PathOpt—A global transition state search approach: Outline of algorithm

We propose a new algorithm to determine reaction paths and test its capability for Ar₁₂ and Ar₁₃ clusters. Its main ingredient is a search for the local minima on a (n?1) dimensional hyperplane (n = dimension of the complete system in Cartesian coordinates) lying perpendicular to the straight line connection between initial and final states. These minima are part of possible reaction paths and are, hence, used as starting points for an uphill search to the next transition state. First, path fragments are obtained from subsequent relaxations starting from these transition states. They can be combined with information from the straight line connection procedure to obtain complete paths. Our test computations for Ar₁₂ and Ar₁₃ clusters prove that PathOpt delivers several reaction paths in one round. © 2013 Wiley Periodicals, Inc.     

Comparison of double-ended transition state search methods

While a variety of double-ended transition state search methods have been developed, their relative performance in characterizing complex multistep pathways between structurally disparate molecular conformations remains unclear. Three such methods (doubly-nudged elastic band, a string method, and a growing string method) are compared for a series of benchmarks ranging from permutational isomerizations of the seven-atom Lennard-Jones cluster (LJ(7)) to highly cooperative LJ(38) and LJ(75) rearrangements, and the folding pathways of two peptides. A database of short paths between LJ(13) local minima is used to explore the effects of parameters and suggest reasonable default values. Each double-ended method was employed within the framework of a missing connection network flow algorithm to construct more complicated multistep pathways. We find that in our implementation none of the three methods definitively outperforms the others, and that their relative effectiveness is strongly system and parameter dependent.     

Superlinearly converging dimer method for transition state search

Algorithmic improvements of the dimer method [G. Henkelman and H. Jonsson, J. Chem. Phys. 111, 7010 (1999)] are described in this paper. Using the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimizer for the dimer translation greatly improves the convergence compared to the previously used conjugate gradient algorithm. It also saves one energy and gradient calculation per dimer iteration. Extrapolation of the gradient during repeated dimer rotations reduces the computational cost to one gradient calculation per dimer rotation. The L-BFGS algorithm also improves convergence of the rotation. Thus, three to four energy and gradient evaluations are needed per iteration at the beginning of a transition state search, while only two are required close to convergence. Moreover, we apply the dimer method in internal coordinates to reduce coupling between the degrees of freedom. Weighting the coordinates can be used to apply chemical knowledge about the system and restrict the transition state search to only part of the system while minimizing the remainder. These improvements led to an efficient method for the location of transition states without the need to calculate the Hessian. Thus, it is especially useful in large systems with expensive gradient evaluations.     

A hierarchical clustering algorithm for MIMD architecture

Hierarchical clustering is the most often used method for grouping similar patterns of gene expression data. A fundamental problem with existing implementations of this clustering method is the inability to handle large data sets within a reasonable time and memory resources. We propose a parallelized algorithm of hierarchical clustering to solve this problem. Our implementation on a multiple instruction multiple data (MIMD) architecture shows considerable reduction in computational time and inter-node communication overhead, especially for large data sets. We use the standard message passing library, message passing interface (MPI) for any MIMD systems.     

A search algorithm for fixed-composition protein design

We present a computational protein design algorithm for finding low-energy sequences of fixed amino acid composition. The search algorithms used in protein design typically do not restrict amino acid composition. However, the random energy model of Shakhnovich suggests that the use of fixed-composition sequences may circumvent defects in the modeling of the denatured state. Our algorithm, FC_FASTER, links fixed-composition versions of Monte Carlo and the FASTER algorithm. As proof of principle, FC_FASTER was tested on an experimentally validated, full-sequence design of the beta1 domain of protein G. For the wild-type composition, FC_FASTER found a lower energy sequence than the experimentally validated sequence. Also, for a different composition, FC_FASTER found the hypothetical lowest-energy sequence in 14 out of 32 trials.     

