Abstract
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 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 VpH required to provide a physical meaning to K w, (where N A is Avogadro’s number). For example, at pH 7 (neutral at 25°C) VpH = 16.6 aL. Any deviation from neutral pH results in a larger VpH 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vesicles and lysosomes, are too small to contain free H+ ions at equilibrium, thus the definition of pH based on K w is no longer valid.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.
Highlights
Our results indicate that many subcellular structures, including coated vesicles and lysosomes, are too small to contain free H+ ions at equilibrium, the definition of pH based on Kw is no longer valid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
The pH scale is based on the thermodynamic equilibrium of the water dissociation process, in simplest terms: H2O ? H+ + OH2, with a dissociation constant given by Eq 1
Summary
Mitochondria have volumes of ca. fL, (90% in mitochondrial matrix, and 10% in the intermembrane space), lysosomes of about 30 aL, and the smallest of them, coated vesicles, of about 30 to 800 zL (10221 L) [2,3,4]. In a coated vesicle we find from 76105 to 26107 water molecules, in a lysosome 76108, and in an average mitochondrion 2.361010 In these organelles, pH values of 6.8 for the mitochondrial intermembrane space, 8.0–8.1 for the matrix, 4–5 for lysosomes, and 5–7 for coated vesicles have been reported [5]. PH values of 6.8 for the mitochondrial intermembrane space, 8.0–8.1 for the matrix, 4–5 for lysosomes, and 5–7 for coated vesicles have been reported [5] These values have been accepted in the biological community and are hardly ever disputed. We examine the physical meaning of these pH values
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