Inorganic anion recognition in aqueous solution by coupling nearby highly hydrophilic and hydrophobic moieties in a macrocyclic receptor.

Receptor L, composed of a tripropylenetetramine chain linking the 2 and 7 positions of an acridine unit via methylene bridges, behaves as a pentaprotic base in aqueous solution. The first four protonation steps occur on the tetra-amine chain, while the acridine nitrogen protonates only below pH 4. The penta-protonated receptor assumes a folded conformation, resulting in a cleft delimited by the aliphatic tetramine and acridine moieties, in which anions of appropriate size can be hosted. Potentiometric titrations reveal that F- forms the most stable complexes, although the stability constants of the Cl- and Br- adducts are unusually only slightly lower than those observed for F- complexes. A remarkable drop in stability is observed in the case of I- adducts. Oxo-anions, including H2PO4-, NO3- and SO42-, are not bound or weakly bound by the protonated receptor, despite the known ability of charged oxygens to form stable O-⋯HN+ salt bridges. This unexpected stability pattern is explained in the light of the X-ray crystal structures of H5LCl5·4H2O, H5LBr5·4H2O, H5L(NO3)5·3H2O and H5L(H2PO4)5·(H3PO4)2·4H2O complexes, coupled with MD simulations performed in the presence of explicit water molecules, which reveal that Cl- and, overall, Br- possess the optimal size to fit the receptor cleft, simultaneously forming strong salt bridging interactions with the ammonium groups and anion⋯π contacts with protonated acridine. I- and oxo-anions are too large to conveniently fit the cavity and are only partially enclosed in the receptor pocket, remaining exposed to solvent, with a lower entropic stabilization of their complexes. Although F- could be enclosed in the cavity, its smaller size favours the F-⋯HN+ salt bridging interaction from outside the receptor pocket. The fluorescence emission of the acridinium unit is quenched by anion binding. The quenching ability parallels the stability of the complexes and is related to the relevance of the anion⋯π contacts in the overall host-guest interaction.

Cu(Proline)2 Complex: A Model of Bio-Copper Structural Ambivalence.

Complexes of Cu2+(d9) with proline may be considered a simple model to address the structural flexibility and electronic properties of copper metalloproteins. To discuss optical electronic spectra and infrared spectral responses, we use quantum chemistry applied to model systems prepared under different geometries and degree of hydration. A comparison of experimental data with calculations indicates that first explicit neighbor water clustering next to the Cu2+(d9) complex is critical for a correct description of the electronic properties of this system. We deduce that the moderately hydrated trans conformer is the main structural form of the complex in water. Further, we suggest that the antisymmetric stretching mode of the carbonyl moieties of the conformer is dominant in the spectrally broadened infrared resonance at 1605 cm-1, where inhomogeneity of the transition at the blue side can be ascribed to a continuum of less optimal interactions with the solvent. Extracted structural properties and hydration features provide information on the structural flexibility/plasticity specific to Cu2+(d9) systems in correlation with the electronic behavior upon photoexcitation. We discuss the role and the nature of the axial ligand in bio-copper structural ambivalence and reactivity.

Ethanol electro-oxidation reaction on the Pd(111) surface in alkaline media: insights from quantum and molecular mechanics.

The ethanol electro-oxidation catalyzed by Pd in an alkaline environment involves several intermediate reaction steps promoted by the hydroxyl radical, OH. In this work, we report on the dynamical paths of the first step of this oxidation reaction, namely the hydrogen atom abstraction CH3CH2OH + OH → CH3CHOH + H2O, occurring at the Pd(111) surface and address the thermodynamic stability of the adsorbed reactants by means of quantum and molecular mechanics calculations, with special focus on the effect of the solvent. We have found that the impact of the solvent is significant for both ethanol and OH, contributing to a decrease in their adsorption free energies by a few dozen kcal mol-1 with respect to the adsorption energy under vacuum. Furthermore, we observe that hydrogen atom abstraction is enhanced for those simulation paths featuring large surface-reactant distances, namely, when the reactants weakly interact with the catalyst. The picture emerging from our study is therefore that of a catalyst whose coverage in an aqueous environment is largely dominated by OH with respect to ethanol. Nevertheless, only a small amount of them, specifically those weakly bound to the catalyst, is really active in the ethanol electro-oxidation reaction. These results open the idea of a rational design of co-catalysts based on the tuning of surface chemical properties to eventually enhance exchange current density.

Computational Investigation of the Selective Cleavage of Diastereotopic Cyclopropane Bonds in 5-Spirocyclopropane Isoxazolidines Rearrangement.

