Tunable electromechanical nanopore trap reveals populations of peripheral membrane protein binding conformations

Abstract

We demonstrate that a naturally occurring nanopore of the mitochondrion, the voltage-dependent anion channel (VDAC), can be used to electromechanically trap and interrogate proteins bound to a lipid surface at the single-molecule level. Electromechanically probing α-synuclein (αSyn), an intrinsically disordered neuronal protein intimately associated with Parkinson’s pathology, reveals wide variation in the time required for individual proteins to unbind from the same membrane surface. The observed distributions of unbinding times span up to three orders of magnitude and depend strongly on the lipid composition of the membrane; surprisingly, lipid membranes to which αSyn binds weakly are most likely to contain sub-populations in which unbinding is very slow. We conclude that unbinding of αSyn from the membrane surface depends not only on membrane binding affinity, but also on the conformation adopted by an individual αSyn molecule on the membrane surface.

The capture and analysis of charged biomolecules by nanopores has revolutionized single-molecule sensing. A nanopore is a small hole in a thin membrane separating two electrically isolated reservoirs filled with electrolyte solution. In a conventional nanopore sensing experiment, a transmembrane potential is applied across the membrane, creating a small ionic current through the nanopore. Often, the transmembrane potential is also responsible for attracting, capturing, and driving the analyte through the interior of the nanopore. Modulations in the ionic current in the presence of large analyte biomolecules such as polynucleic acids or proteins contain information about their structure and dynamics. The membrane can be constructed from either solid state materials or lipid membranes; in the latter case, the nanopore is often a naturally occurring or engineered ion channel. While the primary application of nanopores remains the rapid sequencing of polynucleic acids, proteins and their vast array of known properties and interactions are of continued interest. In this context, nanopores have been used for low-resolution analysis of conformation, shape, and tumbling dynamics,¹ analysis of post-translational modifications and other single-residue alterations,^2–4 and protein fingerprinting. Active development is underway to apply nanopore-based sensing to protein sequencing and proteomic analysis.^5,6

Biological nanopores are embedded in lipid membranes and are thus in close proximity to other membrane-associated proteins in, or transiently interacting with, the membranes. As a result of their strategic location in vivo at the boundaries of cells and their compartments, membrane-associated proteins play an outsized role in how cells process and respond to their environment. While membrane proteins are estimated to constitute only about 20% of the human proteome,⁷ they represent about 70% of modern drug targets.⁸ Their confinement to the crowded two-dimensional membrane surface, however, limits the number of these proteins found in cells and makes them difficult to study by conventional solution-based biochemical and biophysical techniques in which their natural membrane environment is not present.

Peripheral membrane proteins are a subclass of membrane-associated proteins that are only transiently bound to the lipid surface. This property allows these molecules to take advantage both of the enhancement to interaction rate with other membrane proteins that arises from localization on the membrane surface, and, when unbound, of a higher rate of transport through solution. The multicomponent nature of lipid-mediated protein-protein interactions, the transience of the peripheral membrane proteins on lipid membranes, and the differences in their structural and biochemical properties in their membrane-bound and solvated states,^9–11 all complicate the study of peripheral membrane proteins. Dynamical biophysical techniques that allow probing the proteins, or their effects on lipid membranes, in real time and under a wide range of conditions are essential to understanding these proteins and their biological roles.

In this paper, we will demonstrate the use of a single voltage-biased biological nanopore embedded in a lipid bilayer membrane to observe the capture and membrane detachment of intrinsically disordered peripheral membrane proteins or polypeptides at the single molecule level. We will show that the voltage and time scales at which membrane detachment occurs depend strongly on the lipid composition. The single-molecule nature of this technique reveals a wide variation in the time required for individual proteins to unbind from the same membrane surface, and multiple characteristic dissociation times are required to describe molecules on the same lipid surface. Analysis using energy landscape modeling shows that the observed lipid-dependent variation can be attributed to two physical parameters: the energy of membrane dissociation, and the penetration depth, or the length of polypeptide that freely penetrates the nanopore trap before being impeded by the membrane anchor. We conclude that the tunable electromechanical nanopore trap reveals a multiplicity of protein binding conformations, each with unique thermodynamic and kinetic signatures, that are highly dependent on the composition of the lipid membrane surface.

RESULTS

Determination of dissociation rates using the VDAC nanopore

A schematic of the strategy for single-molecule determination of the dissociation rate of a peripheral membrane protein is shown in Figure 1. A single nanopore, in this case recombinant murine voltage-dependent anion channel isoform 1 (VDAC), is reconstituted (see Methods) into a lipid bilayer membrane of the desired lipid composition (Figure 1A). VDAC is a 19-strand beta-barrel, weakly anion selective channel that is primarily responsible for transport of multivalent metabolites across the mitochondrial outer membrane (MOM). In vitro, VDAC has been shown to be very sensitive to charged polyanionic biomolecules, such as the disordered C-terminal domain of tubulin.^12,13 The membrane separates two reservoirs filled with 1 M KCl (M = mol/L) buffered to pH 7.4 with 5 mM HEPES. A transmembrane voltage $V$ is applied using external electronics coupled to the electrolyte-filled reservoirs using Ag/AgCl electrodes. The ionic current $I\left(t\right)$ is continuously recorded. Under these conditions the channel conductance is approximately 4 nS.¹⁴

Figure 1.

Schematic of the electromechanical nanopore trapping process. (A) A VDAC nanopore is reconstituted into a lipid membrane and subjected to a transmembrane potential $V$, setting up an ionic current $I\left(t\right)$ through the nanopore. (B) The peripheral membrane protein α-synuclein (αSyn) has a diblock copolymer-type structure comprising a charged domain and a net neutral membrane binding domain. (C) Schematic of the complex interactions between membrane-bound αSyn and the VDAC nanopore. The charged domain of αSyn is captured by the (negative) transmembrane potential and remains trapped by the opposing action of the electrostatic and mechanical membrane anchoring forces. Eventually it escapes by one of two pathways: (1) retraction from the pore, with characteristic time ${\tau }_{ret};$ or (2) membrane dissociation followed by translocation through the pore, with total characteristic time ${\tau }_{trans}$. Translocation is rate limited by the membrane dissociation process, which occurs with characteristic time ${\tau }_d$, so ${\tau }_{trans}\approx {\tau }_d$. Processes corresponding to escape and capture are denoted by * and †, respectively. (D) $I\left(t\right)$ directly reports on whether an αSyn molecule is trapped in the nanopore. Abrupt changes in the ionic current corresponding to escape and capture processes are marked with the same symbols as in (C). The duration of a single blockage event is ${\tau }_b$. (E) At a constant $V$, distributions of many single molecule observations of ${\tau }_b$ are plotted on a logarithmic time axis. The curves shown are single exponential functions with characteristic escape times ${\tau }_{off}$; more than one can be present and are revealed by interrogating individual molecules. (F) The $V$-dependence of ${\tau }_{off}$ depends sensitively on the balance between ${\tau }_{ret}$ and ${\tau }_{trans}$ and reveals the underlying dynamics. The average retraction time ${\tau }_{ret}$ scales exponentially with $V$ and is shown as the dashed red “retraction line”. Above a transition voltage $V^{*},\mathrm{ }{\tau }_{ret}>{\tau }_{trans}$, translocation dominates, and ${\tau }_{off}\left(V\right)$ deviates from the retraction line.