Sphere-to-cylinder transition in hierarchical electrostatic complexes

We report on the formation of colloidal complexes resulting from the electrostatic co-assembly between anionic surfactants and cationic polyelectrolytes or block copolymers. Combining light and X-ray scattering experiments with cryogenic transmission and optical microscopy, we emphasize a feature rarely addressed in the formation of the electrostatic complexes, namely the role of the mixing concentration on the microstructure. At low mixing concentration, electrostatic complexes made from cationic-neutral copolymers and alkyl sulfate surfactants exhibit spherical core-shell microstructures. With increasing concentration, the complexes undergo a sphere-to-cylinder transition, yielding elongated aggregates with diameter 50 nm and length up to several hundreds of nanometers. From the comparison between homo- and diblock polymer phase behaviors, it is suggested that the unidimensional growth is driven by the ability of the surfactant to self-assemble into cylindrical micelles when complexed with cationic polymers.     

A transition state analogue for an RNA-editing reaction

Deamination at C6 of adenosine in RNA catalyzed by the ADAR enzymes generates inosine at the corresponding position. Because inosine is decoded as guanosine during translation, this modification can lead to codon changes in messenger RNA. Hydration of 8-azanebularine across the C6-N1 double bond generates an excellent mimic of the transition state proposed for the hydrolytic deamination reaction catalyzed by ADARs. Here, we report the synthesis of a phosphoramidite of 8-azanebularine and its use in the preparation of RNAs mimicking the secondary structure found at a known editing site in the glutamate receptor B subunit pre-mRNA. The binding properties of analogue-containing RNAs indicate that a tight binding ligand for an ADAR can be generated by incorporation of 8-azanebularine. The observed high-affinity binding is dependent on a functional active site, the presence of one, but not the other, of ADAR2's two double-stranded RNA-binding motifs (dsRBMs), and the correct placement of the nucleoside analogue into the sequence/structural context of a known editing site. These results advance our understanding of substrate recognition during ADAR-catalyzed RNA editing and are important for structural studies of ADAR.RNA complexes.     

Quantum transition state theory

We derive and discuss upper bound, of transition state form, to the quantum rate constant for bimolecular reactions.     

A degree-distribution based hierarchical agglomerative clustering algorithm for protein complexes identification

Since cellular functionality is typically envisioned as having a hierarchical structure, we propose a framework to identify modules (or clusters) within protein-protein interaction (PPI) networks in this paper. Based on the within-module and between-module edges of subgraphs and degree distribution, we present a formal module definition in PPI networks. Using the new module definition, an effective quantitative measure is introduced for the evaluation of the partition of PPI networks. Because of the hierarchical nature of functional modules, a hierarchical agglomerative clustering algorithm is developed based on the new measure in order to solve the problem of complexes detection within PPI networks. We use gold standard sets of protein complexes to validate the biological significance of predicted complexes. A comprehensive comparison is performed between our method and other four representative methods. The results show that our algorithm finds more protein complexes with high biological significance and a significant improvement. Furthermore, the predicted complexes by our method, whether dense or sparse, match well with known biological characteristics.     

A hierarchical algorithm for calculating the isotopic fine structures of molecules

This article presents a memory efficient algorithm for accurately calculating the isotopic fine structures of molecules. Treating individual isotopic species of a molecule as different mass states, we introduce the concept of transitions between mass states and represent all mass states of the molecule in a hierarchical structure. We show that there exists a simple relationship between two different mass states at two different levels of the hierarchical structure. This allows us to efficiently and accurately compute both the mass and the abundance of every mass state of a small to medium-sized molecule, whose gross structures include small number of fine structures. A truncated calculation of this algorithm can be applied to calculate a majority of isotopic species (99.99% of cumulative abundance) of a large molecule.     

A consensus line search algorithm for molecular potential energy functions

Force field based energy minimization of molecular structures is a central task in computational chemistry and biology. Solving this problem usually requires efficient local minimization techniques, i.e., iterative two‐step methods that search first for a descent direction and then try to estimate the step width. The second step, the so called line search, typically uses polynomial interpolation schemes to estimate the next trial step. However, dependent on local properties of the objective function alternative schemes may be more appropriate especially if the objective function shows singularities or exponential behavior. As the choice of the best interpolation scheme cannot be made a priori, we propose a new consensus line search approach that performs several different interpolation schemes at each step and then decides which one is the most reliable at the current position. Although a naive consensus approach would lead to severe performance impacts, our method does not require additional evaluations of the energy function, imposing only negligible computational overhead. Additionally, our method can be easily adapted to the local behavior of other objective functions by incorporating suitable interpolation schemes or omitting non‐fitting schemes. The performance of our consensus line search approach has been evaluated and compared to established standard line search algorithms by minimizing the structures of a large set of molecules using different force fields. The proposed algorithm shows better performance in almost all test cases, i.e., it reduces the number of iterations and function and gradient evaluations, leading to significantly reduced run times. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

