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Simple evolution of complex crystal species

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Abstract

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.

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Notes

  1. This diagram does not show the molecular structure of a DNA tile (Fu and Seeman 1993; Winfree et al. 1998); it is merely an abstract depiction of the interactions that the DNA tiles have with each other.

  2. For most of the tile sets that we identify as having the potential for more complex evolution, the number of wallpaper patterns that are possible in a given width grows approximately linearly with width, so the number of layers in each pattern is on average exponential in the width of the crystal. Thus, if the number of layers in (the length of) a wallpaper pattern (instead of its width) were used as the measure of complexity, complexity would grow more quickly with width. However, the qualitative result described here, that the complexity of patterns can increase as a result of selection pressure based on the rarity of certain monomer types, would not change.

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Author notes

  1. Rebecca Schulman

    Present address: Johns Hopkins University, Baltimore, MD, 21218, USA

Authors and Affiliations

  1. University of California Berkeley, Berkeley, CA, 94720, USA

    Rebecca Schulman

  2. California Institute of Technology, Pasadena, CA, 91125, USA

    Erik Winfree

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  1. Rebecca Schulman
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  2. Erik Winfree
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Correspondence to Rebecca Schulman.

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Schulman, R., Winfree, E. Simple evolution of complex crystal species. Nat Comput 11, 187–197 (2012). https://doi.org/10.1007/s11047-011-9302-9

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