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Diversity and motif conservation in protein 3D structural landscape: exploration by a new multivariate simulation method

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Abstract

In this paper, diversity and conservation in the ‘landscape’ of random variation of protein tertiary structures are explored for quantitative feature-vector models of major types of functionally important 3D structural motifs. For this, I have deployed a recently developed nonparametric regression (NPR)-based multidimensional copula method of simulation. Apart from improved accuracy of multidimensional random sample generation, the simulation provides additional insight into diversity in the protein structural landscape in terms of random variation in the feature-vector. It shows the relative importance of several features, with biological implications, in conservation of motifs. Mapping of this landscape in distance-preserving 2D eigenspace also shows consistency in demarcation of different motif classes and preservation of their characteristic patterns in this 2D space.

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Acknowledgements

The author would like to thank Srijit Chakrabarty for implementing the initial version of the author’s algorithm as part of his MSc project. The version used in this work has been developed further with significant modifications.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, India

    Rajani R. Joshi

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  1. Rajani R. Joshi
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Correspondence to Rajani R. Joshi.

Appendix

Appendix

(Re: Legend of Figs. 1, 2, 3, 4, 5 and 6)

Let θij(v) denote the coefficient of (Rank or Partial, as the case may be) correlation between Xi and Xj in the Validation sample and let θij(g) denote the same in the Generated sample. Let η(i,j) = | θij(v) - θij(g) |, i, j = 1, .....11.

As the correlation matrices are symmetric, so is the matrix of their difference, i.e., η(i,j) = η(j,i). As each element of the diagonals of the correlation matrices is = 1, (and almost so are their estimates for both the samples with accuracy up to 7th place of decimal), so η(i,i) = 0 for each i. These properties are satisfied in our results for both the methods. Therefore only the values below the diagonal elements (i.e. η(i,j) for i = j+1, to 11, for j = 1, .....,11) are shown in Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

In these bar-diagrams, the integers 1 to 10 along the X-axis indicate the suffix-labels (i, j) = (2,1), .... (11,1) respectively; integers, 11 to 19 indicate the suffix-labels (3,2), .... (11,2) respectively; and so on ....., integers, 53 and 54 indicate the suffix-labels (10,9) and (11,9) respectively; and integer 55 indicates the suffix-label (11,10).

The numerical values of the corresponding η(i,j) are shown along the Y-axis.

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Joshi, R.R. Diversity and motif conservation in protein 3D structural landscape: exploration by a new multivariate simulation method. J Mol Model 24, 76 (2018). https://doi.org/10.1007/s00894-018-3614-y

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