Eigen's paradoxAll organisms face the issue of how to detect and repair germ-line errors.
Modern organisms use sophisticated enzymes to detect and correct errors.
However the complexity of these enzymes needs a highly reliable inheritance mechanism, just to be capable of specifing the information needed to create them.
The difficulty associated with the the creation of error-correcting enzymes by a genetic system that lacks any form of error correction can thus seem like a bit of a chicken-and-egg problem.
Primitive organisms would not have had the ability to manufacture complicated error-correction enzymes. However without the ability to correct errors at all, early organisms would have been very limited to in the amount of information they could carry without suffering from an error catastrophe.
Fortunately, there are error correction mechanisms that work using the principles of self-assembly. These require no enzymatic machinery at all. It is error correction via self-assembly that this essay will be concerned with.
CrystalsThere is really only one known example of an error correction mechanism which occurs in nature outside of biology.
That is the error correction process that is associated with crystal growth.
Crystals self-assemble into huge, highly ordered structures from large numbers of disordered components with a fantastic level of accuracy.
Without any kind of error correction, regular crystals as we know them would not exist. Instead, crystalline solids would be amorphous and disordered.
In fact, real crystals often display a reflection of their lattice structure in their external shape. The orientation of the seed breaks symmetry. The resulting asymmetry is magnified up to macroscopic dimensions during crystal growth - propagating information about the seed's orientation through thousands of layers of crystal in the process.
These pictures illustrate how information about the orientation of an initial seed can be preserved through a large number of layers of crystal, and get magnified up to macroscopic proportions.
Clearly in order to exhibit the large-scale regularities that they do, crystals must have some way of dealing with units that attach themselves to the growing crystal in the 'wrong' place.
Crystal error correctionCrystal growth consists of the repeated addition of units to an existing crystal.
Error correction in crystals occurs because correctly aligned units are more stable than misaligned ones - and because crystal growth proceeds via an iterated process that preserves stable structures better than it preserves unstable ones.
For error correction to occur there needs to be a difference in energy between the rates at which crystal growth or crystal dissolution occur, when there is an error - compared to when there is no error.
When units are attached to a crystal in a manner that does not perpetuate the existing crystal structure, the added units tend to be slightly less stable, and slightly more likely to become detached and return to the solution from which they came, compared to properly aligned ones.
Similarly growth around a misaligned bit of crystal is often hindered - because units do not attach properly to both the existing crystal and the new misaligned units simultaneously.
The combination of hindered forward growth and an accelerated rate of dissolution means misaligned units have a lower probability of persisting than correctly-aligned ones.
The saturation levelNear the edge of super-saturation, crystal growth proceeds via a process analogous to taking five steps forwards and four steps backwards. The iterative nature of this process means that errors are examined many times - and have many opportunities to be corrected.
How near to the edge of super-saturation the surrounding solution is kept at is a critical factor determining both the rate at which crystals grow and to the rate at which misaligned units are added.
The backward steps - where units are lost from the crystal - are of critical importance to the process - since they represent opportunities to correct errors in the existing structure.
If the level of super-saturation is too high, units will be added more frequently than they are removed - and the error correction mechanisms will have less opportunity to operate - resulting in a crystal with more errors and it.
Analysis suggests an that the error rate can be made arbitrarily low - if one is prepared to sacrifice a rapid growth rate in the process - by making the solution only slightly super-saturated.
An extremely low error rate may not be desirable for crystals that are candidates for the category of "organisms". Sometimes these transmit information to their offspring in the form of crystal fault structures.
If eliminating errors will also eliminates any such faults, then too low an error rate may be undesirable.
ReversibilityFor another perspective on the issue of error correction, consider the reversibility of the of the reactions involved. For error correction to take place there should be a difference in how easily reversed the attachment of any units is - which depends on whether the units are correctly positioned or not.
Crystal growth is not a reversible phenomenon on a macroscopic scale. To reverse crystal growth typically requires a power supply to heat the surrounding fluid and melt the crystal.
However, crystal growth processes are normally considered to be microscopically reversible by chemists.
While they do not involve any irreversible chemical reactions, there are nontheless energy differences involved that mean that crystal growth has an irreversible aspect - even when viewed on small scales.
Crystal growth requires a power supply. The potential energy in a super-saturated solution is degraded and partilly converted into heat while being used to generate an ordered crystal.
Consider the phases which a unit typically goes through when becoming attached to a crystal:
First the unit hits the surface of the crystal - at a random location. If it lacks sufficient kinetic energy to bounce off the surface of the crystal, it may become attached to the surface.
