Multifractal Properties of BK Channel Currents in Human Glioblastoma Cells

Potassium channels play an important physiological role in glioma cells. In particular, voltage- and Ca²⁺-activated large-conductance BK channels (gBK in gliomas) are involved in the intensive growth and extensive migrating behavior of the mentioned tumor cells; thus, they may be considered as a drug target for the therapeutic treatment of glioblastoma. To enable appropriate drug design, molecular mechanisms of gBK channel activation by diverse stimuli should be unraveled as well as the way that the specific conformational states of the channel relate to its functional properties (conducting/nonconducting). There is an open debate about the actual mechanism of BK channel gating, including the question of how the channel proteins undergo a range of conformational transitions when they flicker between nonconducting (functionally closed) and conducting (open) states. The details of channel conformational diffusion ought to have its representation in the properties of the experimental signal that describes the ion-channel activity. Nonlinear methods of analysis of experimental nonstationary series can be useful for observing the changes in the number of channel substates available from geometrical and energetic points of view at given external conditions. In this work, we analyze whether the multifractal properties of the activity of glioblastoma BK channels depend on membrane potential, and which states, conducting or nonconducting, affect the total signal to a larger extent. With this aim, we carried out patch-clamp experiments at different levels of membrane hyper- and depolarization. The obtained time series of single channel currents were analyzed using the multifractal detrended fluctuation analysis (MFDFA) method in a standard form and incorporating focus-based multifractal (FMF) formalism. Thus, we show the applicability of a modified MFDFA technique in the analysis of an experimental patch-clamp time series. The obtained results suggest that membrane potential strongly affects the conformational space of the gBK channel proteins and the considered process has nonlinear multifractal characteristics. These properties are the inherent features of the analyzed signals due to the fact that the main tendencies vanish after shuffling the data.