Fabrice Homblé
email: fhomble@ulb.ac.be

Hana Kmita
email: kmita@amu.edu.pl

Hayet Saidani
email: hayettesaiidany@gmail.com

Marc Leonetti
email: leonetti@irphe.univ-mrs.fr

Hanna Kmita

Plant VDAC permeability: molecular basis and role in oxidative stress

Keywords: BiFC, bimolecular fluorescence complementation, VDAC, voltage-dependent anion channel, HK and HXK, hexokinase, Trx, thioredoxin

The mitochondrial voltage-dependent anion-selective channel (VDAC) is highly abundant in the mitochondrial outer membrane. It is permeable to molecules with a size up to about 5kDa and is the main pathway for the exchange of metabolites and ions between the mitochondrial intermembrane space and the cytosol. Experimental studies performed for plant VDAC have shown that the channel displays properties reported for VDACs of other eukaryotic organisms. Firstly, it transports compounds as diverse as inorganic ions (e.g., K + and Cl -), adenylates (e.g., ATP and AMP) and large macromolecules (tRNA and DNA). Secondly, despite its wide pore, the channel displays selectivity towards these compounds, i.e. it distinguishes between K + and Cl -but also between ATP and AMP. The question of how VDAC can selectively transport these different compounds is addressed in this chapter based on data obtained for plant VDAC. It is well known that all organisms have at least one canonical VDAC isoform that shares similar electrophysiological properties and secondary structure with cognate VDAC of other organisms. For instance, this is the case of the mammalian VDAC1, the yeast Saccharomyces cerevisiae VDAC1 and the PcVDAC purified from the bean Phaseolus coccineus seeds. Consequently, Brownian dynamic simulations of monatomic ion permeation through the experimental threedimensional structure of the mammalian VDAC1 and the PcVDAC modeled structure predict fairly well conductance and selectivity of both the proteins. In addition, the data of molecular simulation studies performed on the mammalian VDAC1 agree with the experimental data obtained for PcVDAC, which suggests a similar permeation process for these VDAC proteins. Accordingly, both the experimental and theoretical studies indicate that the selectivity for inorganic ions is a consequence of the excess of positive charges and their distribution inside the pore and the absence of defined pathways for the permeation. In contrast, the permeation of metabolites involves a major binding site located at the N-terminal helix which folded into the pore lumen and occurs through a preferential pathway. The key residues forming the binding site are conserved in the PcVDAC pointing to the conserved permeation process. The process might be affected by VDAC-interaction with other proteins. For example, it is suggested that plant VDAC is involved in the oxidative stress response which includes cytosolic hexokinase and thioredoxin binding to VDAC. This in turn may influence the exchange of molecules between mitochondria and the cytosol.

Introduction

The plant mitochondria are the place of a variety of processes including respiratory substrate oxidation, ATP synthesis, calcium and redox signaling and regulated cell death. Their biochemical activity requires exchange of ions and molecules through the mitochondrial outer membrane (MOM) and the mitochondrial inner membrane (MIM). Due to the co-ordination of the metabolic pathways between different cellular compartments, they also play a role in other plant cellular processes such as photosynthesis, photorespiration and nitrogen metabolism [START_REF] Sweetlove | The impact of oxidative stress on Arabidopsis mitochondria[END_REF][START_REF] Dutilleul | Functional Mitochondrial Complex I Is Required by Tobacco Leaves for Optimal Photosynthetic Performance in Photorespiratory Conditions and during Transients[END_REF][START_REF] Foyer | Respiration and nitrogen assimilation: targeting mitochondria-associated metabolism as a means to enhance nitrogen use efficiency[END_REF][START_REF] Bauwe | Photorespiration has a dual origin and manifold links to central metabolism[END_REF][START_REF] Araújo | On the role of plant mitochondrial metabolism and its impact on photosynthesis in both optimal and sub-optimal growth conditions[END_REF].

The Voltage-Dependent Anion-selective Channel (VDAC) is the major protein in plant MOM [START_REF] Mannella | X-ray diffraction from oriented outer mitochondrial membranes[END_REF]. It is the main transport pathway for ions [START_REF] Krammer | Origin of ion selectivity in Phaseolus coccineus mitochondrial VDAC[END_REF], metabolites [START_REF] Alcántar-Aguirre | ATP produced by oxidative phosphorylation is channeled toward hexokinase bound to mitochondrial porin (VDAC) in beetroots (Beta vulgaris)[END_REF][START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF], and nucleic acids [START_REF] Koulintchenko | Plant mitochondria actively import DNA via the permeability transition pore complex[END_REF][START_REF] Salinas | The voltage-dependent anion channel, a major component of the tRNA import machinery in plant mitochondria[END_REF][START_REF] Salinas | Recent advances in tRNA mitochondrial import[END_REF]. By using molecules of increasing size it has been shown that VDAC of mung bean have a size exclusion limit of about 5kDa [START_REF] Zalman | Mitochondrial outer membrane contains a protein producing nonspecific diffusion channels[END_REF]. Like VDAC of other organisms, VDAC isolated from different plants is voltage-dependent after reconstitution in a planar lipid bilayer. This denotes that at voltage |V|≥20 mV the channel exhibits transition between the open state and lower conductance states. This change in conductance might be of prime importance for the physiological role of plant VDAC because it has been shown that VDAC from Neurospora crassa is permeable to ATP in the open state but not in the subconductance states [START_REF] Rostovtseva | ATP Flux Is Controlled by a Voltage-gated Channel from the Mitochondrial Outer Membrane[END_REF][START_REF] Rostovtseva | VDAC channels mediate and gate the flow of ATP: implications for the regulation of mitochondrial function[END_REF]. This change in permeability to metabolites suggests that VDAC may not only facilitate, but also control the metabolic flux through MOM.

Phylogenetic analysis points to an early evolutionary divergence of VDAC. VDAC from algae, plant, fungi and animals belong to different clades. This suggests that they all derive from a common ancestor [START_REF] Young | The evolutionary history of mitochondrial porins[END_REF][START_REF] Homblé | Plant VDAC: Facts and speculations[END_REF]. Despite differences in their amino acid sequence, at least one VDAC isoform (named 'canonical VDAC') in each clade bears extremely conserved structural and functional features. For instance, the most abundant mammalian isoform VDAC1 shares similar basic electrophysiological properties, secondary structure and fold with the most abundant VDAC isoform of plants and fungi (e.g., [START_REF] Colombini | Voltage gating in the mitochondrial channel, VDAC[END_REF][START_REF] Homblé | Plant VDAC: Facts and speculations[END_REF][START_REF] Mertins | Voltage-dependent anion channels: the wizard of the mitochondrial outer membrane[END_REF].

