Effective Concentration 2
In my post on effective concentration, I noted that the concentration of water in water (about as high as a real concentration can be) is 55 M, while observed effective concentrations are often >55,000 M. This is puzzling until you realize that, for a molecular collision to result in a reaction, it must typically hit a target that is much smaller than an atomic diameter, because the channel through the transition state of a typical reaction is quite narrow. If the transverse restoring forces at the transition state are comparable to those of bond angle-bending, the target size will be about 1/10 the size of an atom. Positioning reactants with similar accuracy in 3 dimensions can have the effect of a 1000-fold increase in concentration. Unless a reactant is a single atom, orientation matters, too, and constraining the mutual orientations of reactants also can greatly increase the reaction rate, and hence the inferred effective concentration.
I learned a lot from Thomas Creighton’s book Proteins: Structures and Molecular Properties (enough that I bought the second edition when it came out), and the concept of effective concentration is pervasive in his lucid and quantitative discussion of the topic. With respect to reaction rates, he cites values as high as 105 M for thiol/disulfides reaction in proteins.
Effective concentration, binding, and self assembly
Effective concentration also provides a way to think about how multiple weak interactions can conspire to create strong binding when all the components are properly aligned, for example, in molecular self assembly. To quote Creighton regarding a simple example:
If both interactions are possible simultaneously, the presence of one interaction will increase the effective concentration of the other two groups, in a mutual manner….Consequently, a second simultaneous interaction is more stable than when it is present alone.
Above, I’ve discussed the concept of effective concentration from a kinetic perspective, but when considering stability of binding, it is usually more useful to think in terms of entropy and free energy. Increased stability results from the reduced entropy of a pre-organized structure, as compared to a similar collection of components that would be free to disperse when unbound. Increased concentration and decreased entropy go hand in hand.
Effective concentration and mechanosynthesis
The most basic characteristic of a mechanosynthetically guided process is that it positions reactive molecules adjacent to their intended reaction partners, and away from other potential reaction partners. In the absence of imposed strain or other influences, the increase in the reaction rate at the intended site is a direct consequence of increased effective concentration, and we’ve seen that this can raise rates by many orders of magnitude. The flip side is at least as important, though: When combined with the ability to excluded unbound reactive molecules, mechanically guided synthesis has the great virtue of suppressing side-reactions at unwanted sites by reducing the effective concentration at these sites to what is effectively zero. Molecules that don’t meet won’t react.
This is the key to enabling long sequences of error-free operations and the fabrication of correspondingly complex atomically precise products.
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