As a model peripheral membrane protein, we choose α-synuclein (αSyn), a 140-residue intrinsically disordered protein of keen contemporary interest due to its role in the pathology of Parkinson disease.¹⁵ αSyn has a diblock copolymer-like structure (Figure 1B), with a 45-residue polyanionic C-terminal domain that carries 15 negative elementary charges on the last 37 residues; the preceding 95 residues are nearly net neutral and are responsible for membrane binding.¹⁶ The membrane binding domain can adopt an α-helical structure on membranes containing anionic or strongly non-lamellar lipids,^16–18 but remains disordered when bound to a wide range of other lipids.¹⁹

The dynamical motion of αSyn in the VDAC nanopore has been extensively characterized and is briefly summarized here.^4,20–22 When αSyn is added to one of the reservoirs contacting the VDAC nanopore, it binds to the membrane surface (Figure 1C). If the voltage has the correct polarity (in this case negative from the side of αSyn addition), the C-terminal domain is then captured into the VDAC nanopore, causing a decrease in the magnitude of the ionic current (shown by † in Figures 1C–D). The anchoring effect of the membrane binding domain prevents the αSyn molecule from immediately passing through the nanopore, or “translocating.” Instead, the αSyn molecule stays in the nanopore trap until the C-terminal domain “retracts” (withdraws from the nanopore, driven by stochastic thermal motion), or the membrane anchor dissociates from the membrane surface, allowing the translocation process to proceed.

Either retraction or translocation, marked with * in Figures 1C–D, restore the ionic current to its open pore level. The total trapping duration, from capture to release, is ${\tau }_b$ (Figure 1D). By observing many single molecules of αSyn, distributions of ${\tau }_b$ are constructed (Figure 1E). When the distribution is consistent with a single exponential distribution characteristic of escape over a high free energy barrier, the single characteristic escape time is ${\tau }_{off}^{(1)}=<{\tau }_b>$, where the brackets denote an average over individual observations. Otherwise, additional characteristic times $({\tau }_{off}^{\left(2\right)},{\tau }_{off}^{\left(3\right)},\dots )$ may be required to describe the distribution. This has previously been observed with mixtures of polypeptides.¹²

In general, the retraction and translocation processes have different characteristic times, labeled ${\tau }_{ret}$ and ${\tau }_{trans}$, respectively. The retraction process involves escape over an energy barrier that is largely electrostatic in nature and thus increases linearly with $V$. As a result, ${\tau }_{ret}\left(V\right)~\mathrm{e}\mathrm{x}\mathrm{p}\left(\left|V\right|\right)$. This is shown as the dashed line on Figure 1F and is denoted the “retraction line”. If translocation is impaired, e.g. by a large globular membrane binding domain that cannot pass through the nanopore,¹² this exponential dependence allows many orders of magnitude in ${\tau }_{ret}$ to be explored with modest changes in $V$.

The translocation time scale ${\tau }_{trans}\left(V\right)$ combines the membrane dissociation time scale and the transit time of αSyn through the nanopore after dissociation. Note that both processes may be voltage-dependent, particularly if membrane binding is destabilized by the tension applied to the αSyn by the transmembrane potential. Indeed, ${\tau }_{trans}\left(V\right)$ is observed to decrease with $\left|V\right|$.²¹ In electrolyte gradient experiments, the average transit time was measured to be ~ 0.4 ms.²² Thus, for ${\tau }_{trans}\left(V\right)\gtrsim 1 \mathrm{m}\mathrm{s}$, membrane dissociation is the rate limiting step of translocation, and ${\tau }_{trans}\left(V\right)\approx {\tau }_d\left(V\right)$, where ${\tau }_d\left(V\right)$ is the average time of αSyn dissociation from the membrane.

The probability that an αSyn molecule translocates before retraction occurs is

$$P_{\mathit{trans}}(V)=\frac{{\tau }_{\mathit{ret}}(V)}{{\tau }_{\mathit{ret}}(V)+{\tau }_{\mathit{trans}}(V)},$$ (1)

while the average escape time is given by

$${\tau }_{\mathit{off}}(V)=P_{\mathit{trans}}(V){\tau }_{\mathit{trans}(V)}+\left(1-P_{\mathit{trans}}(V)\right){\tau }_{\mathit{ret}}(V).$$ (2)

As shown in Figure 1F, the different voltage-dependences of ${\tau }_{ret}\left(V\right)$ and ${\tau }_{trans}\left(V\right)$ lead to a biphasic behavior of ${\tau }_{off}\left(V\right)$ characterized by a crossover potential $V^{*}$ at the maximum observed escape time, ${\tau }_{off}\left(V^{*}\right).$

Off-rates of αSyn-VDAC interaction in the membranes of different lipid compositions

The lipids used for bilayer membranes in this study span a wide range of lipid headgroup chemistries. We varied both charge and the propensity of the lipid headgroups to form lamellar bilayer structures. The particular headgroup choices were focused on lipids that are common in the mitochondrial membranes in which VDAC is found, as well as anionic and nonlamellar lipid species to which αSyn preferentially binds.^17,23 The mammalian MOM is characterized by a high level of phosphatidylcholine (PC) and phosphatidylethanolamine (PE), 55 and 30%, respectively, and by up to ~15% of anionic lipids, mainly phosphatidylinositol (PI).²⁴ Here we use the lipid compositions that closely mimic the high PC (DOPC) and PE (DOPE) content of MOM, along with 50% of anionic phosphoglycerol (DOPG). The positively charged synthetic lipid dioleoyl-trimethylammonium-propane (DOTAP) was chosen as an antipode of DOPG to study the effect of lipid charge on αSyn-VDAC interaction. Dioleoyl acyl chains were used uniformly to isolate the effect of the lipid headgroups.

