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+]x[OH-]. We used K-w [in a reversed way] to calculate the number of undissociated H2O 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(vertical bar pH) - (pKw/2 vertical bar) x 10(pKw/2)/N-A (where N-A is Avogadro's number). For example, at pH 7 (neutral at 25 degrees 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vesicles and lysosomes, are too small to contain free H+ ions at equilibrium, thus the definition of pH based on K-w is no longer valid.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.