Volume 4, Issue 32 October 2007
The Mathematician and the Genome
Lior Pachter is at the leading edge of a new generation of mathematics and biologists. He is not only a professor of mathematics and computer science, but also a QB3 faculty affiliate and a member of Berkeley's Center for Computational Biology. Photo credit: Robert Fisher
The completion of the Human Genome Project in 2001 was hailed as a major breakthrough in science. For the first time, humans could look at their DNA and discover traits ranging from their propensity to alcohol addiction to the likelihood that their children will have blue eyes.
In fact, research into our biochemical blueprints had only just begun. Since then, scientists have added the rat, cow, chicken, dog, and even platypus to the list of creatures whose genes have been read like a biochemical book. Each species has shed new light on the structure and function of our own genetic code.
Darwin's first sketch of an evolutionary tree from his First Notebook on Transmutation of Species (1837). Source: Wikipedia
Lior Pachter has been at the forefront of these new genomic analyses. Officially a UC Berkeley professor of mathematics and computer science, Pachter considers himself a mathematical biologist. He uses the power of mathematical modeling and statistics to evaluate the vast quantities of data in DNA.
Pachter first got interested in biology as a graduate student in mathematics at MIT. There, he began using mathematical techniques to find functional genes within the so-called "junk" sequences in human DNA. Later, while biologists sequenced the mouse genome, he developed methods to compare where the mouse and human genomes were similar by chance versus selection.
Pachter has big plans for his sequence analysis work: he seeks to do nothing less than map the ancestral tree of life. "I want to understand how each one of the 3 billion nucleotides in the human genome arose in the course of evolution," Pachter says. "To make sense of how the genome works, we have to understand its history. That means understanding what we share in common with other organisms, both with other humans and primates but also all other animals."
To date, the genomes of nearly 30 vertebrates with genes relatively similar to ours have been sequenced. Each has made the task of comparing sequences exponentially more useful and complicated. "It's no longer possible for biologists to analyze these results by hand; there's just too much data," Pachter says. "Here, mathematics helps make sense of the data and also provides models of how the actual molecular components work."
Pachter's research comparing genomes has helped define relationships among vertebrate species. The lengths of the branches on this phylogenetic tree, which are based on DNA sequence comparisons, show how closely each animal is related. The numbers next to each species name indicate the amount of sequence (in megabases) that was analyzed. Image credit: E.H. Margulies et al., "Analyses of deep mammalian sequence alignments and constraint predictions for 1% of the human genome," Genome Research (2007).
Pachter likens genome studies to recreating plans for an existing building. "Until now, we've just been labeling the parts, the doorknobs and windows. Only recently have we started to ask about the function of the parts, and how these functions are related to each other."
A genotope representing genetic relationships among individuals. Each point corresponds to an individual from one of four distinct populations. Image credit: P. Huggins et al., "Towards the human genotope," Bulletin of Mathematical Biology (2007).
In addition to sequence data, a profusion of other genetic information is now flooding the field. Measurements of gene expression in different tissues, ways to measure gene variations between individuals, and other information can all help make sense of how our DNA makes us who we are. "Mathematics and statistics provides a good means for synthesizing the data in a reasonable way," Pachter says.
Just this year, Pachter began collaborating on the Human Microbiome Project. This new initiative from the National Institutes of Health seeks to analyze the microbial flora that lives in and on the human body. Scientists estimate that each person carries around 10 times more bacterial than human cells, species ranging from helpful gut microbes to pathogens like streptococci. The project will generate a jumble of gene fragments from both known and new species. Pachter's role is to help determine the rough number of creatures represented in the mix.
"It's fun for me that I can combine both mathematics and biology and participate in these major enterprises," Pachter says. "The best thing is, I get to do a lot of beautiful math to go along with it."