Figures 2A–C show representative segments of ionic current recordings from a single VDAC channel in the presence of 10 nM αSyn on membranes of three different lipid compositions: anionic DOPG/DOPC/DOPE (2:1:1) (2PG/PC/PE) (A), neutral DOPC/DOPE (1:1) (PC/PE) (B), and cationic DOTAP/DOPC/DOPE (2:1:1) (2TAP/PC/PE) (C). The blockage times τ_b, indicated by arrows in Fig. 2A–C, visibly depend on lipid charge, with long-lasting blockage events, labeled ${\tau }_b^{\left(2\right)}$, appearing in the cationic 2TAP/PC/PE (Fig. 2C) and neutral PC/PE membranes (Fig. 2B). At the same time, number of blockage events decreases from anionic to neutral to cationic membranes (Fig. 2A–C) as was previously shown.²⁵

Figure 2.

Kinetics of VDAC blockage by αSyn strongly depend on membrane lipid composition. (A, B, C) Representative current records of VDAC single-channels reconstituted into planar membranes formed from lipid mixtures of 2PG/PC/PE (A), PC/PE (B), and 2TAP/PC/PE (C) in the presence of 10 nM of αSyn added to the cis compartment and observed at −37.5 mV of applied voltage. Wide variation in blockage times is observed for a single lipid composition; red arrows indicate short blockage times, ${\tau }_b^{\left(1\right)}$, observed in all three membranes, while black arrows indicate the long-lasting blockage times, ${\tau }_b^{\left(2\right)}$, observed only in PC/PE (B) and 2TAP/PC/PE (C) membranes but absent in 2PG/PC/PE (A). Horizontal dotted lines indicate VDAC open and blocked by αSyn states; dashed lines indicate zero current. Channel traces were digitally filtered using a 5 kHz lowpass Bessel filter for presentation. The membrane-bathing solution contained 1 M KCl buffered by 5 mM HEPES at pH 7.4. (D, E, F) Representative log-binned distributions of the blockage times in 2PG/PC/PE (D), PC/PE (E), and 2TAP/PC/PE (F) membranes obtained at three different voltages on each membrane. In anionic 2PG/PC/PE membranes (D), distributions of blockage times are well described by a single exponential function (solid lines) at all voltages with characteristic times ${\tau }_{off}^{\left(1\right)}\mathrm{ }=<{\tau }_b^{\left(1\right)}>$ indicated by red arrows. In neutral PC/PE membranes (E) a second, longer component of blockage time, ${\tau }_{off}^{\left(2\right)}$, indicated by black arrows, appears at voltages > 32.5 mV. Solid lines in (E, F) are fits to the sum of two exponential functions of ${\tau }_b$ histograms with characteristic times of ${\tau }_{off}^{\left(1\right)}$ and ${\tau }_{off}^{\left(2\right)}$. In cationic 2TAP/PC/PE membranes (F) the longer blockage times (indicated by black arrows) cannot be satisfactorily described by just a single additional exponential function at |V| > 32.5 mV.

The τ_b distributions show dramatic lipid-dependent differences in the behavior of αSyn in the VDAC nanopore trap. Distributions of τ_b obtained in 2PG/PC/PE membranes are well described by single-exponential functions at all applied voltages (Fig. 2D, solid lines); the characteristic dwell times ${\tau }_{off}^{\left(1\right)}V$ are shown by red arrows in Figure 2D. In membranes formed from an equimolar mixture of two neutral lipids PC/PE (Fig. 2B, E), and in membranes formed from the cationic lipid mixture 2TAP/PC/PE (Fig. 2C, F), the ${\tau }_b$ distributions are qualitatively different. In PC/PE membranes, at ǀVǀ > 32.5 mV (Fig. 2E), the populations of short- and long-lasting ${\tau }_b$ are separated by a factor of 20 and can be satisfactorily described by the sum of two single-exponential functions with characteristic times ${\tau }_{off}^{\left(1\right)}$ and ${\tau }_{off}^{\left(2\right)}$, as in Figure 1E. In cationic 2TAP/PC/PE membranes, the ${\tau }_b$ distributions are even more complex (Fig. 2F). The long-lasting ${\tau }_b$ have broad distributions, even at the lowest voltages, which require the sum of more than two exponential functions to describe them. As a result, we attempt to characterize only ${\tau }_{off}^{\left(1\right)}$, which has a distinct peak. The long-lasting blockages account for a minor but significant fraction of the total events, about 20% and 30% in PC/PE and 2TAP/PC/PE membranes, respectively.

To assess the effect of lamellar versus non-lamellar lipids on the αSyn membrane dissociation rate, we also performed measurements in pure DOPE and DOPC membranes. Single exponential distributions of ${\tau }_b$ are characteristic for pure DOPE but not for pure DOPC (Fig. 3A). For DOPC membranes the distribution of ${\tau }_b$ requires two-exponential fitting (Fig. 3B, right panel, solid lines) with 64 and 36 % contributions of each exponent to the total distribution (of events, and well discriminated characteristic times of 1.0 and 39 ms for ${\tau }_{off}^{\left(1\right)}$ and ${\tau }_{off}^{\left(2\right)}$, respectively.

Figure 3.

(A-B) Log-binned distributions of the αSyn-VDAC blockage times ${\tau }_b$ obtained in neutral DOPE (A) and DOPC (B) membranes. The ${\tau }_b$ distribution in pure DOPE (A) follows a single exponential fitting (solid line). Solid lines in (B) are a two-exponential fit and dashed lines are separate fits of the short and long-time populations for comparison. Data were obtained at −35 mV. (C) Voltage dependences of ${\tau }_{off}^{\left(1\right)}\left(V\right)$ and ${\tau }_{off}^{\left(2\right)}\left(V\right)$ for all membrane lipid compositions: 2PG/PC/PE (red), PC/PE (1:1) (black), and 2TAP/PC/PE (blue). Each data point is a mean of 3-5 independent experiments ± standard error (68% confidence interval of the mean). Membrane bathing solutions contained 1 M KCl buffered by 5 mM HEPES to pH 7.4. Solid lines are fits to an energy landscape model (equation (5)); the dashed line is an estimate of the retraction line for ${\tau }_{off}^{\left(1\right)}\left(V\right)$ for 2PG/PC/PE to guide the eye.

The voltage dependences of ${\tau }_{off}^{\left(1\right)}$ and ${\tau }_{off}^{\left(2\right)}$, where applicable, are shown in Figure 3C for all lipid compositions studied. In each case ${\tau }_{off}^{\left(1\right)}\left(V\right)$ has the characteristic biphasic shape shown in Figure 1F. The retraction lines are similar for all lipid compositions and the times increase exponentially with $V$ (red dashed line). The departure of ${\tau }_{off}$ from the retraction line changes significantly with lipid content; for example, $V^{*}$ is approximately −33 mV, −35, and −42 mV in 2TAP/PC/PE, PC/PE, and 2PG/PC/PE membranes, respectively. The associated values of ${\tau }_{off}^{\left(1\right)}\left(V^{\ast }\right)$ are approximately 0.7, 1.5, and 18 ms, spanning well over an order of magnitude in lipid-dependent membrane dissociation rate. Interestingly, ${\tau }_{off}^{\left(1\right)}\left(V\right)$ is essentially the same for DOPE, DOPC, and mixed PC/PE membranes. Thus, ${\tau }_{off}^{\left(1\right)}$ appears to depend strongly on the lipid headgroup charge but is relatively insensitive to the type of the headgroup (PC vs PE) and lamellar character of the neutral lipid.

