Ultrasonic Relaxations in Aqueous Solutions of Propionic Acid in the Presence and Absence ofβ-Cyclodextrin

QMrebind: incorporating quantum mechanical force field reparameterization at the ligand binding site for improved drug-target kinetics through milestoning simulations

Understanding the interaction of ligands with biomolecules is an integral component of drug discovery and development. Challenges for computing thermodynamic and kinetic quantities for pharmaceutically relevant receptor-ligand complexes include the size and flexibility of the ligands, large-scale conformational rearrangements of the receptor, accurate force field parameters, simulation efficiency, and sufficient sampling associated with rare events. Our recently developed multiscale milestoning simulation approach, SEEKR2 (Simulation Enabled Estimation of Kinetic Rates v.2), has demonstrated success in predicting unbinding (koff) kinetics by employing molecular dynamics (MD) simulations in regions closer to the binding site. The MD region is further subdivided into smaller Voronoi tessellations to improve the simulation efficiency and parallelization. To date, all MD simulations are run using general molecular mechanics (MM) force fields. The accuracy of calculations can be further improved by incorporating quantum mechanical (QM) methods into generating system-specific force fields through reparameterizing ligand partial charges in the bound state. The force field reparameterization process modifies the potential energy landscape of the bimolecular complex, enabling a more accurate representation of the intermolecular interactions and polarization effects at the bound state. We present QMrebind (Quantum Mechanical force field reparameterization at the receptor-ligand binding site), an ORCA-based software that facilitates reparameterizing the potential energy function within the phase space representing the bound state in a receptor-ligand complex. With SEEKR2 koff estimates and experimentally determined kinetic rates, we compare and interpret the receptor-ligand unbinding kinetics obtained using the newly reparameterized force fields for model host-guest systems and HSP90-inhibitor complexes. This method provides an opportunity to achieve higher accuracy in predicting receptor-ligand koff rate constants.

SEEKR2: Versatile Multiscale Milestoning Utilizing the OpenMM Molecular Dynamics Engine

We present SEEKR2 (simulation-enabled estimation of kinetic rates version 2)—the latest iteration in the family of SEEKR programs for using multiscale simulation methods to computationally estimate the kinetics and thermodynamics of molecular processes, in particular, ligand-receptor binding. SEEKR2 generates equivalent, or improved, results compared to the earlier versions of SEEKR but with significant increases in speed and capabilities. SEEKR2 has also been built with greater ease of usability and with extensible features to enable future expansions of the method. Now, in addition to supporting simulations using NAMD, calculations may be run with the fast and extensible OpenMM simulation engine. The Brownian dynamics portion of the calculation has also been upgraded to Browndye 2. Furthermore, this version of SEEKR supports hydrogen mass repartitioning, which significantly reduces computational cost, while showing little, if any, loss of accuracy in the predicted kinetics.

Atomistic description of molecular binding processes based on returning probability theory

The efficiency of molecular binding such as host-guest binding is commonly evaluated in terms of kinetics, such as rate coefficients. In general, to compute the coefficient of the overall binding process, we need to consider both the diffusion of reactants and barrier crossing to reach the bound state. Here, we develop a methodology of quantifying the rate coefficient of binding based on molecular dynamics simulation and returning probability (RP) theory proposed by Kim and Lee [J. Chem. Phys. 131, 014503 (2009)]. RP theory provides a tractable formula of the rate coefficient in terms of the thermodynamic stability and kinetics of the intermediate state on a predefined reaction coordinate. In this study, the interaction energy between reactants is utilized as the reaction coordinate, enabling us to effectively describe the reactants' relative position and orientation on one-dimensional space. Application of this method to the host-guest binding systems, which consist of β-cyclodextrin and small guest molecules, yields the rate coefficients consistent with the experimental results.