Plant VDAC proteins were purified and characterized from maize [START_REF] Smack | Voltage-dependent channels found in the membrane fraction of corn mitochondria[END_REF][START_REF] Aljamal | Purification and Characterization of Porin from Corn (Zea mays L.) Mitochondria[END_REF], potato tuber [START_REF] Heins | Biochemical, molecular, and functional characterization of porin isoforms from potato mitochondria[END_REF], pea seedlings and roots [START_REF] Schmid | Identification of two general diffusion channels in the outer membrane of pea mitochondria[END_REF][START_REF] Fischer | Porins from plants. Molecular cloning and functional characterization of two new members of the porin family[END_REF][START_REF] Clausen | Intracellular localization of VDAC proteins in plants[END_REF]), wheat seedlings [START_REF] Blumenthal | Purification and Characterization of the Voltage-Dependent Anion-Selective Channel Protein from Wheat Mitochondrial Membranes[END_REF])and runner bean seeds (Abrecht et al. 2000b). The conductance, ion selectivity and voltage dependence of these VDACs are very similar and correspond to isoforms highly abundant in the tissue used for purification. Two major mitochondrial VDAC isoforms were purified from bean and lentil seed cotyledons (Abrecht et al. 2000b) and potato tubers [START_REF] Heins | Biochemical, molecular, and functional characterization of porin isoforms from potato mitochondria[END_REF]. However, proteomics studies indicate that more VDAC protein isoforms exists in plant tissues. For instance, there is a perfect matching between the transcriptomic and proteomic data for the model plant Arabidopsis thaliana, indicating the existence of four VDAC protein isoforms [START_REF] Marmagne | Identification of new intrinsic proteins in Arabidopsis plasma membrane proteome[END_REF][START_REF] Heazlewood | Experimental Analysis of the Arabidopsis Mitochondrial Proteome Highlights Signaling and Regulatory Components, Provides Assessment of Targeting Prediction Programs, and Indicates Plant-Specific Mitochondrial Proteins[END_REF][START_REF] Tateda | Molecular and genetic characterization of the gene family encoding the voltage-dependent anion channel in Arabidopsis[END_REF][START_REF] Rao | The proteome of higher plant mitochondria[END_REF]). The 'green plants' (Viridiplantea) VDACs are encoded in the nuclear genome and belong to a small multigene family which is larger than that found in mammals (3) and fungi (2 but only 1 in Neurospora crassa). Most green plants are sessile and this large diversity of VDAC genes might be the source of more physiological plasticity to cope with environmental stresses. In plant, abiotic and biotic stresses are known to impact mitochondrial function and to be correlated with ROS imbalance known to alter VDAC permeability in mammalian and yeast mitochondria [START_REF] Rostovtseva | Voltage gating of VDAC is regulated by nonlamellar lipids of mitochondrial membranes[END_REF][START_REF] Owsianowski | Negative regulation of apoptosis in yeast[END_REF][START_REF] Homblé | Plant VDAC: Facts and speculations[END_REF][START_REF] Mccommis | The role of VDAC in cell death: Friend or foe?[END_REF][START_REF] Takahashi | The functions of voltage-dependent anion channels in plants[END_REF] .

The 3D structure of the mouse and human VDAC isoform1 (VDAC1) and that of the zebrafish VDAC isoform2 (VDAC2) were resolved at atomic resolution [START_REF] Hiller | Solution structure of the integral human membrane protein VDAC-1 in detergent micelles[END_REF][START_REF] Bayrhuber | Structure of the human voltage-dependent anion channel[END_REF][START_REF] Ujwal | The crystal structure of mouse VDAC1 at 2.3 A resolution reveals mechanistic insights into metabolite gating[END_REF][START_REF] Schneider | The Native Conformation of the Human VDAC1 N Terminus[END_REF][START_REF] Schredelseker | High Resolution Structure and Double Electron-Electron Resonance of the Zebrafish Voltage-dependent Anion Channel 2 Reveal an Oligomeric Population[END_REF]. They all display a common fold, which consists in a 19 β-strands β-barrel and one N-terminal helical segment lying inside the pore parallel to the membrane plane at about mid-height of the channel. This structure corresponds most probably to the open state of VDAC. There are clues suggesting that this structure might be conserved at least in the canonical VDACs of the different phylogenetic clades because : a) amino acid sequence analysis has put forward the presence of conserved motifs, long stretches of alternating hydrophobic and hydrophilic amino acid residues typical of β-barrel structure and a region featuring properties of α-helix at N-terminus [START_REF] Young | The evolutionary history of mitochondrial porins[END_REF][START_REF] Kutik | Dissecting membrane insertion of mitochondrial beta-barrel proteins[END_REF][START_REF] Imai | Eukaryote-wide sequence analysis of mitochondrial beta-barrel outer membrane proteins[END_REF][START_REF] Homblé | Plant VDAC: Facts and speculations[END_REF][START_REF] Jores | Characterization of the targeting signal in mitochondrial β-barrel proteins[END_REF]); b) the barrel fold is also confirmed by circular dichroism (CD) and attenuated total reflection Fourier transform infrared (ATR-FTIR) spectroscopy [START_REF] Shao | Circular dichroism studies of the mitochondrial channel, VDAC, from Neurospora crassa[END_REF]Abrecht et al. 2000a;[START_REF] Shanmugavadivu | Correct folding of the beta-barrel of the human membrane protein VDAC requires a lipid bilayer[END_REF]; and c) the electron and atomic force microscopy images corroborate the 3D structure [START_REF] Hiller | The 3D structures of VDAC represent a native conformation[END_REF].

In its open state, VDAC possesses a slight preference for inorganic monatomic anions over cations [START_REF] Smack | Voltage-dependent channels found in the membrane fraction of corn mitochondria[END_REF][START_REF] Schmid | Identification of two general diffusion channels in the outer membrane of pea mitochondria[END_REF][START_REF] Blumenthal | Purification and Characterization of the Voltage-Dependent Anion-Selective Channel Protein from Wheat Mitochondrial Membranes[END_REF][START_REF] Heins | Biochemical, molecular, and functional characterization of porin isoforms from potato mitochondria[END_REF]Abrecht et al. 2000b). Remarkably, most inorganic ions, metabolites and tRNA transported through VDAC are negatively charged. This raises the question of the mechanism(s) used to transport such diverse compounds.

In this review we address two key functional issues about plant VDAC: 1) How inorganic ions and metabolites are transported through the pore? and 2) What is the role of VDAC in the response of plant cells to oxidative stress? For this purpose, we compare the data available for plants and other organisms to highlight the similarities and differences between orthologues.

Transport and selectivity

The main physiological role of VDAC is the transport of chemical compounds of varying size, composition, structure and charge e.g., K + , Cl -, Ca 2+ , HPO4 2-, succinate 2-, ATP 4-or highly charged tRNA through MOM. Since the discovery of VDAC from Paramecium aurelia mitochondria [START_REF] Schein | Reconstitution in planar lipid bilayers of a voltage-dependent anion-selective channel obtained from paramecium mitochondria[END_REF]) the transport function of VDAC has been investigated by electrophysiology following its reconstitution in a planar lipid bilayer. For the sake of clarity, we describe separately the transport of inorganic monatomic ions (consisting of a single atom) and that of inorganic polyatomic ions (consisting of several atoms) and metabolites.

