Elucidation of the key role of Pt···Pt interactions in the directional self-assembly of platinum(II) complexes.

Here, we report the use of an amphiphilic Pt(II) complex, K[Pt{(O3SCH2CH2CH2)2bzimpy}Cl] (PtB), as a model to elucidate the key role of Pt···Pt interactions in directing self-assembly by combining temperature-dependent ultraviolet-visible (UV-Vis) spectroscopy, stopped-flow kinetic experiments, quantum mechanics (QM) calculations, and molecular dynamics (MD) simulations. Interestingly, we found that the self-assembly mechanism of PtB in aqueous solution follows a nucleation-free isodesmic model, as revealed by the temperature-dependent UV-Vis experiments. In contrast, a cooperative growth is found for the self-assembly of PtB in acetone­water (7:1, vol/vol) solution, which is further verified by the stopped-flow experiments, which clearly indicates the existence of a nucleation phase in the acetone­water (7:1, vol/vol) solution. To reveal the underlying reasons and driving forces for these self-assembly processes, we performed QM calculations and show that the Pt···Pt interactions arising from the interaction between the pz and dz2 orbitals play a crucial role in determining the formation of ordered self-assembled structures. In subsequent oligomer MD simulations, we demonstrate that this directional Pt···Pt interaction can indeed facilitate the formation of linear structures packed in a helix-like fashion. Our results suggest that the self-assembly of PtB in acetone­water (7:1, vol/vol) solution is predominantly driven by the directional noncovalent Pt···Pt interaction, leading to the cooperative growth and the formation of fibrous nanostructures. On the contrary, the self-assembly in aqueous solution forms spherical nanostructures of PtB, which is primarily due to the predominant contribution from the less directional hydrophobic interactions over the directional Pt···Pt and π−π interactions that result in an isodesmic growth.

Reactivity of Unsupported Transition Metal-Aluminyl Complexes: A Nucleophilic TM-Al Bond.

Despite the long history of research in transition metal (TM) complexes, the study of TM-aluminyl complexes is still in its early stage of development. It is expected that the presence of an electropositive Al donor atom would open up new possibilities in TM complex reactivity, and indeed TM-aluminyl has shown an early sign of success in small-molecule activation. On the other hand, the existing reports on TM-aluminyl reactivity are often explained to readers with different understanding on individual cases, and a general picture of TM-aluminyl reactivity is still not available. In this work, we have attempted to provide a systematic picture to explain some early explorations in this field, specifically a series of recently reported heteroallene insertion reactions involving unsupported TM-aluminyl complexes. Through density functional theory calculations of a number of TM-aluminyl complexes, covering both Au and Cu centers, we found that their reactivity against heteroallenes (including CO2 and carbodiimides) is mostly based on the strong nucleophilicity of the TM-Al σ-bond.

RPnet: a reverse-projection-based neural network for coarse-graining metastable conformational states for protein dynamics.

The Markov State Model (MSM) is a powerful tool for modeling long timescale dynamics based on numerous short molecular dynamics (MD) simulation trajectories, which makes it a useful tool for elucidating the conformational changes of biological macromolecules. By partitioning the phase space into discretized states and estimating the probabilities of inter-state transitions based on short MD trajectories, one can construct a kinetic network model that could be used to extrapolate long-timescale kinetics if the Markovian condition is met. However, meeting the Markovian condition often requires hundreds or even thousands of states (microstates), which greatly hinders the comprehension of the conformational dynamics of complex biomolecules. Kinetic lumping algorithms can coarse grain numerous microstates into a handful of metastable states (macrostates), which would greatly facilitate the elucidation of biological mechanisms. In this work, we have developed a reverse-projection-based neural network (RPnet) to lump microstates into macrostates, by making use of a physics-based loss function that is based on the projection operator framework of conformational dynamics. By recognizing that microstate and macrostate transition modes can be related through a projection process, we have developed a reverse-projection scheme to directly compare the microstate and macrostate dynamics. Based on this reverse-projection scheme, we designed a loss function that allows the effective assessment of the quality of a given kinetic lumping. We then make use of a neural network to efficiently minimize this loss function to obtain an optimized set of macrostates. We have demonstrated the power of our RPnet in analyzing the dynamics of a numerical 2D potential, alanine dipeptide, and the clamp opening of an RNA polymerase. In all these systems, we have illustrated that our method could yield comparable or better results than competing methods in terms of state partitioning and reproduction of slow dynamics. We expect that our RPnet holds promise in analyzing the conformational dynamics of biological macromolecules.

