Modeling the early stages of self-assembly in nanophase materials. II. Role of symmetry and dimensionality

We study the early stages of self-assembly of elementary building blocks of nanophase materials, considering explicitly their structure and the symmetry and the dimensionality of the reaction space. Previous work [Kozak et al., J. Chem. Phys. 134, 154701 (2007)] focused on characterizing self-assembly on small square-planar templates. Here we consider larger lattices of square-planar symmetry having N = 255 sites, and both hexagonal and triangular lattices of N = 256 sites. Furthermore, to assess the consequences of a depletion zone above a basal layer (λ = 1), we study self-assembly on an augmented diffusion space defined by λ = 2 and λ = 5 stacked layers having the same characteristics as the basal plane. The effective decrease in the efficiency of self-assembly of individual nanophase units when the diffusion space is expanded, by increasing the template size and/or by enlarging the depletion zone, is then quantified. The results obtained reinforce our earlier conclusion that the most significant factor influencing the kinetics of formation of a final self-assembled unit is the number of reaction pathways from one or more precursor states. We draw attention to the relevance of these results to zeolite synthesis and reactions within pillared clays.     

Power‐law scaling of structured poly(p‐xylylene) films deposited by oblique angle

This study describes the evolution and growth of structured polymers by oblique angle deposition of poly(p‐xylylene) (PPX) derivatives. The deposition of structured PPX polymers have been demonstrated recently, but the mechanism of growth has not been studied. Here, we provide experimental evidence for the growth of structured PPX polymers by an atomic force microscope, electron microscope, and a profilometer. Individual columns expand with respect to their heights according to a power‐law, d = ch^p, where d is the column diameter, c and p are constants, and h is the height of a column. Values of p for structured poly(chloro‐p‐xylylene), poly(trifloroacetly‐p‐xylylene‐co‐p‐xylylene), and poly(bromo‐p‐xylylene) films are estimated as 0.11 ± 0.01, 0.15 ± 0.01, and 0.18 ± 0.01, respectively. This result is different from the traditional oblique angle deposition processes of nonpolymeric materials where the surface diffusion is low. Further analysis with two‐dimensional power spectral density (PSD) method showed that the ordering of columns is quasi‐periodic. Additionally, the X‐ray and transmission electron microscope characterization of the columns revealed that the columns are semicrystalline. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 640–648, 2008     

Flexible CDOCKER: Development and application of a pseudo‐explicit structure‐based docking method within CHARMM

Protein‐ligand docking is a commonly used method for lead identification and refinement. While traditional structure‐based docking methods represent the receptor as a rigid body, recent developments have been moving toward the inclusion of protein flexibility. Proteins exist in an interconverting ensemble of conformational states, but effectively and efficiently searching the conformational space available to both the receptor and ligand remains a well‐appreciated computational challenge. To this end, we have developed the Flexible CDOCKER method as an extension of the family of complete docking solutions available within CHARMM. This method integrates atomically detailed side chain flexibility with grid‐based docking methods, maintaining efficiency while allowing the protein and ligand configurations to explore their conformational space simultaneously. This is in contrast to existing approaches that use induced‐fit like sampling, such as Glide or Autodock, where the protein or the ligand space is sampled independently in an iterative fashion. Presented here are developments to the CHARMM docking methodology to incorporate receptor flexibility and improvements to the sampling protocol as demonstrated with re‐docking trials on a subset of the CCDC/Astex set. These developments within CDOCKER achieve docking accuracy competitive with or exceeding the performance of other widely utilized docking programs. © 2015 Wiley Periodicals, Inc.     

New evaluation of reconstructed spatial distribution function from radial distribution functions

Although three dimensional (3D) solvation structure is much more informative than one dimensional structure, its evaluation is difficult experimentally and theoretically. In our previous Communication [Yokogawa et al., J. Chem. Phys. 123, 211102 (2005)], we proposed a new method to present reconstructed spatial distribution function (RC-SDF) from a set of radial distribution functions (RDFs). In this article, we successfully extended the method more accurately with new basis sets. This new method was applied to two liquid solvation structures, methanol and dimethyl sulfoxide, as examples. Their RC-SDFs evaluated here clearly show that the former solvation structure is well defined while the latter one is broad, which agrees well with the SDFs calculated directly from molecular dynamics simulations. These results indicate that the method can reproduce well these 3D solvation structures in reasonable computational cost.     

