1000 Genomes Whole Genome PCA Example
Upshot It’s pretty easy to compute principal components of variants across thousands (or many more) of whole genomes.
This example illustrates principal components (PCA) decomposition of genomic variant data of 2,504 people from the 1000 genomes project1. The example looks for clusters of people with similar genmoic traits by projecting the very high-dimensional genome-wide variant data into a three dimensional subspace.
Genomic variants
Our genomes consist of billions of copies of four base molecules arranged in pairs along our DNA. Sequences of these base pairs define all our genomic traits like eye color and whether we have freckles. Despite the immense length of our genome, there is remarkably little variation from person to person.
Rather than always work with the full sequence of base pairs, we often take advantage of the small variation from one person to the next to simply store differences between a genome and a so-called “reference” genome. The differences are called variants and might consist of, for example, a single difference at one genomic position in a base pair, or an insertion or deletion of a sequence of base pairs at specific point.
 
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| The figure shows an example single base pair variant, otherwise called a SNP for single nucleotide polymorphism 2. |
Storing variants instead of whole genomes results in a significant space savings. For instance, there are only about 81 million differences between the 2,504 people in the NIH 1000 Genomes project.
Identifying and specifying genomic variants is a very involved process, one step in a complex and computationally intensive genomic sequencing workflow. See https://bioconductor.org/help/course-materials/2014/CSAMA2014/3_Wednesday/lectures/VariantCallingLecture.pdf for many details.
Variant analysis
Importantly, the likelihood of certain diseases may be encoded in our genomic sequences. The study of modified DNA from cells degraded by cancer is also an importantly and heavily studied topic.
Scientists analyze genomic variants using a huge and constantly expanding variety of techniques. This note analyzes variant data from the NIH 1000 Genomes Project using a classification method called principal components analysis (PCA). The method is representative of many unsupervised machine learning techniques and good at projecting high-dimensional data down into a lower dimensional subspace to help identify groups of points (people) with lots in common.
The technique used here is discussed in a Google Genomics video here https://www.youtube.com/watch?v=ExNxi_X4qug&feature=youtu.be&t=6m21s although we suspect based on the presented output that only a subset of the genome was used in their analysis, perhaps one or two chromosomes.
Similar techniques are used in cancer genomics to classify tumor cells, in plant and animal breeding genomics, and in many more areas of genomic research.
We present two versions of a whole-genome variant PCA:
- A horizontally-scalable version suitable for clusters of machines with relatively limited RAM
- A fully in-memory SMP version
Both approaches use R.
1000 Genomes Analysis
We arranged variant data from the 1000 Genomes Project ins a very sparse matrix of 2,504 rows (people) by 81,271,844 columns (genomic variants), but with only about 9.8 billion nonzero-elements, that is only a little over 2% fill-in. In other words not every person exhibits all variants.
Our objective is to project these 81,271,844 dimensional data down to just three dimensions using principal components analysis (PCA) and visualize the resulting clusters.
Our approach breaks the problem up into sequences of smaller problems. Solving the problem by breaking it up into manageable pieces has the advantage of promoting scalability. Those pieces can be run on other CPU cores or even networked computers relatively easily.
Results
The 1000 Genomes data contain over 81 million dimensions. We use PCA to project those data into a three-dimensional space, which despite the substantial data reduction still contains a large amount of the information in the original data.
Of course we can see data in three dimensions, so lets look at the result!
The data exhibit obvious groups, and those groups correspond to ethnicities. The above plot colors the data by “Superpopulation”, a designation of each subject’s reported racial heritage. The superpopulations correspond very well to the latent clusters “discovered” in the data by PCA. Notice the level of detail in each cluster, some of which display distinct sub-clusters. Compare with the next illustration computed using only a portion of the variants across the whole genome (similar to the plot shown in the Google Genomics example above).Compare these clusters with those obtained from one chromosome (20) here http://bwlewis.github.io/1000_genomes_examples/PCA.html:
Notice that there is much finer detail in the whole genome plot. Zooming in on some of the clusters shows distinct subclusters.