Inorganic monatomic ions

The functional properties of plant VDAC were mainly inferred from transport studies of inorganic monatomic ions (K + , Na + , Cl -). The obtained data indicate that the open state of plant VDAC can sustain a flow of about 10 7 ions/s in the presence of 0.1MKCl and 10mV and its selectivity for chloride ions over potassium ions is weak (~2Cl -:1K + ) [START_REF] Smack | Voltage-dependent channels found in the membrane fraction of corn mitochondria[END_REF][START_REF] Aljamal | Purification and Characterization of Porin from Corn (Zea mays L.) Mitochondria[END_REF][START_REF] Blumenthal | Purification and Characterization of the Voltage-Dependent Anion-Selective Channel Protein from Wheat Mitochondrial Membranes[END_REF][START_REF] Heins | Biochemical, molecular, and functional characterization of porin isoforms from potato mitochondria[END_REF]Abrecht et al. 2000b). These values are akin to those found for VDACs of other organisms [START_REF] Colombini | Voltage gating in the mitochondrial channel, VDAC[END_REF].

The experimental parameter measured to get information on the channel selectivity is the reversal potential, which is a voltage set up in the presence of a salt concentration gradient across the membrane when there is no net flow of ions (zero current) through the channel. Knowing the value of the reversal potential (mV), an electrodiffusion model is required to quantify the selectivity. Two models are commonly used: the Planck model and the Goldman-Hodgkin-Katz model. Solving the Nernst-Planck equation under the assumption of either electroneutrality (Planck) or constant electric field (Goldman-Hodgkin-Katz) in a channel gives two simple equations to quantify the selectivity [START_REF] Krammer | Origin of ion selectivity in Phaseolus coccineus mitochondrial VDAC[END_REF]. The Goldman-Hodgkin-Katz equation, commonly known as GHK equation, is the most popular one and was applied to quantify the selectivity of plant VDAC using the value of reversal potential measured at a single high salt concentration gradient (e.g., 1M/0.1M KCl) across the membrane. Surprisingly, in a recent work on VDAC purified from Phaseolus coccineus (PcVDAC) [START_REF] Krammer | Origin of ion selectivity in Phaseolus coccineus mitochondrial VDAC[END_REF]) it has been shown that PcVDAC selectivity value calculated by GHK equation changes with KCl concentration gradient, which disagrees with the assumption of a constant permeability ratio in the GHK model. Moreover, the GHK equation did not fit properly to the data showing the change in reversal potential versus the concentration gradient [START_REF] Krammer | Origin of ion selectivity in Phaseolus coccineus mitochondrial VDAC[END_REF]. The inappropriateness of the GHK and Planck models for the description of the selectivity was further demonstrated in an experiment showing the change in reversal potential as a function of salt concentration, at a constant KCl concentration gradient across the membrane (Fig. 1). Under the condition of the constant gradient, the two equations predict that the reversal potential is constant whatever the salt concentration is, and are in contradiction with the experimental results showing that the selectivity towards chloride ion increases at low KCl concentration. The dependence of the reversal potential on the salt concentration indicates the involvement of positive charged amino acid residues at low salt concentration and their screening at high concentration. The PcVDAC selectivity was correctly predicted taking into account the net fixed charge in the pore of the channel. A one-compartment macroscopic electrodiffusion model including both ion diffusion and an effective fixed charge in the pore was sufficient to describe properly the selectivity of the channel. (Fig. 1). Thus, in agreement with published data on yeast Saccharomyces cerevisiae [START_REF] Blachly-Dyson | Selectivity changes in site-directed mutants of the VDAC ion channel: structural implications[END_REF][START_REF] Peng | Large scale rearrangement of protein domains is associated with voltage gating of the VDAC channel[END_REF][START_REF] Zambrowicz | Zero-current potentials in a large membrane channel: a simple theory accounts for complex behavior[END_REF], the fixed charge in the pore governs the selectivity of plant VDAC.

Several plant genomes has been sequenced. The sequences coding for putative VDAC proteins indicate that in plant VDACs the number of positively charged amino acids is equal or higher than that of negatively charged amino acids (Fig. 2), which is consistent with a selectivity favoring chloride ions relative to potassium ions. The electrostatic screening effect is also clearly evidenced when the VDAC conductance normalized in respect to the bulk concentration (G/[KCl] ratio) is plotted versus the bulk concentration (Fig. 3).

Fig. 3. VDAC conductance normalized in respect to the bulk concentration (G/[KCl] ratio) as a function of plotted versus the bulk concentration

At low KCl concentration (0.1M), the screening of the fixed charges of the channel is weak, which favors the accumulation of chloride ions inside the channel because of the excess of positive fixed charges. Consequently, both G/[KCl] ratio and selectivity towards chloride increase. At high KCl concentration (1M), there is a strong screening of the fixed charges and VDAC behaves like a wide neutral pore. Thus, the ion concentration inside the channel will be close to that in solution and thus, the G/[KCl] ratio reaches its lowest value. At 1M KCl, the selectivity towards chloride ions is weak because the diffusion coefficient of chloride and potassium ions have a similar value. As shown in Fig. 1 and3, the fixed charge has a major impact on the G/[KCl] ratio and selectivity at concentrations that prevails in vivo. Therefore, the measurement of the reversal potential at high concentrations is of limited interest to assess plant VDAC selectivity because of the electrostatic screening effect.

Molecular modelling has been used to get insight into the microscopic mechanism for the monatomic ions transport through VDAC. Different simulation techniques have been used to investigate the structure-function relationship of VDAC [START_REF] Noskov | ATP Transport through VDAC and the VDAC-Tubulin Complex Probed by Equilibrium and Nonequilibrium MD Simulations[END_REF]. They require the knowledge of the protein structure at an atomic resolution, which does not exist for plant VDAC. The PcVDAC and the mouse VDAC1 (mVDAC1) share similar electrophysiological and secondary structure features suggesting a conserved mechanism of ion transport and a similar folding. Thus, a 3D model of PcVDAC was constructed using homology modelling and the 3D structure of mVDAC1 determined at a resolution of 2.3 Å as template [START_REF] Homblé | Plant VDAC: Facts and speculations[END_REF]. It features an electrostatic energy ion profile, a β-strand dynamics and a distribution of the hydrophobic and charged residues comparable to those of mVDAC1 [START_REF] Homblé | Plant VDAC: Facts and speculations[END_REF]). These similarities do not prove that the model is the right structure, but they provide a rational basis to use it as a working hypothesis to interpret the data collected on plant VDACs. The conductance and selectivity values of the PcVDAC 3D model calculated using Brownian Dynamics (BD) simulations are consistent with the experimental data, albeit some discrepancies are observed. In addition, BD and Molecular Dynamics (MD) simulations performed for mVDAC1 structure reproduce properly the concentration dependence of the PcVDAC selectivity (Fig. 4) [START_REF] Krammer | Concentration Dependent Ion Selectivity in VDAC: A Molecular Dynamics Simulation Study[END_REF][START_REF] Krammer | Molecular origin of VDAC selectivity towards inorganic ions: A combined molecular and Brownian dynamics study[END_REF][START_REF] Krammer | Origin of ion selectivity in Phaseolus coccineus mitochondrial VDAC[END_REF]. The free energy profile of the ion Fig. 4. Effect of ionic strength on the reversal potential of PcVDAC at a fixed concentration ratio trans/cis = 2. The reversal potential computed from BD trajectories of mVDAC1 (circle, dashed line) and experimentally determined on PcVDAC (square, solid line). Reprinted with permission from Mitochondrion [START_REF] Krammer | Origin of ion selectivity in Phaseolus coccineus mitochondrial VDAC[END_REF] translocation along the pore of mVDAC1 shows a concentration dependence (Fig. 5). The free energy profile of chloride ions is lower than that of potassium ions favoring the transport of chloride ions. The difference between the free energy profiles of these ions decreases at high salt concentration in agreement with the weakest selectivity observed for PcVDAC at 1M KCl. The maximum of the free energy profile of ion permeation coincides with the channel region made up of the N-terminal helix and the surrounding beta-barrel strip, which might be the rate-limiting step for ion transport through VDAC. These conclusions are consistent with results obtained by BD and MD simulations on mVDAC1 [START_REF] Krammer | Concentration Dependent Ion Selectivity in VDAC: A Molecular Dynamics Simulation Study[END_REF][START_REF] Krammer | Molecular origin of VDAC selectivity towards inorganic ions: A combined molecular and Brownian dynamics study[END_REF]. MD also shows that ion transport through mVDAC1 is driven by the global electrostatics due to the distribution of charges in the pore and not by specific pathways or interactions with amino acid residues [START_REF] Krammer | Concentration Dependent Ion Selectivity in VDAC: A Molecular Dynamics Simulation Study[END_REF].