Formation of deprotected fuzzy blobs in chemically amplified resists

The requirement of nanometer dimensional control in photolithographic patterning underlies the future of emerging technologies, including next-generation semiconductors, nanofluids, photonics, and microelectromechanical systems. For chemically amplified resists, dimensional control is mediated by the diffusion and reaction of photogenerated acids within a polymer-based photoresist matrix. The complex nature of the combined processes of reaction and diffusion prohibit the routine measurement of this phenomenon. Using small-angle neutron scattering, we have measured the form of the diffusion–reaction path of a photogenerated acid within a model photoresist matrix with a labeled protection group on the polymer side group. During the deprotection reaction, changes in the scattering form factor result from the shape and form of the deprotected regions. The individual volumes or blobs of reacted material are diffuse, with a fuzzy boundary between the reacted and unreacted regions. The impact of these results on the pattern quality is also discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3063–3069, 2004     

Dynamics of Cu monomer,dimer and trimer on Ag (110) (1 × 2) missing‐row reconstructed surface

The authors aimed to investigate the diffusion of Cu monomer, dimer and trimer on Ag (110) (1×2) missing‐row surface. This problem is addressed through molecular dynamic simulation based on semi‐empirical many‐body potential, derived from the embedded atom method. Within this approach, we have identified and calculated the activation energy of each microscopic mechanism. Thus, for Cu monomer, the diffusion process occurs essentially by simple hopping between nearest‐neighbor sites. While for the Cu dimer, three processes have been identified such as dissociation–reassociation (DR), concerted jump (CJ) and leapfrog mechanisms (LF) with a slight predominance of DR process and a dual competition between CJ and LF processes. But, in the case of small one‐dimensional cluster such as trimer on (110)(1×2) missing‐row reconstructed surface, the main diffusion mechanism is the LF process. These results shed light on the diffusion processes on missing‐row reconstructed surfaces, especially for heterogeneous systems. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical simulation of coupled‐stress case II diffusion in one dimension

This article is concerned with the robust and efficient numerical simulation of case II diffusion, which constitutes an important regime of solvent diffusion into glassy polymers. Even in the one‐dimensional case considered here, the numerical simulation of case II diffusion is made difficult by the extreme nonlinearities and coupling in the governing model equations due to a nonlinear flux law needed to produce sharp solvent fronts, a concentration‐dependent relaxation time of the polymer used to model the glass‐rubber transition, and coupling between the diffusion and deformation phenomena. Having an efficient and accurate solution to such equations is central to advancing a clear understanding of the meaning of such models. The difficulties due to coupling and nonlinearities are highlighted by the consideration of a specific, normalized, one‐dimensional case II diffusion model laid out in a general framework of balance laws. Issues such as the stiffness of the spatially discrete differential algebraic equations obtained from the finite element discretization of the governing equations and their bearing on the choice of time‐stepping schemes are discussed. The key requirements of numerical schemes, namely, robustness and efficiency, are addressed by the use of an implicit, adaptive, second‐order backward differentiation formula with error control for time discretization. Error control is used to maximize the step size to satisfy a target error and the radius of convergence requirements while nonlinear algebraic equations are solved at each time step. An example of an initial boundary value problem is solved numerically to show that the chosen model reproduces case II behavior and to validate that the stated objectives for the numerical simulation are met. Finally, the features and numerical implementation of this model are compared with those of a closely related case II diffusion model due to Wu and Peppas. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2091–2108, 2003     

O2和CO表面催化反应的活性位分布模型

对于O_2和CO表面催化反应，建立了一个新的不可逆Monte Carlo模拟模型。在 二维格子中，引进了表面活性位和非活性位的要领。模型假设，一定浓度的活性位 随机分布在非活性位上，形成了活性位分布的二维格子模型反应器，并在ZGB模型 的基础上，考虑了氧原子和CO分子的表面扩散，特别是引进了吸附粒子的定向表面 扩散。其中，活性位和活性位最近邻是表面吸附物质反应的活性中心，而非活性位 的作用是通过表面扩散传质。当活性位浓度C_a = 1且考虑扩散时，模型还原为增 加了扩散的ZGB模型。当活性位浓度C_a = 1且只考虑氧的扩散时，模拟结果表明， 扩散几率达到某一数值（0.3）时，二级相变点完全消失。当活性位浓度C_a逐渐减 小时，单位活性位产生的CO_2的速率不断增大，这表明活性位的利用率提高了。     

Assessing search strategies for flexible docking

We assess the efficiency of molecular dynamics (MD), Monte Carlo (MC), and genetic algorithms (GA) for docking five representative ligand–receptor complexes. All three algorithms employ a modified CHARMM-based energy function. The algorithms are also compared with an established docking algorithm, AutoDock. The receptors are kept rigid while flexibility of ligands is permitted. To test the efficiency of the algorithms, two search spaces are used: an 11-Å-radius sphere and a 2.5-Å-radius sphere, both centered on the active site. We find MD is most efficient in the case of the large search space, and GA outperforms the other methods in the small search space. We also find that MD provides structures that are, on average, lower in energy and closer to the crystallographic conformation. The GA obtains good solutions over the course of the fewest energy evaluations. However, due to the nature of the nonbonded interaction calculations, the GA requires the longest time for a single energy evaluation, which results in a decreased efficiency. The GA and MC search algorithms are implemented in the CHARMM macromolecular package. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1623–1631, 1998     

