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Edited by: Miguel A. Aon, The Johns Hopkins University School of Medicine, USA

Reviewed by: Nickolay Brustovetsky, Indiana University School of Medicine, USA; Marco Colombini, University of Maryland, USA

*Correspondence: Daniel A. Beard, Department of Molecular and Integrative Physiology, University of Michigan, NCRC Building 10 #A122, 2800 Plymouth Rd., Ann Arbor, MI 48109, USA e-mail:

This article was submitted to Mitochondrial Research, a section of the journal Frontiers in Physiology.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The voltage-dependent anion channel (VDAC) is the main conduit for permeation of solutes (including nucleotides and metabolites) of up to 5 kDa across the mitochondrial outer membrane (MOM). Recent studies suggest that VDAC activity is regulated via post-translational modifications (PTMs). Yet the nature and effect of these modifications is not understood. Herein, single channel currents of wild-type, nitrosated, and phosphorylated VDAC are analyzed using a generalized continuous-time Markov chain Monte Carlo (MCMC) method. This developed method describes three distinct conducting states (open, half-open, and closed) of VDAC activity. Lipid bilayer experiments are also performed to record single VDAC activity under un-phosphorylated and phosphorylated conditions, and are analyzed using the developed stochastic search method. Experimental data show significant alteration in VDAC gating kinetics and conductance as a result of PTMs. The effect of PTMs on VDAC kinetics is captured in the parameters associated with the identified Markov model. Stationary distributions of the Markov model suggest that nitrosation of VDAC not only decreased its conductance but also significantly locked VDAC in a closed state. On the other hand, stationary distributions of the model associated with un-phosphorylated and phosphorylated VDAC suggest a reversal in channel conformation from relatively closed state to an open state. Model analyses of the nitrosated data suggest that faster reaction of nitric oxide with Cys-127 thiol group might be responsible for the biphasic effect of nitric oxide on basal VDAC conductance.

The mitochondrial inner membrane (MIM) and mitochondrial outer membrane (MOM) are the two phospholipid membranes separating the mitochondrial matrix milieu from cytosol. Transport between cytosol and matrix is essential for mitochondrial function. The most abundant protein in the mammalian MOM is a voltage-dependent anion channel (VDAC) (Krimmer et al., ^{2+}, K^{+}, H^{+}) across the MOM. Because VDAC has been linked to both cell survival and apoptosis, it has been described as the “gatekeeper of mitochondrial function and dysfunction (Kerner et al.,

By transporting substrates for the tricarboxylic acid cycle and oxidative phosphorylation across the MOM, VDAC plays a significant role in regulating mitochondrial bioenergetics (Hodge and Colombini,

To study the effects of PTM on VDAC, single channel current recordings of cardiac wild-type (WT) and PTM VDAC reconstituted in planar lipid bilayers are analyzed. Specifically, single VDAC data from two types of PTM are studied: nitrosation of VDAC protein using NO donor PAPA NONOate (PPN) and phosphorylation (phospho-mimetic) of VDAC protein at a serine residue. The nitrosation data is the recently published biphasic effect of PPN on VDAC purified from rat heart (Cheng et al.,

To better understand the kinetics of VDAC activity obtained from the single channel current recordings under these conditions, mathematical modeling is utilized to develop a kinetic model of the channel activity. In particular, a generalized continuous-time Markov-chain Monte Carlo (MCMC) method, based on Siekmann et al. (

Cheng et al. (

VDAC full length cDNA clone from rat heart with the corresponding GenBank accession number BC072484 was purchased from the Mammalian Gene Collection of Open Biosystems (Huntsville, AL). The coding sequence of VDAC was amplified and cloned by standard PCR methods in the BamHI/Not1 sites of

Induction of VDAC expression in BL21(DE3) cells was achieved by incubating the overnight culture for an additional 4 hours after addition of 1 mM isopropyl β-D-10 thiogalactopyranoside. Cells were then pelleted and lysed, and the VDAC containing inclusion bodies were subsequently isolated by centrifugation. The inclusion bodies were dissolved in solubilization buffer and then loaded onto nickel-nitrilotriacetic acid (Ni-NTA) His•Bind Resin (Novagen) columns. Bound proteins were dislodged from the matrix with a Ni-elution buffer. Subsequently, the purified VDAC was refolded by drop-wise dilution in a 1:10 ratio of elution buffer to the refolding buffer. The un-phosphorylated/recombinant VDAC (rVDAC) and phosphomimetic VDAC (S137E) proteins were reconstituted into planar lipid bilayers to measure their respective channel current activities as previously described (Cheng et al.,

Briefly, a mixture of phospholipids in chloroform were mixed and dried under a stream of nitrogen and dissolved in n-decane with a final lipid composition of phosphatidylethanolamine, phosphatidylserine and phosphatidylcholine (Avanti Polar Lipids, Alataster, AL) at a ratio of 5:4:1 (v/v). The lipid bilayers were formed in symmetrical solutions, with both the _{2}, 0.2 MgATP, with pH 7.4. The

