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Density functional theory calculations are used to obtain stable structures and transition states for a network of reactions involving asparagine deamidation, which are a decisive event in chemotherapy-induced apoptosis and a major obstacle in the formulation of monoclonal antibodies. The calculated pH-dependent rates constant agree with the experimental pH dependence and the rate-determining transition state structures help in understanding chemotherapy-induced apoptosis and improve protein formulations.

Equilibrium path sampling method is used for free energy calculations with reactive flux and kinetic Monte Carlo simulations in order to estimate the methane diffusivity within a structure I gas hydrate crystal from a water-vacancy assisted diffusion mechanism. The studies have shown that equilibrium path sampling has computed free energies for a broader class of coordinates than umbrella sampling with molecular dynamics.

The article explains the size dependent nucleation mechanism, which is involved in the solid state polymorph transformations in teraphthalic acid. The mechanism is shown to continuously change with the size of the system.

The specific roles for acid-base catalysis is strictosidine synthase are described by using the data derived from kinetic isotope effects (KIE), rate dependence of pH, and comparisons to a nonenzymatic Pictet-Spengler reaction. The studies have shown that a spiroindolenine intermediate, which is often invoked in the Pictet-Spengler mechanism, does not occur.

A molecular mechanism is described for nucleation for the solid-state polymorph transformation of terephthalic acid. The findings reveal the reaction coordinate approximation is validated by using the committor probability analysis and the transformation has proceeded through a localized, elongated nucleus along the crystal edge formed by fluctuations in the supramolecular synthons, indicating a nucleation and growth mechanism in the macroscopic system.

Crystal growth rates depend on the density of kink sites along step edges, ρ. The supersaturation-dependence of the kink density, ρ(S), is often ignored despite available nonequilibrium models for centrosymmetric crystals. The aim of this work is to derive ρ(S) from a rather simple one-dimensional nucleation framework in a manner that accounts for multiheight kinks. These become more prevalent at higher S and/or lower kink energies where the step front roughens (i.e., higher ρ). We arrive at a density of kinetic kinks that contribute to the step velocity and make comparisons with other models and simulations. Our model almost entirely eliminates systematic errors in predicted step velocities and crystal growth rates. [ABSTRACT FROM AUTHOR]

We develop a theory to account for variable coverage of trace additives that lower the interfacial free energy for nucleation. The free energy landscape is based on classical nucleation theory and a statistical mechanical model for Langmuir adsorption. Dynamics are modeled by diffusion-controlled attachment and detachment of solutes and adsorbing additives. We compare the mechanism and kinetics from a mean-field model, a projection of the dynamics and free energy surface onto nucleus size, and a full two-dimensional calculation using Kramers-Langer-Berezhkovskii-Szabo theory. The fluctuating coverage model predicts rates more accurately than mean-field models of the same process primarily because it more accurately estimates the potential of mean force along the size coordinate. [ABSTRACT FROM AUTHOR]

Nucleationkinetics, induction times, and metastable zone widthsare often modeled in quiescent, quasi-steady, and/or spatially uniformconcentration fields. However, freezing an aqueous solution can concentratethe solute and effectively increase the supersaturation. During thefreezing process, a boundary layer of giant supersaturation developsahead of the moving ice front. We develop stochastic models of nucleationin the boundary layer when the growing ice perfectly excludes thesolute for a one-dimensional system. The models make three simplifyingassumptions: quasi-stationary nucleation kinetics, nuclei that aresmall compared to the boundary layer thickness, and a constant solventcrystallization growth velocity. Whether heterogeneous on the icesurface, or homogeneous in the boundary layer, the models suggestthat nucleation is dramatically accelerated by the growing ice. Formethane hydrates, which form at conditions similar to that of ice,induction times for hydrate nucleation can be reduced by as much as10105times because of the moving supersaturation zone. [ABSTRACT FROM AUTHOR]

The Pictet-Spengler reaction, which yields either a β-carboline or a tetrahydroquinoline product from an aromatic amine and an aldehyde, is widely utilized in plant alkaloid biosynthesis. Here we deconvolute the role that the biosynthetic enzyme strictosidine synthase plays in catalyzing the stereoselective synthesis of a β-carboline product. Notably, the rate-controlling step of the enzyme mechanism, as identified by the appearance of a primary kinetic isotope effect (KIE), is the rearomatization of a positively charged intermediate. The KIE of a nonenzymatic Pictet-Spengler reaction indicates that rearomatization is also rate-controlling in solution, suggesting that the enzyme does not significantly change the mechanism of the reaction. Additionally, the pH dependence of the solution and enzymatic reactions provides evidence for a sequence of acid-base catalysis steps that catalyze the Pictet-Spengler reaction. An additional acid-catalyzed step, most likely protonation of a carbinolamine intermediate, is also significantly rate controlling. We propose that this step is efficiently catalyzed by the enzyme. Structural analysis of a bisubstrate inhibitor bound to the enzyme suggests that the active site is exquisitely tuned to correctly orient the iminium intermediate for productive cyclization to form the diastereoselective product. Furthermore, ab initio calculations suggest the structures of possible productive transition states involved in the mechanism. Importantly, these calculations suggest that a spiroindolenine intermediate, often invoked in the Pictet-Spengler mechanism, does not occur. A detailed mechanism for enzymatic catalysis of the β-carboline product is proposed from these data. [ABSTRACT FROM AUTHOR]