In regards to the transport process of inorganic monatomic ions through VDAC, the molecular simulations emphasizes the major role of the non-uniform charge distribution in Fig. 5. Ion concentration dependent energy profile of mVDAC1. Chloride (solid lines) and potassium(dashed lines) concentration dependent energy profiles computed fromBD simulations performed at 0.1M(red), 0.25 M (blue), 0.5 M (cyan), 0.8 M (orange), and 1.0 M (black) KCl. Reprinted with permission from Mitochondrion [START_REF] Krammer | Origin of ion selectivity in Phaseolus coccineus mitochondrial VDAC[END_REF] VDAC pore. Despite the simplistic assumptions underpinning the macroscopic model, it is remarkable that it fits pretty well to the experimental data and thereby, it provides an easy practical way to quantify the selectivity measured experimentally. The preference for anions relative to cations serves the major physiological role of VDAC, i.e. the transport of metabolites, most of which are anions. This major VDAC function might have undergone pressure of the natural selection, which might explain the conserved transport process of metabolites between the different phylogenetic clades. In agreement with this suggestion, the weak VDAC selectivity of all species studied for monatomic inorganic ions appears as a consequence of the electrostatic properties of the pore (Colombini 2016).

Inorganic polyatomic ions and metabolites

The major function of mitochondria is the transformation of energy for cellular needs. This requires the exchange of inorganic polyatomic ions (e.g., H2PO4 -, HPO4 2-) and metabolites (e.g., ADP 2-, ATP 4-, succinate 2-) between the mitochondrial matrix and the cytosol. The experiment with purified VDAC from Neurospora crassa (NcVDAC) has provided indirect and direct evidences for the permeation of several compounds through VDAC. The flux through VDAC estimated from selectivity measurement indicated that VDAC can discriminate between different compounds according to the sequence H2PO4 -> HPO4 2-= succinate 2-> citrate 3-and that the flux of these compounds is strongly reduced when VDAC switched from the open to a subconductance state [START_REF] Hodge | Regulation of metabolite flux through voltage-gating of VDAC channels[END_REF]. The specificity of nucleotide-VDAC binding was shown for mammalian VDAC by the channel labeling with [α -32 P]BzATP in the presence of various nucleotides [START_REF] Yehezkel | Nucleotide-binding sites in the voltage-dependent anion channel -Characterization and localization[END_REF]. Combining electrophysiology and luciferin/luciferase assay [START_REF] Rostovtseva | ATP Flux Is Controlled by a Voltage-gated Channel from the Mitochondrial Outer Membrane[END_REF]1997) have achieved a direct evidence demonstrating that ATP 4- permeates VDAC in the open state but not in subconductance states. Assuming ATP concentration of 1-10mM and a voltage of 10mV, one can estimate that ATP can permeate VDAC at a rate of about 10 4 -10 5 ATP/s i.e. at least two order of magnitude lower than that of monatomic inorganic ions. The dependence of ATP flux through VDAC channel on ATP concentration is linear up to 100mM ATP suggesting a low-affinity binding site, which is required for an efficient translocation rate.

The VDAC occupancy by ATP interferes with the permeation of inorganic monatomic ions, which results in a decrease of VDAC conductance [START_REF] Rostovtseva | ATP transport through a single VDAC channel, studied by noise analysis[END_REF]. Thus, the change in conductance is an indirect way to probe the occupancy of VDAC channel by metabolites. Mononucleotides (AMP 2-, ADP 3-, UTP 4-) and dinucleotides (NAD -, NADH 2-, and NADPH 4-) were found to decrease the NcVDAC conductance [START_REF] Rostovtseva | Dynamics of Nucleotides in VDAC Channels: Structure-Specific Noise Generation[END_REF]. Accordingly, the conductance of mouse VDAC2 and PcVDAC decreases in the presence of ATP [START_REF] Komarov | New insights into the mechanism of permeation through large channels[END_REF][START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF]. In the case of PcVDAC, the decrease in channel conductance is larger in the presence of ATP than AMP. The magnitude of the conductance change is attenuated at high salt concentration (1M) [START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF] probably due to the electrostatic screening of the metabolites and channel fixed charge.

Altogether, these experimental results point to a common mechanism of metabolite transport shared by VDACs of all organisms. They emphasize firstly that VDACs are channels for the transport of metabolites and organic polyatomic ions and secondly that they may regulate the flow of these compounds. The regulatory property is related to a change in VDAC conductance. Though it is well established that this change in conductance can be triggered by a change in the membrane potential, there is numerous evidences concerning mammalian cells that it could be also induced by interaction with proteins, peptides or small compounds [START_REF] Rostovtseva | VDAC regulation: role of cytosolic proteins and mitochondrial lipids[END_REF][START_REF] Shoshan-Barmatz | VDAC, a multi-functional mitochondrial protein regulating cell life and death[END_REF][START_REF] Rostovtseva | VDAC inhibition by tubulin and its physiological implications[END_REF]. For example, NADH was found to regulate the gating of potato tuber VDAC [START_REF] Lee | Beta-NADH decreases the permeability of the mitochondrial outer membrane to ADP by a factor of 6[END_REF]Zizi et al. 1994).

MD simulations of H2PO4 -diffusion through mVDAC1 revealed a permeation process very similar to that of chloride ions. Thus, both free energy profiles of permeation displayed the same features and no specific pathway was reported for the monovalent anion H2PO4 - , though a few long-lived interactions with some amino acid residues were noticed [START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF]. A completely different scenario was found for the permeation of the divalent anion HPO4 2-, which followed a specific pathway and long-lasting interactions with a limited number of positively charged amino acid residues: K12, R15, K20, K96, K119, and R218 [START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF].

