Conductance recording of single pores
Fluctuations in membrane conductance were induced by applying a voltage step of sufficiently high amplitude (more than 100-150 mV). As described in earlier studies (Abidor et al., 1979
), before the onset of conductance fluctuations, membrane current remained on the background level during some lag-time. We have chosen the voltage applied to be high enough to cause the conductance changes but low enough to provide us with minutes of the conductance recording before the onset of inevitable BLM rupture. For BLMs and membrane patches applied voltages were in the ranges of 150-400 mV and 250-550 mV, respectively. Fig. 1 presents the dependence of the lag-time on voltage amplitude applied to membrane patches.
Most of the observed changes in conductance were abrupt transitions from one conductance level to another. In Fig. 2 the representative recordings of conductance fluctuations are presented. The abruptness of the transitions and the closeness of the initial and final levels of conductance suggest that these fluctuations reflect opening and closure of single lipid pores. Besides the fluctuations presented above, in some experiments a slow drift of the mean conductance accompanied the abrupt transitions between different conductance levels. This slow drift of conductance, which complicated the analysis, was much less frequent for membrane patches than for BLMs. In addition, due to the small area, membrane patches allowed better amplitude and time resolution. Because of the mentioned advantages of membrane patches, most of the quantitative data presented below were obtained for this experimental model.
Analysis of records shows that the amplitude of transition varied in a rather broad interval from 150 to 1500 pS. A histogram of amplitude distribution for the experiments on membrane patches at 450 mV is shown in Fig. 3. It can be fitted by a Gaussian distribution function with a mean value of ~450 pS and dispersion of ~250 pS. Both mean value and dispersion did not significantly depend on membrane voltage in the range of 250-450 mV (Fig. 4). An all-points amplitude histogram of conductance fluctuations observed on BLMs (Fig. 5) is similar to those obtained for experiments on membrane patches (Fig. 3). Importantly, mean amplitudes of the conductance fluctuations were similar for membrane patches and BLMs. Because the area of a BLM was ~10,000 times larger than that of a membrane patch, observed fluctuations most probably reflected opening and closure of single lipid pores, rather than some changes in the integral conductivity of the membrane (see also Chernomordik and Abidor, 1980). The existence of the distinct maximum in the amplitude distribution implies that lipid pores formed in the membrane by electric field are metastable. The existence of long-lived conductance steps with duration of up to hundreds of milliseconds further confirmed the metastable character of lipid pores.
Conductance of 450 pS corresponds to ~1-nm radius of the cylindrical pore as estimated by taking into account the access resistance of the pore and assuming bilayer thickness and conductance of the solution in the pore lumen to be 5 nm and 0.01 S/cm, respectively. A pore of such radius can be expected to restrict passage of large ions such as N-methyl-D-glucamine (NMDG+, 1.1 × 0.5-nm rod) and glutamate ion (0.9 × 0.4-nm rod). (The sizes of the ions were estimated using ChemWindow 6.0, BioRad (Richmond, CA) software.) Indeed, the mean amplitude of conductance fluctuations decreased from ~450 pS to ~100 pS when K+ and Cl
were replaced by NMDG+ and glutamate ion. This decrease was significantly more profound than the 1.5 times decrease in the bulk solution conductance assayed as conductivity of micropipettes filled with different solutes. Assuming that the change of solute does not affect pore size, these data can be interpreted as an indication that the radius of the voltage-induced pore is close to the size of the large ions and thus restricts their passage.
Analysis of conductance recordings allowed us to evaluate not only the size but also lifetimes of the voltage-induced pores. The transition to a new level of conductance was often followed by a return back to the initial conductance within a few milliseconds. The mean duration of such conductance spikes appeared to be independent of the voltage (3.0 ± 0.8, 1.2 ± 0.1, 2.5 ± 0.3, and 5.7 ± 0.8 ms for 250, 350, 400, and 450 mV, respectively; n > 1000 for each voltage). As already mentioned, besides short-lived spikes, we also observed another type of electrical activity, conductance steps. In this case, after abrupt establishing of a new conductance level, this level was stable for up to several hundred milliseconds.
Reversible changes in conductance induced by electric field were observed not only on DPhPC membranes but also on membranes made of azolectin, DPhPC/diphytanoyl phosphatidylethanolamine mixtures 2:1 and 1:1, and bacterial phosphatidylethanolamine with 3 mol % lauroyl lysophosphatidylcholine. However, the thorough investigation of the influence of the lipid composition on the properties of the pores was complicated by the differences in voltage amplitudes required for inducing pore formation in membranes of different lipid compositions.