Superatomic Ligand-Field Splitting in Ligated Gold Nanoclusters.

Gold nanoclusters are attractive because of their electronic and optical properties. Many theoretical models have been proposed to explain their electronic structures through an electron-counting approach. However, subtle features may not be well explained by electron-counting rules. In this work, we have discovered a unique example of ligand-controlled skeletal bonding in two recently reported gold nanoclusters with very similar compositions and geometries. We have shown that the superatomic orbitals of the common kernel of the two clusters undergo different ligand-field splitting because of the different ligand-field strengths in the two clusters. Such a difference is clearly revealed by constructing the Jellium orbitals via an orbital alignment process, and a subsequent localization of the Jellium orbitals allows us to obtain localized bonding models. Finally, on the basis of localized bonding models, we predict the existence of a ligated gold cluster with a [Au32]4+ kernel.

Principal interacting spin orbital: understanding the fragment interactions in open-shell systems.

Due to the recent rise in the interest and research efforts on first-row transition metal catalysis and other radical-related reactions, open-shell systems play a much more important role in modern chemistry. However, the development of bonding analysis tools for open-shell systems is still lagging behind. In this work, we present the principal interacting spin orbital (PISO) analysis, which is an analysis framework developed based on our previously reported principal interacting orbital (PIO) analysis. We will demonstrate the power of our framework to analyse different kinds of open-shell systems, ranging from simple organic radicals to much more complicated coordination complexes, from which we can see how different kinds of odd-electron bonds could be identified. We will also illustrate its advantage when used in the analysis of chemical reactions, through which we can observe subtle patterns that could be helpful for tuning or rational design of related reactions.

Remote Bonding in Clusters [Pd3Ge18R6]2-: Modular Bonding Model for Large Clusters via Principal Interacting Orbital Analysis.

Main group cluster compounds have attracted increasing attention in the past decades. Despite recent developments in their synthesis, the description of their electronic structures is usually limited to simply applying Wade's rule originally developed for borane compounds. This traditional approach is once again challenged by two recently reported group 14 metalloid clusters in the form of [Pd3Ge18R6]2-. In this work, we put forward a modular bonding model for these two clusters, via principal interacting orbital (PIO) analysis. The site preference for six substituents has also been analyzed.

TAPS: A traveling-salesman based automated path searching method for functional conformational changes of biological macromolecules.

Locating the minimum free energy paths (MFEPs) between two conformational states is among the most important tasks of biomolecular simulations. For example, knowledge of the MFEP is critical for focusing the effort of unbiased simulations that are used for the construction of Markov state models to the biologically relevant regions of the system. Typically, existing path searching methods perform local sampling around the path nodes in a pre-selected collective variable (CV) space to allow a gradual downhill evolution of the path toward the MFEP. Despite the wide application of such a strategy, the gradual path evolution and the non-trivial a priori choice of CVs are also limiting its overall efficiency and automation. Here we demonstrate that non-local perpendicular sampling can be pursued to accelerate the search, provided that all nodes are reordered thereafter via a traveling-salesman scheme. Moreover, path-CVs can be computed on-the-fly and used as a coordinate system, minimizing the necessary prior knowledge about the system. Our traveling-salesman based automated path searching method achieves a 5-8 times speedup over the string method with swarms-of-trajectories for two peptide systems in vacuum and solution, making it a promising method for obtaining initial pathways when investigating functional conformational changes between a pair of structures.

Unravelling Chemical Interactions with Principal Interacting Orbital Analysis.