The molecular simulation of metabolites permeation through VDAC is all but trivial. According to the experimental flux measurements [START_REF] Rostovtseva | ATP Flux Is Controlled by a Voltage-gated Channel from the Mitochondrial Outer Membrane[END_REF] , the transport of one ATP through the VDAC lasts about 10-100 µs and this is a major bottleneck regarding MD simulations. Several approaches were used to unravel the mechanism of ATP permeation by the use of molecular simulation [START_REF] Noskov | ATP Transport through VDAC and the VDAC-Tubulin Complex Probed by Equilibrium and Nonequilibrium MD Simulations[END_REF]. They all indicated that the phosphate moiety of ATP interacts with positively charged amino acid residues of the pore (R15, K20, K96) and point the N-terminus α-helix as a probable weak binding site for ATP [START_REF] Noskov | ATP Transport through VDAC and the VDAC-Tubulin Complex Probed by Equilibrium and Nonequilibrium MD Simulations[END_REF][START_REF] Choudhary | Structure-guided simulations illuminate the mechanism of ATP transport through VDAC1[END_REF][START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF]) that corresponds to experimental data [START_REF] Yehezkel | Nucleotide-binding sites in the voltage-dependent anion channel -Characterization and localization[END_REF][START_REF] Yehezkel | An N-terminal nucleotide-binding site in VDAC1: Involvement in regulating mitochondrial function[END_REF][START_REF] Villinger | Nucleotide Interactions of the Human Voltage-dependent Anion Channel[END_REF]. As ATP, AMP interacts with the binding site but more weakly. Though there is a general agreement about the identification of the binding site, the question on how ATP arrives to and leaves from the binding site is a matter of debate. [START_REF] Choudhary | Structure-guided simulations illuminate the mechanism of ATP transport through VDAC1[END_REF] identified five different pathways for ATP permeation, while [START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF] pointed to a preferential pathway recruiting K12, R15, K20, K96, K119, and R218. Their key position in the structure and their long and flexible side chains might favor the permeation of the phosphate ions and metabolites through VDAC via a brush-like mechanism [START_REF] Yehezkel | Nucleotide-binding sites in the voltage-dependent anion channel -Characterization and localization[END_REF][START_REF] Villinger | Nucleotide Interactions of the Human Voltage-dependent Anion Channel[END_REF][START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF]) (Fig. 6). Even though the occurrence of long-lasting interaction between H2PO4 -and some amino acid residues is relatively less frequent, it occurs notably with R15 and K20 of the binding site. Thus, according to the minimum in the free energy profile of the studied compounds, the probability of interaction with the binding site decreases according to the sequence ATP 4-> HPO4 2-> AMP 2-> H2PO4 -. Fig. 6. The charged brush mechanism of VDAC. Schematic representation of the positively charged key residues acting as a charged brush to facilitate permeation of the divalent form of Pi, AMP, and ATP along the VDAC pore. Below are represented successive MD conformations (in green and purple) showing these positively charged side chains undergoing a sweeping motion assisting the translocation of Pi along the pore. Pi are shown as balls and sticks, and the basic residues as thick sticks. CYT and IS stand for the cytosolic and the intermembrane side, respectively. Reprinted with permission from PLoS ONE [START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF] As regard to the mechanism of permeation through plant VDAC conserved features have been noticed [START_REF] Krammer | Dual Mechanism of Ion Permeation through VDAC Revealed with Inorganic Phosphate Ions and Phosphate Metabolites[END_REF]. Namely, the N-terminal helical segment and the cluster of positively charged amino acid residues forming the binding site, K12, R15 and K20 are conserved in PcVDAC. When the effect of ATP and AMP on the PcVDAC conductance is considered, it is observed that the decrease in conductance is higher in the presence of ATP because of its long dwelling time inside the pore, which restricts the diffusion of inorganic monatomic ions. At high NaCl concentration (1M) change in the conductance is weaker than at 0.1M NaCl because the electrostatic screening of the charges inside the pore shallows the free energy profile for ATP and AMP, that decreases their probability of interaction with the binding site and thereof reduces dwelling time inside the VDAC pore.

3. VDAC involvement in oxidative stress and regulated cell death.

The role of mitochondria in oxidative stress

In Eukaryotic cells, oxidative stress can be defined as a process resulting from an imbalance between the production of reactive oxygen species (ROS) and capacity of cellular antioxidant defenses. The defense mechanisms, include upregulation of various endogenous molecules, such as glutathione, ROS catalytic removal by enzymes like superoxide dismutase, catalase, and peroxidase and repair of ROS-modified molecules [START_REF] Barber | Oxidative stress in ALS: A mechanism of neurodegeneration and a therapeutic target[END_REF][START_REF] Radak | Age-associated neurodegeneration and oxidative damage to lipids, proteins and DNA[END_REF][START_REF] Mailloux | Unearthing the secrets of mitochondrial ROS and glutathione in bioenergetics[END_REF]). Among ROS there are the free radicals of oxygen (e.g. singlet oxygen (1 O2), superoxide anion (O2  ) and hydroxyl radical (•OH)), which are atoms or molecules with an unpaired electron that can be rapidly donated making them highly reactive molecular species. Hydrogen peroxide (H2O2) is not a free radical but it belongs to ROS, and it is capable of producing oxidative stress. The main site of ROS production in cells are mitochondria (e.g., [START_REF] Ott | Mitochondria, oxidative stress and cell death[END_REF][START_REF] Murphy | How mitochondria produce reactive oxygen species[END_REF]) and chloroplasts in photosynthetic tissues [START_REF] Woodson | Coordination of gene expression between organellar and nuclear genomes[END_REF][START_REF] Van Aken | Licensed to Kill: Mitochondria, Chloroplasts, and Cell Death[END_REF]. In mitochondria, They are mainly generated at Complex I and III of the respiratory chain as a result of respiratory chain reactions. The oneelectron reduction of molecular oxygen produces a relatively stable intermediate, i.e. O2  , which serves as the precursor of most ROS but the detail mechanism of their generation is beyond the scope of the review (for review, see for example, [START_REF] Murphy | How mitochondria produce reactive oxygen species[END_REF]. In chloroplast site of production. The details of ROS production in chloroplast is beyond the scope of the chapter as VDAC is highly abundant in mitochondria.

