Multivariate Analyses of Codon Usage Biases

Jean R. Lobry

• Publisher: ISTE Press - Elsevier
• Year: 2018
• Print ISBN: 9781785482960
• eBook ISBN: 9780128172513
• Topic: Biological Sciences
• Subtopic: Molecular Biology
• Index: Biological Sciences

A complete case study with all coding sequences from the bacteria Borrellia burgdorferi illustrates how multivariate analyses reveals evolutionary mechanisms acting at the molecular level. They are either mutationnal (symmetric and asymmetric directionnal mutation pressure) or selective (selection against head-on collisions or linked to gene expressivity or subcellular location).- The main objective is to provide a complete and reproducible example of the power of multivariate analyses in this application field

1

Introduction to Correspondence Analysis

Abstract

This multivariate data analysis technique1 is well suited for amino acid and codon count tables. Its application, however, is not without pitfalls and its popularity not as high as one may expect. Its primary goal is to transform a table of counts into a graphical representation, in which each gene (or protein) and each codon (or amino acid) is depicted as a point. Correspondence analysis (CA) may be defined as a special case of principal components analysis (PCA) with a different underlying metric. The purpose of this chapter is to introduce CA for someone who is already familiar with dimension reduction methods such as PCA. The underlying metric is progressively introduced and some useful properties of CA are then mentioned.

Keywords

Correspondence analysis; Euclidean distance; Histogram; Metric choice; Protein profiles; Scree plot; Symmetric

1.1 Chapter objectives

This multivariate data analysis technique¹ is well suited for amino acid and codon count tables. Its application, however, is not without pitfalls [PER 02] and its popularity not as high as one may expect [TEK 16]. Its primary goal is to transform a table of counts into a graphical representation, in which each gene (or protein) and each codon (or amino acid) is depicted as a point. Correspondence analysis (CA) may be defined as a special case of principal components analysis (PCA) with a different underlying metric. The purpose of this chapter is to introduce CA for someone who is already familiar with dimension reduction methods such as PCA. The underlying metric is progressively introduced and some useful properties of CA are then mentioned.

1.2 Metric choice

1.2.1 A small data set example

The interest of the metric in CA, that is the way we measure the distance between two individuals, is illustrated here with a very simple example, inspired by [GAU 87] and given in Figure 1.1, with only three proteins having only three amino acids, so that the consequences of the metric choice are exactly represented on a map.

Figure 1.1 Balloonplot. For a color version of this figure, see www.iste.co.uk/lobry/multivariate.zip

data(toyaa)toyaa Ala Val Cys1 130 70 02 60 40 03 60 35 5

Notes on Table 1.1

A contingency table between two categorical varia...

Table of contents

• Cover image
• Title page
• Table of Contents
• Dedication
• Copyright
• Acknowledgments
• Introduction
• 1: Introduction to Correspondence Analysis
• 2: Global Correspondence Analysis
• 3: Within and Between Correspondence Analysis
• 4: Internal Correspondence Analysis
• Conclusion
• Appendix 1
• Appendix 2
• References
• Index