Complexation Kinetics of Cyclodextrins with Bile Salt Anions: Energy Barriers for the Threading of Ionic Groups

Binding constants for thousands of cyclodextrin complexes have been reported in the literature, but much less is known about the kinetics of these host-guest complexes. In the present study, inclusion complexes of bile salts with β-cyclodextrin, γ-cyclodextrin, and a methylated β-cyclodextrin were studied by nuclear magnetic resonance (NMR) lineshape analysis to explore the structural factors that govern the complexation kinetics. For complexes with β-cyclodextrin, the association rate constants ranged from 2 × 10⁶ to 2 × 10⁷ M^-1 s^-1 while the dissociation rate constants ranged from 12 to 6000 s^-1 at 25 °C. The kinetics were thus significantly slower than for any other β-cyclodextrin complex reported in the literature, due to the large energy barrier for threading the ionic sidechains of the bile salt anions. Bile salts with taurine and glycine sidechains had identical binding affinities, but the kinetics differed by a factor of 10. Introduction of a single hydroxyl group at the binding site of the bile salts reduced the lifetimes and binding constants of the complexes by more than 50 times. The strong temperature dependence of the rate constants revealed that the large activation energies were mainly enthalpic with a small contribution from entropy. The larger γ-cyclodextrin was threaded by the nonionic end of the bile salts, and the kinetics were too fast to be accurately determined. The study demonstrates that ionic groups on guest molecules constitute significant energy barriers for the threading and dethreading of β-cyclodextrin hosts.

Quantitative Ranking of Ligand Binding Kinetics with a Multiscale Milestoning Simulation Approach

Efficient prediction and ranking of small molecule binders by their kinetic ( kon and koff) and thermodynamic ( Δ G) properties can be a valuable metric for drug lead optimization, as these quantities are often indicators of in vivo efficacy. We have previously described a hybrid molecular dynamics, Brownian dynamics, and milestoning model, Simulation Enabled Estimation of Kinetic Rates (SEEKR), that can predict kon's, koff's, and Δ G's. Here we demonstrate the effectiveness of this approach for ranking a series of seven small molecule compounds for the model system, β-cyclodextrin, based on predicted kon's and koff's. We compare our results using SEEKR to experimentally determined rates as well as rates calculated using long time scale molecular dynamics simulations and show that SEEKR can effectively rank the compounds by koff and Δ G with reduced computational cost. We also provide a discussion of convergence properties and sensitivities of calculations with SEEKR to establish "best practices" for its future use.

Binding Thermodynamics and Kinetics Calculations Using Chemical Host and Guest: A Comprehensive Picture of Molecular Recognition

Understanding the fine balance between changes of entropy and enthalpy and the competition between a guest and water molecules in molecular binding is crucial in fundamental studies and practical applications. Experiments provide measurements. However, illustrating the binding/unbinding processes gives a complete picture of molecular recognition not directly available from experiments, and computational methods bridge the gaps. Here, we investigated guest association/dissociation with β-cyclodextrin (β-CD) by using microsecond-time-scale molecular dynamics (MD) simulations, postanalysis and numerical calculations. We computed association and dissociation rate constants, enthalpy, and solvent and solute entropy of binding. All the computed values of kon, koff, ΔH, ΔS, and ΔG using GAFF-CD and q4MD-CD force fields for β-CD could be compared with experimental data directly and agreed reasonably with experiment findings. In addition, our study further interprets experiments. Both force fields resulted in similar computed ΔG from independently computed kinetics rates, ΔG = -RT ln(kon·C0/koff), and thermodynamics properties, ΔG = ΔH - TΔS. The water entropy calculations show that the entropy gain of desolvating water molecules are a major driving force, and both force fields have the same strength of nonpolar attractions between solutes and β-CD as well. Water molecules play a crucial role in guest binding to β-CD. However, collective water/β-CD motions could contribute to different computed kon and ΔH values by different force fields, mainly because the parameters of β-CD provide different motions of β-CD, hydrogen-bond networks of water molecules in the cavity of free β-CD, and strength of desolvation penalty. As a result, q4MD-CD suggests that guest binding is mostly driven by enthalpy, while GAFF-CD shows that gaining entropy is the major driving force of binding. The study deepens our understanding of ligand-receptor recognition and suggests strategies for force field parametrization for accurately modeling molecular systems.

