Discriminative Link Prediction using Local Links, Node Features and Community Structure

A link prediction (LP) algorithm is given a graph, and has to rank, for each node, other nodes that are candidates for new linkage. LP is strongly motivated by social search and recommendation applications. LP techniques often focus on global properties (graph conductance, hitting or commute times, Katz score) or local properties (Adamic-Adar and many variations, or node feature vectors), but rarely combine these signals. Furthermore, neither of these extremes exploit link densities at the intermediate level of communities. In this paper we describe a discriminative LP algorithm that exploits two new signals. First, a co-clustering algorithm provides community level link density estimates, which are used to qualify observed links with a surprise value. Second, links in the immediate neighborhood of the link to be predicted are not interpreted at face value, but through a local model of node feature similarities. These signals are combined into a discriminative link predictor. We evaluate the new predictor using five diverse data sets that are standard in the literature. We report on significant accuracy boosts compared to standard LP methods (including Adamic-Adar and random walk). Apart from the new predictor, another contribution is a rigorous protocol for benchmarking and reporting LP algorithms, which reveals the regions of strengths and weaknesses of all the predictors studied here, and establishes the new proposal as the most robust.Comment: 10 pages, 5 figure

Learning and Forecasting Opinion Dynamics in Social Networks

Social media and social networking sites have become a global pinboard for exposition and discussion of news, topics, and ideas, where social media users often update their opinions about a particular topic by learning from the opinions shared by their friends. In this context, can we learn a data-driven model of opinion dynamics that is able to accurately forecast opinions from users? In this paper, we introduce SLANT, a probabilistic modeling framework of opinion dynamics, which represents users opinions over time by means of marked jump diffusion stochastic differential equations, and allows for efficient model simulation and parameter estimation from historical fine grained event data. We then leverage our framework to derive a set of efficient predictive formulas for opinion forecasting and identify conditions under which opinions converge to a steady state. Experiments on data gathered from Twitter show that our model provides a good fit to the data and our formulas achieve more accurate forecasting than alternatives

Computational studies of the structure, dynamics, and catalysis of the hepatitis delta virus ribozyme