The reconstituted VDAC activity recorded from the planar lipid bilayer experiments is sampled with a time-interval of fixed length (τ) and represented as a sequence of discrete-time channel events _{k})^{N}_{k = 1}, where _{k} is the single channel current at time _{k}. A typical VDAC current recording has multiple open and closed (or minimally open) states with a dominant sub-state that can be regarded as half-open or a half-closed state. Thresholding of VDAC current is employed to identify channel openings and closures which are classified into three distinct conductance states: open (_{S}), or closed (_{O}| > |_{C}|. The thresholds _{O} and _{C} are set at fixed values to identify distinct VDAC conductance states. These threshold values are different for WT and PTMed VDAC activity, however were chosen to be same within a given data type (i.e., WT, S137E, etc.). The threshold values used are tabulated in Table _{k})^{N}_{k = 1} obtained in Equation 1 can be represented by a Markov model. A Markov model is a symmetric directed graph. The set of vertices contain distinct Markov states {_{1}, _{2}, … _{n}} and the set of edges contain the non-negative constants _{ij} (i,j: 1, 2, …, n) that govern the transition rate from state _{i} to state _{j}. Figure

^{a} |
^{a} |
||||
---|---|---|---|---|---|

_{C} |
−20 | −9 | −38 | −21.5 | −20 |

_{O} |
−15 | −6.7 | −34 | −14.5 | −15 |

^{−1})^{b} |
|||||

_{13} |
141.6 ± 6.4 | 230 ± 1.8 | 120 ± 1.3 | 130.3 ± 14.8 | 135.3 ± 2.59 |

_{31} |
9.79 ± 4.8 | 3 ± 1.3 | 0.66 ± 0.27 | 47.5 ± 7.8 | 1.26 ± 0.49 |

_{15} |
177.3 ± 9.7 | 95 ± 1 | 139 ± 1.3 | 118.6 ± 14.8 | 152.2 ± 9.13 |

_{51} |
148.1 ± 5.5 | 220 ± 1.1 | 118 ± 1 | 161.2 ± 8 | 137.4 ± 20.17 |

_{34} |
253.3 ± 11.0 | 110 ± 1.1 | 157 ± 0.85 | 237.2 ± 8.1 | 169.9 ± 2.5 |

_{43} |
0.24 ± 0.12 | 0.12 ± 0.21 | 0.094 ± 0.02 | 0.36 ± 0.33 | 0.61 ± 0.2 |

_{24} |
332.6 ± 9.5 | 0.46 ± 0.13 | 165 ± 7 | 296.1 ± 13 | 143.8 ± 19.8 |

_{42} |
0.4 ± 0.07 | 0.048 ± 0.014 | 0.075 ± 0.016 | 3.6 ± 0.8 | 0.83 ± 0.29 |

_{1}–_{5} represent distinct VDAC conformations. _{3}: Maximally open VDAC conformation; (_{5}, _{1}, _{4}): Sub-conductance state of VDAC (all three have the same conductance level); _{2}: Minimally open or closed state of VDAC. _{3} and _{2} refer to maximally open and minimally open VDAC state, respectively.

In general, a given channel event can be represented by more than one Markov state. For example, _{5}, _{1}, _{4} represent the same event _{S} for the Markov model shown in Figure _{k}) can yield same event sequence (_{k}). To circumvent this problem and identify the best Markov model, Siekmann et al. (_{k})|(_{k}), _{ij} (

Let _{0} be vector containing the initial probability distributions for the set of Markov states. Then the time evolution of the Markov state probabilities, _{i} to _{j} in a given sampling interval (τ) is computed:

To account for different conducting states of VDAC activity the Siekmann et al. (Siekmann et al., _{O}, θ_{OS}, θ _{C} which correspond to the three possible events i.e., _{S}, _{i}(_{k−1}) to _{j}(_{k}) if _{j}(_{k}) ∉ _{k}. This is done by modifying the transition probability matrix _{τ} according to an event at a given time _{k}, such that:

Such projection matrices are useful in developing Markov models of channels with multiple sub-conducting states such as, VDAC. Here, the Metropolis–Hastings (MH) algorithm is used for sampling different Markov models (Brooks,

Random walk MH updating is used to generate a new model candidate _{ij} = _{ij} + _{ij}, _{ij} ∈ _{i}_{ij} = _{ji} π_{j}. Here, π is the stationary distribution to which Markov state probabilities

The candidate model

Here, ^{−1} for all the VDAC dataset—unless very small values are used (Siekmann et al.,

Independent runs of the algorithm tested different competing Markov models (shown in Figure

To validate the robustness of the Markov model, open-time, half-open-time, and close-time distribution of the VDAC activity are computed and are compared with the open-time, half-open-time, and close-time distributions derived from the experimental data. These probability density functions govern the time for which the channel remains in open state, half-open state or closed state. Colquhoun et al. (Colquhoun and Hawkes,

