Protein Structure Classification and Loop Modeling Using Multiple Ramachandran Distributions

Najibi, Seyed Morteza; Maadooliat, Mehdi; Zhou, Lan; Huang, Jianhua Z.; Gao, Xin

doi:10.1016/j.csbj.2017.01.011

Cited by 20 publications

(15 citation statements)

References 64 publications

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“…This idea has been used in a generalized mixture model to iteratively update the smoothing parameter . Schellhase and Kauermann and Najibi et al extended this approach for density estimation. We borrow their formulation and use the parameter estimates in the i t h step to update the tuning parameter, ie,

{\overset{λ}{true}}_{i + 1}

, through

{\overset{λ}{true}}_{i + 1}^{- 1} = \frac{trace ((), {\overset{Θ}{true}}_{i}^{⊤} boldR {\overset{Θ}{true}}_{i})}{sans-serifdf false({\overset{λ}{true}}_{i} false) - false(a - 1 false)},

where a is the order of the differences (derivative) used in the penalty matrix R (see Section 2.5).…”

Section: Methodsmentioning

confidence: 99%

“…From what we have seen in the implementation of the new procedure, updating the tuning parameter within the Newton‐Raphson iterations, on average, does not increase the number of iterations required for convergence. Therefore, the new procedure obtains the final result p times faster than the old procedure, where p is the number of λ s used in the grid search to minimize the AIC (see the work of Najibi et al for details).…”

Section: Methodsmentioning

confidence: 99%

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Nonparametric collective spectral density estimation with an application to clustering the brain signals

Maadooliat

Sun

Chen

2018

Statistics in Medicine

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In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the collection of the log-SDFs is estimated as a low-dimensional manifold of a large space spanned by a prespecified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the coefficients of the basis expansion, and these coefficients can be used for visualization, clustering, and classification purposes.The Whittle pseudo-maximum likelihood approach is used to fit the model and an alternating blockwise Newton-type algorithm is developed for the computation. A web-based shiny App found at "https://ncsde.shinyapps.io/NCSDE" is developed for visualization, training, and learning the SDFs collectively using the proposed technique. Finally, we apply our method to cluster similar brain signals recorded by the for identifying synchronized brain regions according to their spectral densities. KEYWORDS roughness penalty, time series clustering, Whittle likelihood INTRODUCTIONNonparametric techniques for estimating functional structures have been developed in a variety of settings including regression, density estimation, and survival analysis. In time series analysis, the spectral density function plays an important role in characterizing the frequency content of a signal. Mainly, the estimated spectral density can be used to detect the periodicities of the signals in the frequency domain.In practice, it is common to utilize a discrete Fourier transform (DFT) of the input signal and provide a mathematical approximation of the full integral solution of the Fourier transformation. The squared-magnitude of a DFT of the data is called periodogram. However, the raw periodogram is not a consistent estimator for the spectral density of a stationary random process. One classical method to obtain a consistent estimator is to smooth the periodogram across frequencies. Yuen 1 analyzed the performance of three methods of periodogram smoothing for spectrum estimation. Wahba 2 developed an objective optimum smoothing procedure for estimating the log-spectral density using the spline to smooth the log-periodogram. A discrete spectral average estimator and lag window estimators were introduced in the work of Brockwell and Davis. 3 Both of the two methods are consistent. Brillinger 4 introduced periodogram kernel smoothing.Statistics in Medicine. 2018;37:4789-4806.wileyonlinelibrary.com/journal/sim

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{\overset{λ}{true}}_{i + 1}

, through

{\overset{λ}{true}}_{i + 1}^{- 1} = \frac{trace ((), {\overset{Θ}{true}}_{i}^{⊤} boldR {\overset{Θ}{true}}_{i})}{sans-serifdf false({\overset{λ}{true}}_{i} false) - false(a - 1 false)},

where a is the order of the differences (derivative) used in the penalty matrix R (see Section 2.5).…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Nonparametric collective spectral density estimation with an application to clustering the brain signals

Maadooliat

Sun

Chen

2018

Statistics in Medicine

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“…() by using non‐parametric density estimation, focusing on modelling loop regions of a protein; see also Najibi et al . (). Motivated by direct modelling of the evolution of a protein, Golden et al .…”