Ribozymes represent a unique class of RNA that is capable of catalyzing biochemical reactions. Since their discovery three decades ago, ribozymes have been shown to be involved in numerous crucial biological processes, such as gene regulation, translation, and RNA splicing. Similar to protein enzymes, these catalytic RNAs fold into well-defined tertiary structures with organized active sites to carry out catalysis. While their side chains do not possess the variety in functional groups accessible to the side chains of their protein counterparts, their efficiency as biological catalysts is often comparable to protein enzymes, making their catalytic strategies highly interesting. The study of ribozymes is also motivated by their possible significance in evolutionary biology. The hepatitis delta virus (HDV) ribozyme is a small nucleolytic RNA that performs a phosphodiester self-cleavage reaction generating products with a 2’, 3’-cyclic phosphate and a 5’ -hydroxyl termini. This ribozyme was initially discovered in the RNA genome of the human pathogen HDV, where it played a crucial role in the viral life cycle, cleaving site-specifically the multimeric copies of the RNA genome into monomeric pieces. More recently, HDV-like ribozymes have been shown to be widespread across all kingdoms of life. Since their discovery, the HDV ribozymes have been intensely studied from structural as well as mechanistic perspectives, and much is known about their structure and catalytic strategies. The HDV ribozyme has a compact double-pseudoknot structure and uses a combination of metal ion and nucleobase catalysis to effect its self-cleavage reaction. An active site cytosine C75 is thought to act as a general acid in the catalytic reaction by donating a proton to the 5’-hydroxyl of the leaving group, and an active site Mg2+ ion has been purported to play the role of a Lewis acid and activate the O2’ nucleophile. The exact role of this putative catalytic ion is still uncertain. A crystal structure also revealed a rare reverse G•U wobble close to the active site interacting with the putative catalytic ion. This base pair has been hypothesized to play an important role in positioning the metal ion for catalysis. In this dissertation, the HDV ribozyme was studied using a variety of computational approaches. Classical molecular dynamics (MD) simulations and non-linear Poisson-Boltzmann (NLPB) calculations were utilized to study the metal binding characteristics of the reverse G•U wobble close to the active site of the ribozyme. These studies revealed that the reverse wobble creates a highly negative pocket that allows it to interact with metal ions and helps to shift the pKa of the nucleobase C75, thereby facilitating its protonation. MD simulations were also used to investigate the impact of C75 protonation and Mg2+ ion interaction at the reverse G•U wobble on the structure as well as the motions of the HDV ribozyme. The protonated state of C75 was found to be essential for keeping the active site organized for catalysis. A localized, ‘chelated’ metal ion interaction was observed at the reverse G•U wobble, in contrast to a ‘diffused’ metal ion interaction observed at a standard G•U wobble also located close to the active site. The effects of mutation of the reverse G•U wobble, as well as the standard G•U wobble, to a Watson-Crick GC base pair were also studied. The overall tertiary structure and thermal motions of the ribozyme were not found to be significantly affected by C75 protonation, mutation of the reverse and standard wobbles, or the metal ion interaction at the two wobbles, suggesting that small local motions at the active site, rather than large-scale global motions, dominate the ribozyme reaction pathway. Quantum mechanical/molecular mechanical (QM/MM) calculations were used to study the HDV ribozyme self-cleavage reaction and elucidate the role of the catalytic metal ion. The calculations suggested a concerted mechanism of the catalytic reaction in the presence of a divalent ion at the active site but a sequential mechanism in the presence of a monovalent ion at the same position. The divalent ion at the active site was found to lower the pKa of the nucleobase C75, making its proton donation more facile and thereby favoring the concerted mechanism. QM/MM calculations were also used to study the effects of phosphorothioate substitutions of the non-bridging oxygens at the scissile phosphate, commonly known as the ‘thio effects’, in the HDV ribozyme. In the case of the RP sulfur substrate, the calculations revealed a reactant state with pronounced active site distortion and an unfavorable reaction pathway with a high energetic barrier. In contrast, the reactant state of the SP sulfur substrate showed minimal distortion at the active site compared to the oxo-substrate. The results from these studies are consistent with several biochemical experimental studies. The mechanism of the HDV ribozyme was further investigated using QM/MM free energy simulations to include conformational sampling and entropic effects. Umbrella sampling simulations were combined with a finite temperature string method to generate the multidimensional free energy surface underlying the self-cleavage reaction. The results of these simulations were qualitatively consistent with the previous QM/MM calculations, indicating a concerted mechanism in the presence of a Mg2+ ion at the catalytic site and a sequential mechanism in the presence of a Na+ ion. However, several new mechanistic insights were provided by the QM/MM free energy simulations, including the observation of proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate to stabilize the phosphorane intermediate in the sequential mechanism. The free energy barrier along the concerted pathway in the presence of the catalytic Mg2+ ion was consistent with the intrinsic reaction rate of the HDV ribozyme cleavage reaction measured experimentally. The differences in the reaction pathways of the cleavage reaction in the presence of the Mg2+ ion and the Na+ ion illustrated several key roles of the catalytic metal ion in the HDV ribozyme catalysis, including activation of the O2’ nucleophile, acidification of the general acid C75, and stabilization of the non-bridging oxygen of the scissile phosphate

Importance of MM Polarization in QM/MM Studies of Enzymatic Reactions: Assessment of the QM/MM Drude Oscillator Model

For accurate quantum mechanics/molecular mechanics (QM/MM) studies of enzymatic reactions, it is desirable to include MM polarization, for example by using the Drude oscillator (DO) model. For a long time, such studies were hampered by the lack of well-tested polarizable force fields for proteins. Following up on a recent preliminary QM/MM-DO assessment (<i>J. Chem. Theory. Comput.</i> <b>2014</b>, <i>10</i>, 1795–1809), we now report a comprehensive investigation of the effects of MM polarization on two enzymatic reactions, namely the Claisen rearrangement in chorismate mutase and the hydroxylation reaction in p-hydroxybenzoate hydroxylase, using the QM/CHARMM-DO model and two QM methods (B3LYP, OM2). We compare the results from extensive geometry optimizations and free energy simulations at the QM/MM-DO level to those obtained from analogous calculations at the conventional QM/MM level

Glutamine Amide Flip Elicits Long Distance Allosteric Responses in the LOV Protein Vivid

