Simple Evolution Of Complex Crystal Sequences

1409 words - 6 pages

In 1966 Graham Cairns-Smith proposed that the first genetic material
on earth was not organic, but crystalline, and resided in the
particular morphologies of clays. One of the primary objections to
this theory is that it is not clear how non-trivial crystal genotypes
could be selected for. It is therefore of interest to ask whether
crystals and physical conditions for their assembly exist where
complex crystal morphologies could evolve. DNA tile crystals are
particularly suitable for this kind of investigation because DNA tile
monomers are programmable---new molecules with particular affinities
can be easily designed and synthesized. While it has previously been
suggested that arbitrarily complex morphologies of DNA tile crystals
could form as the result of an evolutionary process, the crystals
which could develop these morphologies contain thousands of monomer
types, and are therefore too complex to assemble or study.
Additionally, the physical conditions under which this process might
occur would be difficult or impossible to reproduce experimentally.
Here, we suggest how evolution of crystals produced by a small set of
tiles could yield crystals with complex patterns under achievable
environmental conditions. The crystals consist of a set of 12 tiles
that copy a 2-dimensional pattern along a ribbon-shaped crystal. Each
of these tile sets can form some large, complex crystals which only
rarely use specific molecules during growth. Simple, thin crystals
constructed from these tiles must use the specific molecules more
often. When these molecules are available only at very low
concentrations, the large, complex crystals that only rarely use these
molecules grow faster than thin, simple ones. Thus, large, complex
crystals are selected for. Because the number of these molecules that
are required for growth decreases as the width of the crystals
increases, by making the concentration of these required molecules
arbitrarily small it is in principle possible to select for
arbitrarily large, complex crystals. We describe a family of tile
sets whose members contain tile sets that meet the above criteria and
investigate the crystal evolution that occurs with these tile sets
using both a simple analytical model of crystal growth and stochastic
simulations. The molecules and the environments described are
sufficiently simple that evolution of complex crystal forms could be
tested in the laboratory in the near future. The described mechanism
for evolution is also sufficiently general that it may apply to other
DNA crystal forms such as nanotubes, or even to natural clay crystals,
suggesting that the crystals Cairns-Smith imagined might have evolved
complex forms because of a relative lack of some crystal monomer
types.

\section{Introduction}

A plausible hypothesis for the origin of life must explain both how a
self-replicating system emerged spontaneously and how Darwinian
evolution of this...

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