O2  produced by mitochondria Complex I is released into the mitochondrial matrix whereas O2  produced by Complex III appears on both sides of the inner membrane. As summarized by [START_REF] Ott | Mitochondria, oxidative stress and cell death[END_REF], within the mitochondrial matrix, MnSOD (manganese containing superoxide dismutase) converts O2  to H2O2, which can be further metabolized by glutathione peroxidase (Gpx1) and peroxiredoxin (PrxIII), or diffuse from the mitochondria into the cytosol. O2  located in the intermembrane space can be released into the cytosol and/or converted into H2O2 by CuZnSOD (copper and zinc containing superoxide dismutase). Accordingly, mitochondria contribute 20-30% of the cytosolic steady-state concentration of H2O2 [START_REF] Han | Voltage-dependent Anion Channels Control the Release of the Superoxide Anion from Mitochondria to Cytosol[END_REF]. The conversion of O2  into H2O2 proceeds also in the cytosol due to the presence of cytosolic CuZnSOD and the H2O2 may be then decomposed to water and oxygen by catalase located mainly in peroxisomes (Del [START_REF] Río | Plant Peroxisomes, Reactive Oxygen Metabolism and Nitric Oxide[END_REF]. Importantly, about 1% of ROS escapes elimination [START_REF] Ott | Mitochondria, oxidative stress and cell death[END_REF]. Likewise excessive O2  generation by the mitochondrial respiratory chain and consequently other ROS production can lead to oxidation of macromolecules including DNA, proteins and membrane lipids that may influence cell viability and trigger cell death 1 (e.g., [START_REF] Shoshan-Barmatz | The mitochondrial voltage-dependent anion channel 1 in tumor cells[END_REF]. Moreover, it is proposed that the steady state concentration of O2  in the mitochondrial matrix is about 5-to 10-fold higher than that in the cytosol or nucleus making mitochondria a possible primary target for the damaging effects of ROS [START_REF] Ott | Mitochondria, oxidative stress and cell death[END_REF]. This denote that mitochondria may generate and/or propagate oxidative stress. However, the mechanisms of O2  transport via the outer membrane of mitochondria and the control of this process are still not clear.

VDAC and the regulated cell death

In mammals, the O2  release from rat heart mitochondria is inhibited by known VDAC inhibitor [START_REF] Han | Voltage-dependent Anion Channels Control the Release of the Superoxide Anion from Mitochondria to Cytosol[END_REF]. It has been also reported that closure of VDAC1 may impede the efflux of O2 •-from the intermembrane space to the cytosol that results in internal oxidative stress and promotion of mitochondrial membrane permeability changes related to regulated cell death [START_REF] Tikunov | Closure of VDAC causes oxidative stress and accelerates the Ca2+-induced mitochondrial permeability transition in rat liver mitochondria[END_REF]). In addition, silencing of VDAC1 expression results in inhibition of oxidative stress-induced regulated cell death whereas overexpression of the protein enhances the regulated cell death in mammalian cells (e.g., [START_REF] Liu | Increased susceptibility to apoptosis in CD45+ myeloma cells accompanied by the increased expression of VDAC1[END_REF][START_REF] Simamura | Furanonaphthoquinones cause apoptosis of cancer cells by inducing the production of reactive oxygen species by the mitochondrial voltage-dependent anion channel[END_REF][START_REF] Tomasello | Outer membrane VDAC1 controls permeability transition of the inner mitochondrial membrane in cellulo during stress-induced apoptosis[END_REF][START_REF] Chen | Inhibition of VDAC1 prevents Ca2+-mediated oxidative stress and apoptosis induced by 5-aminolevulinic acid mediated sonodynamic therapy in THP-1 macrophages[END_REF].

In yeasts, it has been shown that isogenic wild type and por1 S. cerevisiae mitochondria depleted of YVDAC1 differ distinctly in the level of O2  release [START_REF] Budzińska | The TOM complex is involved in the release of superoxide anion from mitochondria[END_REF]). The expression level of CuZnSOD and MnSOD proteins is influenced by the absence of either YVDAC isoform and both YVDAC1 and YVDAC2 are required for the homeostasis of the mitochondrial redox state [START_REF] Galganska | Communication between mitochondria and nucleus: Putative role for VDAC in reduction/oxidation mechanism[END_REF].

There are strong evidences indicating that regulated cell death occurs in plants and it is coupled to the mtROS production [START_REF] Rhoads | Mitochondrial Reactive Oxygen Species. Contribution to Oxidative Stress and Interorganellar Signaling[END_REF][START_REF] Love | Timing is everything: regulatory overlap in plant cell death[END_REF][START_REF] Zancani | The Permeability Transition in Plant Mitochondria: The Missing Link[END_REF][START_REF] Van Aken | Licensed to Kill: Mitochondria, Chloroplasts, and Cell Death[END_REF][START_REF] Huang | Roles of mitochondrial reactive oxygen species in cellular signalling and stress response in plants[END_REF]. The synthesis of mtROS occurs during respiratory activity of plant cells. Under normal conditions, mtROS detoxification by dismutation and redox reactions prevent their deleterious effects on proteins, lipids and DNA molecules. In addition, the electron transport chain of plant mitochondria contains an alternative oxidase (AOX) that catalyses the oxidation of ubiquinol and reduces oxygen to water, which minimizes the formation of mtROS [START_REF] Møller | PLANT MITOCHONDRIA AND OXIDATIVE STRESS: Electron Transport, NADPH Turnover, and Metabolism of Reactive Oxygen Species[END_REF][START_REF] Vanlerberghe | Alternative Oxidase: A Mitochondrial Respiratory Pathway to Maintain Metabolic and Signaling Homeostasis during Abiotic and Biotic Stress in Plants[END_REF]. There is a growing body of evidence pointing at enhanced mtROS production and consecutive redox signaling during the plant response to biotic and abiotic stresses [START_REF] Love | Timing is everything: regulatory overlap in plant cell death[END_REF][START_REF] Van Aken | Licensed to Kill: Mitochondria, Chloroplasts, and Cell Death[END_REF].

