Atomistic description of molecular binding processes based on returning probability theory

Flexible framework of computing binding free energy using the energy representation theory of solution

Host-guest binding plays a crucial role in the functionality of various systems, and its efficiency is often quantified using the binding free energy, which represents the free-energy difference between the bound and dissociated states. Here, we propose a methodology to compute the binding free energy based on the energy representation (ER) theory of solution, which enables us to evaluate the free-energy difference between the systems of interest with the molecular dynamics (MD) simulations. Unlike the other free-energy methods, such as the Bennett acceptance ratio (BAR), the ER theory does not require the MD simulations for hypothetical intermediate states connecting the systems of interest, leading to reduced computational costs. By constructing the thermodynamic cycle of the binding process that is suitable for the ER theory, a robust calculation of the binding free energy is realized. We apply the present method to the self-association of N-methylacetamide in different solvents and the binding of aspirin to β-cyclodextrin (CD) in water. In the former case, the present method estimates that the binding free energy decreases as the solvent polarity decreases. This trend is consistent with the experimental finding. For the latter system, the binding free energies for the two representative CD-aspirin bound complexes, primary (P) and secondary (S) complexes, are estimated to be -5.2 ± 0.1 and -5.03 ± 0.09 kcal mol-1, respectively. These values are satisfactorily close to those from the BAR method [-4.2 ± 0.2 and -4.1 ± 0.2 kcal mol-1 for P and S, respectively]. Furthermore, the interaction-energy component analysis reveals that the van der Waals interaction between aspirin and CD dominantly contributes to the stabilization of the bound complexes, which is in harmony with the well-known binding mechanism in the CD systems.

Amide cyclodextrin that recognises monophosphate anions in harmony with water molecules

Anion recognition in water by synthetic host molecules is a popular and challenging topic. It has been considered difficult because the water molecules compete for the recognition units. In this study, we have successfully created a novel macrocycle that achieves precise recognition through multipoint hydrogen bonding in harmony with water molecules. Specifically, an N-methylpyridinium amide β-cyclodextrin (β-CD) derivative 1(OTf)7 was synthesized, whose amide groups are directly attached to each pyranose ring. The pyridinium amide CD encapsulated a monophosphate anion in water, but it did not show interactions with sulfonates or carboxylates, thus a remarkable selectivity was demonstrated. Two monophosphates with different substituents, phenyl phosphate (PhOPO3 2-) and adamantyl phosphate (AdOPO3 2-), exhibited interesting contrasting pictures in the inclusion process, which were revealed by a combination of NOESY experiments, ITC measurements, and MD simulations. PhOPO3 2- was positioned slightly "upper" (closer to the pyridinium amide side) in 17+ with the oxygen atom of the phosphate ester R-O-P involved in the hydrogen bonds with the amide N-H, and configurational entropy plays a key role in the inclusion. Meanwhile, AdOPO3 2- was positioned "lower" (closer to the methoxy rim of CD) with the terminal -PO3 2- forming hydrogen bonds with the amides, and the hydrophobic effect is a major contributing driving force of the inclusion. The molecular design presented herein to achieve the precise recognition in water and clarification of the detailed mechanisms including the hydration phenomenon greatly contribute to the development of functional molecules that work in aqueous environments.

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.

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.

Diffusion theory of molecular liquids in the energy representation and application to solvation dynamics

The generalized Langevin equation (GLE) formalism is a useful theoretical fundament for analyzing dynamical phenomena rigorously. Despite the systematic formulation of dynamics theories with practical approximations, however, the applicability of GLE-based methods is still limited to simple polyatomic liquids due to the approximate treatment of molecular orientations involved in the static molecular liquid theory. Here, we propose an exact framework of dynamics based on the GLE formalism incorporating the energy representation theory of solution, an alternative static molecular liquid theory. A fundamental idea is the projection of the relative positions and orientations of solvents around a solute onto the solute-solvent interaction, namely the energy coordinate, enabling us to describe the dynamics on a one-dimensional coordinate. Introducing systematic approximations, such as the overdamped limit, leads to the molecular diffusion equation in the energy representation that is described in terms of the distribution function of solvents on the energy coordinate and the diffusion coefficients. The present theory is applied to the solvation dynamics triggered by the photoexcitation of benzonitrile. The long-time behavior of the solvation time correlation function is in good agreement with that obtained by the molecular dynamics simulation.