Here, “A” is the subset of Markov states representing only the VDAC open states, _{AA} = {_{ij} : _{A} is a column vector with _{A} entries which are all equal to one. Φ is the initial (row) vector that defines the relative probability of an opening starting in a given Markov open state. π_{B} is the stationary distribution of the Markov states which do not represent the VDAC open state and _{BA} = {_{ij} : _{0} and _{A} are unity and can be omitted, and the distribution reduces to a simple exponential distribution. For a more comprehensive detail of this approach the reader is referred to Colquhoun and Hawkes (

We applied the generalized continuous-time MCMC method, using the Markov model shown in Figure

In the current recordings analyzed here, the VDAC activity has at least three conducting states which are identified using the thresholds (_{O} and _{C}). For example, the WT VDAC data shown in Figures _{3} if |_{k})| ≥ (|_{O}| = 20) or closed state S_{2} if |_{k})| ≤ (|_{C}| = 15) or else half-open state(s) _{1}, _{4}, _{5}. Similarly, distinct conducting events for nitrosated VDAC data are also identified using the threshold values listed in Table

It is apparent from Figure

The rVDAC activity behaves differently than the purified or WT VDAC activity. Compare the data shown in Figures

The parameter convergence plots are shown in Figure _{4} in our model), therefore transitions to a higher conductance state (_{3}) or a lower conductance state (_{2}) seldom happen. The model captures this aspect of WT VDAC.

The open-time, half-open-time, and close-time distributions are computed from the experimental data (shown in Figure

It is apparent from Figure _{4} irrespective of the type of experimental data (WT or PTM). Therefore, it is excluded from the distributions shown in Figure _{1}, _{2}, _{3}, _{5}). Stationary distributions, shown in Figure _{2}) as compared to other states (_{1}, _{3}, _{5}). Un-phosphorylated and phosphorylated VDAC also share significant differences in their stationary distributions. The S137E data based stationary distributions (see Figure

_{4} was omitted from computations because it seemed to be the dominant dwell state which did not change significantly with different conditions. Y-axis: probability (unitless); X-axis: C and O correspond to _{2} and _{3}, respectively.

In Figures _{13} and _{51} have significantly increased, and _{31}, _{24} and _{42} have significantly decreased. As a result of these changes the PPN25 VDAC gating kinetics are much faster, as compared to purified WT and PPN 100 μM VDAC data. The phosphorylated VDAC (S137E) closes much less as compared to the recombinant VDAC. This behavior is captured by the significant differences in the _{31}, _{34}, _{24}, and _{42} parameters of both the data types (see Figure

Conduction kinetics of single VDAC was analyzed to identify a Markov model for the channel. The identified model was used to probe the effects of (possible) nitrosation on purified WT VDAC activity via NO donor PPN. The model was also used to study the effect of phosphorylation at a serine residue (phosphor-mimetic) on recombinant VDAC activity. To analyze current recordings from single channels, the statistical method of Siekmann et al. (

Several competing Markov models, shown in Figures _{1}) to closed state (_{2}) via open state (_{3}) and half-open state (_{4}).

Comparison of parameter profiles for rVDAC and S137E data suggests that phosphomimetic mutant has lower rate of transition to the closed states (_{2}) and higher rate of transition to the open state (_{3}). Although not obvious from the raw experimental data, the phosphomutant has a higher probability of being in the open state as compared to the closed state. This phenomenon is revealed by computing the stationary distributions of the Markov model associated with rVDAC and S137E data (see Figures

The parameter profiles of the purified WT and nitrosated VDAC suggest differences in the kinetics of the VDAC nitrosated using PPN 25 μM and PPN 100 μM. The kinetics of PPN100 VDAC is similar to WT VDAC, while the conductance of the WT VDAC is about half of PPN100 VDAC. The kinetics of PPN25 VDAC is different than WT or PPN100 VDAC. PPN 25 μM not only reduces the conductance of VDAC but it also significantly increases the dwell-time of VDAC in its closed state (~99%; see Figure

While the MCMC method reveals information on the gating kinetics of WT VDAC and VDAC that underwent PTMs, it does not reveal how the VDAC conductance is modified as a result of different PTMs. This is an important aspect of VDAC activity as changes in VDAC conductance not only signify a change in conductance but also changes in ion selectivity. Previously, alternative methods like molecular dynamic simulations have been applied on VDAC (Krammer et al.,

Although the proposed model is based on experiments performed at −10 mV, the VDAC current-voltage relationship remains linear at voltages between −30 and +30 mV (Colombini,

It is thought that solutes and metabolites across MOM via VDAC can freely enter the MIS so that there is no ionic gradient across the membrane. This rationale has been supported by two observations: VDAC remains open most of the time at low voltages (~10 mV) and its big pore size (2.5–3 nm). VDAC undergoes transitions to lower conducting state (change in ion selectivity) when voltage is increased beyond ±30 mV but the potential mechanisms of MOM potential generation are not known. However, several mechanisms have been proposed for generation of an electrostatic potential maintenance of ionic gradients across the MOM (Colombini,

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This work was supported by the National Institute of Health grant P50-GM094503. Bradley J. Otto was supported by a Medical Student Anesthesia Research Fellowship from the Foundation for Anesthesia Education and Research.