The complete path of the Brandi-Guarna rearrangement of 5-spirocyclopropane isoxazolidines has been investigated by means of density functional theory calculations to rationalize the competing formation of tetrahydropyridones and enaminones by the determination of the minimum energy reaction paths. Our calculations confirm that the rearrangement is triggered by the homolysis of the isoxazolidine N-O bond followed by cleavage of one of the two C-CH2 cyclopropane bonds as previously proposed by the Fabian group [ Eur. J. Org. Chem. 2001, 2001, 4223]. In addition, the results of this work suggest that in the presence of a stereogenic center at isoxazolidine C-4', the formation of a piperidinone or an enaminone as the final product depends on which of the two diastereotopic C-CH2 bonds of cyclopropane is cleaved in the second step of the process. The result can be of great interest for the understanding of other processes involving the opening of a cyclopropane ring.

Imidazole in Aqueous Solution: Hydrogen Bond Interactions and Structural Reorganization with Concentration.

The structural and dynamic properties of imidazole in aqueous solution have been studied by means of classical and ab initio molecular dynamics simulations. We developed a new force field for the imidazole molecule with improved modeling of the electrostatic interactions, specifically tailored to address the well-known drawbacks of existing force fields based on the atomic fractional charge approach. To this end, we reparametrized the charge distribution on the heterocyclic ring, introducing an extra site accounting for the lone pair on the deprotonated nitrogen. The accuracy of the model in describing the hydrogen bond pattern in the aqueous solvent has been confirmed by comparing the classical results on imidazole-water interactions to accurate Car-Parrinello molecular dynamics simulations. It reproduces satisfactorily the experimental water/octanol partition coefficient of imidazole, as well as the structure of the imidazole molecular crystal. The force field has been finally applied to simulate aqueous solutions at various imidazole concentrations to obtain information on both imidazole-water and imidazole-imidazole interactions, providing a description of the different molecular arrangements in solution.

A Photochromic Azobenzene Peptidomimetic of a ß-Turn Model Peptide Structure as a Conformational Switch.

The insertion of azobenzene moiety in complex molecular protein or peptide systems can lead to molecular switches to be used to determine kinetics of folding/unfolding properties of secondary structures, such as α-helix, ß-turn, or ß-hairpin. In fact, in azobenzene, absorption of light induces a reversible trans ↔ cis isomerization, which in turns generates a strain or a structure relaxation in the chain that causes peptide folding/unfolding. In particular azobenzene may permit reversible conformational control of hairpin formation. In the present work a synthetic photochromic azobenzene amino acid derivative was incorporated as a turn element to modify the synthetic peptide [Pro7,Asn8,Thr10]CSF114 previously designed to fold as a type I ß-turn structure in biomimetic HFA/water solution. In particular, the P-N-H fragment at positions 7-9, involved in a ß-hairpin, was replaced by an azobenzene amino acid derivative (synthesized ad hoc) to investigate if the electronic properties of the novel peptidomimetic analog could induce variations in the isomerization process. The absorption spectra of the azopeptidomimetic analog of the type I ß-turn structure and of the azobenzene amino acid as control were measured as a function of the irradiation time exciting into the respective first ππ* and nπ* transition bands. Isomerization of the azopeptidomimetic results strongly favored by exciting into the ππ* transition. Moreover, conformational changes induced by the cis↔ trans azopeptidomimetic switch were investigated by NMR in different solvents.

Correspondence between light-absorption spectrum and nonequilibrium work distribution as a mean to access free energy differences between electronic states.

The problem of recovering the free energy difference between two electronic states has been investigated by Frezzato [Chem. Phys. Lett. 533, 106 (2012)], exploring the equivalence between light-absorption spectra and work distribution, hence opening to the application of a spectroscopic version of the Jarzynski equality (JE) [Phys. Rev. Lett. 78, 2690 (1997)]. Here, assuming the validity of the time-dependent perturbation theory, we demonstrate that such equivalence does not lead to the known form of the JE. This is ascribed to the fact that light-absorption processes cannot be described as stochastic processes. To emphasize such an aspect, we devise a stochastic model for the UV-vis (ultraviolet and visible) absorption, suitable for determining the free energy difference between two generic quantum manifolds in a JE-like fashion. However, the model would require explicit knowledge of the transition dipole moments, which are in general not available. Nonetheless, we derive a spectroscopic version of the JE that allows us to recover the free energy difference between the ground and an excited electronic state when the latter state is the only one observed in the spectrum.

Structural Insights into the Osteopontin-Aptamer Complex by Molecular Dynamics Simulations.

