The cross-correlation-based analysis to digest the conformational dynamics of the mitoBK channels in terms of their modulation by flavonoids

Abstract

The activity of mitochondrial large-conductance voltage- and [Formula: see text]-activated [Formula: see text] channels (mitoBK) is regulated by a number of biochemical factors, including flavonoids. In particular, naringenin (Nar) and quercetin (Que) reached reasonable scientific attention due to their well-pronounced channel-activating effects. The open-reinforcing outcomes of Nar and Que on the mitoBK channel gating have been already reported. Nevertheless, the molecular picture of the corresponding channel-ligand interactions remains still to be revealed. In this work, we investigate the effects of the Nar and Que on the conformational dynamics of the mitoBK channel. In this aim, the cross-correlation-based analysis of the single-channel signals recorded by the patch-clamp method is performed. The obtained results in the form of phase space diagrams enable us to visually monitor the effects exerted by the considered flavonoids at the level of temporal characteristics of repetitive sequences of channel conformations. It turns out that the mitoBK channel activation by naringenin and quercetin does not lead to the change in the number of clusters within the phase space diagrams, which can be related to the constant number of available channel macroconformations regardless of the flavonoid administration. The localization and occupancy of the clusters of cross-correlated sequences suggest that mitoBK channel stimulation by flavonoids affects the relative stability of channel conformations and the kinetics of switching between them. For most clusters, greater net effects are observed in terms of quercetin administration in comparison with naringenin. It indicates stronger channel interaction with Que than Nar.

Keywords: Channel gating dynamics; Conformational dynamics; Cross-correlations; Dwell-time series; Flavonoids; MitoBK channels.

Fig. 1

Chemical structures of the flavonoids, including the general structure (left), quercetin (middle) and naringenin (right)

Fig. 2

Exemplary kinetic scheme representing channel gating. The substates $O_i$ and $C_i$ denote the possible open and closed conformations, respectively. The arrows stand for the possible transitions between the channel substates

Fig. 3

The phase space representation of the clusters of the cross-correlated O–C–O (top) and C–O–C (bottom) sequences at $R_0$ = 0.75 threshold, describing channel’s gating dynamics induced by the naringenin and quercetin binding, and their individual control groups. Each cluster is encircled by a dashed line and numbered. The coordinates are represented by consecutive dwell-times (${\tau }_i$). The position of circles represent the average sequence of dwell-times forming a given cluster. The size of circles are proportional to the normalized cardinality

Fig. 4

The distances between the centers of the sets of cross-correlated O–C–O sequences obtained at mitoBK channel stimulation by naringenin (Nar) and quercetin (Que) and the corresponding controls. The presented data correspond to the clusters presented and numbered in Fig. 3 (top). Each cluster is tagged by its average occupancy (VERY LOW <10%, LOW 10–35%, MEDIUM >35%). The presented errors on the bar chart are calculated as the standard error of the mean. The statistical significance calculated for $\mathrm{\Delta }\tau$s obtained at different concentrations of a given flavonoid (3 and 10 $\mu$M) via non-parametric Mann Whitney U test is also included in the graphs. For the statistically significant results at the level of $\alpha =0.05$, the results are marked with the asterisks

Fig. 5

The distances between the centers of the sets of cross-correlated C–O–C sequences obtained at mitoBK channel stimulation by naringenin (Nar) and quercetin (Que) and the corresponding controls. The presented data correspond to the clusters presented and numbered in Fig. 3 (bottom). Each cluster is tagged by its average occupancy (VERY LOW <10%, LOW 10–35%, MEDIUM 35–55%, HIGH >55%). The presented errors on the bar chart are calculated as the standard error of the mean. The statistical significance calculated for $\mathrm{\Delta }\tau$s obtained at different concentrations of a given flavonoid (3 and 10 $\mu$M) via non-parametric Mann Whitney U test is also included in the graphs. For the statistically significant results at the level of $\alpha =0.05$, the results are marked with the asterisks

Fig. 6

The possible energetic picture of the impact of flavonoid binding (naringenin—Nar and quercetin—Que) on the activation energy ($U(b)-U(a)$) of the conformational change between the most frequently occupied open (O) and closed (C) substates of the mitoBK channel, according to the Kramers Reaction Rate theory. Reaction coordinates “a” and “b” denote the conformation corresponding to the energetic minimum and the potential barrier that separates it from the next state in sequence, respectively. On the left, the energetic changes corresponding to the open-closed switching are depicted. On the right, the changes in energy corresponding to the conformational change from closed to open. Note, the reference potential is unknown—we can infer only about the changes in barrier height

Fig. 7

The values of the $<dis{t}_{\tau }>$ parameter for the C–O–C and O–C–O clusters obtained at mitoBK channel stimulation by flavonoids (Nar/Que) and their controls. The presented bar chart errors were estimated by the formula of the total differential

Fig. 8

The phase space representation of the clusters of the O–C–O (top) and C–O–C (bottom) sequences describing channel’s conformational dynamics induced by the naringenin and quercetin binding and their common control group. Clusters are encircled and numbered. The coordinates are represented by the dwell-times (${\tau }_i$) forming the cross-correlated sequences (at $R_0$ = 0.75) belonging to a given cluster. The size of circles are proportional to the normalized cardinality