Study of Self-Diffusion ofn-Decane in NaX Zeolite by the Pulsed Magnetic-Field Gradient NMR Method

Translational mobility of n-decane molecules in a porous space of NaX zeolite was studied within the wide ranges of diffusion times and temperatures. The dependence of the effective self-diffusion coefficient on diffusion time was established. Confined mobility of diffusant molecules inside the crystallite was observed both for complete and partial filling of NaX pores with a liquid, when the adsorption barrier was absent at the interface between intra- and intercrystallite regions. It was suggested that obstacles are present at the surface of NaX crystallites complicating the transfer of liquid molecules from crystallite channels to intercrystallite space. True value of self-diffusion coefficient ofn-decane in the itracrystallite space of NaX was determined and its dependence on the concentration of liquid molecules in zeolite channels was considered. A special attention was paid to the study of molecular exchange between intra- and intercrystallite-confined liquids.     

Polymer reversal rate calculated via locally scaled diffusion map

A recent study on the dynamics of polymer reversal inside a nanopore by Huang and Makarov [J. Chem. Phys. 128, 114903 (2008)] demonstrated that the reaction rate cannot be reproduced by projecting the dynamics onto a single empirical reaction coordinate, a result suggesting the dynamics of this system cannot be correctly described by using a single collective coordinate. To further investigate this possibility we have applied our recently developed multiscale framework, locally scaled diffusion map (LSDMap), to obtain collective reaction coordinates for this system. Using a single diffusion coordinate, we obtain a reversal rate via Kramers expression that is in good agreement with the exact rate obtained from the simulations. Our mathematically rigorous approach accounts for the local heterogeneity of molecular configuration space in constructing a diffusion map, from which collective coordinates emerge. We believe this approach can be applied in general to characterize complex macromolecular dynamics by providing an accurate definition of the collective coordinates associated with processes at different time scales.     

Simulation of aggregating particles in complex flows by the lattice kinetic Monte Carlo method

We develop and validate an efficient lattice kinetic Monte Carlo (LKMC) method for simulating particle aggregation in laminar flows with spatially varying shear rate, such as parabolic flow or flows with standing vortices. A contact time model was developed to describe the particle-particle collision efficiency as a function of the local shear rate, G, and approach angle, θ. This model effectively accounts for the hydrodynamic interactions between approaching particles, which is not explicitly considered in the LKMC framework. For imperfect collisions, the derived collision efficiency [?=1 - ∫(0)(π/2) sinθ exp(-2cotθΓ(agg)/G)dθ] was found to depend only on Γ(agg)∕G, where Γ(agg) is the specified aggregation rate. For aggregating platelets in tube flow, Γ(agg)=0.683 s(-1) predicts the experimentally measured ε across a physiological range (G = 40-1000 s(-1)) and is consistent with α(2b)β(3)-fibrinogen bond dynamics. Aggregation in parabolic flow resulted in the largest aggregates forming near the wall where shear rate and residence time were maximal, however intermediate regions between the wall and the center exhibited the highest aggregation rate due to depletion of reactants nearest the wall. Then, motivated by stenotic or valvular flows, we employed the LKMC simulation developed here for baffled geometries that exhibit regions of squeezing flow and standing recirculation zones. In these calculations, the largest aggregates were formed within the vortices (maximal residence time), while squeezing flow regions corresponded to zones of highest aggregation rate.     

Multiple ligand simultaneous docking: Orchestrated dancing of ligands in binding sites of protein

Present docking methodologies simulate only one single ligand at a time during docking process. In reality, the molecular recognition process always involves multiple molecular species. Typical protein–ligand interactions are, for example, substrate and cofactor in catalytic cycle; metal ion coordination together with ligand(s); and ligand binding with water molecules. To simulate the real molecular binding processes, we propose a novel multiple ligand simultaneous docking (MLSD) strategy, which can deal with all the above processes, vastly improving docking sampling and binding free energy scoring. The work also compares two search strategies: Lamarckian genetic algorithm and particle swarm optimization, which have respective advantages depending on the specific systems. The methodology proves robust through systematic testing against several diverse model systems: E. coli purine nucleoside phosphorylase (PNP) complex with two substrates, SHP2NSH2 complex with two peptides and Bcl‐xL complex with ABT‐737 fragments. In all cases, the final correct docking poses and relative binding free energies were obtained. In PNP case, the simulations also capture the binding intermediates and reveal the binding dynamics during the recognition processes, which are consistent with the proposed enzymatic mechanism. In the other two cases, conventional single‐ligand docking fails due to energetic and dynamic coupling among ligands, whereas MLSD results in the correct binding modes. These three cases also represent potential applications in the areas of exploring enzymatic mechanism, interpreting noisy X‐ray crystallographic maps, and aiding fragment‐based drug design, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Discover binding pathways using the sliding binding-box docking approach: application to binding pathways of oseltamivir to avian influenza H5N1 neuraminidase