Some of the most potent antifreeze proteins (AFPs) are approximately rigid helical structures that bind with one side in contact with the ice surface at specific orientations. These AFPs take random orientations in solution; however, most orientations become sterically inaccessible as the AFP approaches the ice surface. The effect of these inaccessible orientations on the rate of adsorption of AFP to ice has never been explored. Here, we present a diffusion-controlled theory of adsorption kinetics that accounts for these orientational restrictions to predict a rate constant for adsorption ( k on , in m/s) as a function of the length and width of the AFP molecules. We find that k on decreases with length and diameter of the AFP and is almost proportional to the inverse of the area of the binding surface. We demonstrate that the restricted orientations create an entropic barrier to AFP adsorption, which we compute to be approximately 7 k B T for most AFPs and up to 9 k B T for Maxi, the largest known AFP. We compare the entropic resistance 1/ k on to resistances for diffusion through boundary layers and across typical distances in the extracellular matrix and find that these entropic and diffusion resistances could become comparable in the small confined spaces of biological environments.

Of all plastics, the most abundantly produced is polyethylene, most of which is destined for landfills, shipping ports, and natural environments. The limited degradability and recyclability of this synthetic polymer motivates the development of chemical recycling methods. One possible approach consists of selective depolymerization to propylene with tandem olefin metathesis and double bond isomerization catalysts. In this paper, we transform thousands of coupled rate equations, pseudo-steady-state approximations, and local density approximations into one simple and analytically solvable Fokker-Planck type equation. The Fokker-Planck equation gives concise expressions for the rate of propylene production and polymer molecular weight evolution as functions of catalyst concentrations, rate constants, and ethylene concentrations.

The slow nucleation of clathrate hydrates is a central challenge for their use in the storage and transportation of natural gas. Molecules that strongly adsorb to the clathrate-water interface decrease the crystal-water surface tension, lowering the barrier for clathrate nucleation. Surfactants are widely used to promote the nucleation and growth of clathrate hydrates. It has been proposed that these amphiphilic molecules bind to the clathrate surface via hydrogen bonding. However, recent studies reveal that PVCap, an amphiphilic polymer, binds to clathrates through hydrophobic moieties. Here we use molecular dynamic simulations and theory to investigate the mode and strength of binding of surfactants to the clathrate-water interface and their effect on the nucleation rate. We find that the surfactants bind to the clathrate-water interface exclusively through their hydrophobic tails. The binding is strong, driven by the entropy of dehydration of the alkyl chain, as it penetrates empty cavities at the hydrate surface. The hydrophobic attraction of alkyl groups to the clathrate surface also results in strong adsorption of alkanes. We identify two regimes for the binding of surfactants as a function of their density at the hydrate surface, which we interpret to correspond to the two steps of the Langmuir adsorption isotherm observed in experiments. Our results indicate that hydrophobic attraction to the clathrate-water interface is key for the design of soluble additives that promote the nucleation of hydrates. We use the calculated adsorption coefficients to estimate the concentration of sodium dodecyl sulfate (SDS) required to reach nucleation rates for methane hydrate consistent with those measured in experiments. To our knowledge, this study is the first to quantify the effect of surfactant concentration in the nucleation rate of clathrate hydrates.

Recent theories and simulations suggest that molecular additives can bind to the surfaces of nuclei, lower the surface energy, and accelerate nucleation. Experiments have shown that oligomeric and polymeric additives can also modify nucleation rates of proteins, ice, and minerals; however, general design principles for oligomeric or polymeric promoters do not yet exist. Here we investigate oligomeric additives for which each segment of the oligomer can bind to surfaces of nuclei. We use semigrand canonical Monte Carlo simulations in a Potts lattice gas model to study the effects of oligomer chain length, volume fraction, and binding strength. We find that increasing each of those parameters lowers the nucleation barrier. At extremely low oligomer concentrations, the nucleation kinetics can be modeled as though each oligomer is a heterogeneous nucleation site in solution.

Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.

