pH fluctuations in unilamellar vesicles

pH fluctuations in small unilamellar vesicles (SUV) are theoretically estimated. We determine that these fluctuations are dependent on macroscopic variables such as pH, pK(a), buffer group concentration and surface electrical potential. Based on a previously reported definition of buffer electrical capacitance (Procopio and Fornes, Phys. Rev. E, 1995, 51, 829) an equation is derived which relates the pH fluctuation, the buffering power and the SUV size. We also derived an equation for the mean square charge thermal fluctuation using the fluctuation-dissipation theorem which coincides with that independently obtained by Kirkwood and Shumaker (Proc. Natl. Acad. Sci., 1952, 38, 863) using mechanical statistical methods. From our results it is inferred that measurement of pH in small systems has to be performed near the pK of the buffer groups in order that the fluctuational errors be minimized. We show that pH fluctuations diminish with increasing the size of the SUV and the predicted pH fluctuations decrease as the surface potential becomes less negative as a consequence of decreasing density of charged groups in the inner vesicular surface. It is predicted that measurable effects will appear on the fluorescence detection due to protonic fluctuations close to the pH sensing region of the probes.