Math of strategy can describe molecular competition, cooperation
At first glance, it seems strange to think that math used for describing business competition, fighting terrorists and playing poker would also have anything to do with the origin of life. But you never know.
Game theory — the branch of math used for describing strategic interactions — was conceived as a mathematical exercise to explain parlor games. Originally the idea was to analyze two-person games where one player lost whatever the other player won (a “zero sum” game). John von Neumann, the mathematician-physicist-computer scientist who also liked poker, developed game theory math in the 1920s to quantify the relative merits of different strategic choices, such as whether to raise or call. Later, in the 1940s, von Neumann collaborated with the economist Oskar Morgenstern to write Theory of Games and Economic Behavior, a tome intended to revolutionize economics with game-theoretic insight.
Game theory caught on slowly in economics, but was adopted in other arenas, such as analyzing Cold War strategies. It got a boost in the 1950s from the work of John Nash, the troubled mathematician whose life inspired the book and movie A Beautiful Mind.
Nash perceived that game theory could be applied to complicated gamelike situations, with multiple players each able to pursue multiple strategies. Even in such complex situations, Nash showed, there was always at least one combination of everybody’s strategies that allowed each player to get the best deal possible assuming all competitors played their best choices. In such a case, no one had any incentive to change strategies. That means that the game (or economic system, or international situation) had achieved a stable state, or equilibrium.
This notion of “Nash equilibrium” became the central concept in game theory, making it useful to a variety of disciplines studying human behavior, including psychology, sociology, political science and economics. In the 1970s, game theory invaded biology, when George Price and John Maynard Smith showed how with minor adjustments, the Nash equilibrium idea could be applied to competition among species for survival. An ecosystem in which all the niches promoted the best survival chances for all its members suggested that they had collectively found an “evolutionary stable strategy.”
In other words, animals can choose from among different possible strategies, just as humans do. Cats, for instance, can choose whether to hunt for mice or purr in your face till you reach for the Purina. For most creatures, though, strategies are not so much choices as behaviors. On an island populated by hawks and doves, hawks play an aggressive strategy and doves play a passive strategy just because that’s the way those birds behave. An evolutionary stable strategy can be reached when the relative number of hawks and doves offers no advantage to the next bird that comes along to behave one way or another.
If animals can play games just by virtue of their innate behavior, it’s not really all that great a stretch to imagine that game theory could also apply to biological molecules, as some scientists have noticed.
“Not only organisms as a whole, but also macromolecules that have (indirect) influence on their reproductive success can be considered as players in the sense of game theory,” Katrin Bohl and collaborators wrote in a paper published last year in Molecular BioSystems. “Many of their properties can be viewed as strategies.… Cognitive and rational capabilities are no prerequisites of players in game-theoretical models.”
In fact, there’s a very real sense in which chemical reactions are a sort of competition among molecules to reach an arrangement that achieves some optimal state. Just as in economics, where competitors want to maximize their profits, a collection of molecules wants to maximize energetic stability — which is achieved by reaching a state with minimum energy. It’s no accident that Nash called a stable situation in game theory an “equilibrium”; he explicitly compared game equilibria to the equilibrium states reached in chemical reactions. (Nash was a chemistry and chemical engineering student before he switched to math.)
Within living things, molecules can have different strategies (or properties) that contribute to the survival of the organism they inhabit. Genes, for instance, are key contributors to an organism’s survival and ability to reproduce. Some genes obviously possess properties that play the role of cooperative strategies that benefit the organism. But sometimes genes possess properties (play strategies) that aren’t so good for the body but allow the gene to “free ride” on the cooperation of others — and therefore continue on to future generations. These “parasites of the genome,” as Bohl and colleagues call them, are like people who benefit from society’s services but do everything they can to avoid paying taxes.
Other examples of molecules acting like game players have been identified. Certain proteins fold into a rigid form; others are more flexible. Still others can become rigid or stay flexible depending on the property of the proteins they interact with. Rigidity and flexibility can be considered strategies, so such protein interactions can be analyzed in game-theoretic terms. Similar game theory analysis can be applied to viruses — genetic material on the borderline between life and nonlife. Game theory’s insights could be very valuable in this case, indicating better strategies for fighting infections by the biomedical game players known as doctors.
It’s a small step from viruses to suppose that during the Earth’s early days, preceding life’s origins, molecules may have been interacting in ways suitable for a game theory analysis. Bohl and colleagues have pointed out that ribozymes — RNA fragments exhibiting catalytic ability — can self-assemble into networks that might produce sufficient complexity to lead to life. In 2012, Nilesh Vaidya of Portland State University and collaborators showed experimentally how that can happen. They reported in Nature that one ribozyme can catalyze the creation of a second that in turn can catalyze the creation of a third; the third one then catalyzes the creation of the first one. Such ribozymes that assist in the assembly of others can be considered “cooperators” in a primordial soup of molecules; other “selfish” ribozymes replicate only themselves. It appears that the cooperating strategy might outcompete the selfish strategy in producing greater prebiological complexity, making the emergence of actual life more probable.
“Our experiments highlight the advantages of cooperative behavior even at the molecular stages of nascent life,” Vaidya and collaborators wrote.
So the next time I write a blog post speculating that game theory could explain the origin of life, don’t laugh. Even if it is a joke.
Follow me on Twitter: @tom_siegfried