Isolating the first spark of life on Earth is a matter of biology, geology, and chemistry - but it's also an amazing math problem. At least, that's how Varun Varanasi '24 viewed it when he was a Yale undergraduate.
The question, in a nutshell, is this: How did the primordial soup of interacting molecules on the Earth's surface billions of years ago transform itself from complete chaos to an organized system of self-sustaining, reproducing chemicals? Did this occur gradually over millions of years, or was it abrupt?
Researchers have been mulling over this question for a century. Inspired by a class he took as a Yale undergraduate, which was taught by Yale geophysicist Jun Korenaga, Varanasi decided it was his turn.
That inspiration would become Varanasi's senior thesis, which is now the basis for a new study in the journal Physical Review E. (It is co-authored by Korenaga, a professor of Earth and planetary sciences in Yale's Faculty of Arts and Sciences.)
"Our work offers a direct way to connect the underlying chemistry of prebiotic environments to the spontaneous emergence of life-like structures," said Varanasi, now a Ph.D. student in biophysics at Harvard. "It adds to exciting recent advancements in origin of life research and RNA autocatalysis, taking us a step closer to answering one of life's greatest mysteries."
Autocatalysis is a leading theory on the origin of life nearly four billion years ago. It proposes that groups of molecules collectively began to support the formation of new molecules through catalytic interactions. But what did that process look like?
Varanasi and Korenaga say it was like a light switch being flipped on after millions of years of preparation. The probability of a self-sustaining chemical network in the primordial soup sharply rose from zero to a near-certainty.
"Using a mathematical framework based on Kauffman networks, the paper derives an explicit prediction for when these life-like structures become overwhelmingly likely to appear," said Korenaga.
Kauffman networks, also known as Random Boolean Networks, are abstract math models of self-organizing collective action. They are named for theoretical biologist Stuart Kauffman, who first applied the concept to gene regulation networks in the late 1960s. The networks have also been used to study other complex systems, such as economic models of production.
Varanasi and Korenaga say their findings offer a bridge between abstract theories of complex systems and real-world systems themselves. They noted that similar mathematical prediction models could be applied to biological and interdisciplinary systems.
Varanasi said the research was inspired by a Yale course, "The Science of Complex Systems," which introduces undergraduate students to mathematical approaches for studying emergent behavior in such systems.
"I remember learning about the competitive Lotka-Volterra model, which describes predator-prey population dynamics," Varanasi said. "Jun had just finished a couple of lectures describing mathematical phenomena arising from differential equations and then introduced this classical model explaining why certain ecological systems can support themselves while others cannot."
He added, "I was fascinated by how much complexity in the real world could be captured by some neat equations we learned in a couple of weeks. By the end of the course, I felt like I had learned a new way to think about the world."
Korenaga, who describes himself as a "freestyle" geophysicist, was only too happy to help Varanasi take his interest to the next level.
"Seeing a project that started in an undergraduate classroom evolve into a published study in a peer-reviewed journal has been immensely rewarding," he said.