Decomposing chemical interactions into bonds and other higher order interactions is a common practice to analyse chemical structures, and gave birth to many chemical concepts, despite the fact that the decomposition itself might be subjective in nature. Fragment molecular orbitals (FMOs) offer a more rigorous alternative to such intuition, but might be less interpretable due to extensive delocalisation in FMOs. Inspired by the Principal Component Analysis in statistics, we hereby present a novel framework, Principal Interacting Orbital (PIO) analysis, that can very quickly identify the "dominant interacting orbitals" that are semi-localised and easily interpretable, while still maintaining mathematical rigor. Many chemical concepts that are often taken for granted, but could not be easily inferred from other computational techniques like FMO analysis, can now be visualised as PIOs. We have also illustrated, through various examples covering both organic and inorganic chemistry, how PIO analysis could help us pinpoint subtle features that might play determining roles in bonding and reactions.

An efficient Bayesian kinetic lumping algorithm to identify metastable conformational states via Gibbs sampling.

Markov State Model (MSM) has become a popular approach to study the conformational dynamics of complex biological systems in recent years. Built upon a large number of short molecular dynamics simulation trajectories, MSM is able to predict the long time scale dynamics of complex systems. However, to achieve Markovianity, an MSM often contains hundreds or thousands of states (microstates), hindering human interpretation of the underlying system mechanism. One way to reduce the number of states is to lump kinetically similar states together and thus coarse-grain the microstates into macrostates. In this work, we introduce a probabilistic lumping algorithm, the Gibbs lumping algorithm, to assign a probability to any given kinetic lumping using the Bayesian inference. In our algorithm, the transitions among kinetically distinct macrostates are modeled by Poisson processes, which will well reflect the separation of time scales in the underlying free energy landscape of biomolecules. Furthermore, to facilitate the search for the optimal kinetic lumping (i.e., the lumped model with the highest probability), a Gibbs sampling algorithm is introduced. To demonstrate the power of our new method, we apply it to three systems: a 2D potential, alanine dipeptide, and a WW protein domain. In comparison with six other popular lumping algorithms, we show that our method can persistently produce the lumped macrostate model with the highest probability as well as the largest metastability. We anticipate that our Gibbs lumping algorithm holds great promise to be widely applied to investigate conformational changes in biological macromolecules.

Adaptive partitioning by local density-peaks: An efficient density-based clustering algorithm for analyzing molecular dynamics trajectories.

We present an efficient density-based adaptive-resolution clustering method APLoD for analyzing large-scale molecular dynamics (MD) trajectories. APLoD performs the k-nearest-neighbors search to estimate the density of MD conformations in a local fashion, which can group MD conformations in the same high-density region into a cluster. APLoD greatly improves the popular density peaks algorithm by reducing the running time and the memory usage by 2-3 orders of magnitude for systems ranging from alanine dipeptide to a 370-residue Maltose-binding protein. In addition, we demonstrate that APLoD can produce clusters with various sizes that are adaptive to the underlying density (i.e., larger clusters at low-density regions, while smaller clusters at high-density regions), which is a clear advantage over other popular clustering algorithms including k-centers and k-medoids. We anticipate that APLoD can be widely applied to split ultra-large MD datasets containing millions of conformations for subsequent construction of Markov State Models. © 2016 Wiley Periodicals, Inc.

Path lumping: An efficient algorithm to identify metastable path channels for conformational dynamics of multi-body systems.

Constructing Markov state models from large-scale molecular dynamics simulation trajectories is a promising approach to dissect the kinetic mechanisms of complex chemical and biological processes. Combined with transition path theory, Markov state models can be applied to identify all pathways connecting any conformational states of interest. However, the identified pathways can be too complex to comprehend, especially for multi-body processes where numerous parallel pathways with comparable flux probability often coexist. Here, we have developed a path lumping method to group these parallel pathways into metastable path channels for analysis. We define the similarity between two pathways as the intercrossing flux between them and then apply the spectral clustering algorithm to lump these pathways into groups. We demonstrate the power of our method by applying it to two systems: a 2D-potential consisting of four metastable energy channels and the hydrophobic collapse process of two hydrophobic molecules. In both cases, our algorithm successfully reveals the metastable path channels. We expect this path lumping algorithm to be a promising tool for revealing unprecedented insights into the kinetic mechanisms of complex multi-body processes.

