A sequence of nucleotides, if you talk about nucleic acids, has say N positions, N and a G in a thousand positions or whatever. If you write a sequence space then each position will define a dimension. In other words, if you are standing on a certain point you can migrate into N different directions, regarding... to the position which changes. Let's say you have a given sequence and now there is a change in the tenth position. Alright. You go in that dimension. Or there is a change in the 150th position. You go that way. So it's very similar as doing a mountain trip. What are you doing if you go on a mountain?
[Q] So I understand that using a landscape, a multi-dimensional landscape for what we have no real imagination is, so to speak, a analogy to explain the status of the nucleic acid. In the sense that you just say that... how big is the chance of having a mutant here and there? So it is just a transposition into another world to explain the complexity of a nucleic... is that right?
That's correct. But you have to say in addition it doesn't need to be nucleic acid, but nucleic acid is something we can quantify... a sequence. We can exactly say which base is in that position, and we can compare to the other... is it the same or is it a different one? Now, the assumption behind it is that changing any of the bases will change the property of the molecule. Or later, if it is going to be translated into a protein, will change the property of the protein. Sometimes this will not change, then we talk about neutral mutants. So wherever you have some complex - and you had this in population genetics too, these were humans or animals or so - but you couldn't quantify it. But the properties are also consisting of many, many influences and elements and so, in order to describe them quantitatively you need high dimensional spaces. For each property you need a dimension. And that's exactly what happens if we do evolution, let's say, of a sequence of nucleic acids. We are in a high dimensional landscape, we need populations, that's very important, that's filling the basin with water droplets. If you have only one water molecule, nothing would happen, you must build up a population. The same is true with nucleic acids. Evolution without populations doesn't make sense, not a single molecule or a single entity doesn't evolve, a population evolves, and that this population is extended in space here means that it consists of many different mutants. And you see, if you have a sufficiently large population and you are in this high dimensional space, it's not so difficult to reach the next optimal step.