Section: Mathematical Formulation: Unlabelled Shape Analysismentioning

confidence: 99%

“…For example, Boomsma et al (2008) used hidden Markov models as generative models for protein structure. Lennox et al (2009) used Dirichlet process mixtures for density estimation of the distribution of dihedral angles: a problem also considered by Maadooliat et al (2016) by using non-parametric density estimation, focusing on modelling loop regions of a protein; see also Najibi et al (2017). Motivated by direct modelling of the evolution of a protein, Golden et al (2017) described the shape of a protein as a sequence of dihedral angles on the torus; their model captures dependences between sequence and structure evolution through a diffusion process on the torus.…”

Section: Mathematical Formulation: Unlabelled Shape Analysismentioning

confidence: 99%

Bayesian Protein Sequence and Structure Alignment

Fallaize

Green

Mardia

et al. 2020

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary The structure of a protein is crucial in determining its functionality and is much more conserved than sequence during evolution. A key task in structural biology is to compare protein structures to determine evolutionary relationships, to estimate the function of newly discovered structures and to predict unknown structures. We propose a Bayesian method for protein structure alignment, with the prior on alignments based on functions which penalize ‘gaps’ in the aligned sequences. We show how a broad class of penalty functions fits into this framework, and how the resulting posterior distribution can be efficiently sampled. A commonly used gap penalty function is shown to be a special case, and we propose a new penalty function which alleviates an undesirable feature of the commonly used penalty. We illustrate our method on benchmark data sets and find that it competes well with popular tools from computational biology. Our method has the benefit of being able potentially to explore multiple competing alignments and to quantify their merits probabilistically. The framework naturally enables further information such as amino acid sequence to be included and could be adapted to other situations such as flexible proteins or domain swaps.

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“…The prediction accuracies have improved gradually over the years [4, 5, 6] and are approaching the ones estimated from NMR chemical shifts [6]. It has been demonstrated that the predicted torsion angles are useful to improve ab initio structure prediction [7, 8], sequence alignment [9], secondary structure prediction [10, 11], template-based tertiary structure prediction and fold recognition [12, 13, 14], protein structure classification and loop modeling [15,16], and protein comformation sampling [17].…”

Section: Introductionmentioning

confidence: 99%

Prediction of Protein Backbone Torsion Angles Using Deep Residual Inception Neural Networks

Fang

Shang

2019

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Prediction of protein backbone torsion angles (Psi and Phi) can provide important information for protein structure prediction and sequence alignment. Existing methods for Psi-Phi angle prediction have significant room for improvement. In this paper, a new deep residual inception network architecture, called DeepRIN, is proposed for the prediction of Psi-Phi angles. The input to DeepRIN is a feature matrix representing a composition of physico-chemical properties of amino acids, a 20-dimensional position-specific substitution matrix (PSSM) generated by PSI-BLAST, a 30-dimensional hidden Markov Model sequence profile generated by HHBlits, and predicted eight-state secondary structure features. DeepRIN is designed based on inception networks and residual networks that have performed well on image classification and text recognition. The architecture of DeepRIN enables effective encoding of local and global interatcions between amino acids in a protein sequence to achieve accruacte prediction. Extensive experimental results show that DeepRIN outperformed the best existing tools significantly. Compared to the recently released state-of-the-art tool, SPIDER3, DeepRIN reduced the Psi angle prediction error by more than 5 degrees and the Phi angle prediction error by more than 2 degrees on average. The executable tool of DeepRIN is available for download at http://dslsrv8.cs.missouri.edu/~cf797/MUFoldAngle/.

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Protein Structure Classification and Loop Modeling Using Multiple Ramachandran Distributions

Cited by 20 publications

References 64 publications

Nonparametric collective spectral density estimation with an application to clustering the brain signals

Nonparametric collective spectral density estimation with an application to clustering the brain signals

Bayesian Protein Sequence and Structure Alignment

Prediction of Protein Backbone Torsion Angles Using Deep Residual Inception Neural Networks

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