Steered transition path sampling

We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying the dynamics based on that probability, and then reweighting to calculate averages. Because the progress constraint can be formulated in terms of occurrences of events within time intervals, the method is particularly well suited for controlling the sampling of currents of dynamic events. We demonstrate the method for calculating transition probabilities in barrier crossing problems and survival probabilities in strongly diffusive systems with absorbing states, which are difficult to treat by shooting. We discuss the relation of the algorithm to other methods.     

The dynamics of water exchange in gadolinium DOTA complexes studied by transition path sampling and potential of mean force methods

The mechanism of water exchange at the Gd centre of the two isomers of [Gd(iii)DOTA](-) (gadolinate(1-), [1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetato(4-)-N1,N4,N7,N10,O1,O4,O7,O10]) has been explored using transition path sampling and potential of mean force methods to sample those regions of phase space inaccessible to standard molecular dynamics simulation. We find that there are definite differences in the details of the solvent rearrangement accompanying the exchange of the capping water molecule for the two isomers. We conclude that these solvent effects, rather than any differences in the binding energy of the capping water, are central in determining the exchange rate. We find that the potential of mean force studies yield absolute and relative rates of water exchange for the two isomers that are in good agreement with experiment.     

Improved transition path sampling methods for simulation of rare events

The free energy surfaces of a wide variety of systems encountered in physics, chemistry, and biology are characterized by the existence of deep minima separated by numerous barriers. One of the central aims of recent research in computational chemistry and physics has been to determine how transitions occur between deep local minima on rugged free energy landscapes, and transition path sampling (TPS) Monte-Carlo methods have emerged as an effective means for numerical investigation of such transitions. Many of the shortcomings of TPS-like approaches generally stem from their high computational demands. Two new algorithms are presented in this work that improve the efficiency of TPS simulations. The first algorithm uses biased shooting moves to render the sampling of reactive trajectories more efficient. The second algorithm is shown to substantially improve the accuracy of the transition state ensemble by introducing a subset of local transition path simulations in the transition state. The system considered in this work consists of a two-dimensional rough energy surface that is representative of numerous systems encountered in applications. When taken together, these algorithms provide gains in efficiency of over two orders of magnitude when compared to traditional TPS simulations.     

Unprejudiced identification of reaction mechanisms from biased transition path sampling

A method for unprejudiced investigation of reaction mechanisms from molecular-dynamics simulations is presented. It combines the transition path sampling approach with a biasing strategy, which (a) allows optimization of transition paths crossing an energy minimum of the transition state surface. The bias is then used to (b) find reaction pathways, which follow different mechanistic routes. In the first step the manifold of similar trajectories that correspond to the same mechanism is reduced to a single characteristic dynamical path. Our method then allows a systematic search for further reaction mechanisms and the related energy barriers. It is illustrated at the example of a single particle in a two-dimensional potential and of the rather complex process of the pressure-induced insertion of a helium atom into a C60 buckyball molecule.     

Efficient transition path sampling for systems with multiple reaction pathways

A new algorithm is developed for sampling transition paths and computing reaction rates. To illustrate the use of this method, we study a two-dimensional system that has two reaction pathways: one pathway is straight with a relatively high barrier and the other is roundabout with a lower barrier. The transition rate and the ratio between the numbers of the straight and roundabout transition paths are computed for a wide range of temperatures. Our study shows that the harmonic approximation for fluctuations about the steepest-descent paths is not valid even at relatively low temperatures and, furthermore, that factors related to entropy have to be determined by the global geometry of the potential-energy surface (rather than just the local curvatures alone) for complex reaction systems. It is reasonable to expect that this algorithm is also applicable to higher dimensional systems.     

