Simple evolution of complex crystal species
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Cairns-Smith has proposed that life began as structural patterns in clays that self-replicated during cycles of crystal growth and fragmentation. Complex, evolved crystal forms could then have catalyzed the formation of a more advanced genetic material. A crucial weakness of this theory is that it is unclear how complex crystals might arise through Darwinian evolution and selection. Here we investigate whether complex crystal patterns could evolve using a model system for crystal growth, DNA tile crystals, that is amenable to both theoretical and experimental inquiry. It was previously shown that in principle, the evolution of crystals assembled from a set of thousands of DNA tile types under very specific environmental conditions could produce arbitrarily complex patterns. Here we show that evolution driven only by the dearth of one monomer type could produce complex crystals from just 12 monomer types. When a monomer type is rare, crystals that use few of this monomer type are selected for. We use explicit enumeration to show that there are situations in which crystal species that use a particular monomer type less frequently will grow faster, yet to do so requires that the information contained in the crystal become more complex. We show that this feature of crystal organization could allow more complex crystal morphologies to be selected for in the right environment, using both analysis in a simple model of self-assembly and stochastic kinetic simulations of crystal growth. The proposed mechanism of evolution is simple enough to test experimentally and is sufficiently general that it may apply to other DNA tile crystals or even to natural crystals, suggesting that complex crystals could evolve from simple starting materials because of relative differences in concentrations of the materials needed for growth.