Drug binding and unbinding are transient processes which are hardly observed by experiment and difficult to analyze by computational techniques. In this paper, we employed a cost-effective method called “pathway docking” in which molecular docking was used to screen ligand-receptor binding free energy surface to reveal possible paths of ligand approaching protein binding pocket. A case study was applied on oseltamivir, the key drug against influenza a virus. The equilibrium pathways identified by this method are found to be similar to those identified in prior studies using highly expensive computational approaches.     

Fully automated flexible docking of ligands into flexible synthetic receptors using forward and inverse docking strategies

The prediction of the structure of host-guest complexes is one of the most challenging problems in supramolecular chemistry. Usual procedures for docking of ligands into receptors do not take full conformational freedom of the host molecule into account. We describe and apply a new docking approach which performs a conformational sampling of the host and then sequentially docks the ligand into all receptor conformers using the incremental construction technique of the FlexX software platform. The applicability of this approach is validated on a set of host-guest complexes with known crystal structure. Moreover, we demonstrate that due to the interchangeability of the roles of host and guest, the docking process can be inverted. In this inverse docking mode, the receptor molecule is docked around its ligand. For all investigated test cases, the predicted structures are in good agreement with the experiment for both normal (forward) and inverse docking. Since the ligand is often smaller than the receptor and, thus, its conformational space is more restricted, the inverse docking approach leads in most cases to considerable speed-up. By having the choice between two alternative docking directions, the application range of the method is significantly extended. Finally, an important result of this study is the suitability of the simple energy function used here for structure prediction of complexes in organic media.     

Colloid filtration theory and the Happel sphere-in-cell model revisited with direct numerical simulation of colloids

The transport of colloids and bacterial cells through saturated porous media is a complex phenomenon involving many interrelated processes that are often treated via application of classical colloid filtration theory (CFT). This paper presents a numerical investigation of CFT from the Lagrangian perspective, to evaluate the role of some of the classical assumptions underlying the theory and to demonstrate a means to include processes relevant to bacterial transport that were inadequately characterized or neglected in the original formulation, including Brownian diffusion and potentially hysteretic potential functions. The methodology is based on conducting a Lagrangian trajectory analysis within Happel's sphere-in-cell porous media model to obtain the collection efficiency (eta), the frequency at which colloids or bacteria make contact with the solid phase of the porous medium. The Lagrangian framework of our model lends itself to mechanistic modeling of the biological processes that may be important in subsurface bacterial transport. The numerical study presented here focuses on the size range of bacterial colloids and smaller (down to 10 nm). Results of our model runs are in good agreement with the deterministic trajectory analysis of Rajagopalan and Tien (when diffusion is neglected) and in excellent agreement with the analytical solution to the Smoluchowski-Levich approximation of the convective-diffusion equation (when external forces and interception are neglected). Simple addition of our result for the deterministic eta to our result for the Smoluchowski-Levich eta matches the overall Rajagopalan and Tien eta to within 5% error or less for all cases studied. When we simulate diffusion and the deterministic forces together, our results diverge from the Rajagopalan and Tien eta as the particle size decreases, with discrepancies as large as 73%. These results suggest that accurate prediction of eta values for bacteria-sized (and all submicrometer) colloids requires simultaneous consideration of the primary transport mechanisms.     

Long-timescale simulations of diffusion in molecular solids

Kinetic processes play a crucial role in the formation and evolution of molecular layers. In this perspective we argue that adaptive kinetic Monte Carlo is a powerful simulation technique for determining key kinetic processes in molecular solids. The applicability of the method is demonstrated by simulating the diffusion of a CO admolecule on a water ice surface, which is an important process for the formation of organic compounds on interstellar dust grains. CO diffusion is found to follow Arrhenius behavior and the corresponding effective activation energy for diffusion is determined to be 50 ± 1 meV. A coarse graining algorithm is applied which greatly enhances the efficiency of the simulations at low temperatures, down to 10 K, without altering the underlying physical processes. Eventually, we argue that a combination of both on- and off-lattice kinetic Monte Carlo techniques is a good way for simulating large-scale processes in molecular solids over long time spans.     

Flexible protein‐protein docking based on Best‐First search algorithm

We developed a new high resolution protein‐protein docking method based on Best‐First search algorithm that loosely imitates protein‐protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; “high,” “medium,” “acceptable,” and “incorrect”). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side‐chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side‐chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein‐protein docking and is of interest even with the current use of a simple energy function. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010