An efficient transition path sampling algorithm for nanoparticles under pressure

We apply transition path sampling to the simulation of nanoparticles under pressure. As a barostat we use a bath of ideal gas particles that form a stochastically updated atmosphere around the nanoparticle. We justify this algorithm by showing that it preserves the distribution of an ideal gas at constant temperature and pressure by satisfying detailed balance. Based on this result, we present a simple and efficient transition path sampling scheme for the study of activated processes in nanoparticles under pressure. As a first application, we investigate the h-MgO to rocksalt transformation in faceted CdSe nanocrystals. Starting from an artificial mechanism involving a uniform motion of all atoms, trajectories quickly converge towards the dominant mechanism of nucleation and growth along parallel (100) planes.     

Mechanism of enantioseparation of DL-pantothenic acid in ligand exchange capillary electrophoresis using a diol-borate system

Borate complexes formed in the ternary system at pH 9.2 containing borate, (S)-3-amino-1,2-propanediol (SAP), and DL-pantothenic acid (DL-PTA) were identified by 13C and 11B NMR, and it is confirmed that the binary complexes, [B(OH)2(SAP)], [B(SAP)2]+ [B(OH)2(D- or L-PTA)]2-, and [B(D- or L-PTA)2]3- (including [B(D-PTA)(L-PTA)]3-), and the ternary complexes, [B(SAP)(D- or L-PTA)]-, coexist at equilibrium in the ternary system. Thermodynamic experiments by variable-temperature 11B NMR revealed that the ternary complex, [B(SAP)(D-PTA)]-, is entropically more stable than [B(SAP)(L-PTA)]-. Because two geometrical isomers are possible for the respective ternary complexes, semi-empirical molecular orbital calculations were performed by PM5, PM3, and AM1 methods in order to obtain the optimized structures. It is indicated from the calculated heats of formation and experimentally obtained thermodynamic parameters that the (S)-isomer is more probable for the respective ternary complexes with D- and L-PTA. In the optimized structure of (S)-[B(SAP)(D-PTA)]- in water, the SAP and D-PTA ligands were oppositely oriented to form a rather linear structure, while the diastereomer, (S)-[B(SAP)(L-PTA)]-, had a folded structure. Because such a difference in the solvated structure of the ternary complexes can give a different electrophoretic velocity in CE, the enantioseparation of DL-PTA in CE is reasonably attributed to a difference in the observed electrophoretic mobility for the equilibrated ternary systems containing the respective ternary complexes.     

Glass-liquid transition of vapor-deposited hexane studied using TOF-SIMS

Thermodynamic connection between liquid and glass is not obvious for poor glass formers. In this study, microscopic molecular diffusivity and macroscopic fluidity of vapor-deposited thin films of n-hexane were investigated using TOF-SIMS to elucidate the mechanism of the glass-liquid transition. The C 6H 14 film deposited at 15 K is characterized by a porous structure, as inferred from the intermixing with adsorbed C 6D 14 and D 2O molecules, as well as the formation of D 2O nanoclusters on the surface. The hexane molecules are reoriented at temperatures higher than 60-70 K, resulting in smoothing of the surface and densification of the film. Self-diffusion of the hexane molecules commences at 110 K; then, the film dewets the Ni(111) substrate after some aging time. Results indicate that ultraviscous liquid formed at the glass transition temperature of 110 K transforms into fluidized liquid immediately before crystallization. The D 2O molecules adsorbed onto the surface play a role as a surfactant, as evidenced by quenching the film dewetting. The ultraviscous liquid is likely to be a distinct phase, which might explain the absence of calorimetric glass transition for poor glass formers like hexane.     

Significant enhancement of docking sensitivity using implicit ligand sampling

The efficient and accurate quantification of protein-ligand interactions using computational methods is still a challenging task. Two factors strongly contribute to the failure of docking methods to predict free energies of binding accurately: the insufficient incorporation of protein flexibility coupled to ligand binding and the neglected dynamics of the protein-ligand complex in current scoring schemes. We have developed a new methodology, named the 'ligand-model' concept, to sample protein conformations that are relevant for binding structurally diverse sets of ligands. In the ligand-model concept, molecular-dynamics (MD) simulations are performed with a virtual ligand, represented by a collection of functional groups that binds to the protein and dynamically changes its shape and properties during the simulation. The ligand model essentially represents a large ensemble of different chemical species binding to the same target protein. Representative protein structures were obtained from the MD simulation, and docking was performed into this ensemble of protein conformation. Similar binding poses were clustered, and the averaged score was utilized to rerank the poses. We demonstrate that the ligand-model approach yields significant improvements in predicting native-like binding poses and quantifying binding affinities compared to static docking and ensemble docking simulations into protein structures generated from an apo MD simulation.     

