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# 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

IN THE BEGINNING: Uses dynamical equations to probe whether the evolutionary force of selection preceded replication, a process that could explain how the polymers of life came to be." data-pin-do="buttonBookmark">

MARTIN A. NOWAK
A BIG DEAL: Lured to Harvard University in 2003 when he was granted the school’s first joint appointment between the math and biology departments.
NUMBERS GAME: Coined the term "evolutionary dynamics," which mathematically models how populations of genes, organisms and other biological entities change over time.
IN THE BEGINNING: Uses dynamical equations to probe whether the evolutionary force of selection preceded replication, a process that could explain how the polymers of life came to be.
Image: Erik Jacobs Jacobs Photographic

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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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1. 1. ScareBear 02:28 PM 10/7/08

Wow, I knew you could try to prove anything with math. I wonder if there is a mathematical equation I could use to prove the sky is indeed purple.

2. 2. Mithremakor in reply to ScareBear 09:41 PM 10/9/08

You've got it backwards. Nowak's mathematical model is not designed to 'prove' anything. As always in science, the model is a theory saying 'look, this is how life may have began' now it's up to experimenters to verify or disprove the theory. If experimental biologists can make his model work in the lab then we can say this is very probably the way life started.

3. 3. alphachapmtl 01:41 PM 10/10/08

Self-organization. Fascinating!

4. 4. laconic 09:03 AM 10/11/08

i find the idea of self-organization hard to believe in. Nonliving matter combining to form enzymes or proteins? By itself? I've never even heard of anything similar or even close to in nature.

5. 5. agodbout 12:08 PM 10/11/08

what if some kind of proto energetic-consciensness is "embodied in"and self evolving towards more complex forms of being?

6. 6. Assegai 04:17 PM 10/11/08

I believe there is some mathematical relation in most things, to understand anything one must put it in maths even if it is not accurate, but in mathematical notation it can be understood and then explained to the general public in simpler terms, I think he is on to something.

7. 7. lhpd in reply to Assegai 08:42 PM 10/12/08

It is true that mathematics explain our physical world. Yet, I am not convinced that it will prove anything. No one has proven in details which conditions existed on the earth before life arose. Some talk about RNA or DNA templates, but where did the RNA or DNA bases come from? How would they have associated themselves to the ribose moieties and phosphates to form nucleotides? How did the genetic base pairing rule come to be? A-T , A-U, G-C? If enzymes were needed to catalyze the reactions, how did they form? Where did the L-amino acids come from and why just L and not D? How did they form on the earth and if they came from a meteorite as some say, how did they form there? Or where does imidazole come from to bind to the nucleotides to make them more reactive? Yes, he can assign mathematical formulae to explain how "evolution works", but I think that Mr. Nowak is skipping many steps here, not starting at the real beginning of things. Let's hear how math can predict the way the atmospheric conditions of the earth were in those days and which chemical elements were abundant and how these elements came together to make more complex molecules before calculating distributions of RNA strands. People still debate whether the RNA world explanation is valid. Yes, his accomplishment is noteworthy, but please start at the beginning!

8. 8. lhpd in reply to lhpd 08:55 PM 10/12/08

In addition, the statement made that he would be able to explain the transition from no-life to life is pure exaggeration! Again, start from the beginning. I don't really like the way this article was presented. It seems too sensationalized to make you think that this man has solved the problem using his equations. He has solved nothing so far.

9. 9. Geodesic 09:36 PM 10/12/08

The topic of self-organization reminds me of that of (social) network research: people keep re-inventing the wheel. While this article seems to present self-organization mathematics as something new, we find many research articles and careers already well underway. One thinks of Ross Ashby in the '40s and so on. Of some significance here would of course be the work of molecular biologist Stuart Kauffman, reviewed in SciAm June 2008.

10. 10. frgough 10:53 AM 10/13/08

As a trained biochemist, Nowak should quit ignoring the chemistry. Chemical compounds form according to the laws of physics, and his monomers simply cannot form outside of living organisms without violating those laws. He might as well be using mathematics to demonstrate how a reactionless drive will propel spacecraft. The resulting equations would be the same sort of meaningless gibberish.

11. 11. Tan Boon Tee 09:49 PM 10/14/08

I have my reservation on your assertion that Nowak can explain the change from no life to life.

It is not so much of explanation, rather more of a formulation of a mathematical model to fit in what is already known about the plausibility of the emergence of life on earth. Moreover, no one can exactly describe how life came into being as yet.

While one may construe that math is the true language of science, it is still a tool, albeit a very versatile and essential tool.
(Tan Boon Tee)

12. 12. jana 06:57 AM 10/18/08

it is logical that the faster monomers appear more in a population.

13. 13. emil47 07:17 AM 10/18/08

The human mind isn't properly wired to understand what really means "one milliard years", because we only live under 100 years. Given enough time, "the blind watchmaker" (Mother Nature) will give rise to life. The mathematical models of self-organization can help us to "visualize" that sort of things.

14. 14. isrocolombiano 01:57 PM 12/3/08

I agree math will be telling us very much about the origin of life. I also agree with Ihpd that we need better understanding of the Real beginnigs.
Selection prior replication sounds persuasive. New experiments should verified this.

15. 15. anditico in reply to emil47 04:59 PM 9/29/10

"one milliard years"
What you say is true enough.. except for this...

Given enough time, "the blind watchmaker" (Mother Nature) will give rise to life.

That's a belief, not a statement of what we know. You may as well say, "God created life". There's no difference.

It's true the mathematical models will help us visualize the possibilities. The certainties still elude us completely.

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