Such a unit loses one degree of translational freedom in the process but retains the ability to move around in two dimensions on the crystal surface - rather like an ice skater.
Next, the unit may run into an edge - which takes away another degree of translational freedom.
Finally, the unit may run into a corner - where it may become totally immobilised.
None of these steps is fully reversible - since each sends shock waves into the crystal - as the incoming particle loses its kinetic energy. To reverse such steps completely, shock waves within the crystal would have to conspire to converge upon a point on the surface - overally a less likely set of affairs - unless the initial conditions are contrived to favour it.
Having said and what type of reversability is under discussion, it is time to examine how reactions that position units correctly and incorrectly differ in their reversibility.
An analogy is useful at this stage. Consider the energy of balls falling into holes in the ground, and adopting the positions in the following diagram:
Here, the blue ball has lost more kinetic energy falling into the hole and is less likely to be ejected again if the ground is shaken.
Falling into a deep hole is a situation which is less easily reversed and falling into a shallow one.
In the analogy the blue ball corresponds to a correctly- positioned unit. Such units have a reduced probability of being shaken loose - due to the strength of the bonds with the surrounding crystal.
Saturation level fluctuationsThe iterative nature of the error correction process requires that local fluctuations in the level of saturation of the surrounding solution take place.
In practice these fluctuations may have many sources:
Firstly it should be noted that whenever a unit leaves solution to become attached to the surface of a crystal, it makes the surrounding solution slightly less super- saturated. This results in a force favouring the detachment of the newly-attached unit - or one of its neighbours.
A highly significant source of small fluctuations in the level of super-saturation is simple thermal noise.
Another possible source of such fluctuations is turbulent fluid flow.
Finally other environmental fluctuations may be responsible for changes in super-saturation on a larger scale.
Error rate factorsCrystals vary in the extent to which error correction mechanisms operate in them.
One factor is how rapidly additional units are added around misplaced ones, locking them in place in the process.
Factors such as weather the crystal has triangular, rectangular or hexagonal unit cell influence this.
Another factor whether growth takes place on many fronts simultaneously.
Parallel growth fronts allow units to rapidly form on top of each other, locking in existing errors.
Some configurations reduce the extent to which growth takes place in parallel. In particular, screw dislocation and tubular crystals can reduce the opportunity for growth taking place in parallel.
Lastly, some types of units simply fit together more satisfyingly. An analogy with a jigsaw puzzle may help illustrate this:
In the "loose fit" case, there may not be much difference between the energy needed to shake free a correctly-positioned unit and an incorrectly-positioned one - because even correct bonds are relatively weak.
However, in the "tight fit" case, correctly-assembled units more strongly resist disassembly.
More advanced error correctionSince the probability of errors being corrected depends partly on to what extend growth around errors is inhibitied, the question arises of to what extent it is possible to prevent new units from being added adjacent to incorrectly positioned ones.
It turns out that it is possible to do to a remarkably good job of preventing growth around incorrectly positioned units - if the units are of an appropriate shape.
A diagram illustrates the basic idea:
In this diagram, misplaced units (marked with '?') are effective at preventing more units from being added around them.
An error during assembly can only be followed by a series of subsequent errors.
This is a kind of roadblock to growth - and it gives the unstable units more time to dissolve back into solution again.
Theoretical possibilitiesStill more sophisticated error correction during self-assembly is possible - in theory:
As before, an error during assembly can only be followed by a series of subsequent errors.
Here, an error during assembly cannot occur alone. It must be accompanied by at least one other error. With more sophisticated sets of tiles, the number of subsequent errors that must occur if a mutation is to be produced can be configured - at the expense of increasing the overall redundancy. Such configuration allows a energy barrier of a configurable height to be erected - which any mutations need to climb.
While this kind of scheme is effective at reducing the error rate, it requires redundancy in the underlying message - and results in larger genomes and slower growth and reproduction.
More complex variations on this theme can requires relatively complex rules about how the units can be combined. While this kind of scheme has been implemented by those experimenting with DNA crystals, it would be surprising if any clay minerals took this kind of approach very far.
ConclusionsThe unique capabilities of crystal growth processes to copy information while applying error correction techniques are what make crystal growth the leading candidate inheritance mechanism for the first organisms.
No other high-fidelity information copying process - or error correction process - outside of the products of modern biological systems - has ever been demonstrated or observed.