Activation energy for a model ferrous-ferric half reaction from transition path sampling

Activation parameters for the model oxidation half reaction of the classical aqueous ferrous ion are compared for different molecular simulation techniques. In particular, activation free energies are obtained from umbrella integration and Marcus theory based thermodynamic integration, which rely on the diabatic gap as the reaction coordinate. The latter method also assumes linear response, and both methods obtain the activation entropy and the activation energy from the temperature dependence of the activation free energy. In contrast, transition path sampling does not require knowledge of the reaction coordinate and directly yields the activation energy [C. Dellago and P. G. Bolhuis, Mol. Simul. 30, 795 (2004)]. Benchmark activation energies from transition path sampling agree within statistical uncertainty with activation energies obtained from standard techniques requiring knowledge of the reaction coordinate. In addition, it is found that the activation energy for this model system is significantly smaller than the activation free energy for the Marcus model, approximately half the value, implying an equally large entropy contribution.     

Catalytic asymmetric deprotonation using a ligand exchange approach

A novel ligand exchange approach to catalytic asymmetric deprotonation-electrophilic trapping has been developed that uses 1.3 equiv of s-BuLi, 0.06-0.2 equiv of chiral diamine ((-)-sparteine or a (+)-sparteine surrogate), and 1.2 equiv of achiral bispidine. The methodology is illustrated with a range of examples and gives access to either enantiomer of useful chiral products in good yields using substoichiometric amounts of chiral diamines.     

A transition path sampling study of the reaction catalyzed by the enzyme chorismate mutase

The study of the chemical steps in enzyme-catalyzed reactions represents a challenge for molecular simulation techniques. One concern is how to calculate paths for the reaction. Common techniques include the definition of a reaction coordinate in terms of a small set of (normally) geometrical variables or the determination of minimum energy paths on the potential energy surface of the reacting system. Both have disadvantages, the former because it presupposes knowledge of which variables are likely to be important for reaction and the latter because it provides a static picture and dynamical effects are ignored. In this paper, we employ the transition path sampling method developed by Chandler and co-workers, which overcomes some of these limitations. The reaction that we have chosen is the chorismate-mutase-catalyzed conversion of chorismate into prephenate, which has become something of a test case for simulation studies of enzyme mechanisms. We generated an ensemble of approximately 1000 independent transition paths for the reaction in the enzyme and another approximately 500 for the corresponding reaction in solution. A large variety of analyses of these paths was performed, but we have concentrated on characterizing the transition state ensemble, particularly the flexibility of its structures with respect to other ligands of the enzyme and the time evolution of various geometrical and energetic properties as the reaction proceeds. We have also devised an approximate technique for locating transition state structures along the paths.     

Electrochromatographic enantioseparation using chiral ligand exchange monolithic sol-gel column

This paper describes the development of a monolithic sol-gel column modified with l-hydroxyproline as a ligand exchange chiral stationary phase. It has been demonstrated that the monolithic chiral stationary phase can be used for the enantioseparation of dansyl amino acids, free amino acids, hydroxy acids, and dipeptides by capillary electrochromatography and micro-liquid chromatography. The recommended mobile phase was acetonitrile/0.50 mM Cu(Ac)₂-50 mM NH₄Ac (7:3) adjusted to pH 6.5. The characteristics of the monolithic column using hydroxyproline as chiral selector in CEC have been discussed.     

