant enzymes and substrates. We find that close proximity between enzymes does not guarantee optimal reaction rates, as the benefit of decreasing enzyme separation is countered by the volume excluded by adjacent enzymes. We further quantify the extent to which the electrostatic potential increases the efficiency of transferring substrate between enzymes, which supports the existence of electrostatic channeling in nature. Here, a major finding is that the role of attractive electrostatic interactions in confining intermediate substrates in the vicinity of the enzymes can contribute more to net reactive throughput than the directional properties of the electrostatic fields. These findings shed light on the interplay of long-range interactions and enzyme distributions in coupled enzyme-catalyzed reactions, and their influence on signaling in biological systems.

Influence of neighboring reactive particles on diffusion-limited reactions.

Competition between reactive species is commonplace in typical chemical reactions. Specifically the primary reaction between a substrate and its target enzyme may be altered when interactions with secondary species in the system are substantial. We explore this competition phenomenon for diffusion-limited reactions in the presence of neighboring particles through numerical solution of the diffusion equation. As a general model for globular proteins and small molecules, we consider spherical representations of the reactants and neighboring particles; these neighbors vary in local density, size, distribution, and relative distance from the primary target reaction, as well as their surface reactivity. Modulations of these model variables permit inquiry into the influence of excluded volume and competition on the primary reaction due to the presence of neighboring particles. We find that the surface reactivity effect is long-ranged and a strong determinant of reaction kinetics, whereas the excluded volume effect is relatively short-ranged and less influential in comparison. As a consequence, the effect of the excluded volume is only modestly dependent on the neighbor distribution and is approximately additive; this additivity permits a linear approximation to the many-body effect on the reaction kinetics. In contrast, the surface reactivity effect is non-additive, and thus it may require higher-order approximations to describe the reaction kinetics. Our model study has broad implications in the general understanding of competition and local crowding on diffusion-limited chemical reactions.

Restructuring of a model hydrophobic surface: Monte Carlo simulations using a simple coarse-grained model.

A lattice model is proposed to explain the restructuring of an ionic surfactant absorbed on a charged surface. When immersed in water, an ionic mica plate initially covered by a monolayer of surfactants rearranges to a surface inhomogeneously covered by patches of surfactant bilayer and bare mica. The model considers four species that can cover lattice sites of a surface. These species include (i) a surfactant molecule with its headgroup down, (ii) surfactant molecule with the headgroup up, (iii) a surfactant dimer arranged in a tail-to-tail configuration, which is a part of a bilayer, and (iv) a mica lattice site covered by water. We consider that only nearest neighbors on the lattice interact and describe the interactions by an interaction matrix. Using this model, we perform Monte Carlo simulations and study how the structure of the inhomogeneous surface depends on the interaction between water covered lattice site and its neighboring surfactant species covered sites. We observe that when this interaction is absent, the system undergoes phase separation into a bilayer phase and mica surface covered with water. When this interaction is taken into account, patches of surfactant bilayer and water are present in our system. The interaction between mica surfaces covered by patches of ionic surfactants is studied in experiments to understand the nature of long-ranged "hydrophobic" forces.

Molecular dynamics simulation study of the water-mediated interaction between zwitterionic and charged surfaces.

We calculated the potential of mean force (PMF) for the interaction between a model zwitterionic bilayer and a model charged bilayer. To understand the role of water, we separated the PMF into two components: one due to direct interaction and the other due to water-mediated interaction. In our calculations, we observed that water-mediated interaction is attractive at larger distances and repulsive at shorter. The calculation of the entropic and enthalpic contributions to the solvent-mediated components of the PMF showed that attraction is entropically dominant, while repulsion is dominated by the enthalpy.

Restructuring of hydrophobic surfaces created by surfactant adsorption to mica surfaces.

Hydrophobic surfaces created by the adsorption of a monolayer of surfactants, such as CTAB or DODAB, to mica display long-range mutual attraction when placed in water. Initially, this attraction was considered to be due to hydrophobic interaction, but more careful measurements using AFM showed that the surfactant monolayer undergoes rearrangements to produce charged patches on the surface; therefore, the nature of the long-range interaction is due to the electrostatic interaction between patches. The monolayer rearrangement depends on the nature of the surfactant and its counterion. To study possible monolayer rearrangements in molecular detail, we performed detailed molecular dynamics computer simulations on systems containing a monolayer of surfactants RN(CH(3))(3)(+)Cl(-) (R indicates a saturated hydrocarbon chain) adsorbed on a mica surface and immersed in water. We observe that when chain R is 18 carbons long the monolayer rearranges into a micelle but it remains a monolayer when the chain contains 24 carbons.

Molecular dynamics simulation study of interaction between model rough hydrophobic surfaces.

We study some aspects of hydrophobic interaction between molecular rough and flexible model surfaces. The model we use in this work is based on a model we used previously (Eun, C.; Berkowitz, M. L. J. Phys. Chem. B 2009, 113, 13222-13228), when we studied the interaction between model patches of lipid membranes. Our original model consisted of two graphene plates with attached polar headgroups; the plates were immersed in a water bath. The interaction between such plates can be considered as an example of a hydrophilic interaction. In the present work, we modify our previous model by removing the charge from the zwitterionic headgroups. As a result of this procedure, the plate character changes: it becomes hydrophobic. By separating the total interaction (or potential of mean force, PMF) between plates into the direct and the water-mediated interactions, we observe that the latter changes from repulsive to attractive, clearly emphasizing the important role of water as a medium. We also investigate the effect of roughness and flexibility of the headgroups on the interaction between plates and observe that roughness enhances the character of the hydrophobic interaction. The presence of a dewetting transition in a confined space between charge-removed plates confirms that the interaction between plates is strongly hydrophobic. In addition, we notice that there is a shallow local minimum in the PMF in the case of the charge-removed plates. We find that this minimum is associated with the configurational changes that flexible headgroups undergo as the two plates are brought together.

Fluctuations in number of water molecules confined between nanoparticles.

We used molecular dynamics computer simulations to study the character of interactions between two nanoscale graphene plates in water and also between plates made of "carbon" atoms that have different interaction strength with water. Fluctuations in the number of water molecules in the confined space between plates are qualitatively similar when the plates are made of graphene or when the plates contain "carbon" atoms with weaker "carbon"-water interaction strength. We also observed that these fluctuations are strongly enhanced compared to the fluctuations observed next to a single plate. If the character of water fluctuations in the confined space determines the character of interactions, then it is possible to conclude that the interaction between graphene plates in water is hydrophobic.

A revisit to the one form kinetic model of prothrombinase.

Thrombin is generated enzymatically from prothrombin by two pathways with the intermediates of meizothrombin and prethrombin-2. Experimental concentration profiles from two independent groups for these two pathways have been re-analyzed. By rationally combining the independent data sets, a simple mechanism can be established and rate constants determined. A structural model is consistent with the data-derived finding that mechanisms that feature channeling or ratcheting are not necessary to describe thrombin production.