The generalized transition state method

Current theories of unimolecular reaction rates are based on the transition state method which replaces internal reactant dynamics by an assumption of internal equilibrium. The present work is devoted to the development of generalized transition state method which allows effects such as nonergodicity and non-exponential decay to be accounted for within a simple theoretical framework. The derivation is quantum mechanical and not limited by any weak perturbation assumption. An effective hamiltonian is constructed for the reactant dynamics. The loss of amplitude due to reaction is accounted for by a dissipative term in the hamiltonian which is obtained on a phenomenological basis. The diagonalization of the hamiltonian allows the decay of reactant state to be predicted. The decay information is then used to set up a non-markovian master equation which in turn yields the rate coefficient for the reaction. The accuracy of the method is tested in one-dimensional model calculations in which particular attention is paid to decay by quantum mechanical tunneling through a potential barrier.     

On nonadiabatic transition state theory

A nonseparable semiclassical transition state approximation for reactions involving more than one electronic surface is suggested. The single surface formulation in terms of quasiprobability distributions used by Miller is discussed along with a separable semiclassical approximation for the nonadiabatic rate suggested in the Soviet literature. A thermally averaged nonadiabatic rate is defined, and a semiclassical approximation is presented, wherein the surface through which flux is calculated in the transition state approach is determined by the intersection of adiabatic electronic surfaces viewed as functions of imaginary (or complex) time.     

A note on the transition state of radical addition reactions

An ab initio MO study of the reaction of F¹ atoms and CH^?₃ radicals with ethylene indicates that the transition state occurs later in the F¹ atom reaction and that there is considerable charge polarization in the alkene arising mainly from transfer of a β electron to fluorine.     

A hierarchical algorithm for fast debye summation with applications to small angle scattering

Debye summation, which involves the summation of sinc functions of distances between all pair of atoms in three‐dimensional space, arises in computations performed in crystallography, small/wide angle X‐ray scattering (SAXS/WAXS), and small angle neutron scattering (SANS). Direct evaluation of Debye summation has quadratic complexity, which results in computational bottleneck when determining crystal properties, or running structure refinement protocols that involve SAXS or SANS, even for moderately sized molecules. We present a fast approximation algorithm that efficiently computes the summation to any prescribed accuracy ? in linear time. The algorithm is similar to the fast multipole method (FMM), and is based on a hierarchical spatial decomposition of the molecule coupled with local harmonic expansions and translation of these expansions. An even more efficient implementation is possible when the scattering profile is all that is required, as in small angle scattering reconstruction (SAS) of macromolecules. We examine the relationship of the proposed algorithm to existing approximate methods for profile computations, and show that these methods may result in inaccurate profile computations, unless an error‐bound derived in this article is used. Our theoretical and computational results show orders of magnitude improvement in computation complexity over existing methods, while maintaining prescribed accuracy. © 2012 Wiley Periodicals, Inc.     

Oxygen adsorption induced superhydrophilic-to-superhydrophobic transition on hierarchical nanostructured CuO surface

Hierarchical nanostructured CuO surface was embellished to amplify the wettability. The pristine superhydrophilic CuO surface spontaneously transited to be superhydrophobic after exposed in air at room temperature for about 3 weeks. The wettability change is attributed to the adsorption of oxygen molecules on the topmost layer according to the surface chemical analysis. The adsorbed oxygen molecules could be removed by dipping the sample into l-Ascorbic acid solution for 10 s, leading to the recovery of the pristine superhydrophilicity.     

Quantum variational transition state theory revisited

A quantum version of classical variational transition state theory suggested by McLafferty and Pechukas is refined. In this new quantum version, the variational property of the theory leads to the identification of an optimal smeared dividing surface. This optimal function is shown to be the eigenfunction associated with the lowest eigenvalue of a positive quantum transition state theory operator. The lowest eigenvalue is the optimal bound on the quantum rate. Application of the theory to the parabolic barrier provides better bounds but does not give an essential improvement when compared to previous quantum transition state theories.