Statistical Approaches to Three Key Challenges in Protein Structural Bioinformatics

Mardia, Kanti V.

doi:10.1111/rssc.12003

Cited by 20 publications

(15 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We show how this new prior can be incorporated in the fully Bayesian framework of Green and Mardia (2006), and how a Markov chain Monte Carlo (MCMC) scheme can be implemented in light of the changes to the model due to this prior. (See also Mardia (2013), who considered alignment preserving sequence order, but with a uniform prior over all possible such alignments.) This methodology can give biologically meaningful alignments on challenging problems, as well as accounting for uncertainty in the alignment and transformation parameters in a fully Bayesian manner.…”

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…A.1 Additional Illustrations Figure 13: Illustration of a dihedral angle defined by four atoms or three bonds, it is the opening angle between to pages of a book. (Reproduced from Mardia (2013). )…”

Section: A Supplementary Materialsmentioning

confidence: 99%

Torus principal component analysis with applications to RNA structure

Eltzner¹,

Huckemann²,

Mardia³

2018

Ann. Appl. Stat.

Self Cite

View full text Add to dashboard Cite

There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied. There are two existing general methods: tangent space PCA and geodesic PCA. However, unlike tangent space PCA, our torus-PCA honors the cyclic topology of the data space whereas, unlike geodesic PCA, our torus-PCA produces a variety of non-winding, non-dense descriptors. This is achieved by deforming tori into spheres and then using a variant of the recently developed principle nested spheres analysis. This PCA analysis involves a step of small sphere fitting and we provide an improved test to avoid overfitting. However, deforming tori into spheres creates singularities. We introduce a data-adaptive pre-clustering technique to keep the singularities away from the data. For the frequently encountered case that the residual variance around the PCA main component is small, we use a post-mode hunting technique for more fine-grained clustering. Thus in general, there are three successive interrelated key steps of torus-PCA in practice: pre-clustering, deformation, and post-mode hunting. We illustrate our method with two recently studied RNA structure (tori) data sets: one is a small RNA data set which is established as the benchmark for PCA and we validate our method through this data. Another is a large RNA data set (containing the small RNA data set) for which we show that our method provides interpretable principal components as well as giving further insight into its structure.

show abstract

“…Let

false(x_{i}, y_{i}, z_{i} false), i = 1, \dots, n

be n consecutive points on a helix. For the

α

‐helix, we take these n points for our study here to be

C_{α}

atoms which are the key atoms of a protein chain (see for example Mardia, ). The

C_{α}

is the central atom of each residue and is commonly used to trace an

α

‐helix in display programmes.…”

Section: The Straight Helix Modelmentioning

confidence: 99%

“…Proteins are considered the workhorses of life. There have been recent studies into the statistical aspects of the 3D atomic configuration of protein structures (see Mardia, ). The shape of a protein plays an important role in its function, and proteins contain some specific shapes (secondary structures) such as helices.…”

Section: Introductionmentioning

confidence: 99%

A Statistical Model for Helices with Applications

2018

Self Cite

View full text Add to dashboard Cite

Motivated by a cutting edge problem related to the shape of α -helices in proteins, we formulate a parametric statistical model, which incorporates the cylindrical nature of the helix. Our focus is to detect a "kink," which is a drastic change in the axial direction of the helix. We propose a statistical model for the straight α -helix and derive the maximum likelihood estimation procedure. The cylinder is an accepted geometric model for α -helices, but our statistical formulation, for the first time, quantifies the uncertainty in atom positions around the cylinder. We propose a change point technique "Kink-Detector" to detect a kink location along the helix. Unlike classical change point problems, the change in direction of a helix depends on a simultaneous shift of multiple data points rather than a single data point, and is less straightforward. Our biological building block is crowdsourced data on straight and kinked helices; which has set a gold standard. We use this data to identify salient features to construct Kink-detector, test its performance and gain some insights. We find the performance of Kink-detector comparable to its computational competitor called "Kink-Finder." We highlight that identification of kinks by visual assessment can have limitations and Kink-detector may help in such cases. Further, an analysis of crowdsourced curved α -helices finds that Kink-detector is also effective in detecting moderate changes in axial directions.

show abstract

Statistical Approaches to Three Key Challenges in Protein Structural Bioinformatics

Cited by 20 publications

References 51 publications

Bayesian Protein Sequence and Structure Alignment

Bayesian Protein Sequence and Structure Alignment

Torus principal component analysis with applications to RNA structure

A Statistical Model for Helices with Applications

Contact Info

Product

Resources

About