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Register a new userHidden Semi-Markov Models for Single-Molecule Conformational Dynamics
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The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable. However, the evolution of the conformational states of proteins mostly shows non-Markovian behavior, recognizable by non-monoexponential state dwell time histograms. The application of a Hidden Markov Model technique to a cyclic system demonstrating semi-Markovian dynamics is presented in this paper and the required extension of the model design is discussed. As standard ranking criteria of models cannot deal with these systems properly, a new approach is proposed considering the shape of the dwell time histograms. We observed the rotational kinetics of a single F1-ATPase alpha3beta3gamma sub-complex over six orders of magnitude of different ATP to ADP and Pi concentration ratios, and established a general model describing the kinetics for the entire range of concentrations. The HMM extension described here is applicable in general to the accurate analysis of protein dynamics.
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1. Movement is the primary means by which animals obtain resources and avoid hazards. Most movement exhibits directional bias that is related to environmental features (taxis), such as the location of food patches, predators, ocean currents, or wind. Numerous behaviours with directional bias can be characterized by maintaining orientation at an angle relative to the environmental stimuli (menotaxis), including navigation relative to sunlight or magnetic fields and energy-conserving flight across wind. However, no statistical methods exist to flexibly classify and characterise such directional bias. 2. We propose a biased correlated random walk model that can identify menotactic behaviours by predicting turning angle as a trade-off between directional persistence and directional bias relative to environmental stimuli without making a priori assumptions about the angle of bias. We apply the model within the framework of a multi-state hidden Markov model (HMM) and describe methods to remedy information loss associated with coarse environmental data to improve the classification and parameterization of directional bias. 3. Using simulation studies, we illustrate how our method more accurately classifies behavioural states compared to conventional correlated random walk HMMs that do not incorporate directional bias. We illustrate the application of these methods by identifying cross wind olfactory foraging and drifting behaviour mediated by wind-driven sea ice drift in polar bears (Ursus maritimus) from movement data collected by satellite telemetry. 4. The extensions we propose can be readily applied to movement data to identify and characterize behaviours with directional bias toward any angle, and open up new avenues to investigate more mechanistic relationships between animal movement and the environment.
Metabolic heterogeneity is widely recognised as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular events. However, metabolism has been traditionally viewed as a purely deterministic process, on the basis that highly abundant metabolites tend to filter out stochastic phenomena. Here we bridge this gap with a general method for prediction of metabolite distributions across single cells. By exploiting the separation of time scales between enzyme expression and enzyme kinetics, our method produces estimates for metabolite distributions without the lengthy stochastic simulations that would be typically required for large metabolic models. The metabolite distributions take the form of Gaussian mixture models that are directly computable from single-cell expression data and standard deterministic models for metabolic pathways. The proposed mixture models provide a systematic method to predict the impact of biochemical parameters on metabolite distributions. Our method lays the groundwork for identifying the molecular processes that shape metabolic heterogeneity and its functional implications in disease.
Non-coding RNA molecules fold into precise base pairing patterns to carry out critical roles in genetic regulation and protein synthesis. We show here that coupling systematic mutagenesis with high-throughput SHAPE chemical mapping enables accurate base pair inference of domains from ribosomal RNA, ribozymes, and riboswitches. For a six-RNA benchmark that challenged prior chemical/computational methods, this mutate-and-map strategy gives secondary structures in agreement with crystallographic data (2 % error rates), including a blind test on a double-glycine riboswitch. Through modeling of partially ordered RNA states, the method enables the first test of an interdomain helix-swap hypothesis for ligand-binding cooperativity in a glycine riboswitch. Finally, the mutate-and-map data report on tertiary contacts within non-coding RNAs; coupled with the Rosetta/FARFAR algorithm, these data give nucleotide-resolution three-dimensional models (5.7 {AA} helix RMSD) of an adenine riboswitch. These results highlight the promise of a two-dimensional chemical strategy for inferring the secondary and tertiary structures that underlie non-coding RNA behavior.
Generalizing manipulation skills to new situations requires extracting invariant patterns from demonstrations. For example, the robot needs to understand the demonstrations at a higher level while being invariant to the appearance of the objects, geometric aspects of objects such as its position, size, orientation and viewpoint of the observer in the demonstrations. In this paper, we propose an algorithm that learns a joint probability density function of the demonstrations with invariant formulations of hidden semi-Markov models to extract invariant segments (also termed as sub-goals or options), and smoothly follow the generated sequence of states with a linear quadratic tracking controller. The algorithm takes as input the demonstrations with respect to different coordinate systems describing virtual landmarks or objects of interest with a task-parameterized formulation, and adapt the segments according to the environmental changes in a systematic manner. We present variants of this algorithm in latent space with low-rank covariance decompositions, semi-tied covariances, and non-parametric online estimation of model parameters under small variance asymptotics; yielding considerably low sample and model complexity for acquiring new manipulation skills. The algorithm allows a Baxter robot to learn a pick-and-place task while avoiding a movable obstacle based on only 4 kinesthetic demonstrations.
This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. Multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for chemical and biological problems. Extensive numerical experiments involving more than 4,000 protein-ligand complexes from the PDBBind database and near 100,000 ligands and decoys in the DUD database are performed to test respectively the scoring power and the virtual screening power of the proposed topological approaches. It is demonstrated that the present approaches outperform the modern machine learning based methods in protein-ligand binding affinity predictions and ligand-decoy discrimination.
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