Light-oxygen-voltage (LOV) domains sense blue light through the photochemical formation of a cysteinyl-flavin covalent adduct. Concurrent protonation at the flavin N5 position alters the hydrogen bonding interactions of an invariant Gln residue that has been proposed to flip its amide side chain as a critical step in the propagation of conformational change. Traditional molecular dynamics (MD) and replica-exchange MD (REMD) simulations of the well-characterized LOV protein Vivid (VVD) demonstrate that the Gln182 amide indeed reorients by ∼180° in response to either adduct formation or reduction of the isoalloxazine ring to the neutral semiquinone, both of which involve N5 protonation. Free energy simulations reveal that the relative free energies of the flipped Gln conformation and the flipping barrier are significantly lower in the light-adapted state. The Gln182 flip stabilizes an important hinge-bβ region between the PAS β-sheet and the N-terminal cap helix that in turn destabilizes an N-terminal latch region against the PAS core. Release of the latch, observed both experimentally and in the simulations, is known to mediate light-induced VVD dimerization. This computational study of a LOV protein, unprecedented in its agreement with experiment, provides an atomistic view of long-range allosteric coupling in a photoreceptor

Learning a linear influence model between actors from transient opinion dynamics

Many social networks are characterized by actors (nodes) holding quantitative opinions about movies, songs, sports, people, colleges, politicians, and so on. These opinions are influenced by network neighbors. Many models have been proposed for such opinion dynamics, but they have some limitations. Most consider the strength of edge influence as fixed. Some model a discrete decision or action on part of each actor, and an edge as causing an ``infection'' (that is often permanent or self-resolving). Others model edge influence as a stochastic matrix to reuse the mathematics of eigensystems. Actors' opinions are usually observed globally and synchronously. Analysis usually skirts transient effects and focuses on steady-state behavior. There is very little direct experimental validation of estimated influence models. Here we initiate an investigation into new models that seek to remove these limitations. Our main goal is to estimate, not assume, edge influence strengths from an observed series of opinion values at nodes. We adopt a linear (but not stochastic) influence model. We make no assumptions about system stability or convergence. Further, actors' opinions may be observed in an asynchronous and incomplete fashion, after missing several time steps when an actor changed its opinion based on neighbors' influence. We present novel algorithms to estimate edge influence strengths while tackling these aggressively realistic assumptions. Experiments with Reddit, Twitter, and three social games we conducted on volunteers establish the promise of our algorithms. Our opinion estimation errors are dramatically smaller than strong baselines like the DeGroot, flocking, voter, and biased voter models. Our experiments also lend qualitative insights into asynchronous opinion updates and aggregation

Quantum mechanical/molecular mechanical free energy simulations of the self-cleavage reaction in the hepatitis delta virus ribozyme

The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mechanical/molecular mechanical (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg²⁺ at the catalytic site, the self-cleavage mechanism is observed to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from experimental studies. With Na⁺ at the catalytic site, the mechanism is observed to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2–4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate observed experimentally with monovalent ions, we hypothesize that the activation of the O2′ nucleophile by deprotonation and orientation is less favorable with Na⁺ ions than with Mg²⁺ ions. To explore this hypothesis, we experimentally measure the p<i>K</i>_a of O2′ by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theoretical and experimental results indicate that the catalytic Mg²⁺ ion may play three key roles: assisting in the activation of the O2′ nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it

Quantum Mechanical/Molecular Mechanical Study of the HDV Ribozyme: Impact of the Catalytic Metal Ion on the Mechanism

A recent crystal structure of the precleaved HDV ribozyme along with biochemical data support a mechanism for phosphodiester bond self-cleavage in which C75 acts as a general acid and bound Mg²⁺ ion acts as a Lewis acid. Herein this precleaved crystal structure is used as the basis for quantum mechanical/molecular mechanical calculations. These calculations indicate that the self-cleavage reaction is concerted with a phosphorane-like transition state when a divalent ion, Mg²⁺ or Ca²⁺, is bound at the catalytic site but is sequential with a phosphorane intermediate when a monovalent ion, such as Na⁺, is at this site. Electrostatic potential calculations suggest that the divalent metal ion at the catalytic site lowers the p<i>K</i>_a of C75, leading to the concerted mechanism in which the proton is partially transferred to the leaving group in the phosphorane-like transition state. These observations are consistent with experimental data, including p<i>K</i>_a measurements, reaction kinetics, and proton inventories with divalent and monovalent ions