To put dates on events in evolutionary history, biologists count how many mutations have accumulated over time in a species’ genes. But these “molecular clocks” can be fickle. A paper in the 28 September Physical Review Letters mathematically relates erratic “ticking” of the clock to properties of the DNA sequence. Researchers may eventually use the results to select which genes make the best clocks.
Although mutations in DNA are rare, they are crucial for evolution. Each mutation in a gene changes one small piece of a protein molecule’s structure–sometimes rendering it non-functional and occasionally improving it. The vast majority of mutations, however, neither hurt nor help, often because they affect an unimportant part of their protein. Such a “neutral” mutation usually dies out over the generations, but occasionally one proliferates until virtually every individual has it, permanently “fixing” the mutation in the evolving species.
Over thousands of generations, these fixed mutations accumulate. To gauge the time since two species diverged from a common ancestor, biologists count the number of differences between stretches of their DNA. But different DNA segments (genes) often give different answers, and those answers differ by much more than would be expected if the average rate of mutations remained constant over evolutionary time. Sometimes they also disagree with dates inferred from fossils. Now Alpan Raval, of the Keck Graduate Institute and Claremont Graduate University, both in Claremont, California, has put precise mathematical limits on this variation.
Raval’s work is based on representing possible DNA sequences for a gene as a network of interconnected points or “nodes.” Each point represents a version of the gene sequence that differs by exactly one neutral mutation–a single DNA “letter”–from its immediate neighbors. The network contains only neutral mutations; non-functional versions of the sequence aren’t part of the network.
Models and simulations had suggested that if the number of neighbors varies from point to point–that is, if some sequences allow more neutral mutations than others–mutations accumulate erratically over time, making the molecular clock unreliable. Raval calculates precise limits on how unsteady the clock could get, based on properties of the network, such as the average number of neighbors for each node or the number of “jumps” connecting any two randomly chosen nodes. “The great strength of this paper is that it’s now mathematically worked out in much more detail than before,” says Erik van Nimwegen of the University of Basel and the Swiss Institute of Bioinformatics in Switzerland, who developed the framework that Raval uses.
Still, the relevant network properties are “not very intuitive,” van Nimwegen observes. Raval agrees. “The real question from this point on would be to identify what kinds of proteins would be good molecular clocks.” He says that according to his results, for a protein to be a good clock, “virtually all single mutations [should] be neutral”–many neighbors per node–but “as you start accumulating double and triple mutants, it should quickly become dysfunctional.” Raval is working to relate these network features to protein properties that researchers could measure in the lab.
Researchers have suggested other explanations for the erratic behavior of molecular clocks, such as variations in the mutation rate because of changes in the environment. But such environmental changes are relatively fast, so their effect should average out over evolutionary time, says David Cutler of Emory University in Atlanta. He says that in network models, by contrast, changes in the mutation rate are naturally slow because the point representing the current sequence moves slowly around the network as mutations accumulate.
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