The well-defined exponential distributions of ${\tau }_b^{\left(2\right)}$ in PC/PE and PC membranes allow accurate calculation of ${\tau }_{off}^{\left(2\right)}\left(V\right)$, exposing a striking difference with ${\tau }_{off}^{\left(1\right)}\left(V\right)$ (Fig. 3C). ${\tau }_{off}^{\left(2\right)}$ rises exponentially up to $V=-45 \mathrm{m}\mathrm{V}$ for both PC/PE and PC membranes without deviating from its retraction line; thus, $V^{*}$ is not achieved and ${\tau }_{off}^{\left(2\right)}$ rises to values that are more than 100 times greater than the maximum ${\tau }_{off}^{\left(1\right)}\approx 2 \mathrm{m}\mathrm{s}.$ The retraction line associated with ${\tau }_{off}^{\left(2\right)}$ is also offset from that of ${\tau }_{off}^{\left(1\right)}$ by a factor of about 4. Together, these results reveal the surprisingly complex nature of αSyn membrane association. While it is to be expected that average membrane dissociation rates differ with membrane composition, the single-molecule nanopore trap reveals that even αSyn molecules bound to the same lipid surface have vastly different membrane dissociation rates when interrogated with the VDAC nanopore.

Effect of electrolyte concentration

The foregoing experiments were performed under conditions where the lipid and protein charges are largely screened. To further elucidate the role of electrostatics in interactions between the highly negatively charged the C-terminus of αSyn and net positively charged VDAC pore, and between the αSyn membrane binding domain and the lipid surface, we explored the effect of lipid charge in a more physiologically relevant 150 mM KCl electrolyte buffer. The results are shown in Figure 4, and two major differences with the data shown in Figures 2–3 emerge. First, there is no longer a ${\tau }_{off}^{\left(2\right)}$ in PC/PE membranes at any voltage (Fig. 4A, middle panel), and the contribution of ${\tau }_{off}^{\left(2\right)}$ in 2TAP/PC/PE membranes is small but remains too broad to be described by the sum of just two exponential functions (Fig. 4A, lower panel). Therefore, in Fig. 4B we compare only ${\tau }_{off}^{\left(1\right)}\left(V\right)$ in 1 M and 150 mM KCl for the three lipid compositions.

Figure 4.

Effect of reduced electrolyte concentration (150 mM KCl). (A) Log-binned distributions of ${\tau }_b$ obtained in 150 mM KCl in 2PG/PC/PE, PC/PE, and 2TAP/PC/PE membranes. Distributions of τ_b in 2PG/PC/PE and PC/PE follow a single exponential (solid line). In 2TAP/PC/PE membrane there is a small fraction of longer events, but the distribution is too broad to describe with just two exponential functions (shown individually as dashed lines and their sum as the solid line). All data were obtained at −35 mV. (B) Voltage dependences of ${\tau }_{off}^{\left(1\right)}$. Solid lines are fits to an energy landscape model (equation (5)); dashed lines of the same color show the fits to the voltage-dependence of ${\tau }_{off}^{\left(1\right)}$ in 1 M KCl (Figure 3B). Each data point is a mean of 3-5 independent experiments ± standard error (68% confidence interval of the mean). Membrane bathing solutions were buffered by 5 mM HEPES at pH 7.4.

Second, ${\tau }_{off}^{\left(1\right)}\left(V\right)$ is affected by electrolyte concentration in a lipid-dependent manner (Fig. 4B). The retraction lines are independent of ionic strength for all three lipid compositions; however, $V^{*}$ and ${\tau }_{off}\left(V^{*}\right)$ depend strongly on electrolyte concentration. In 2PG/PC/PE membranes $V^{*}$ is not observed in 150 mM KCl (Fig. 4B, red symbols and lines) up to $-47.5\mathrm{ }\mathrm{m}\mathrm{V}$. In PC/PE membrane, $V^{*}$ increases from about $-33 \mathrm{m}\mathrm{V}$ in 1 M KCl to $-38 \mathrm{m}\mathrm{V}$ in 150 mM KCl (Fig. 4B, black symbols and lines), and ${\tau }_{off}^{\left(1\right)}\left(V^{*}\right)$ increases by an order of magnitude. In 2TAP/PC/PE membranes, the relation between ${\tau }_{off}^{\left(1\right)}\left(V\right)$ in high and low salt is reversed in comparison with the two other membranes. In particular, ${\tau }_{off}^{\left(1\right)}\left(V^{*}\right)$ decreases from 1 M KCl to 150 mM KCl (Fig. 4B, blue symbols and lines) and is comparable to the 450 μs estimate of the time between membrane dissociation and the completion of the translocation process.²² This suggests that the membrane anchoring function of the membrane binding domain of αSyn on 2TAP/PC/PE membranes is essentially nonexistent.

Long membrane dissociation times correspond to smaller translocation probability

For lipid membrane compositions from which αSyn has multiple characteristic dissociation times, the exponential increase of the slower dissociation component is suggestive that these molecules escape primarily by retraction. To demonstrate this, we use a method that allows discrimination of retraction and translocation events on the single-molecule level.²² Briefly, the VDAC nanopore is subjected to a gradient of electrolyte concentration (Figure 5A). These conditions reveal the altered ionic selectivity of the VDAC channel when the charged or uncharged region of the αSyn molecule is in the channel. Thus, the ionic current reports not only on the presence of an αSyn molecule, but also which domain is in the channel at a given time.^21,22 Of particular interest is the end of each blockage event; if the charged C-terminal domain was in the pore, the molecule retracted, while if the uncharged N-terminal domain was in the pore, the molecule translocated. Two such representative blockage events are shown in Figure 5A from an experiment using 10 nM αSyn and a 1:1 DOPC:DOPE lipid membrane with a 0.2 M cis / 1.0 M trans KCl electrolyte gradient. Note that under these conditions, higher voltages are required to observe translocation, i.e. $V^{*}$ increases, because the osmotic gradient abets retraction.

Figure 5.