Nonconductive pre-pores
One of the important features of conductance records under high voltage was the existence of the bursts of activity with multiple consecutive spikes coming one after another separated by short gaps, tg 
1 ms (mean value for 250 mV is 2.0 ± 0.4; n > 100), with the background conductance. The mean value of tg did not depend on the voltage applied. In many records, the bursts of electrical activity were separated by rather long (compared with tg) intervals during which membrane conductance remained at the background level (Fig. 6). tg was also much shorter than the lag-time before the onset of electrical activity, which in the experiments with BLMs had a mean value of 1.9 ± 3.8 s (n = 15) for 300 mV and decreased with the voltage increase.
Our observation that conductance spikes usually come in bursts rather than singly implies that there is more than one closed or shut state. This important conclusion was substantiated by statistical analysis. We tested whether apparent clustering of short-lived closed states in bursts of activity occurs by chance in a random series of closed states, or indeed reflects a correlation between adjacent closed states. To test for correlation we analyzed the representative conductance record obtained for BLMs clamped at 180 mV using a runs test (Colquhoun and Sigworth, 1995). First we divided all closed states (which were determined as states with conductance within 1.5 times of background variance) by their duration into two groups containing either short-lived (duration = " align="bottom" src="http://www.biophysj.org/math/12pt/normal/ge.gif" /> 20 ms) states. The number of runs Nr (i.e., uninterrupted sequences of the closed states of the same type) was counted. We then asked whether runs occur with the frequency expected for independent events or, for instance, short-lived closed states tend to follow each other, as expected if the closed state between the bursts of spikes is different from the closed state within the burst. The test statistic, which characterizes the randomness of the series of the runs, is z = [Nr 
E(Nr)]/[var(Nr)]1/2, where E(Nr) and var(Nr) stand for the mean and variance of Nr (Colquhoun and Sigworth, 1995). The value of z for our record, |z| = 60, was much higher than the value of 
2 expected for the random distribution, indicating that the probability for clustered closed states in the analyzed recording to occur by chance is less than 0.001. Replacing the 20-ms threshold duration of the closed state used in the analysis with values within the range from 5 to 50 ms did not change the conclusion: |z| remained much higher than 2.
The histogram of the number of closed states in bursts presented in Fig. 7 confirms that the number of longer bursts containing many consecutive short-lived closed states is increased in comparison with that generated by computer simulation for independent events (shown by solid line).
These results indicated that the series of the conductance spikes within a burst reflect the transitions between 1) a conductive, open pore and 2) a closed precursor or pre-pore, which differs from the intact membrane by an increased probability to form open pores. Note that our operational definition of the pre-pore state involves reopening of the pore within the same burst of electric activity. Thus, we cannot exclude the possibility that the first opening of a pore in the burst does not proceed through the pre-pore state, which in this case forms only upon resealing of the existing pore.
The existence of the pre-pore state was further substantiated by the experiments with two consecutive pulses of high voltage (250-500 mV) separated by an inter-pulse interval (varied from 20 ms to 5 s) at 50 mV. Changes in the conductance for different inter-pulse intervals (50 ms and 1 s) are shown on Fig. 8. A voltage drop at the end of the first step resulted in a rapid ( relaxation of membrane conductance toward background level. During the inter-pulse interval, conductance remained at the background level. The conductance behavior during the second voltage step depended on the duration of the inter-pulse interval. In the case of rather short intervals ( voltage pulse resulted in an immediate upsurge in conductance; i.e., there was no lag-time detectable with our 1-ms time resolution (Fig. 8 a). In the case of longer (>500-ms) inter-pulse intervals, lag-time observed in the beginning of the second voltage step was similar to the response observed during the first step (Fig. 8 b). Thus, although conductance between pulses was the same as in the initial state, the membrane "remembered" for some time the previous pulse. Taking into account the size of our pores (~1.0 nm, see above), we do not expect them to demonstrate the non-ohmic behavior described in Glaser et al. (1988). Thus, our data indicate that after the end of the first pulse the open pore quickly turns into some non-conductive but activated state (pre-pore), which is ready to reopen in response to the second pulse. The pre-pore is a metastable structure and without a second pulse it reseals with a relaxation time of the order of 100-1000 ms. Note that this type of experiment (Fig. 8) is feasible only for relatively long-lived conductive pores (conductance steps, see above).
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