Osteopontin is an intrinsically disordered protein involved in tissue remodeling. As a biomarker for pathological hypertrophy and fibrosis, the protein is targeted by an RNA aptamer. In this work, we model the interactions between osteopontin and its aptamer, including mono- (Na+) and divalent (Mg2+) cations. The molecular dynamics simulations suggest that the presence of divalent cations forces the N-terminus of osteopontin to bind the shell of divalent cations adsorbed over the surface of its RNA aptamer, the latter exposing a high negative charge density. The osteopontin plasticity as a function of the local concentration of Mg is discussed in the frame of the proposed strategies for osteopontin targeting as biomarker and in theranostic.

Binding Free Energies of Host-Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Illustrative Calculations and Numerical Validation.

In the companion article (Giovannelli et al., 10.1021/acs.jctc.7b00594), we presented an alchemical approach, based on nonequilibrium molecular dynamics simulations, to compute absolute binding free energies of a generic host-guest system. Two alternative computational routes, called binded-domain and single-point alchemical-path schemes, have been proposed. This study is addressed to furnish numerical validation and illustrative examples of the above-mentioned alchemical schemes. Validation is provided by comparing binding free-energy data relative to two poses of a Zn(II)·anion complex with those recovered from an alternative approach, based on steered molecular dynamics simulations. We illustrate important technical and theoretical aspects for a good practice in applying both alchemical schemes, not only through the calculations on the Zn(II)·anion complex, but also estimating absolute binding free energies of 1:1 complexes of ß-cyclodextrin with aromatic compounds (benzene and naphthalene). Comparison with experimental data and previous molecular dynamics simulation studies further confirms the validity of the present nonequilibrium-alchemical methodology.

Binding Free Energies of Host-Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Theoretical Framework.

The fast-switching decoupling method is a powerful nonequilibrium technique to compute absolute binding free energies of ligand-receptor complexes (Sandberg et al., J. Chem. Theory Comput. 2014, 11, 423-435). Inspired by the theory of noncovalent binding association of Gilson and co-workers (Biophys. J. 1997, 72, 1047-1069), we develop two approaches, termed binded-domain and single-point alchemical-path schemes (BiD-AP and SiP-AP), based on the possibility of performing alchemical trajectories during which the ligand is constrained to fixed positions relative to the receptor. The BiD-AP scheme exploits a recent generalization of nonequilibrium work theorems to estimate the free energy difference between the coupled and uncoupled states of the ligand-receptor complex. With respect to the fast-switching decoupling method without constraints, BiD-AP prevents the ligand from leaving the binding site, but still requires an estimate of the positional binding-site volume, which may not be a simple task. On the other side, the SiP-AP scheme allows avoidance of the calculation of the binding-site volume by introducing an additional equilibrium simulation of ligand and receptor in the bound state. In the companion article (DOI: 10.1021/acs.jctc.7b00595), we show that the extra computational effort required by SiP-AP leads to a significant improvement of accuracy in the free energy estimates.

Insights on the Realgar Crystal Under Pressure from XP-PCM and Periodic Model Calculations.

The spectroscopic properties of As4S4 with pressure have been computed by the quantum mechanical XP-PCM method and by density functional theory periodic calculations. The comparison has allowed the interpretation of the available experimental data. By comparison of the two methods and with experiments, we show that the XP-PCM method is able to reproduce the same behavior of the periodic calculations with much lower computational cost allowing to be adopted as a first choice computational tool for a qualitative interpretation of molecular crystals properties under pressure.

Photochemical Reactivity of 1,6-Methano[10]annulene.

1,6-Methano[10]annulene solutions in cyclohexane have been subjected to continuous and pulsed UV irradiation. Photolysis occurs in both cases, giving naphthalene as a minor and major product, respectively. The wavelength dependence of the reaction in solution indicates that the photochemical process occurs, exciting 1,6-methano[10]annulene in the second and third singlet electronic excited states. The reaction kinetics has been determined under pulsed irradiation. From the time dependence of concentrations, along with support of density functional theory calculations and early published data, two mechanisms are proposed for naphthalene production. Reaction steps such as direct migration of the bridging methylene of 1,6-methano[10]annulene to cyclohexane and 1,6-methano[10]annulene isomerization to benzotropilidene have been identified. The calculated energy diagrams relative to the ground and lowest excited states allow one to relate these steps to processes such as electrocyclic closure and sigmatropic shift. The norcaradienic form of 1,6-methano[10]annulene results in the critical species for methylene migration and the sigmatropic [1,5] shift. The present results and those arising from photolysis in the gas phase are good examples of the photochemical reactivity of 1,6-methano[10]annulene.