Measurement of translocation probability for αSyn on a 1:1 PC:PE membrane. (A) Identification of single blockage events as retractions or translocations based on the ionic current through the VDAC nanopore at the end of each event. Current traces measured for one retraction (left) and one translocation (right) event are shown. The two current levels marked by the red and green dashed lines correspond to the presence of the C-terminal (CT) or N-terminal (NT) domains in the nanopore, respectively, and arise from differences in the pore selectivity by the charge density of the αSyn. Darker traces show the result of postprocessing with an order 9 median filter. (B) ${\tau }_b$ histograms for retraction and translocation events, showing the presence of ${\tau }_{off}^{\left(2\right)}$ above ${\tau }_b=10 \mathrm{m}\mathrm{s}$. The inset corresponds to the region in the dashed box; the relative incidence of retraction and translocation events is reversed from ${\tau }_{off}^{\left(1\right)}$ to ${\tau }_{off}^{\left(2\right)}$. (C) Voltage dependence of translocation events and short (${\tau }_{off}^{\left(1\right)}$) and long (${\tau }_{off}^{\left(2\right)}$) retractions; dashed lines are estimates of the retraction lines of the short and long retraction data. For long retractions, only data for which ${\tau }_{off}^{\left(2\right)}$ could be determined are included. (Inset) Fraction of time spent by the C-terminal domain in the VDAC nanopore for short and long events, separated at ${\tau }_b=10 \mathrm{m}\mathrm{s}$. Long events are associated with a low C-terminal domain occupancy. (D) Dependence of translocation probability on voltage and blockage time. The translocation probability increases from right to left (increasing $\left|V\right|$), but decreases from bottom to top (increasing blockage time). (E) Translocation probability as a function of voltage at constant observed blockage time. Higher voltages are required to cause translocation for molecules with longer blockage times. The orange and black data points correspond to the horizontal dashed lines with the same colors in (D). (F) Translocation probability as a function of observed blockage time at constant voltage. Longer blockage times are associated with a lower translocation probability. The orange and black data correspond to the vertical dashed lines with the same colors in (D). Error bars are 68% confidence intervals estimated using bootstrap analysis.

When this determination is performed for many individual molecules, histograms of ${\tau }_b$ can be accumulated for events identified as either retractions or translocations, as shown for $V=-47.5 \mathrm{m}\mathrm{V}$ in Figure 5B. As in the symmetric case for a 1:1 DOPC:DOPE membrane, but unlike previous measurements on DPhyPC membranes,²² the ${\tau }_b$ histograms have two clear components separated at ${\tau }_b\approx 10\mathrm{ }\mathrm{m}\mathrm{s}$. The ${\tau }_b$ histogram for retraction has characteristic times ${\tau }_{off}^{\left(1\right)}=2.06\pm 0.11 \mathrm{m}\mathrm{s}$ and ${\tau }_{off}^{\left(2\right)}=21.1\pm 2.4 \mathrm{m}\mathrm{s}$. The ${\tau }_{off}^{\left(1\right)}$ peak is larger for translocations than for retractions; thus, smaller ${\tau }_{off}$ corresponds primarily to translocations. The opposite is true for ${\tau }_{off}^{\left(2\right)}$ (Figure 5B, inset), which is dominated by retraction events. Thus, the larger ${\tau }_{off}$ corresponds to primarily retraction events. For each $t_b$ histogram bin, the fraction of translocation events is the observed translocation probability $P_{trans}$.

The voltage dependence of ${\tau }_{off}^{\left(1\right)}$ and ${\tau }_{off}^{\left(2\right)}$ for retraction events, and the dominant ${\tau }_{off}^{\left(1\right)}$ for translocation events, are shown in Figure 5C, showing the same qualitative features as observed in Figure 3C for PC:PE membranes without the electrolyte gradient. The inset shows the average fraction of time spent by the C-terminal domain in the nanopore, showing a large difference between long and short events (both retraction and translocation events were included in this analysis).

Figure 5D shows $P_{trans}$ as a function of both $V$ and $t_b$. Cuts through the data shown as vertical and horizontal orange and black dashed lines correspond to the data points of the same color in Figures 5E, F. Figure 5E shows a striking shift to higher voltages in the transition from retraction to translocation when considering events with longer blockage times. The black data points correspond to ${\tau }_b={10}^{-0.4} \mathrm{m}\mathrm{s}$, or ${\tau }_{off}^{\left(1\right)}$, while the orange data correspond to ${\tau }_b={10}^{1.6}\mathrm{ }\mathrm{m}\mathrm{s},\mathrm{ }\mathrm{o}\mathrm{r}\mathrm{ }{\tau }_{off}^{\left(2\right)}$. At a given voltage, the translocation probability is significantly smaller for data corresponding to ${\tau }_{off}^{\left(2\right)}$, confirming that this peak represents primarily molecules that eventually retract from the VDAC nanopore. Similarly, Figure 5F confirms that at same voltage, longer events correspond to a lower translocation probability, i.e. are more likely to be retraction events.

DISCUSSION

Energy landscape model of αSyn/VDAC interaction

The interaction of αSyn with the VDAC nanopore shown in Figure 1C is complex enough to produce a rich variety of observed behaviors, particularly the biphasic dependence of ${\tau }_{off}\left(V\right)$.²⁰ The “diblock copolymer”-like architecture of αSyn, with its charged C-terminal domain and net uncharged N-terminal domain, provides a molecular fiducial point at the junction that allows the progress of the molecule through the VDAC nanopore to be monitored in real time;²² this is the basis for the data in Figure 5. These features have allowed the development and validation of free energy landscape models for the αSyn/VDAC interaction.²¹ These models have proven quantitatively predictive for the effect of mimic post-translational modifications to αSyn⁴ as well as for the interactions of the various disordered C-terminal tails in the plethora of tubulin isotypes with the VDAC nanopore.¹²

Energy landscape modeling entails construction of a one-dimensional free energy profile that describes the interaction energy between a polypeptide and a nanopore and from which a prediction of ${\tau }_{off}\left(V\right)$ can be calculated (Figure 6A). The process is shown in Figure 6B, C. The single spatial dimension, $x$, represents the length of polypeptide that has threaded through the nanopore constriction. The domain of $x$ runs from 0—when one end of the molecule is in the constriction, and the capture process is beginning or the retraction process completing—to $L$, the total length of the polypeptide. For αSyn, $L=56 \mathrm{n}\mathrm{m}$, assuming 0.4 nm per amino acid;²⁶ the boundary between the C-terminal domain and N-terminal domain is at $x=16 \mathrm{n}\mathrm{m}$. At $x=L$, the translocation process is complete.

Figure 6.

