The Second Version

24/11/08

Reaction Rates and Randomness

In a thread over at Misha's there is this significant snippet:
Cortillaen,

The mathematical chances of a simple 200 chain (all left or all right handed) amino acid is .1 in 10 to the minus 40,000. In plain english that number would be expressed as ZERO.

Reference: Evolution; A Theory in Crisis, by Dr. Michael Denton
I suspect that the probability quoted in there is calculated as it were the probability of obtaining a certain string from randomly picked letters (the explanation is not at all clear), which is the wrong way to look at the issue.

Because chemistry is definitely not random.
Even leaving aside the specific properties of biological evolution.

Let's take initially a simple model system one in which a molecule A can react with either a molecule B or a similar but not identical molecule C (say, acid-catalyzed aromatic alkylation where A is benzene, B ethylene and C propylene). The two reactions, and respective rates, are:

A + B --> X r1
A + B --> Y r2

What happens in this worls is that, except for very rare cases, r1 and r2 are different. The difference can be tiny or relevant but it is nearly inescapable.

The study of reaction rates and what factors influence them is the realm of chemical kinetics, and a great deal of effort went into it. Many clever and competent scientists spent a lot of time using sophisticate instruments to investigate reaction mechanisms and rates - and they obtained many good results.

It turns out that the main driver of reaction rates is molecular orbitals - the shape and electron distribution of molecules; however, thinking in terms of molecular orbitals is not the easiest task and in many cases it is enough to refer to a subset of molecular properties such as charge distribution and molecular size and shape - for example, a small molecule can gain access to a reactive centre while a bigger one can not.

The second factor is temperature, which in turn alters the collision rates and energy distribution of molecules (especially in the fluid phase) - molecules must not only collide in order to react, but they have to do so within a defined energy range.

This is only an extremely brief overview of what in fact is a vast field; there are many subtle distinctions and lesser effects and particular cases. The main point is that the structure of molecules determines their reactivty.

Going back to our model system, the difference between r1 and r2 results in different quantities (and generally concentrations) of X and Y; the difference can be tiny initially but - and this is another important point - if the supply of reactants is enough to let the reaction proceed for a long time, eventually the difference of quantities will become relevant - in some cases, also the initial ratios of reactants will influence the final state of the system.

In any case, we will end up with a certain degree of order which did not happen by random chance but neither was deliberataly designed.

Knowledgeable readers will notice that I have left out two or three aspects - namely, reaction thermodynamics and, exact form of rate expressions and the difference between reaction rates and rate constants. The first two are not so important in the context of this discussion, and this just a blog post, not a thesis. The third is in fact more important, but I prefer not to overload a post which is already quite technical.

If the reactants in our models systems were three α-aminoacids (pick the ones you like the most), things would become fantastically more complicate altogether: aminoacids can react with each other and thus form all possible products (AA, BB, CC, AB, AC, CB) each with its own reaction rate; the dipeptides from this first stage can react further producing longer chains, which can in turn react again becoming longer (or eventually be hydrolized at some point), and so on.

A template effect can also kick in, where the peptides already present influence the formation of new ones - to the point of self-replication, as it has been observed.

Even considering only the first reaction stage (dipeptides), in order to have a random distribution of the six products, the six reaction rates would have to be the same - but we have seen that the circumstance has only a near-zero probability of occurring: the distribution of products will not be random.

What will happen next... a random (normal) distribution of reaction rates should be unable to eliminate the non-randomness originating from the distribution of concentration of reactants.

But even if the longer peptides had a completely random sequence of aminoacids, they would not have all the same structure: some sequences would able to fold or coil (as in the omnipresent alpha helix) acquiring different properties regarding both thermodynamics and kinetics.

Some structures may fold in conformations that leave them more exposed to hydrolysis or other degradations and consequently be destroyed.

The first structure able to self-replicate, even imperfectly, would then gain an advantage and tend to grow in concentration at the expense of others.

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