Crystal evolutions
Recent developments in DNA have established that computations can now be embedded in crystals. It has been speculated that crystal computations have a possible connection to the origin of life. Support for this hypothesis has been postulated but Graham Cairns-Smith on the assumptions that primitive ‘organisms’ were clay crystals. One of the key strengths behind Cairns-Smith’s theory is that it answers Darwinians evolution that could have begun through a geological process. Taking into consideration the simplicity and conceptual evolution of crystals this provides wide range of open evolutions.
Another great advancement in this area is the case of ‘crystal metabolism’ where it has shown that crystals can sense the environments and adapt themselves in response to their environments. This in particular has prompted the interest into the evolution of complex crystal metabolism. To better explain evolution is important to establish three aspects of evolutionary process. First is the self-replication entity that carries information and stipulates behaviors. Secondly is the possibility of certain environments that have the advantage of availing stimulus that enable the evolution of complex solutions. Finally in order for evolution to be quickly achieved there must be a route through mutations in which complex behaviors increments in steps. The importance behind these understanding best serves the future goals in crystal evolution studies.
Zigzag approach
Unlike previous suggestions that DNA tiles could evolve through cycles of crystal growth and splitting, the zigzag approach produces ribbon-like crystals that copy information along the crystal length. Hence when a growth occurs according to the tiles assembly model, tiles are added to a ribbon in a zig-zag pattern as the technique name depicts.
The propagation behind the working of the zig-zag approach is that the growth of the crystals increases the number of copies of the original information in every ribbon but does not result in new growth fronts therefore a constant rate of copying is achieved. This repeated fragmentation will greatly amplify the initial pieces of information. Therefore such copying errors, inevitable in any physical implementation of tiles will lead to evolution if ribbons with certain sequences happens to grow faster than others.
Zig-zag ribbon metabolism
It has been found that the rate of attachment of a tile to a crystal is proportional to the concentration of the tile in the solution, thus the growth rate of crystals can be made faster by increasing their concentration of their components in the tile solution. Unlike the previous examples of zig-zag ribbon that had to be complicated so as to achieve complex selection in biology it has been found that single chemistry in biology has led to evolution of more complex organisms.
Key to these findings illustrated by ‘computation tiles’ tends exhibit Boolean functionality. This facilitates the existence of a principle that allows a crystal to perform local computations that modify sequence upon inputs whereby its resulting outputs server as inputs for future computation steps.
On the issue of a suitable assembly for the environment, it has been established that fit assemblies are those which have the highest replication rates. It has then been assumed that if all assemblies split at the same time, a fit environment would depict the fastest growth rate. Due to the fact that the environment changes over time, the fittest assembly is the one that has the average growth rate.
Evolution of universal sensing and response
A Turing machine refers to a long work tape which has a sequence of symbols written on it, and the head represents a finite number of states. The head examines the work tape one simple at a time, and providing symbols observed locally.
If the correlation between measurement and resource tiles were very complex, it is possible that by the time assembly finished simulating computations, the concentration of the resources in the tiles would have changed already. This best depicts that a complex program may not be selected for. It can be established that the pattern of increasing and decreasing concentrations of measurement and resource tile is sufficiently slowed down then it can be established that the prediction of the right resource tiles would be fit.
Further discussions
Since it is now possible to increase the complexity of selective pressures by increasing the complexity of tile sets used for growth, we can draw a suggestion that the tile sets exist allows crystals to encode and execute programs that can predict arbitrary complex environmental changes.
Therefore such evolutions using tiles set as a medium shows possibilities of producing very complex sequence that are able to grow well because of their ability to predict changes in growth conditions. This further suggests growth logically support open-ended evolutions with arbitrarily complex fitness landscapes.
Despite the argument presented that some assemblies will be more fit relies on their growth rates however being fit requires assemblies to not only grow quickly but also to shear frequently. However not sufficient information is known about shearing frequencies to make sound predictions since these rates dependent on the kind of forces that produce the shearing in practice. Though it might be certain to make an assumption that zig-zag assemblies would shear less frequently than thin ones in most cases, all this could have the effects of favoring correct and concise programs for prediction of resource tile concentrations such as the natural implementation of Occam razor.
However since our conclusions at this point is limited, we tend to neglect several key real life features of crystal growth, For instance, while our models prohibit any tile that matches more than two bonds from attaching, still such attachments occur at rates dependent on the physical conditions of the assembly. In the case where this error rates are too large, two things are apparent. First of all large programs that takes longer to run maybe difficult to accurately compute without mistakes and may as well favors preference for robust programs in this case if such programs already exists for the tiles used which compute an answer correctly even in the presence of assembly errors.
Secondly it may be possible for assemblies that seek for absent resources within their environments to eventually attach the available to the available non-matching resource environment. Also considering the fact that the effects of backward growth on the fitness of crystal landscapes. For some environment however as depicted by the tiles, backward growth cannot be determined quickly hence this leads to configurations that cannot be furthered except by making an error in which results in the case of backward growth stalling and being neglected.
However despite all other limitations to the present study we believe that qualitative features of the described mechanisms should be looked into in a more realistic model of crystal growth. It also brings about an interesting question about minimal requirements for open-ended evolution of crystals.
Reference
Rebecca Schulman, E. W. (2008). How crystals that sense and respond to their environments could evolve. Nat Comput , 219–237.