Markov State Models Reveal a Two-Step Mechanism of miRNA Loading into the Human Argonaute Protein: Selective Binding followed by Structural Re-arrangement.

Argonaute (Ago) proteins and microRNAs (miRNAs) are central components in RNA interference, which is a key cellular mechanism for sequence-specific gene silencing. Despite intensive studies, molecular mechanisms of how Ago recognizes miRNA remain largely elusive. In this study, we propose a two-step mechanism for this molecular recognition: selective binding followed by structural re-arrangement. Our model is based on the results of a combination of Markov State Models (MSMs), large-scale protein-RNA docking, and molecular dynamics (MD) simulations. Using MSMs, we identify an open state of apo human Ago-2 in fast equilibrium with partially open and closed states. Conformations in this open state are distinguished by their largely exposed binding grooves that can geometrically accommodate miRNA as indicated in our protein-RNA docking studies. miRNA may then selectively bind to these open conformations. Upon the initial binding, the complex may perform further structural re-arrangement as shown in our MD simulations and eventually reach the stable binary complex structure. Our results provide novel insights in Ago-miRNA recognition mechanisms and our methodology holds great potential to be widely applied in the studies of other important molecular recognition systems.

An [Au13]5+ Approach to the Study of Gold Nanoclusters.

Recently, many examples of gold nanoclusters have been synthesized due to their exceptional spectroscopic properties and potential applications in nanotechnology. In this work we put forward an approach based on the icosahedral [Au13]5+ unit and summarize three possible extensions of the unit: wrapping, bonding, and vertex sharing. We show that the electronic structure of such clusters can be treated in a more localized manner and show how the approach could be applied to understand the structure and bonding of a large variety of gold nanoclusters.

Elucidation of the conformational dynamics of multi-body systems by construction of Markov state models.

Constructing Markov State Models (MSMs) based on short molecular dynamics simulations is a powerful computational technique to complement experiments in predicting long-time kinetics of biomolecular processes at atomic resolution. Even though the MSM approach has been widely applied to study one-body processes such as protein folding and enzyme conformational changes, the majority of biological processes, e.g. protein-ligand recognition, signal transduction, and protein aggregation, essentially involve multiple entities. Here we review the attempts at constructing MSMs for multi-body systems, point out the challenges therein and discuss recent algorithmic progresses that alleviate these challenges. In particular, we describe an automatic kinetics based partitioning method that achieves optimal definition of the conformational states in a multi-body system, and discuss a novel maximum-likelihood approach that efficiently estimates the slow uphill kinetics utilizing pre-computed equilibrium populations of all states. We expect that these new algorithms and their combinations may boost investigations of important multi-body biological processes via the efficient construction of MSMs.

Catalytic enantioselective intermolecular desymmetrization of azetidines.

The first catalytic asymmetric desymmetrization of azetidines is disclosed. Despite the low propensity of azetidine ring opening and challenging stereocontrol, smooth intermolecular reactions were realized with excellent efficiency and enantioselectivity. These were enabled by the suitable combination of catalyst, nucleophile, protective group, and reaction conditions. The highly enantioenriched densely functionalized products are versatile precursors to other useful chiral molecules. Mechanistic studies, including DFT calculations, revealed that only one catalyst molecule is involved in the key transition state, though both reactants can be activated. Also, the Curtin-Hammett principle dictates the reaction proceeds via amide nitrogen activation.

Computational Insight into Nickel-Catalyzed Carbon-Carbon versus Carbon-Boron Coupling Reactions of Primary, Secondary, and Tertiary Alkyl Bromides.

The nickel-catalyzed alkyl-alkyl cross-coupling (C-C bond formation) and borylation (C-B bond formation) of unactivated alkyl halides reported in the literature show completely opposite reactivity orders in the reactions of primary, secondary, and tertiary alkyl bromides. The proposed Ni(I) /Ni(III) catalytic cycles for these two types of bond-formation reactions were studied computationally by means of DFT calculations at the B3LYP level. These calculations indicate that the rate-determining step for alkyl-alkyl cross-coupling is the reductive elimination step, whereas for borylation the rate is determined mainly by the atom-transfer step. In borylation reactions, the boryl ligand involved has an empty p orbital, which strongly facilitates the reductive elimination step. The inability of unactivated tertiary alkyl halides to undergo alkyl-alkyl cross-coupling is mainly due to the moderately high reductive elimination barrier.

