The final frontier of pH and the undiscovered country beyond

The comparison of volumes of cells and subcellular structures with the pH values reported for them leads to a conflict with the definition of the pH scale. The pH scale is based on the ionic product of water, K(w) = [H(+)]×[OH(-)].We used K(w) [in a reversed way] to calculate the number of undissociated H(2)O molecules required by this equilibrium constant to yield at least one of its daughter ions, H(+) or OH(-) at a given pH. In this way we obtained a formula that relates pH to the minimal volume V(pH) required to provide a physical meaning to K(w), V(pH)=10(pH-pK(w/2) x 10(pK(w/2)/N(A) (where N(A) is Avogadro's number). For example, at pH 7 (neutral at 25°C) V(pH) =16.6 aL. Any deviation from neutral pH results in a larger V(pH) value. Our results indicate that many subcellular structures, including coated vesicles and lysosomes, are too small to contain free H(+) ions at equilibrium, thus the definition of pH based on K(w) is no longer valid. Larger subcellular structures, such as mitochondria, apparently contain only a few free H(+) ions. These results indicate that pH fails to describe intracellular conditions, and that water appears to be dissociated too weakly to provide free H(+) ions as a general source for biochemical reactions. Consequences of this finding are discussed.