# Using Math to Explain How Life on Earth Began

How did self-replicating molecules come to dominate the early Earth? Using the mathematics of evolutionary dynamics, Martin A. Nowak can explain the change from no life to life

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.”

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