Reference interaction site model with hydrophobicity induced density inhomogeneity: An analytical theory to compute solvation properties of large hydrophobic solutes in the mixture of polyatomic solvent molecules.

Reference interaction site model (RISM) has recently become a popular approach in the study of thermodynamical and structural properties of the solvent around macromolecules. On the other hand, it was widely suggested that there exists water density depletion around large hydrophobic solutes (>1 nm), and this may pose a great challenge to the RISM theory. In this paper, we develop a new analytical theory, the Reference Interaction Site Model with Hydrophobicity induced density Inhomogeneity (RISM-HI), to compute solvent radial distribution function (RDF) around large hydrophobic solute in water as well as its mixture with other polyatomic organic solvents. To achieve this, we have explicitly considered the density inhomogeneity at the solute-solvent interface using the framework of the Yvon-Born-Green hierarchy, and the RISM theory is used to obtain the solute-solvent pair correlation. In order to efficiently solve the relevant equations while maintaining reasonable accuracy, we have also developed a new closure called the D2 closure. With this new theory, the solvent RDFs around a large hydrophobic particle in water and different water-acetonitrile mixtures could be computed, which agree well with the results of the molecular dynamics simulations. Furthermore, we show that our RISM-HI theory can also efficiently compute the solvation free energy of solute with a wide range of hydrophobicity in various water-acetonitrile solvent mixtures with a reasonable accuracy. We anticipate that our theory could be widely applied to compute the thermodynamic and structural properties for the solvation of hydrophobic solute.

Application of Markov State Models to simulate long timescale dynamics of biological macromolecules.

Conformational changes of proteins are an*Author contributed equally with all other contributors. essential part of many biological processes such as: protein folding, ligand binding, signal transduction, allostery, and enzymatic catalysis. Molecular dynamics (MD) simulations can describe the dynamics of molecules at atomic detail, therefore providing a much higher temporal and spatial resolution than most experimental techniques. Although MD simulations have been widely applied to study protein dynamics, the timescales accessible by conventional MD methods are usually limited to timescales that are orders of magnitude shorter than the conformational changes relevant for most biological functions. During the past decades great effort has been devoted to the development of theoretical methods that may enhance the conformational sampling. In recent years, it has been shown that the statistical mechanics framework provided by discrete-state and -time Markov State Models (MSMs) can predict long timescale dynamics from a pool of short MD simulations. In this chapter we provide the readers an account of the basic theory and selected applications of MSMs. We will first introduce the general concepts behind MSMs, and then describe the existing procedures for the construction of MSMs. This will be followed by the discussions of the challenges of constructing and validating MSMs, Finally, we will employ two biologically-relevant systems, the RNA polymerase and the LAO-protein, to illustrate the application of Markov State Models to elucidate the molecular mechanisms of complex conformational changes at biologically relevant timescales.

A fast parallel clustering algorithm for molecular simulation trajectories.

We implemented a GPU-powered parallel k-centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370-residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k-centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.

Marriage of High-Throughput Gradient Surface Generation With Statistical Learning for the Rational Design of Functionalized Biomaterials.

Functional biomaterial is already an important aspect in modern therapeutics; yet, the design of novel multi-functional biomaterial is still a challenging task nowadays. When several biofunctional components are present, the complexity that arises from their combinations and interactions will lead to tedious trial-and-error screening. In this work, a novel strategy of biomaterial rational design through the marriage of gradient surface generation with statistical learning is presented. Not only can parameter combinations be screened in a high-throughput fashion, but also the optimal conditions beyond the experimentally tested range can be extrapolated from the models. The power of the strategy is demonstrated in rationally designing an unprecedented ternary functionalized surface for orthopedic implant, with optimal osteogenic, angiogenic, and neurogenic activities, and its optimality and the best osteointegration promotion are confirmed in vitro and in vivo, respectively. The presented strategy is expected to open up new possibilities in the rational design of biomaterials.