We present new algorithms for conducting transition path sampling (TPS). Permutation shooting rigorously preserves the total energy and momentum of the initial trajectory and is simple to implement even for rigid water molecules. Versions of aimless shooting and permutation shooting that use flexible-length trajectories have simple acceptance criteria and are more computationally efficient than fixed-length versions. Flexible-length permutation shooting and inertial likelihood maximization are used to identify the reaction coordinate for vacancy migration in a two-dimensional trigonal crystal of Lennard-Jones particles. The optimized reaction coordinate eliminates nearly all recrossing of the transition state dividing surface.

We examine the capabilities and foundations of three landmark rate theories: harmonic transition state theory, classical nucleation theory, and the Marcus theory of electron transfer. Each of the three classic rate theories is widely used to predict rates and trends. They are also used "in reverse" to interpret experimental data with no computation at all. Their common foundations include a quasi-equilibrium assumption and dimensionality reduction to a physically meaningful, one-dimensional, and broadly applicable reaction coordinate. Many applications lie beyond the scope of the classic theories, so rare events research has pursued trajectory-based methods that efficiently predict accurate rate constants even when the reaction coordinate and mechanistic details are unknown. Trajectory based rare events methods achieved these ambitious goals, but (by construction) they provide rates rather than mechanistic understanding. We briefly discuss recent efforts to identify reaction coordinates, including methods which provide abstract statistically defined coordinates and those which identify physical collective variables. Finally, we note some natural synergies between existing simulation methods which might help discover simple and powerful quasi-equilibrium theories for the many applications that fall beyond the scope of the classic rate theories.

From a hypothetical perfect dividing surface, all trajectories commit to opposite basins in forward and backward time without recrossing, transition state theory is exact, the transmission coefficient is one, and the committor distribution is perfectly focused at 1/2. However, chemical reactions in solution and other real systems often have dynamical trajectories that recross the dividing surface. To separate true dynamical effects from effects of a nonoptimal dividing surface, the dividing surface and/or reaction coordinate should be optimized before computing transmission coefficients. For NaCl dissociation in TIP3P water, we show that recrossing persists even when the 1/2-committor surface itself is used as the dividing surface, providing evidence that recrossing cannot be fully eliminated from the dynamics for any configurational coordinate. Consistent with this finding, inertial likelihood maximization finds a combination of ion-pair distance and two solvent coordinates that improves the committor distribution and increases the transmission coefficient relative to those for ion-pair distance alone, but recrossing is not entirely eliminated. Free energy surfaces for the coordinates identified by inertial likelihood maximization show that the intrinsic recrossing stems from anharmonicity and shallow intermediates that remain after dimensionality reduction to the dynamically important variables.

Classical nucleation theory is notoriously inaccurate when using the macroscopic surface free energy for a planar interface. We examine the size dependence of the surface free energy for TIP4P/2005 water nanodroplets (radii ranging from 0.7 to 1.6 nm) at 300 K with the mitosis method, that is, by reversibly splitting the droplets into two subclusters. We calculate the Tolman length to be -0.56 ± 0.09 Å, which indicates that the surface free energy of water droplets that we investigated is 5-11 mJ/m(2) greater than the planar surface free energy. We incorporate the computed Tolman length into a modified classical nucleation theory (δ-CNT) and obtain modified expressions for the critical nucleus size and barrier height. δ-CNT leads to excellent agreement with independently measured nucleation kinetics.

The formation of peroxorhenium complexes by activation of H2O2 is key in selective oxidation reactions catalyzed by CH3ReO3 (methyltrioxorhenium, MTO). Previous reports on the thermodynamics and kinetics of these reactions are inconsistent with each other and sometimes internally inconsistent. New experiments and calculations using density functional theory with the ωB97X-D and augmented def2-TZVP basis sets were conducted to better understand these reactions and to provide a strong experimental foundation for benchmarking computational studies involving MTO and its derivatives. Including solvation contributions to the free energies as well as tunneling corrections, we compute negative reaction enthalpies for each reaction and correctly predict the hydration state of all complexes in aqueous CH3CN. New rate constants for each of the forward and reverse reactions were both measured and computed as a function of temperature, providing a complete set of consistent activation parameters. New, independent measurements of equilibrium constants do not indicate strong cooperativity in peroxide ligand binding, as was previously reported. The free energy barriers for formation of both CH3ReO2(η(2)-O2) (A) and CH3ReO(η(2)-O2)2(H2O) (B) are predominantly entropic, and the former is much smaller than a previously reported value. Computed rate constants for a direct ligand-exchange mechanism, and for a mechanism in which a water molecule facilitates ligand-exchange via proton transfer in the transition state, differ by at least 7 orders of magnitude. The latter, water-assisted mechanism is predicted to be much faster and is consequently in much closer agreement with the experimentally measured kinetics. Experiments confirm the predicted catalytic role of water: the kinetics of both steps are strongly dependent on the water concentration, and water appears directly in the rate law.