Figure 2 illustrates the bimodal effect of G2-NH
2 PAMAM
cis-solution addition on the ionic current through a single PA
63 channel incorporated into planar lipid bilayer membranes. To obtain reliable statistics on G2-NH
2/PA
63 interaction, we performed the single channel measurements in 1 M KCl. A decrease in salt concentration led to a dramatic increase in the blocker lifetimes, suggesting the involvement of the long-range Coulomb interactions. Quantitative analysis of the process at lower, e.g., physiological salt concentrations, proved impossible over the course of our experiments. Previously, the PAMAM dendrimers were reported to be ~100–900 times more effective when added to the
cis-side of the membrane, which is also the side of PA
63 addition [
5]. PA
63 insertion was shown to be almost exclusively unidirectional [
2,
9,
33], with the bud, LF/EF binding part of the channel, facing the
cis-side solution (corresponding to the endosome interior), and the stem part facing the
trans-side solution (corresponding to the cytosol or ILV interior). The single channel current recordings show that, in a manner similar to the cationic β-cyclodextrin [
14] and G1-NH
2 PAMAM dendrimer blockers [
5], the G2-NH
2 inhibitive action is bimodal (
Figure 2A). Firstly, G2-NH
2 addition generates complete but reversible blockages of ion current through a single channel (marked with two blue ovals,
Figure 2A). Frequency of these events increases in a concentration-dependent manner and is a strong function of the applied transmembrane voltage (
Figure 2B). Note:
cis-positive sign of the applied transmembrane voltages corresponds to the inside-positive voltage gradient across endosomal limiting membranes. Secondly, G2-NH
2 addition led to a dramatic increase in the voltage-dependent gating of PA
63 channels (
Figure S2), seen as prolonged closing events (marked with red ovals,
Figure 2A, middle and right). Higher concentrations of G2-NH
2 and higher voltages compared to the ones reported earlier (
KD = (7.2 ± 4.7) × 10
−9 M at
V = 20 mV) in the multichannel systems were needed because of the increased supporting electrolyte concentrations (1 M vs. 0.1 M) that, by electrostatically screening charges on both the blocker and the channel, weakened blocker binding.
The fast reversible current fluctuation induced by G2-NH
2 in the parts of current tracks with excluded voltage-dependent gating can be described as a two-state memoryless Markov process, where both the residence time in the blocked state and the channel lifetime in the unblocked state (the time between blockages) are described by exponential distributions. This is demonstrated by the Lorentzian shape of the power spectral density of G2-NH
2-induced current fluctuations at
f < 1000 Hz (
Figure 2C, spectrum in grey fitted by the smooth blue solid line through the experimental curve). This relatively straightforward kinetic analysis was to a certain extent complicated by a number of factors, namely the two types of complex non-Markovian channel gating described in detail previously [
14,
15]. The first type of gating is induced by the applied voltage that brings the PA
63 channel into a nonconductive state, which seems to be characteristic for β-barrel channels in general [
38]. This voltage dependent gating was especially prominent at
cis-side negative voltages [
33]; thus applied voltages as low as − (10–20) mV led to the prolonged channel closures. The fact that the β-barrel PA
63 channel tends to stay closed when positioned under non-physiological inside-negative voltage gradients, adds fuel to the little rusty but still very interesting debate about the significance [
39] and mechanism [
40] of voltage gating for the unconventional channel [
41] function. Note that while some researchers show that the voltage-dependent β-barrel channel closure represents nothing more than an artifact of bilayer lipid experiments [
42], others report clear evidence of physiological significance of voltage gating in β-barrel channels [
43,
44]. In one way or another, this circumstance has largely limited our ability to collect reliable statistics on channel/blocker binding reaction at negative and high positive voltages, especially because in many cases the dendrimer addition has significantly enhanced the voltage sensitivity of the channel. The second type of PA
63 non-Markov gating is the so-called voltage-independent fast flickering 1/
f noise between the open and completely closed states that was earlier described as a universal intrinsic property of the pore-forming components of AB type toxins, PA
63, C2IIa, and Ib, both at the single [
2,
3,
14,
15] and multi-channel [
8,
9] level. The current noise power spectrum of the non-modified PA
63 channel contains a 1/
f-like voltage-independent [
14,
15] component (
Figure 2C, see the spectrum in green and the corresponding current track (left insert) shown at 0.2 ms time resolution). Even though the 1/
f flickering is not among the immediate points of interests of the current publication, the universality of the 1/
f flickering and the fact that the F427A mutant of PA
63, which lacks the φ-clamp [
7] and therefore A-component translocation functionality, was devoid of the 1/
f noise behavior, deserves to be studied more closely. Within the limits of this study, we had to be very careful to uncouple the 1/
f fast-flickering events and the dendrimer-induced reversible blockages, especially under conditions where the closed time distributions of these events partially overlap. For example, in
Figure 2A (left) we show several relatively long 1/
f flickering events that are still seen even at low, 50 ms time resolution. To quantify kinetic parameters of the G2-NH
2-induced reversible blockages, we primarily used current noise spectral analysis (
Figure 2C) instead of the direct counting of open and closed event durations. The direct counting approach does not allow us to distinguish between open times of the 1/
f noise closures and the dendrimer-induced reversible blockages, because a combined open time distribution for these two processes was single-exponential, which may be explained by the fact that there is only one open state of the channel. The average lifetime of G2-NH
2 in the channel pore (
) and average time between blockages (
) were found correspondingly as
and
, where
is the corner frequency of Lorentzian and
is the probability of finding PA
63 in the blocked state [
45]. Ideally, the probability of the channels being in the blocked state could be directly determined as
, where
is the ion current through the completely open channel, and
is the average ion channel current modified by the blocker. However here, to account for the 1/
f fast flickering, the equation was corrected, assuming independence of these two processes as follows:
, where
is the average current through the PA
63 channel measured in blocker-free solutions [
14]. Note: to determine
and
, the prolonged voltage gating closures (both intrinsic and dendrimer-induced) were excluded from the open and closed states probability analysis.
The second mode of dendrimer-induced current inhibition was hard to describe quantitatively because the blocker-induced channel closures often appeared to be irreversible, lasting for minutes or longer. To reopen the channel, we either had to apply 0 mV or to reverse the voltage sign (shown in
Figure 2A, middle) which did not allow us to collect reliable statistics on kinetic parameters of the second mode of channel blockage. Moreover, as described above, the voltage-induced closures were also recorded in the absence of blocker, and voltage-sensitivity and probability of finding a channel in the closed state varied from channel to channel. However qualitatively, this process evinced all the key characteristics of the voltage-induced gating of β-barrel channels, such as strong voltage dependence, prolonged closures (minutes), and difficulties in reopening channels even when voltage was reduced to zero. Paradoxically, channel reopening was often possible with abrupt second-long pulses of high voltages of opposite sign (marked in
Figure 2A, middle track), that, in turn, also induced voltage dependent closures if applied longer.