Exploring reaction pathways with transition path and umbrella sampling: application to methyl maltoside

The transition path sampling (TPS) method is a powerful approach to study chemical reactions or transitional properties on complex potential energy landscapes. One of the main advantages of the method over potential of mean force methods is that reaction rates can be directly accessed without knowledge of the exact reaction coordinate. We have investigated the complementary nature of these two differing approaches, comparing transition path sampling with the weighted histogram analysis method to study a conformational change in a small model system. In this case study, the transition paths for a transition between two rotational conformers of a model disaccharide molecule, methyl beta-D-maltoside, were compared with a free energy surface constrained by the two commonly used glycosidic (phi,psi) torsional angles. The TPS method revealed a reaction channel that was not apparent from the potential of mean force method, and the suitability of phi and psi as reaction coordinates to describe the isomerization in vacuo was confirmed by examination of the transition path ensemble. Using both transition state theory and transition path sampling methods, the transition rate was estimated. We have estimated a characteristic time between transitions of approximately 160 ns for this rare isomerization event between the two conformations of the carbohydrate. We conclude that transition path sampling can extract subtle information about the dynamics not apparent from the potential of mean force method. However, in calculating the reaction rate, the transition path sampling method required 27.5 times the computational effort than was needed by the potential of mean force method.     

Transformations of metal species in ageing humic hydrocolloids studied by competitive ligand and metal exchange

Transformations of metal species (particularly Al, Ca, Fe, Mg, Mn, Zn) in ageing humic hydrocolloids were studied, applying a competitive ligand and metal exchange approach. For this purpose, metal-containing hydrocolloids, freshly collected from humic-rich German bog lake waters (Hohlohsee (HO), Black Forest; Venner Moor (VM), Muensterland; Arnsberger Wald (AW), Northrhine-Westfalia) and conventionally pre-filtered through 0.45 m membranes, were subjected on-site to an exchange with EDTA and Cu(II) ions, respectively, as a function of time. EDTA complexes gradually formed, metal fractions exchanged by Cu(II) (as well as free Cu(II) concentrations) were operationally discriminated by means of a small time-controlled tangential-flow ultrafiltration unit (nominal cut-off: 1 kDa). Metal and DOM (dissolved organic matter) fractions obtained this way were determined off-site using instrumental methods (AAS, ICP-OES, carbon analyzer). After weeks of storage, the collected hydrocolloids were studied again by this approach. The EDTA availability of colloid-bound metals (particularly Al and Fe) exhibited different ageing trends, dependent on the sample (VM: decrease of Fe availability (98–76%), HO: increase of Fe availability (76–82%)). In contrast, the Cu(II) exchange equilibria of colloid-bound metals revealed merely low availability of Al (16–38%) and Fe (5–11%) towards Cu(II) ions, also dependent on ageing effects. In particular, the conditional copper exchange constants K_ex obtained from the exchange between Cu(II) ions and available metal species (such as Ca, Mg, Mn, Zn) exhibited a strong decrease (by a factor of 2–100) during sample storage, indicating considerable non-equilibria complexation of these metal ions in the original bogwaters studied on-site.     

Mechanism and kinetics of ligand exchange between ferric citrate and desferrioxamine B

The kinetics of ligand exchange between ferric citrate and desferrioxamine B (DFB) was investigated at pH 8.0 and high citrate/Fe molar ratios (500-5000) with particular attention given to understanding the precise mechanism of ligand exchange. Ferric citrate complexes present in a test solution and therefore involved in the reaction with the incoming ligand (DFB) were initially examined by evaluating ferric citrate speciation on the basis of published thermodynamic constants. The speciation analysis indicated that mononuclear (mono- and dicitrate) ferric complexes are the major species responsible for the ligand exchange with DFB under the conditions examined in the present work. Given the tendency of DFB to adjunctively associate with the ferric citrate complexes, we propose a kinetic model containing the following three mechanisms: (i) direct association of DFB to the ferric dicitrate complex prior to any dissociation of citrate molecules from the Fe center, (ii) adjunctive association of DFB toward ferric monocitrate complex following dissociation of one molecule of citrate from the parent complex, and (iii) complexation of hydrated Fe by DFB after sequential dissociation of two molecules of citrate from the Fe center. Overall rates for the ligand exchange were determined by spectrophotometrically monitoring the formation of ferrioxamine B. Further analysis in quantifying the rate of each mechanism by use of published and determined rate constants of relevant elemental reactions suggested that the first and second mechanisms were significant under our experimental conditions where [Cit] ? [DFB] with the relative importance of these two pathways depending on citrate concentration.     