Statistical Mechanics of Ligand-Receptor Noncovalent Association, Revisited: Binding Site and Standard State Volumes in Modern Alchemical Theories.

The present paper is intended to be a comprehensive assessment and rationalization, from a statistical mechanics perspective, of existing alchemical theories for binding free energy calculations of ligand-receptor systems. In detail, the statistical mechanics foundation of noncovalent interactions in ligand-receptor systems is revisited, providing a unifying treatment that encompasses the most important variants in the alchemical approaches from the seminal double annihilation method [ Jorgensen et al. J. Chem. Phys. 1988 ; 89 , 3742 ] to the double decoupling method [ Gilson et al. Biophys. J. 1997 ; 72 , 1047 ] and the Deng and Roux alchemical theory [ Deng and Roux J. Chem. Theory Comput. 2006 ; 2 , 1255 ]. Connections and differences between the various alchemical approaches are highlighted and discussed.

II. Dissociation free energies in drug-receptor systems via nonequilibrium alchemical simulations: application to the FK506-related immunophilin ligands.

The recently proposed fast switching double annihilation (FS-DAM) [Cardelli et al., J. Chem. Theory Comput., 2015, 11, 423] is aimed at computing the absolute standard dissociation free energies for the chemical equilibrium RL ⇌ R + L occurring in solution through molecular dynamics (MD) simulations at the atomistic level. The technique is based on the production of fast nonequilibrium annihilation trajectories of one of the species (the ligand) in the solvated RL complex and in the bulk solvent. As detailed in the companion theoretical paper, the free energies of these two nonequilibrium annihilation processes are recovered by using an unbiased unidirectional estimate derived from the Crooks theorem exploiting the inherent Gaussian nature of the annihilation work. The FS-DAM technique was successfully applied to the evaluation of the dissociation free energy of the complexes of Zn(ii) cations with an inhibitor of the Tumor Necrosis Factor α converting enzyme. Here we apply the technique to a real drug-receptor system, by satisfactorily reproducing the experimental dissociation free energies of FK506-related bulky ligands towards the native FKBP12 enzyme and by predicting the dissociation constants for the same ligands towards the mutant I56D. The effect of such mutations on the binding affinity of FK506-related ligands is relevant for assessing the thermodynamic forces regulating molecular recognition in FKBP12 inhibition.

Elastic Barrier Dynamical Freezing in Free Energy Calculations: A Way To Speed Up Nonequilibrium Molecular Dynamics Simulations by Orders of Magnitude.

An important issue concerning computer simulations addressed to free energy estimates via nonequilibrium work theorems, such as the Jarzynski equality [Phys. Rev. Lett. 1997, 78, 2690], is the computational effort required to achieve results with acceptable accuracy. In this respect, the dynamical freezing approach [Phys. Rev. E 2009, 80, 041124] has been shown to improve the efficiency of this kind of simulations, by blocking the dynamics of particles located outside an established mobility region. In this report, we show that dynamical freezing produces a systematic spurious decrease of the particle density inside the mobility region. As a consequence, the requirements to apply nonequilibrium work theorems are only approximately met. Starting from these considerations, we have developed a simulation scheme, called "elastic barrier dynamical freezing", according to which a stiff potential-energy barrier is enforced at the boundaries of the mobility region, preventing the particles from leaving this region of space during the nonequilibrium trajectories. The method, tested on the calculation of the distance-dependent free energy of a dimer immersed into a Lennard-Jones fluid, provides an accuracy comparable to the conventional steered molecular dynamics, with a computational speedup exceeding a few orders of magnitude.

Simulations in generalized ensembles through noninstantaneous switches.

Generalized-ensemble simulations, such as replica exchange and serial generalized-ensemble methods, are powerful simulation tools to enhance sampling of free energy landscapes in systems with high energy barriers. In these methods, sampling is enhanced through instantaneous transitions of replicas, i.e., copies of the system, between different ensembles characterized by some control parameter associated with thermodynamical variables (e.g., temperature or pressure) or collective mechanical variables (e.g., interatomic distances or torsional angles). An interesting evolution of these methodologies has been proposed by replacing the conventional instantaneous (trial) switches of replicas with noninstantaneous switches, realized by varying the control parameter in a finite time and accepting the final replica configuration with a Metropolis-like criterion based on the Crooks nonequilibrium work (CNW) theorem. Here we revise these techniques focusing on their correlation with the CNW theorem in the framework of Markovian processes. An outcome of this report is the derivation of the acceptance probability for noninstantaneous switches in serial generalized-ensemble simulations, where we show that explicit knowledge of the time dependence of the weight factors entering such simulations is not necessary. A generalized relationship of the CNW theorem is also provided in terms of the underlying equilibrium probability distribution at a fixed control parameter. Illustrative calculations on a toy model are performed with serial generalized-ensemble simulations, especially focusing on the different behavior of instantaneous and noninstantaneous replica transition schemes.

