Interpretation of 1/f fluctuations in ion conducting membranes

The main objective of this work is to resolve some uncertainties associated with the analysis of conductance fluctuations that exhibit 1/f spectral density. To this end, we derive mathematical conditions under which a discrete summation of Lorentzian functions best approximates a strictly 1/f density over a given frequency range. The intrinsic errors associated with spectral density estimates are considered and used as a constraint to determine the smallest number of optimally chosen Lorentzians required to fit a 1/f-like spectrum in a statistically acceptable manner. The results provide criteria concerning the extent to which mechanisms generating a strictly 1/f spectra may be distinguished from those generating sums of Lorentzian spectra. It is found, in particular, that 1/f-like fluctuation spectra observed in a variety of biological and model membranes may well arise from the summation of a few Lorentzian components having appropriate amplitudes and corner frequencies. Consideration of physically realistic models of ion conductive channels indicates that 1/f-like conductance fluctuation spectra could originate naturally as a direct consequence of thermodynamic constraints upon the coefficients of Lorentzian components.