Collective Estimation of Multiple Bivariate Density Functions With Application to Angular-Sampling-Based Protein Loop Modeling

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

doi:10.1080/01621459.2015.1099535

Cited by 10 publications

(16 citation statements)

References 74 publications

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“…First, more robust methods for the fourth-digit prediction are needed. The increasing number of enzymes that have experimentally validated functions, as well as the advance in method development for learning from imbalanced-data and small samples ( Maadooliat et al , 2016 ), provide potential solutions to the problem. Second, instead of predicting the EC numbers for enzymes, it is practically useful to predict enzymatic reactions of the enzymes.…”

Section: Discussionmentioning

confidence: 99%

DEEPre: sequence-based enzyme EC number prediction by deep learning

et al. 2017

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MotivationAnnotation of enzyme function has a broad range of applications, such as metagenomics, industrial biotechnology, and diagnosis of enzyme deficiency-caused diseases. However, the time and resource required make it prohibitively expensive to experimentally determine the function of every enzyme. Therefore, computational enzyme function prediction has become increasingly important. In this paper, we develop such an approach, determining the enzyme function by predicting the Enzyme Commission number.ResultsWe propose an end-to-end feature selection and classification model training approach, as well as an automatic and robust feature dimensionality uniformization method, DEEPre, in the field of enzyme function prediction. Instead of extracting manually crafted features from enzyme sequences, our model takes the raw sequence encoding as inputs, extracting convolutional and sequential features from the raw encoding based on the classification result to directly improve the prediction performance. The thorough cross-fold validation experiments conducted on two large-scale datasets show that DEEPre improves the prediction performance over the previous state-of-the-art methods. In addition, our server outperforms five other servers in determining the main class of enzymes on a separate low-homology dataset. Two case studies demonstrate DEEPre’s ability to capture the functional difference of enzyme isoforms.Availability and implementationThe server could be accessed freely at http://www.cbrc.kaust.edu.sa/DEEPre.Supplementary information Supplementary data are available at Bioinformatics online.

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Section: Discussionmentioning

confidence: 99%

DEEPre: sequence-based enzyme EC number prediction by deep learning

et al. 2017

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“…() used Dirichlet process mixtures for density estimation of the distribution of dihedral angles: a problem also considered by Maadooliat et al . () by using non‐parametric density estimation, focusing on modelling loop regions of a protein; see also Najibi 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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“…Ting et al [34] and Joo et al [35] also used this technique with further modification to produce near-native loop structures. In another approach, Maadooliat et al [36] proposed a penalized spline collective density estimator (PSCDE) to represent the log-densities based on some shared basis functions. This method showed some significant improvements for loop modeling of the hard cases in a benchmark dataset where existing methods do not work well [36] .…”

Section: Introductionmentioning

confidence: 99%

“…The PSCDE method is constructed based on Bernstein-Bézier spline basis functions defined over triangles to estimate the log-densities in a complex domain [36] . In simple words, in PSCDE,we artificially extended the constraints of the adjacent triangles to the triangles in boundaries in order to estimate the densities in a two-dimensional circular domain.…”

Section: Introductionmentioning

confidence: 99%

Protein Structure Classification and Loop Modeling Using Multiple Ramachandran Distributions

Najibi

Maadooliat

Zhou

et al. 2017

Computational and Structural Biotechnology Journal

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Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. The proposed method takes into account the circular nature of the angular data using trigonometric spline which is more efficient compared to existing methods. This collective density estimation approach is widely applicable when there is a need to estimate multiple density functions from different populations with common features. Moreover, the coefficients of adaptive basis expansion for the fitted densities provide a low-dimensional representation that is useful for visualization, clustering, and classification of the densities. The proposed method provides a novel and unique perspective to two important and challenging problems in protein structure research: structure-based protein classification and angular-sampling-based protein loop structure prediction.

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Collective Estimation of Multiple Bivariate Density Functions With Application to Angular-Sampling-Based Protein Loop Modeling

Cited by 10 publications

References 74 publications

DEEPre: sequence-based enzyme EC number prediction by deep learning

DEEPre: sequence-based enzyme EC number prediction by deep learning

Bayesian Protein Sequence and Structure Alignment

Protein Structure Classification and Loop Modeling Using Multiple Ramachandran Distributions

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