Computing Free Energy Differences of Configurational Basins.

A simulation-based approach is proposed to estimate free energy differences between configurational states A and B, defined in terms of collective coordinates of the molecular system. The computational protocol is organized into three stages that can be carried on simultaneously. Two of them consist of independent simulations aimed at sampling, in turn, A and B states. In order to limit the evolution of the system around A and B, biased sampling simulations such as umbrella sampling can be employed. These simulations allow us to estimate local configuration integrals associated with A and B, which can be viewed as vibrational contributions to the free energy. Free energy evaluation is completed by the linking-path stage, in which the potential of mean force difference is estimated between two arbitrary points of the configurational surface, located the first around A and the second around B. The linking path in the space of the collective coordinates is arbitrary and can be computed with any method, starting from adaptive biasing potential/force approaches to nonequilibrium techniques. As an illustrative example, we present the calculation of free energy differences between conformational states of the alanine dipeptide in the space of backbone dihedral angles. The basic advantage of this method, that we term "path-linked domains" scheme, is to prevent accurate calculation of the whole free energy hypersurface in the space of the collective coordinates, thus limiting the statistical sampling to a minimum. Path-linked domains schemes can be applied to a variety of biochemical processes, such as protein-ligand complexation or folding-unfolding interconversion.

A fluorescent receptor for halide recognition: clues for the design of anion chemosensors.

The chemosensing properties of the polyaza-macrocycle 1-(6,7)-acridine-3,6,9,12-tetraaza-tridecaphane have been investigated by means of emission fluorescence spectroscopy, considering halide ions as substrates. As in the case of the free ligand, the fluorescence emission of the complexes is due to the acridinium species which are formed after photoinduced proton transfer reaction. The complexation constants have been obtained for the bi- and tri-protonated ligands in deoxygenated aqueous solutions. Two different emission behaviours have been observed varying the anion. Fluoride and chloride give rise to fluorescence enhancement whereas bromide and iodide strongly quench the emission. The macrocycle shows an unusual higher selectivity towards the chloride anion rather than fluoride. The fluorescence emission has been modelled considering a modified Stern-Volmer equation, taking into account the quenching effects of the largest anions, which can be considered negligible for fluoride and chloride anions. Ab initio calculations allow us to interpret the fluorescence emission of the complexes in terms of activation energy related to the proton transfer reaction responsible for the emission process.

Annealed importance sampling with constant cooling rate.

Annealed importance sampling is a simulation method devised by Neal [Stat. Comput. 11, 125 (2001)] to assign weights to configurations generated by simulated annealing trajectories. In particular, the equilibrium average of a generic physical quantity can be computed by a weighted average exploiting weights and estimates of this quantity associated to the final configurations of the annealed trajectories. Here, we review annealed importance sampling from the perspective of nonequilibrium path-ensemble averages [G. E. Crooks, Phys. Rev. E 61, 2361 (2000)]. The equivalence of Neal's and Crooks' treatments highlights the generality of the method, which goes beyond the mere thermal-based protocols. Furthermore, we show that a temperature schedule based on a constant cooling rate outperforms stepwise cooling schedules and that, for a given elapsed computer time, performances of annealed importance sampling are, in general, improved by increasing the number of intermediate temperatures.

Combining path-breaking with bidirectional nonequilibrium simulations to improve efficiency in free energy calculations.

An important limitation of unidirectional nonequilibrium simulations is the amount of realizations of the process necessary to reach suitable convergence of free energy estimates via Jarzynski's relationship [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)]. To this regard, an improvement of the method has been achieved by means of path-breaking schemes [R. Chelli et al., J. Chem. Phys. 138, 214109 (2013)] based on stopping highly dissipative trajectories before their normal end, under the founded assumption that such trajectories contribute marginally to the work exponential averages. Here, we combine the path-breaking scheme, called probability threshold scheme, to bidirectional nonequilibrium methods for free energy calculations [G. E. Crooks, Phys. Rev. E 61, 2361 (2000); R. Chelli and P. Procacci, Phys. Chem. Chem. Phys. 11, 1152 (2009)]. The method is illustrated and tested on a benchmark system, i.e., the helix-coil transition of deca-alanine. By using path-breaking in our test system, the computer time needed to carry out a series of nonequilibrium trajectories can be reduced up to a factor 4, with marginal loss of accuracy in free energy estimates.