When mtROS formation exceeds the normal ROS level despite the existence of an endogenous protective capacity, it may induced mitochondrial retrograde regulation as well as regulated cell death [START_REF] Garcia-Brugger | Early Signaling Events Induced by Elicitors of Plant Defenses[END_REF][START_REF] Rhoads | Mitochondrial Reactive Oxygen Species. Contribution to Oxidative Stress and Interorganellar Signaling[END_REF][START_REF] Woodson | Coordination of gene expression between organellar and nuclear genomes[END_REF][START_REF] Huang | Roles of mitochondrial reactive oxygen species in cellular signalling and stress response in plants[END_REF]. It has been suggested that VDAC is involved in plant stress responses through its involvement in regulated cell death [START_REF] Vianello | The mitochondrial permeability transition pore (PTP) -An example of multiple molecular exaptation?[END_REF][START_REF] Takahashi | The functions of voltage-dependent anion channels in plants[END_REF]. Several experimental data support this hypothesis. Either the overexpression of the rice OsVDAC4 or the human HVDAC1 in mammalian cell lines (Yurkat T-cell) induces apoptosis [START_REF] Godbole | VDAC is a conserved element of death pathways in plant and animal systems[END_REF]. This indicate that OsVDAC4 can substitute for HVDAC1to trigger PCD in mammalian cells. Regulated cell death was also induced by the overexpression of OsVDAC4 in tobacco BY2 cells and leaves [START_REF] Godbole | Mitochondrial VDAC and hexokinase together modulate plant programmed cell death[END_REF] or after the overexpression of Pennisetum glaucum VDAC in rice [START_REF] Desai | Structural and functional analysis of a salt stress inducible gene encoding voltage dependent anion channel (VDAC) from pearl millet (Pennisetum glaucum)[END_REF]). In addition, regulated cell death induced by biotic or abiotic stress is correlated to an upregulation of VDAC transcript and protein level [START_REF] Lacomme | Identification of new early markers of the hypersensitive response in Arabidopsis thaliana[END_REF][START_REF] Kawai-Yamada | Mammalian Bax-induced plant cell death can be down-regulated by overexpression of Arabidopsis Bax Inhibitor-1 (AtBI-1)[END_REF][START_REF] Bitar | Sequence analysis, transcriptional and posttranscriptional regulation of the rice vdac family[END_REF][START_REF] Swidzinski | A proteomic analysis of plant programmed cell death[END_REF][START_REF] Desai | Structural and functional analysis of a salt stress inducible gene encoding voltage dependent anion channel (VDAC) from pearl millet (Pennisetum glaucum)[END_REF][START_REF] Tateda | Plant voltage-dependent anion channels are involved in host defense against Pseudomonas cichorii and in Baxinduced cell death[END_REF][START_REF] Kusano | Voltage-dependent anion channels: their roles in plant defense and cell death[END_REF]). The mammalian anti-apoptotic factors Bcl-xL and its functional homolog Ced-9 in Caenorhabditis are known to suppress regulated cell death in non-plant cells. Though there is no homologue proteins to the BCL-2 familly in plant genome the heterologous expression of Bcl-2, Bcl-xL and Ced-9 cDNA in tobacco plants under the control of a strong promoter inhibits plant regulated death induced by different abiotic stresses or by the non virulent pathogen tobacco mosaic virus [START_REF] Mitsuhara | Animal cell-death suppressors Bcl-xL and Ced-9 inhibit cell death in tobacco plants[END_REF][START_REF] Qiao | Enhanced Resistance to Salt, Cold and Wound Stresses by Overproduction of Animal Cell Death Suppressors Bcl-xL and Ced-9 in Tobacco Cells -Their Possible Contribution Through Improved Function of Organella[END_REF]. The overexpression of mammalian Bax gene in tobacco plants causes regulated cell death [START_REF] Lacomme | Bax-induced cell death in tobacco is similar to the hypersensitive response[END_REF][START_REF] Tateda | Plant voltage-dependent anion channels are involved in host defense against Pseudomonas cichorii and in Baxinduced cell death[END_REF] in agreement with the pro-apoptotic function of Bax proteins.

Altogether, these data highlight the involvement of plant VDAC in the regulated cell death.

VDAC-protein interaction

The function of a protein is often regulated through interaction with other proteins. The occurrence of protein-protein interactions is ubiquitous and is essential for proper functioning of cells. Cytosolic and mitochondrial proteins have been found to interact directly with the mammalian VDAC1 to mediate signaling between cytosol and mitochondria [START_REF] Rostovtseva | VDAC regulation: role of cytosolic proteins and mitochondrial lipids[END_REF][START_REF] Rostovtseva | VDAC inhibition by tubulin and its physiological implications[END_REF][START_REF] Shoshan-Barmatz | The mitochondrial voltage-dependent anion channel 1 in tumor cells[END_REF]. Here, we will focus on hexokinase and thioredoxin, which have been studied in plants.

VDAC-hexokinase interaction

Interaction of mammalian VDAC1 with hexokinase (HK) isoforms is important for cell protection against oxidative stress and consecutive cell death (e.g., [START_REF] Shoshan-Barmatz | The mitochondrial voltage-dependent anion channel 1 in tumor cells[END_REF]. It has been observed for HEK cells that HK I and HK II bounding to VDAC1 decreases ROS release from mitochondria [START_REF] Sun | Glucose Phosphorylation and Mitochondrial Binding Are Required for the Protective Effects of Hexokinases I and II[END_REF]). HK interaction with VDAC1 affects its channel properties, but the question of whether the binding to VDAC leads to its closure or to its opening is still not answered although the available data allow for suggestion that binding of HK II to VDAC1 protects it from closing [START_REF] Robey | Mitochondrial hexokinases, novel mediators of the antiapoptotic effects of growth factors and Akt[END_REF][START_REF] Sun | Glucose Phosphorylation and Mitochondrial Binding Are Required for the Protective Effects of Hexokinases I and II[END_REF]) whereas binding of HK I induces it closure [START_REF] Azoulay-Zohar | In self-defence: hexokinase promotes voltage-dependent anion channel closure and prevents mitochondriamediated apoptotic cell death[END_REF]). Such alteration of the channel conductance may have detrimental effect for cell because it has been shown that excessive VDAC closure induces mitochondrial swelling and regulated cell death in mammalian cells [START_REF] Majewski | Hexokinase-Mitochondria Interaction Mediated by Akt Is Required to Inhibit Apoptosis in the Presence or Absence of Bax and Bak[END_REF][START_REF] Rostovtseva | On the Role of VDAC in Apoptosis: Fact and Fiction[END_REF].

Plant hexokinases, named HXKs, are the only enzymes that can phosphorylate glucose2 [START_REF] Granot | Role of tomato hexose kinases[END_REF]. The HXKs that interact with mitochondria harbor a N-terminal putative membrane anchor sequence and are classified in 'type B HXK' (HXK1) [START_REF] Granot | Substantial roles of hexokinase and fructokinase in the effects of sugars on plant physiology and development[END_REF]). Hexokinase1 (HXK1) has a dual function: it catalyzes glucose phosphorylation and acts as a glucose sensor [START_REF] Jang | Sugar sensing in higher plants[END_REF][START_REF] Granot | Substantial roles of hexokinase and fructokinase in the effects of sugars on plant physiology and development[END_REF] In plants, hexokinase has been shown to play a role in pathogen induced and H2O2induced cell death [START_REF] Kim | Mitochondria-associated hexokinases play a role in the control of programmed cell death in Nicotiana benthamiana[END_REF][START_REF] Camacho-Pereira | Reactive Oxygen Species Production by Potato Tuber Mitochondria Is Modulated by Mitochondrially Bound Hexokinase Activity[END_REF][START_REF] Kusano | Voltage-dependent anion channels: their roles in plant defense and cell death[END_REF]). Kim's seminal work [START_REF] Kim | Mitochondria-associated hexokinases play a role in the control of programmed cell death in Nicotiana benthamiana[END_REF]) has shown that Nicotiana benthamiana HXK1was associated with the mitochondria. Using virus-induced gene silencing they have shown that the downregulation of HXK1 acivated regulated cell death whereas the overexpression of the mitochondria-associated Arabidopsis hexokinases, HXK1 and HXK2, enhanced the resistance to regulated cell death of cells subjected to (experiencing undergoing) an oxidative stress. In addition, HXK1 prevented the H2O2-induced cytochrome c release if it harbor its N-terminal membrane anchor.

Another study has shown that transiently expressed OsVDAC4 and NtKxK3 Nicotiana benthamiana hexokinase into tobacco BY2 cells are localize to mitochondria. The co-expression of the two proteins in plant leafs were more efficient to prevent the induction of regulated cell death than NtKxK3 alone [START_REF] Godbole | Mitochondrial VDAC and hexokinase together modulate plant programmed cell death[END_REF]. Finally, a detergent solubilized membrane proteins from beetroot mitochondria was shown to contain a complex HXK-VDAC suggesting that VDAC and HXK might interact in the MOM [START_REF] Alcántar-Aguirre | ATP produced by oxidative phosphorylation is channeled toward hexokinase bound to mitochondrial porin (VDAC) in beetroots (Beta vulgaris)[END_REF].