Principles of energy landscape analysis for lipid-dependent membrane dissociation of αSyn. (A) Schematic of the effect on ${\tau }_{off}\left(V\right)$ of the membrane dissociation energy $E_b$ and the penetration depth $x_b$. (B-C) Construction of the free energy profiles leading to the effects in (A). (B) Electrokinetic free energy was calculated at −35 mV (black curve) and includes entropy. The membrane dissociation free energy is modeled as an error function with height $E_b$ and position $x_b$. The colored lines show variations with $E_b$ and $x_b.\mathrm{ }{E}_b$ is 15 $k_{B}T$ (red and blue) or 20 $k_{B}T$ (green); $x_b$ is 11 nm (red and green) or 16 nm (blue). The vertical dashed line shows the boundary at $x=16 \mathrm{n}\mathrm{m}$ between the C-terminal domain (CT) and the N-terminal domain (NT). (C) The sum of the electrokinetic free energy and the membrane dissociation free energy profiles in (B) reveals the nanopore trap, marked with *. The heights of the free energy barriers to retraction and to translocation (dashed arrows) depend strongly on $E_b$ and $x_b$. The free energy barrier to translocation depends primarily on $E_b$, while the free energy barrier to retraction increases with $x_b$.

The free energy calculation is performed using a Python-based version of the PPDiffuse engine.²⁷ Briefly, the electrokinetic forces are calculated by first converting the amino acid sequence into a linear charge density ${\sigma }_n\left(x\right)$ that responds to $V$. Hydrodynamic forces from electroosmotic flow in the nanopore, which arises from the action of the electric field on ions in the pore, are also linear in $V$, reducing the effective charge density to a fraction $m_{EOF}$ of its intrinsic value. Similarly, the nonzero charge density of the pore interior sets up an electroosmotic flow even in the absence of charge from the polypeptide; this offset is $b_{EOF}$. Thus, the electric field acts on an effective charge density ${\sigma }_{EOF}\left(x\right)=m_{EOF}{\sigma }_n\left(x\right)+b_{EOF}$. For VDAC in 1 M KCl, these values are known from previous studies to be $m_{EOF}=0.659$, indicating that electroosmotic flow cancels about a third of the intrinsic charge density, and $b_{EOF}=-0.262\mathrm{ }{e}^{-}/\mathrm{n}\mathrm{m}$, the effective charge density corresponding to the intrinsic hydrodynamic flow in the VDAC pore. For αSyn in VDAC at −35 mV, the black curve in Figure 6B shows the sum of the electrokinetic free energy profile and an entropic term $U_S\left(x\right)=0.59k_{B}T\left[\ln x/L+\ln \left(1-x/L\right)\right].\mathrm{ }{U}_S\left(x\right)$ accounts for the multiplicity of molecular configurations at a position $x$ and is small throughout; its maximum magnitude of $3.3k_{B}T$ occurs for the first and last residues only ($x=0.2 \mathrm{n}\mathrm{m}$ or $x=55.8 \mathrm{n}\mathrm{m}$).

The membrane dissociation energy is modeled as an error function barrier with height $E_b$, position $x_b$, and width $w_b=7.13 \mathrm{n}\mathrm{m}$ (colored lines in Figure 6B, where $w_b=4\mathrm{ }\mathrm{n}\mathrm{m}$ for clarity). The height $E_b$ is best interpreted as the activation energy required for membrane dissociation. The position $x_b$ is the penetration depth of the polypeptide and can be considered as the length of the polypeptide that can move freely through the nanopore before its motion is impeded by the membrane anchor. The relatively broad width suggests that the unbinding process may involve a series of fast steps to which the nanopore experiment is not immediately sensitive. This is consistent with the multiple rate constants required to describe unbinding of peptides from lipid bilayer surfaces in force microscopy experiments.^28,29

The total free energy is the sum of the electrostatic, entropic, and membrane association terms. The expression is:

$$U(x)=eV{\int }_0^x\sigma (x^{\prime })d{x}^{\prime }+U_S(x)+E_b\mathrm{erf}\left(\frac{x-x_b}{w_b\sqrt{2}}\right),$$ (3)

Example curves showing the variation with $E_b$ and $x_b$ are shown in Figure 6C, where the free energy minimum, or trap position, is marked with * for each profile.

At a given time $t$, the dynamics are described by function $P\left(x,t;x_0, U\left(x\right)\right)$ representing the probability that the system is at $x$ given an initial position $x_0$ at $t=0$. The average escape time ${\tau }_{off}^{\prime }\left(x_0\right)$ is then calculated as the mean first passage time from the domain of $x$ of a system subject to drift forces represented by $U\left(x\right)$ and with a position-independent diffusion constant $D=0.309 \mathrm{\mu }{\mathrm{m}}^2 {\mathrm{s}}^{-1}$. The boundaries at $x=0,L$ are taken to be absorbing, due to the vanishing probability that a molecule that has retracted or translocated (Figure 6C, dashed arrows) is recaptured into the nanopore. The expression is, for $\tilde{U}\left(x\right)=U\left(x\right)/k_{B}T$:³⁰

$$\begin{gathered} D{\tau }_{off}^{\prime }\left(x_0\right)=\left[\underset{0}{\overset{L}{\int }}dx\left(e^{\tilde{U}(x)}\underset{0}{\overset{x}{\int }}{e}^{-\tilde{U}\left(x^{\prime }\right)}d{x}^{\prime }\right)\right]\left[{\underset{0}{\overset{x_0}{\int }}{e}^{\tilde{U}\left(x^{\prime }\right)}d{x}^{\prime }}^{\text{}}\right]{\left[\underset{0}{\overset{L}{\int }}{e}^{\tilde{U}\left(x^{\prime }\right)}d{x}^{\prime }\right]}^{-1} \\ -\underset{0}{\overset{x_0}{\int }}dx\left(e^{\tilde{U}(x)}\underset{0}{\overset{x}{\int }}{e}^{-\tilde{U}\left(x^{\prime }\right)}d{x}^{\prime }\right), \end{gathered}$$ (4)

To avoid dependence on the choice of $x_0$, the escape times to be compared to experiments are averaged over a distribution $P\left(x_0\right)$ of initial positions between 5 and 20 nm, weighted by a Boltzmann distribution, i.e. $P\left(x_0\right)=e^{-\tilde{U}\left(x_0\right)}/\int e^{-\tilde{U}\left(x_0\right)}d{x}_0$. Thus,

$${\tau }_{off}=\underset{5\mathrm{nm}}{\overset{20\mathrm{nm}}{\int }}{\tau }_{off}^{\prime }\left(x_0\right)P\left(x_0\right)d{x}_0.$$ (5)

Of particular interest for the current study is the effect on ${\tau }_{off}$ of the membrane dissociation energy parameters $E_b$ and $x_b$. This is shown schematically in Figure 6A. Increasing $E_b$ increases the barrier to translocation but does not alter retraction; thus, $V^{*}$ increases, and ${\tau }_{off}\left(V\right)$ shifts along the retraction line. Increasing $x_b$, on the other hand, allows more of the charged C-terminal domain to interact with the applied voltage, suppressing retraction and shifting the ${\tau }_{off}\left(V\right)$ curve to larger times and a new retraction line. For the calculations in this manuscript, $w_b$ was fixed at the previously determined $7.1 \mathrm{n}\mathrm{m}$. In this case the effects of $E_b$ and $x_b$ are not as independent as suggested by Figure 6A, but the general trends remain the same.