Discovery of a non classic host guest complexation mode in a β-cyclodextrin/propionic acid model

A non-classic complexation mode was discovered upon spectroscopic, thermodynamic, crystallographic and computational studies of a β-cyclodextrin/propionic acid complex. A "fully immersed" complexation phenomenon, where both the guest's hydrophobic and polar moieties are located inside the host and are stabilized by it, was found and calculated as the most favorable configuration.

Octylglucopyranoside and cyclodextrin in water. Self-aggregation and complex formation

At 25 degrees C ultrasonic attenuation spectra between 100 kHz and 400 MHz as well as sound velocities and densities of aqueous solutions of the surfactant n-octyl-beta-d-glucopyranoside and of the cage compound alpha-cyclodextrin have been measured. The liquid system reveals a critical association concentration (cac) exceeding the cmc of the surfactant almost by the cyclodextrin concentration and thus indicating a significant formation of cyclodextrin-surfactant inclusion complexes. The ultrasonic spectra display altogether four relaxation regions. The one with largest relaxation time (0.27 mus < or = tau(1) < or = 1.6 mus) exhibits a noticeable amplitude at surfactant concentrations larger than the cac only. It is assigned to the monomer exchange between the micelles and the suspending phase. A term with relaxation time tau(2) (33 ns < or = tau(2) < or = 135 ns) is characteristic for solutions containing both solutes. It is assumed to reflect the inclusion complex formation. Complexes with 1:1, 2:1, and 1:2 stoichiometry appear to exist. The terms at higher frequencies (4.8 ns < or = tau(3) < or = 9.8 ns; 0.8 ns <or = tau(4) < or = 2 ns) are due to fluctuations of the carbohydrate residues around the glucosidic bond angles and to the rotational isomerization of the exocyclic hydroxymethyl groups, respectively.

Kinetic Study for the Inclusion Complex of Carboxylic Acids with Cyclodextrin by the Ultrasonic Relaxation Method

Ultrasonic absorption coefficients in the frequency range of 0.8-95 MHz were measured in aqueous solutions containing both beta-cyclodextrin (beta-CD) (host) and butanoic acid (in its dissociated form and undissociated one) (guest). A single relaxational phenomenon was observed only when the solutes were coexisting, although no relaxation was found in the beta-CD solution or in the acid solutions. The absorption was also measured in a solution of pentanoic acid (dissociated form) with beta-CD, and single relaxation was detected. The ultrasonic relaxation observed in these solutions was due to a perturbation of a chemical equilibrium related to a reaction of an inclusion complex formed by the host and guest. The equilibrium constant was obtained from the dependence of the maximum absorption per wavelength on the guest concentration. The rate constant for the inclusion process of the guest into a cavity of beta-CD and that for the leaving process from the cavity were determined from the obtained relaxation frequency and the equilibrium constant. The standard volume change of the reaction was also computed from the maximum absorption per wavelength. These results were compared with those in solutions containing both beta-CD and different guest molecules. It was found that the hydrophobicity of guest molecules played an important role in the formation of the inclusion complex and also that the charge on the carboxylic group had a considerable effect on the kinetic characteristics of the complexation reaction.

Dynamic Study of Interaction between β-Cyclodextrin and Aspirin by the Ultrasonic Relaxation Method

