Back in March the press went crazy for Martin A. Nowak’s study on the value of punishment. A Harvard University mathematician and biologist, Nowak had signed up some 100 students to play a computer game in which they used dimes to punish and reward one another. The popular belief was that costly punishment would promote cooperation between two equals, but Nowak and his colleagues proved the theory wrong. Instead they found that punishment often triggers a spiral of retaliation, making it detrimental and destructive rather than beneficial. Far from gaining, people who punish tend to escalate conflict, worsen their fortunes and eventually lose out. “Nice guys finish first,” headlines cheered.

It wasn’t the first time Nowak’s computer simulations and mathematics forced a rethinking of a complex phenomenon. In 2002 he worked out equations that can predict the way cancer evolves and spreads, such as when mutations emerge in a metastasis and chromosomes become unstable. And in the early 1990s his model of disease progression demonstrated that HIV develops into AIDS only when the virus replicates fast enough so that the diversity of strains reaches a critical level, one that overwhelms the immune system. Immunologists later found out he had the mechanism right [see “How HIV Defeats the Immune System,” by Martin A. Nowak and Andrew J. McMichael; Scientific American, August 1995]. Now Nowak is out to do it again, this time by modeling the origin of life. Specifically, he is trying to capture “the transition from no life to life,” he says.

Trained as a biochemist, the 43-year-old Nowak believes that mathematics is the “true language of science” and the key to unlocking the secrets of the past. He began exploring the mathematics of evolution as a graduate student at the University of Vienna, working with fellow Austrian Karl Sigmund, a leader in evolutionary game theory. Evolutionary dynamics, as Nowak named the field, involves creating formulas that describe the building blocks of the evolutionary process, such as selection, mutation, random genetic drift and population structure. These formulas track, for example, what happens when individuals with different characteristics reproduce at different rates and how a mutant can produce a lineage that takes over a population.

At the home of the Program for Evolutionary Dy­­namics at Harvard, the blackboard is chalked with equations. Nowak has been busy working on how to whittle down the emergence of life into the simplest possible chemical system that he can describe mathematically. He uses zeroes and ones to represent the very first chemical building blocks of life (most likely compounds based on adenine, thymine, guanine, cytosine or uracil). Nowak refers to them as monomers, which, in his system, randomly and spontaneously assemble into binary strings of information.

Nowak is now studying the chemical kinetics of this system, which means describing how strings with different sequences will grow. The fundamental principles of this idealized scheme, he says, will hold true for any laboratory-based chemical system in which monomers self-assemble, “in the same way as Newton’s equations describe how any planet goes around the sun, and it doesn’t matter what that planet is made of,” Nowak explains. “Math helps us to see what the most crucial and interesting experiment is. It describes a chemical system that can be built, and once it’s built, you can watch the origin of evolution.”

Could it really be that simple? Right now the system exists only on paper and in the computer. Although it is easy to model mathematically, making the system in the lab is tricky because it starts without any enzymes or templates to help the monomers assemble. “It’s hard to imagine an easy way to make nucleic acids,” says David W. Deamer, a biomolecular engineer at the University of California, Santa Cruz. “There had to be a starting material, but we’re very much into a murky area, and we don’t have good ideas about how to re-create it in the laboratory or how to get it to work using just chemistry and physics without the help of enzymes.”

[break]

In the 1980s biochemist Leslie E. Orgel and his group at the Salk Institute for Biological Studies in San Diego showed that a strand of RNA can act as a template for making another strand of complementary RNA—a phenomenon called nonenzymatic template-directed polymerization. Figuring out how nucleotides might self-assemble without templates, however, has proved harder. “I want a process that can comprise polymers,” Nowak says.

Irene Chen, a cellular origins researcher at Harvard, says one way that monomers of RNA or DNA might form polymers in the absence of enzymes is by adding a compound called imidazole to one end of the monomers, making them more reactive and their polymerization quicker and easier. Lipids or clay might also be essential—other researchers have shown that they can help speed up the reaction. At Rensselaer Polytechnic Institute, for instance, chemist James P. Ferris induced adenine nucleotides to assemble into short polymers of RNA—strands 40 to 50 nucleotides long—on a kind of mineral clay that may have been common in the prebiotic world.

Using his mathematical model, Nowak looks at chemical reactions that lead to these kinds of strands and assigns rate constants to the reactions. That is, he imagines that strings with different binary information grow at different rates, with some taking in monomers faster than others. Then he calculates their distributions. Small differences in growth rates, he has noticed, result in small differences in abundance; sequences that grow slower are less common in the population, getting outcompeted by faster ones. “This I find great,” Nowak exclaims, “because now you have selection prior to replication in a completely natural way.”

Some strands mutate, and sometimes one sequence accelerates the reaction rates of other sequences, demonstrating the kind of cooperation that Nowak has long argued is a fundamental principle of evolution. Taken together, he says, the result is a lifelike chemical system ripe with evolutionary dynamics. He calls this system “prelife” because “it has the qualities of life—genetic diversity, selection and mutation—but not replication.”

Typically mutation and selection are seen as consequences of replication. If suddenly, for example, only large, hard seeds were available to the finches of the Galápagos Islands, those with bigger, stronger beaks would be more likely to survive and, generation after generation, would become more common in the population. Selection for a trait, be it beak size or something else, depends on passing down the genes for that trait to offspring. But Nowak says his model shows there can be selection prior to replication—which means that maybe there is selection for replication. If this kind of selection is possible, he notes, maybe it can help explain the origin of life.

All that is necessary is for a few strings to suddenly develop the ability to make copies of themselves—the way some researchers believe certain strands of RNA first became dominant on the primitive earth. Enough free monomers would have to be around to make replication advantageous, Nowak points out, and the replicating strings must be able to use up the monomers faster than the nonreplicating strings. According to his calculations, only when the rate of replication went beyond a certain threshold would the equilibrium of the system change, allowing life to emerge. “Life destroys prelife,” he states. “All of this happened at some stage.”

Nowak hopes that his model will guide experiments. When it comes to understanding the beginning of evolution, building the chemical system he describes mathematically—a system in which only two types of monomers self-assemble and then self-replicate—“is the simplest thing you can do,” he says. “Mathematics is the proper language of evolution. I don’t know what the ‘ultimate understanding’ of biology will look like, but one thing is clear: it’s all about getting the equations right.”