Both membrane dissociation energy and penetration depth depend on lipid composition

Equation (5) was fit to each ${\tau }_{off}\left(V\right)$ with just two free parameters for each lipid composition, $E_b$ and $x_b$. The only exception were the data at 150 mM KCl on the 1:1 PC:PE mixture, which were of sufficient quality to additionally determine the electroosmotic flow parameters for reduced ionic strength. These were determined to be $m_{EOF}=0.749\pm 0.068$ and $b_{EOF}=-0.525\pm 0.049$ (68% confidence intervals). The larger absolute value of $m_{EOF}$ relative to 1 M KCl is consistent with increased electrical forces at reduced ionic strength, as predicted by Poisson-Boltzmann calculations in solid-state nanopores.³¹ On the other hand, at reduced ionic strength the intrinsic charge of the nanopore has a larger effect, as reflected by the increased absolute value of $b_{EOF}$.

The fit results to equation (5) are shown by the solid lines in Figures 3 and 4B, demonstrating excellent agreement with the experimental ${\tau }_{off}\left(V\right)$, including both ${\tau }_{off}^{\left(1\right)}\left(V\right)$ and ${\tau }_{off}^{\left(2\right)}\left(V\right)$. The fit parameters are plotted in Figure 7. The horizontal axis shows penetration depth, while the vertical axis is membrane dissociation energy. The inset details the closely clustered points representing most of the observations. Data markers are identical to those used in previous figures and are shown in the legend at right.

Figure 7.

Lipid-dependent membrane dissociation of αSyn is described by two parameters of an energy landscape model, $E_b$ and $x_b$. All other model parameters were fixed to known values for the VDAC nanopore. Points connected by graded lines show ${\tau }_{off}^{\left(1\right)}$ and ${\tau }_{off}^{\left(2\right)}$ from the same lipid composition. The vertical dashed line shows the boundary between the C-terminal (CT) domain and the N-terminal (NT) domain. Data in the dashed box are shown in greater detail in the inset. Error bars are 95% confidence intervals estimated from posterior distributions of optimized parameters and where not visible are smaller than the data points shown.

Figure 7 reveals the physical origin of the complex observations reported here. For αSyn on 2PG/PC/PE membranes, the penetration depth is near the boundary between the C-terminal and N-terminal domains, suggesting that the αSyn binding conformation in the case of the 2PG/PC/PE composition allows the C-terminal domain to almost completely enter the VDAC nanopore. The same is true for PC/PE at 150 mM KCl, but at 1 M KCl the C-terminal domain penetrates several nm less. Most remarkable is the case of 2TAP/PC/PE in 1 M KCl, where less than half of the C-terminal domain can penetrate the nanopore. A natural explanation is that the anionic C-terminal domain electrostatically binds to the cationic 2TAP/PC/PE surface.

This explanation is borne out by comparing the membrane dissociation energies for 2PG/PC/PE, PC/PE, and 2TAP/PC/PE compositions, with the dissociation constants of 46 μM, 1500 μM, and 116 μM for αSyn on lipid membranes of these compositions in 150 mM KCl determined from fluorescence correlation spectroscopy (FCS).²⁵ While αSyn binds 2TAP/PC/PE membranes almost as strongly as 2PG/PC/PE membranes, it is apparent from these data that this is almost entirely due to the association of the C-terminal domain with the cationic surface. When the C-terminal domain is sequestered in the nanopore trap, the dissociation energy is significantly reduced relative to that of αSyn on 2PG/PC/PE or PC/PE membranes. The $5k_{B}T$ difference in dissociation energies for αSyn on 2PG/PC/PE or PC/PE membranes is close to the natural logarithm of the ratio of dissociation constants, suggesting that at least for these constructs differences in membrane binding strength can be quantified in this manner.

Importantly, the data in Figure 7 show that the accessibility of the C-terminal domain to the nanopore depends significantly on lipid composition, and that this in turn has profound effects on the observed ${\tau }_{off}^{\left(1\right)}\left(V\right)$.

Multiple characteristic dissociation times arise from disordered binding configurations

Perhaps the most striking observation in Figures 2 and 3 is the lipid composition-dependent appearance of a population of αSyn molecules that manifest a very long lifetime, ${\tau }_{off}^{\left(2\right)}\left(V\right)$, in the VDAC nanopore. In the experiments reported here, ${\tau }_{off}^{\left(2\right)}$ was observed for PC/PE, 2TAP/PC/PE, and pure PC membranes. It is suggestive that none of these lipid compositions, unlike PE or 2PG/PC/PE,^17,18 are known to induce helical ordering of the membrane binding domain of αSyn.¹⁹ Figure 7 shows the energy landscape modeling results for ${\tau }_{off}^{\left(2\right)}\left(V\right)$ in PC/PE and PC membranes. Because the translocation regime is not clearly observed in ${\tau }_{off}^{\left(2\right)}$, the parameters are poorly constrained; however, lower bounds on both parameters can be established and are shown by the edges of the 95% confidence intervals in the plot. For both PC/PE and PC membranes, the penetration depth is such that αSyn is trapped with the uncharged N-terminal domain in the nanopore. This is precisely what is found in the electrolyte gradient experiment (Figure 5C, inset); the occupancy of the C-terminal domain in the VDAC nanopore is significantly reduced for longer events corresponding to ${\tau }_{off}^{\left(2\right)}$. These observations are consistent with a disordered binding configuration that, unlike the binding configuration leading to ${\tau }_{off}^{\left(1\right)}$, allows the C-terminal domain to fully pass through the VDAC nanopore constriction, so the trapped molecule does not experience the strong electrical forces that would enhance membrane dissociation by acting on the highly charged C-terminal domain. Thus, ${\tau }_{off}^{\left(2\right)}$ reveals the presence of two (or more) distinct binding conformations populated by αSyn molecules on the same membrane surface. Depending on its binding conformation, the observed dynamics of αSyn in the VDAC nanopore trap, and particularly the release of αSyn from the membrane surface, differ by orders of magnitude, as revealed by the single molecule measurement.

