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I wouldn't really know the mechanisms involved. I get this whole idea from some reading about how the immune system works (in Michael Behe's book, Darwin's Black Box--his point was the irreducible complexity of the system, but that is not my point here). The t-cells or b-cells (or some kind of cells) can do some neat DNA shuffling just to try out different binding sites (if I remember how it works...forgive the vagueness).
Ok, I think I know where you are trying to go with this.
The b-cells are responsible for producing antibodies. When a b-cell matures it rearranges a set of genes. Those genes make up the antigen binding portion (ie the portion that binds to the germs) of the antibody. That mature b-cell can only express that antibody for the entirety of it's life span. The immune system works by creating a bank of these b-cells that all have a randomly created antigen binding site. During an infection, the b-cells that bind antigen are turned on. They then start dividing and pumping out large volumes of this antibody. In some ways, the immune system uses the mechanisms of mutation and natural selection to produce antibodies that are specific to certain antigens. There is absolutely no foresight into which combination of genes goes into each antibody. Rather, the b-cells are selected for by the ability to bind antigen.
This is very similar to how evolution occurs, where the mutations are not created with foresight but are actually selected for by the environment. In the same way, the DNA replication system is allowed to be somewhat sloppy to allow for mutations to occur, although mutations will always happen. For example, humans have mutated the enzymes involved in DNA replication and some of those mutants are actually better at copying DNA without errors. There are also bacteria that live on x-ray equipment. These bacteria have extensive DNA repair mechanisms. From this we know that the DNA repair mechanisms and DNA replication systems are allowed to be a little less accurate than they could be.
However, this is a trait that would be selected for. If mutations were not allowed to happen, or were extremely rare, that species would not be able to adapt to new environments as quickly as they do now. It is always a balancing act between the production of detrimental mutations and the production of beneficial mutations. There is a "sweet spot" where the mutation rate produces detrimental mutations at a rate where natural selection can remove them without harming the overall population.
I always like analogies, so I thought up one for this situation. Let's equate the mutation rate with highway speed limits. On the highways we always balance two things, the ability to get somewhere fast and safety. The faster you can travel the quicker you get somewhere, but there is also an increase in the chances of serious car accidents. The speed is the mutation rate. The ability to get somewhere quickly is the occurrence of beneficial mutations. The accident rate is the occurrence of detrimental mutations. So the balancing act is having a "highway speed" that is both beneficial and poses an acceptable rate of accidents.
This "highway speed" is then selected for by the environment, no need for a intelligent designer to program it in. Those species that do not mutate quickly enough will be outcompeted for new niches. Those species that mutate too quickly will be too unhealthy to adapt to new environments because of the occurrence of too many detrimental mutations. The "Goldylocks" species will have a mutation rate that is "just right".
So random mutations can arise naturally without the need for an intelligent designer to insert the mechanism for creating them. The pattern of mutations shows us that no foresight is involved, even in the case of b-cells and the immune system. For me, we could conclude that a Designer was possibly involved if the same mutation appeared in 10% of the population in one generation. This would show that mutations are not random and that they are produced through foresight. However, this is not seen.
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