Design principles, growth laws, and competition of minimal autocatalysts.

The difficulty of designing simple autocatalysts that grow exponentially in the absence of enzymes, external drives or ingenious internal mechanisms severely constrains scenarios for the emergence of evolution by natural selection in chemical and physical systems. Here, we systematically analyze these difficulties in the simplest and most generic autocatalyst: a dimeric molecule that duplicates by templated ligation. We show that despite its simplicity, such an autocatalyst can achieve exponential growth autonomously.

On the exclusion of exponential autocatalysts by sub-exponential autocatalysts.

Selection among autocatalytic species fundamentally depends on their growth law: exponential species, whose number of copies grows exponentially, are mutually exclusive, while sub-exponential ones, whose number of copies grows polynomially, can coexist. Here we consider competitions between autocatalytic species with different growth laws and make the simple yet counterintuitive observation that sub-exponential species can exclude exponential ones while the reverse is, in principle, impossible. This observation has implications for scenarios pertaining to the emergence of natural selection.

On Kinetic Constraints That Catalysis Imposes on Elementary Processes.

Catalysis, the acceleration of product formation by a substance that is left unchanged, typically results from multiple elementary processes, including diffusion of the reactants toward the catalyst, chemical steps, and release of the products. While efforts to design catalysts are often focused on accelerating the chemical reaction on the catalyst, catalysis is a global property of the catalytic cycle that involves all processes. These are controlled by both intrinsic parameters such as the composition and shape of the catalyst and extrinsic parameters such as the concentration of the chemical species at play.