Effective Molarity

 A reaction or interaction between two different molecules in dilute solution is relatively straightforward and is governed by their concentrations in that solution, plus the appropriate rate or equilibrium constant. In more complex situations, however, the situation may differ from that expected from the bulk concentrations of two reactants. If they attract each other, for example by electrostatic or hydrophobic interactions, their effective molarities will be greater than their bulk concentrations. Similarly, a nonpolar reagent that partitions into the interiors of membranes, or any reagent that concentrates in one organelle or compartment, will react there at a much greater rate than if it were dispersed evenly throughout the system.

 A special situation occurs when two reactive or interactive groups are part of the same macromolecule, such as a protein or nucleic acid. The rate constant for reaction between two such groups, or their association constant, might be known when they are individual molecules, when the observed rate or equilibrium is given by this constant times their respective concentrations, but for an intramolecular reaction or interaction, their concentration within the solution is irrelevant. Instead, it is the effective concentration of the two groups within the macromolecule that is important for the intramolecular interaction. The effective molarity will depend upon the structure of the macromolecule, in particular the extent to which it brings the two reactants together or keeps them apart, plus the environment in which the two groups are kept. The effective molarity for the intramolecular reaction will be essentially zero if the macromolecular structure keeps the two groups

apart (of course, groups on different molecules can still react, and their bulk concentrations still govern this intermolecular reaction). At the other extreme, when the macromolecular structure keeps the two groups in the correct proximity and orientation for reaction, their effective molarity can be extremely large, up to 10 ¹⁰ M, concentrations that are not feasible with two independent molecules. Such values are predicted by theoretical considerations (1) and are also observed experimentally, from the ratio of the rate or equilibrium constants for the same reaction when the groups are on the same molecule and on separate molecules (2).

The large effective concentrations that are observed are believed to be due primarily to the much smaller loss of entropy that occurs when two groups on the same molecule interact. Two independent molecules that interact in solution must lose substantial translational and rotational entropy when they interact, depending upon the rigidity of the interaction. Two groups attached to the same macromolecule have already lost varying degrees of this entropy. In the ideal case, when the two reactive groups are held by the macromolecular structure in precisely the correct position for them to interact, so that there is no change in their entropy, the maximum effect and the maximum effective molarity are observed. Of course, other considerations also apply, such as if the environment of the groups is different in the macromolecule, or if they are strained and this strain is relieved upon their reaction.

Whatever the exact reason for the large effective molarities that can be measured in macromolecules, this has important consequences for understanding the stabilities of the folded structures of macromolecules. For example, the question of the role of hydrogen bonds in stabilizing protein structures has been very controversial. One might expect a priori that hydrogen bonds would contribute nothing to the net stability because any hydrogen bonds in the folded state would be replaced by equivalent hydrogen bonds, with the water, in the unfolded protein. But the two cases differ because the hydrogen bonds in the folded state are intramolecular, whereas those with the solvent are intermolecular. If the hydrogen bonding groups have effective molarities in the folded state greater than the solvent concentration, 55 M for water, the hydrogen bonds in the folded state will be more stable than those in the unfolded state, and they will stabilize the folded conformation. Another way of thinking about this is to consider the increased entropy of the water molecules that are liberated when the protein folds and forms intramolecular hydrogen bonds. Effective molarities of up to 10 5 M have been measured between cysteine residues in forming disulfide bonds during protein folding (3). Consequently, it is not surprising that folded macromolecular structures can be stabilized by many intramolecular interactions that individually are very weak in an unfolded conformation, but occur simultaneously and cooperate to generate a folded conformation (4). The large effective molarities of reactive groups in the active sites of enzymes are also important for explaining enzymatic catalysis.

References

1. M. I. Page and W. P. Jencks (1971) Proc. Natl. Acad. Sci. USA 68, 1678–1683. 

2. A. J. Kirby (1980) Adv. Phys. Org. Chem. 17, 183–278. 

3.  T. E. Creighton and D. P. Goldenberg (1984) J. Mol. Biol. 179, 497–526. 

4. T. E. Creighton (1983) Biopolymers 22, 49–58.