Comparing $E_b$ for ${\tau }_{off}^{\left(2\right)}$ and ${\tau }_{off}^{\left(1\right)}$ for the same compositions (see graded lines connecting each pair of PC and PC/PE membrane data points in Figure 7), the membrane dissociation energy corresponding to ${\tau }_{off}^{\left(2\right)}$ is at least 5 $k_{B}T$ greater than that of ${\tau }_{off}^{\left(1\right)}$. It is counterintuitive that binding conformations that allow αSyn to penetrate further into the VDAC nanopore have a larger apparent binding energy, as less polypeptide would then be available to interact with the lipid surface, but it is by no means impossible. One source of apparent excess binding energy may be the nature of a disordered binding domain, which may spread its binding energy over individual subdomains that interact with the lipid surface.³² Each subdomain is in dynamic equilibrium between bound and dissociated states. All subdomains must simultaneously dissociate for the molecule to translocate, in principle leading to very slow unbinding kinetics that in the context of the energy landscape model would be interpreted as binding energy. An alternative but equally likely source of excess dissociation energy for ${\tau }_{off}^{\left(2\right)}$ is αSyn oligomerization on the lipid surface. Oligomer association could provide both the additional membrane binding energy and the C-terminal tail accessibility deduced from the energy landscape modeling. The lipid dependence would then reflect the ability of lipid membrane surfaces of differing compositions to either maintain bound oligomeric structures or reorganize oligomeric αSyn from solution into membrane-bound monomers.^33,34

CONCLUSIONS

We have shown that the VDAC nanopore embedded in a voltage-biased phospholipid bilayer membrane creates an electromechanical trap to study mechanistic features of membrane-bound αSyn dissociation. The αSyn molecule remains trapped until one of two slow events occurs: its charged C-terminal domain escapes due stochastic thermal forces against the electrical forces, or its membrane binding domain detaches from the surface, allowing translocation to proceed. The trap depth is tunable via the transmembrane potential, allowing orders of magnitude of characteristic escape times to be explored. The measurement reveals that the membrane dissociation time is very sensitive to the membrane phospholipid composition. Surprisingly, for certain lipid compositions, the membrane dissociation of αSyn on the same lipid membranes obeys multiple characteristic rates, suggesting the presence of multiple binding conformations on the surface. Each binding conformation can be parameterized by two physical quantities: the membrane dissociation free energy, and the length of the αSyn polypeptide that is available to penetrate the pore before being arrested by the membrane binding domain.

In sum, an electromechanical trap such as that described here provides a local, single-molecule probe of dissociation kinetics of membrane-bound proteins. The results presented in this work have profound implications for our understanding of protein-lipid interactions, and particularly the roles that disordered membrane binding domains and their inherent stochasticity play in recruiting peripheral proteins to, and preventing their exit from, the surfaces of phospholipid membranes.

METHODS

Protein Purification.

Recombinant mouse VDAC1 (VDAC) was a kind gift of Dr. Adam Kuszak (Laboratory of Chemical Physics, NIDDK, NIH). VDAC1 was expressed, refolded, and purified using a protocol described previously.^25,35 αSyn WT, was a generous gift of Dr. Jennifer Lee (NHLBI, NIH, Bethesda, USA). αSyn was expressed, purified, and characterized as previously described.²⁰

Channel Reconstitution.

The mixtures of lipids were prepared from 10 mg/ml aliquots of two or three lipid solutions in chloroform, followed by drying with nitrogen and then re-dissolving them in pentane to a total lipid concentration of 5 mg/ml. 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE), 1,2-dioleoyl-sn-glycero-3-phospho-(1’-rac-glycerol) (DOPG), 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP) were purchased from Avanti Polar Lipids (Alabaster, AL). Planar bilayer membranes were formed from two opposing lipid monolayers across ~70 μm aperture in the 15-μm-thick Teflon partition separating two ~1.2-mL compartments as previously described.³⁶ VDAC insertion was achieved by adding recombinant murine VDAC1 in 2.5 % triton X-100 buffer³⁷ to the aqueous phase of 1 M or 150 mM KCl buffered with 5 mM Hepes at pH 7.4 in the cis compartment. Potential is defined as positive when it is greater at the side of VDAC addition (cis). αSyn at a final concentration of 10 nM was added symmetrically to the both sides of the membrane after VDAC channel reconstitution. In selectivity experiments, the trans side was filled with a solution of 1.0 M KCl and the cis side with a 0.2 M KCl solution, both buffered with 5 mM HEPES at pH 7.4. αSyn was added to the trans side at 5 nM concentration. Junction potentials with the Ag/AgCl electrodes were minimized because in all experiments the electrodes were connected with 2 M KCl / 2% agarose bridges.

Conductance measurements were performed as described previously²⁰ using an Axopatch 200B amplifier (Axon Instruments, Inc., Foster City, CA) in the voltage clamp mode. Data were filtered by a low pass 8-pole Butterworth filter (Model 900, Frequency Devices, Inc., Haverhill, MA) at 15 kHz and a low pass Bessel filter at 10 kHz, and directly saved into computer memory with a sampling frequency of 50 kHz.

Open and blockage times analysis.

For data analysis by Clampfit 10.3, a digital 8-pole Bessel low pass filter set at 5 kHz or 2 kHz was applied to current recordings in 1 M KCl and 150 mM KCl, respectively, and then individual events of current blockages were discriminated and kinetic parameters were acquired by fitting single exponentials to logarithmically binned histograms ³⁸ as described previously.^20,39 Four different logarithmic probability fits were generated using different fitting algorithms and the mean of the fitted time constants was used as the mean for the characteristic open and blockage times. Each channel experiment was repeated 3-7 times on different membranes. Statistical analysis of the blockage events began 15 min after αSyn addition to ensure a steady state.

Data analysis in selectivity experiments was performed as described previously.²² αSyn capture and release processes were detected with a threshold algorithm. A threshold was set at 0.75 times the open pore current at each applied voltage. Captures were detected when the absolute current level dropped below the threshold; releases (due to either retraction or translocation) are recorded when the absolute current level rose above the threshold. An “event” was defined as the time between a capture and its subsequent release. Data sampled at 4 μs were filtered with a median filter (order 21) such that the minimum event length was approximately 80 μs. Average currents were calculated by fitting a Gaussian function to a histogram of the filtered current for each voltage. These average currents were then used to differentiate between sublevels of each event corresponding to occupancy of VDAC by the C-terminal or N-terminal domain of αSyn.

Modeling and Optimization.

The model was implemented using custom Python code. Optimization was performed on the Bridges^40,41 high performance computing system using the DREAM Markov Chain Monte Carlo (MCMC) algorithm⁴² implemented in the software package Bumps.⁴³ Confidence intervals on parameters and model predictions are calculated from the last 24,528 of at least 744,528 total DREAM samples.