Generation of initial trajectories for transition path sampling of chemical reactions with ab initio molecular dynamics

Transition path sampling is an innovative method for focusing a molecular dynamics simulation on a reactive event. Although transition path sampling methods can generate an ensemble of reactive trajectories, an initial reactive trajectory must be generated by some other means. In this paper, the authors have evaluated three methods for generating initial reactive trajectories for transition path sampling with ab initio molecular dynamics. The authors have tested each of these methods on a set of chemical reactions involving the breaking and making of covalent bonds: the 1,2-hydrogen elimination in the borane-ammonia adduct, a tautomerization, and the Claisen rearrangement. The first method is to initiate trajectories from the potential energy transition state, which was effective for all reactions in the test set. Assigning atomic velocities found using normal mode analysis greatly improved the success of this method. The second method uses a high temperature molecular dynamics simulation and then iteratively reduces the total energy of the simulation until a low temperature reactive trajectory is found. This was effective in generating a low temperature trajectory from an initial trajectory run at 3000 K of the tautomerization reaction, although it failed for the other two. The third uses an orbital based bias potential to find a reactive trajectory and uses this trajectory to initiate an unbiased trajectory. The authors found that a highest occupied molecular orbital-lowest unoccupied molecular orbital bias could be used to find a reactive trajectory for the Claisen rearrangement, although it failed for the other two reactions. These techniques will help make it practical to use transition path sampling to study chemical reaction mechanisms that involve bond breaking and forming.     

Strong complex formation of carbohydrates with metal ions at alkaline pH studied by ligand exchange chromatography

Summary At alkaline pH, carbohydrates are highly retained on a sulphonated polystyrene resin loaded with rare earth or uranyl metal ions. The complex formation is governed by the ionization of the carbohydrate moiety. pH and the type of metal ion were found to have a decisive influence on the complex formation. Binding of the metal ion to the cation exchanger and to different carbohydrates is described. The competitive complexation between solute and hydroxide to the metal ions is described as a ligand exchange reaction and a retention model is proposed. The ligand exchange column was used as precolumn in a coupled column separation system and the high selectivity is demonstrated by the separation of paracetamol glucuronide from a urine sample after filtration and direct injection.     

Molecular path for ligand search

A ligand is a small molecule bind to several residues of a receptor.We adapt the concept of molecular path for effective ligand search with its contacting residues.Additionally,we allow wild type definitions on atoms and bonds of molecular paths for fuzzy algorithms on structural match.We choose hydrogen bond interactions to characterize the binding mode of a ligand by several proper molecular paths and use them to query the deposited ligands in PDBe that interact with their residues in the same way. Expression of molecular path and format of database entries are described with examples.Our molecular path provides a new approach to explore the ligand-receptor interactions and to provide structural framework reference on new ligand design.     

Mechanism in Brill transition of polyamide 66 studied by two-dimensional correlation infrared spectroscopy

The Brill transition of polyamide 66 was investigated by temperature-dependent infrared spectroscopy combined with moving-window two-dimensional (MW2D) correlation spectroscopy. The temperature range of the Brill transition determined by MW2D correlation spectroscopy was 90–170 °C. We employed generalized 2D correlation spectroscopy to study the sequential order of polyamide 66 chains with linear increment of temperature. The movement of the methylene segments near to NH is earlier than those on the CO sides. At the same time, the methylene which is close to NH varies before the inner methylene. Three kinds of NH groups in polyamide 66 were found. The sequential order of their motions is as follows. The free hydrogen-bonded NH groups change first, and then the disordered hydrogen-bonded NH groups. Finally, the ordered hydrogen-bonded NH groups start to change. We also found that the changes of the ordered hydrogen-bonded NH groups follow with the methylene groups.