A single ultrasonic relaxational phenomenon was observed in aqueous solutions containing both beta-cyclodextrin (beta-CD) as host and nonionized or ionized acetylsalicylic acid (aspirin) as guest. The observed relaxation was responsible for a dynamic complexation reaction between beta-CD and aspirin molecules, concomitant with a volume change during the reaction. The kinetic and equilibrium constants for the complexation in the acid (nonionized) form of the aspirin system were derived from the guest concentration dependence of the relaxation frequency. The equilibrium constant for the carboxylate (ionized) form of aspirin was determined from the concentration dependence of a maximum absorption per wavelength, and the rate constants were calculated by using the determined equilibrium constant and the observed relaxation frequencies, which remained nearly almost constant over the concentration range studied. The results showed that the effect of charge on the aspirin molecule was reflected only in the dissociation process from the beta-CD cavity, while no remarkable change was seen in the association process whose rate was diffusion controlled. The results could be explained on the basis of the difference of the hydrophobic moieties in the two guests that were included in the host cavity. The results of the standard volume change for the complexation reaction were closely related to the number of expelled water molecules originally located in the beta-CD cavity and the volume of the aspirin molecule incorporated into the beta-CD cavity.

Dynamic Interaction between Alkylammonium Ions and β-Cyclodextrin by Means of Ultrasonic Relaxation

Ultrasonic absorption measurements in the frequency range from 0.8 to 220 MHz were carried out in aqueous solutions of pentylammonium chloride (PEACL) and hexylammonium chloride (HEACL) with beta-cyclodextrin (beta-CD) at pH approximately 7.2 and 25 degrees C. A single relaxational absorption was attributed to a perturbation of a chemical relaxation associated with the formation of a complex between beta-CD and the alkylammonium chlorides. The rate and equilibrium constants for the complexation reaction were determined from the concentration dependence of the relaxation frequency. Increasing the chain length of the alkylammonium ion led to an increase in the stability of the complex and slowed the exit rate of the ion from the beta-CD cavity. The standard volume change of the reaction was obtained from a maximum absorption per wavelength and was attributed to water molecules being expelled from the cavity with concomitant alkylammonium ion insertion.

Ultrasonic relaxation due to inclusion complex of amino acid by beta-cyclodextrin in aqueous solution

Ultrasonic absorption coefficients in the frequency range of 0.8-95 MHz were measured in aqueous solutions of L-methionine or L-norleucine (guest) in the presence and absence of beta-cyclodextrin (beta-CD, host) at 25 degrees C. A single relaxational absorption was observed only in the solutions containing the guest and host. The ultrasonic relaxation was attributed to a perturbation of a chemical equilibrium associated with an interaction between beta-CD and the amino acid to form the host-guest complex. The kinetic and thermodynamic parameters in the system of L-norleucine with beta-CD were determined from the concentration dependence of the relaxation frequency and the maximum absorption per wavelength. Because of the concentration independence of the relaxation frequency in L-methionine system with beta-CD, the equilibrium constant and the standard volume change of the complexation reaction were estimated first from the concentration dependence of maximum absorption per wavelength, and subsequently the rate constants were calculated with the help of the estimated equilibrium constant and the observed relaxation frequency. The results obtained in this study were compared with those for systems of beta-CD with other amino acids or alcohols having comparable hydrophobicity.

Ultrasonic absorption in aqueous solutions of amino acids at neutral pH

Ultrasonic absorption coefficients in aqueous solutions of glycine, L-alanine, imidazole, L-phenylalanine, L-histidine and L-tryptophan at neutral pH were measured in the range from 0.8 to 220 MHz at 25 degrees C. A characteristic ultrasonic relaxation phenomenon was observed only in the solution of L-histidine with a relaxation frequency at around 2 MHz at neutral pH. It was proposed from the concentration independent relaxation frequency and the linear concentration dependence of the maximum absorption per wavelength that the relaxation mechanism was associated with a perturbation of the rotational isomeric equilibrium of the L-histidine molecule. The existence of two rotational isomeric forms of L-histidine in water was examined by semiempirical quantum chemical methods, in order to determine the free energy difference between the two states. The forward and backward rate constants were determined from the relaxation frequency and the energy change. Also, the standard volume change of the reaction was estimated from the concentration dependence of the maximum absorption per wavelength. It was speculated that L-histidine fulfills a specific function among amino acids because of the rotational motion in the molecule, in addition to its well-established acid-base properties.