Structural dissimilarity sampling with dynamically self‐guiding selection

Structural dissimilarity sampling (SDS) has been proposed as an enhanced conformational sampling method for reproducing the structural transitions of a given protein. SDS consists of cycles of two steps: (1) Selections of initial structures with structural dissimilarities by referring to a measure. (2) Conformational resampling by restarting short‐time molecular dynamics (MD) simulations from the initial structures. In the present study, an efficient measure is proposed as a dynamically self‐guiding selection to accelerate the structural transitions from a reactant state to a product state as an extension to the original SDS. In the extended SDS, the inner product (IP ) between the reactant and the snapshots generated by short‐time MD simulations are evaluated and ranked according to the IP s at every cycle. Then, the snapshots with low IP s are selected as initial structures for the short‐time MD simulations. This scheme enables one to choose dissimilar and distant initial structures from the reactant, and thus the initial structures dynamically head towards the product, promoting structural transitions from the reactant. To confirm the conformational sampling efficiency, the extended SDS was applied to maltodextrin binding protein (MBP), and we successfully reproduced the structural transition from the open to closed states with submicrosecond‐order simulation times. However, a conventional long‐time MD simulation failed to reproduce the same structural transition. We also compared the performance with that obtained by the ordinary SDS and other sampling techniques that have been developed by us to characterize the possible utility of the extended SDS for actual applications. © 2017 Wiley Periodicals, Inc.     

Temperature‐shuffled parallel cascade selection molecular dynamics accelerates the structural transitions of proteins

Parallel cascade selection molecular dynamics (PaCS‐MD) is an enhanced conformational sampling method for searching structural transition pathways from a given reactant to a product. Recently, a temperature‐aided PaCS‐MD (Vinod et al., Eur. Biophys. J. 2016, 45, 463) has been proposed as its extension, in which the temperatures were introduced as additional parameters in conformational resampling, whereas the temperature is fixed in the original PaCS‐MD. In the present study, temperature‐shuffled PaCS‐MD is proposed as a further extension of temperature‐aided PaCS‐MD in which the temperatures are shuffled among different replicas at the beginning of each cycle of conformational resampling. To evaluate their conformational sampling efficiencies, the original, temperature‐aided, and temperature‐shuffled PaCS‐MD were applied to a protein‐folding process of Trp‐cage, and their minimum computational costs to identify the native state were addressed. Through the evaluation, it was confirmed that temperature‐shuffled PaCS‐MD remarkably accelerated the protein‐folding process of Trp‐cage compared with the other methods. © 2017 Wiley Periodicals, Inc.     

Adaptive‐numerical‐bias metadynamics

A metadynamics scheme is presented in which the free energy surface is filled with progressively adding adaptive biasing potentials, obtained from the accumulated probability distribution of the collective variables. Instead of adding Gaussians with assigned height and width in conventional metadynamics method, here we add a more realistic adaptive biasing potential to the Hamiltonian of the system. The shape of the adaptive biasing potential is adjusted on the fly by sampling over the visited states. As the top of the barrier is approached, the biasing potentials become wider. This decreases the problem of trapping the system in the niches, introduced by the addition of Gaussians of fixed height in metadynamics. Our results for the free energy profiles of three test systems show that this method is more accurate and converges more quickly than the conventional metadynamics, and is quite comparable (in accuracy and convergence rate) with the well‐tempered metadynamics method. © 2017 Wiley Periodicals, Inc.     

Absolute Minimal Sampling of Homonuclear 2D NMR TOCSY Spectra for High-Throughput Applications of Complex Mixtures

Modern applications of 2D NMR spectroscopy to diagnostic screening, metabolomics, quality control, and other high-throughput applications are often limited by the time-consuming sampling requirements along the indirect time domain t₁. 2D total correlation spectroscopy (TOCSY) provides unique spin connectivity information for the analysis of a large number of compounds in complex mixtures, but standard methods typically require >100 t₁ increments for an accurate spectral reconstruction, rendering these experiments ineffective for high-throughput applications. For a complex metabolite mixture it is demonstrated that absolute minimal sampling (AMS), based on direct fitting of resonance frequencies and amplitudes in the time domain, yields an accurate spectral reconstruction of TOCSY spectra using as few as 16 t₁ points. This permits the rapid collection of homonuclear 2D NMR experiments at high resolution with measurement times that previously were only the realm of 1D experiments.     

A Gibbs sampling method to determine biomarkers for asthma

PurposeTo identify potential biomarkers and to uncover the mechanisms underlying asthma based on Gibbs sampling.MethodsThe molecular functions (MFs) with genes greater than 5 were determined using AnnotationMFGO of BAGS package, and the obtained MFs were then transformed to Markov chain (MC). Gibbs sampling was conducted to obtain a new MC. Meanwhile, the average probabilities of MFs were computed via MC Monte Carlo (MCMC) algorithm, followed by identification of differentially expressed MFs based on the probabilities of MF more than 0.6. Moreover, the differentially expressed genes (DEGs) and their correlated genes were screened and merged, called as co-expressed genes. Pathways enrichment analysis was implemented for the co-expressed genes.ResultsBased on the gene set more than 5, overall 396 MFs were determined. After Gibbs sampling, 5 differentially expressed MF were acquired according to alfa.pi > 0.6. Moreover, the genes in these 5 differentially expressed MF were merged, and 110 DEGs were identified. Subsequently, 338 co-expressed genes were gained. Based on the P value < 0.01, the co-expressed genes were significantly enriched in 6 pathways. Among these, ubiquitin mediated proteolysis contained the maximum numbers of 35 co-expressed genes, and cell cycle were enriched by the second largest number of 11 co-expressed genes, respectively.ConclusionsThe identified pathways such as ubiquitin mediated proteolysis and cell cycle might play important roles in the development of asthma and may be useful for developing the credible therapeutic approaches for diagnosis and treatment of asthma in future.     

The direct and inverse problem for an inclusion within a heat-conducting layered medium

This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously.     

Periodic Nonuniform Dynamical Sampling in ℓ2(ℤ) and Shift-Invariant Spaces

In this article, we mainly study the periodic nonuniform dynamical sampling in ?²(?) and shift-invariant spaces. We first provide a su?cient and necessary condition for c∈?²(?) which can be reconstructed by its spatial and temporal samples. Then we give a concrete example to show that the su?cient and necessary condition is feasible. Finally, we discuss the periodic nonuniform dynamic sampling problem in shift-invariant spaces.     

Variational Bayes With Intractable Likelihood

Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes their use in many interesting situations such as in state--space models and in approximate Bayesian computation (ABC), where application of VB methods was previously impossible. This article extends the scope of application of VB to cases where the likelihood is intractable, but can be estimated unbiasedly. The proposed VB method therefore makes it possible to carry out Bayesian inference in many statistical applications, including state--space models and ABC. The method is generic in the sense that it can be applied to almost all statistical models without requiring too much model-based derivation, which is a drawback of many existing VB algorithms. We also show how the proposed method can be used to obtain highly accurate VB approximations of marginal posterior distributions. Supplementary material for this article is available online.