These results indicate that mitochondrial-associated hexokinase play a role in the regulated cell death and suggest that the interaction between HK and VDAC might be the functional unit.

These data support the conclusion that plant VDAC have a role in the regulated cell death through its interaction with soluble proteins. It has long be thought that VDAC was a constituent of a protein complex named the permeability transition pore (PTP) that increases the permeability of MIM to solutes. However, the existence of the PTP is now questioned because the permeability transition occurs in the absence of the major components of the PTP. For instance, the peripheral benzodiazepine receptor (TSPO), the adenosine nucleotide translocase (ANT) and the VDAC are dispensable for the permeability transition [START_REF] Kokoszka | The ADP/ATP translocator is not essential for the mitochondrial permeability transition pore[END_REF][START_REF] Krauskopf | Properties of the permeability transition in VDAC1-/-mitochondria[END_REF][START_REF] Baines | Voltage-dependent anion channels are dispensable for mitochondrial-dependent cell death[END_REF][START_REF] Šileikytė | Regulation of the Mitochondrial Permeability Transition Pore by the Outer Membrane Does Not Involve the Peripheral Benzodiazepine Receptor (Translocator Protein of 18 kDa (TSPO))[END_REF][START_REF] Gutiérrez-Aguilar | Genetic manipulation of the cardiac mitochondrial phosphate carrier does not affect permeability transition[END_REF]. Recent data point to the role of the F-ATP synthase dimer in the formation of the PTP in MIM [START_REF] Zancani | The Permeability Transition in Plant Mitochondria: The Missing Link[END_REF].

VDAC-thioredoxin interaction

Thioredoxins are regulatory disulfide proteins that mediate the cellular redox homeostasis allowing disulfide bridge reduction of the target protein. Trx are recruited by Trx-dependent peroxidases (Prxs) to scavenge hydrogen peroxide. In addition, through the control of the redox state of proteins they may also regulated the ROS signaling [START_REF] Sevilla | The thioredoxin/peroxiredoxin/sulfiredoxin system: current overview on its redox function in plants and regulation by reactive oxygen and nitrogen species[END_REF].

Four VDAC isoforms have been characterized In Arabidopsis [START_REF] Yan | Voltage-Dependent Anion Channel 2 of Arabidopsis thaliana (AtVDAC2) Is Involved in ABA-Mediated Early Seedling Development[END_REF][START_REF] Tateda | Molecular and genetic characterization of the gene family encoding the voltage-dependent anion channel in Arabidopsis[END_REF][START_REF] Bauwe | Photorespiration has a dual origin and manifold links to central metabolism[END_REF][START_REF] Robert | Voltage-dependent-anion-channels (VDACs) in Arabidopsis have a dual localization in the cell but show a distinct role in mitochondria[END_REF][START_REF] Tateda | The Arabidopsis voltage-dependent anion channel 2 is required for plant growth[END_REF][START_REF] Li | The Voltage-Dependent Anion Channel 1 (AtVDAC1) Negatively Regulates Plant Cold Responses during Germination and Seedling Development in Arabidopsis and Interacts with Calcium Sensor CBL1[END_REF]. Recently, Zhang et al. [START_REF] Zhang | Arabidopsis mitochondrial voltage-dependent anion channel 3 (AtVDAC3) protein interacts with thioredoxin m2[END_REF] have performed a yeast two-hybrid screen have to identify the interaction between the Arabidopsis thaliana VDAC isoform 3 (AtVDAC3) and the chloroplast protein thioredoxin m2 (AtTrx m2) in the regulation of the ROS signaling occurring in respon. This interaction is specific for AtVDAC3 since AtVDAC1, AtVDAC2, and AtVDAC4 failed to interact with AtTrx m2 in the Y2H essay. The co-expression of AtTrx m2-GFP N and AtVDAC3-GFP C in BY2 tobacco cells localize the two proteins in the mitochondria. The localization of AtTrx m2 at the mitochondrial is not surprising since it has been shown that it is targeted to the cytosol when interacting with cytosolic proteins [START_REF] Meyer | Alternative targeting of Arabidopsis plastidic glucose-6-phosphate dehydrogenase G6PD1 involves cysteine-dependent interaction with G6PD4 in the cytosol[END_REF][START_REF] Hölscher | Dual-Targeting of Arabidopsis 6-Phosphogluconolactonase 3 (PGL3) to Chloroplasts and Peroxisomes Involves Interaction with Trx m2 in the Cytosol[END_REF]. The authors present evidence that AtVDAC3 and AtTrx m2 participate to the regulated cell death. They have shown that hat AtVDAC3 and AtTrx m2 genes were up-regulated when wildtype Arabidopsis plants were treated with H2O2, mannitol or NaCl. [START_REF] Zhang | Arabidopsis mitochondrial voltage-dependent anion channel 3 (AtVDAC3) protein interacts with thioredoxin m2[END_REF] have also analyzed transgenic Arabidopsis plants that overexpress either AtVDAC3 OE or AtTrx m2 OE . Both wildtype and transgenic plants were treated with either NaCl (salt stress) or H2O2. Interestingly, AtVDAC3 OE and AtTrx m2 OE transgenic lines displayed opposite effects in the presence of the abiotic stress. In regards to the wildtype, the seedling growth lower and the ROS production was enhanced in AtVDAC3 OE cell line whereas the seedling growth was higher and the ROS production reduced in AtTrx m2 OE cell line. Altogether, these data suggest that AtVDAC3 and AtTrx m2 might be involved in the regulated cell death. How their interaction might affect the regulated cell death deserves further investigations.

Conclusion

Despite early evolutionary divergence of VDAC proteins and their weak amino acid sequence similarity between different organisms, both the experimental and theoretical data indicate at conservation of the permeation process. The deciphering of the mechanisms underlying inorganic ion and metabolite permeation through VDAC is important, as the most of the chemical species entering or leaving mitochondria are anions significant for energy transformation .The change in VDAC permeability may be imposed by oxidative stress. It has been observed for plant cells that oxidative stress may result in VDAC interaction with other proteins such as cytosolic hexokinase and thioredoxin although the way of their binding to plant VDAC and their impact on its functional properties remains to be elucidated. This in turn should allow for explanation of VDAC contribution to plant cell regulated death.

Fig. 1 .

 1 Fig. 1. Effect of ionic strength on the reversal potential of PcVDAC at a fixed concentration ratio trans/cis = 2. A nonlinear least square regression was used to fit the data to a fixed charge model (continuous line) (DCl/DK = 1.02, effective fixed charge concentration X=0.1 M, goodness of the fit R 2 = 0.994). The reversal potential calculated using the voltage GHK equation (with the PCl/PK = 1.10 at at concentration ratio 2/1 M KCl (trans/cis)) is shown as a dashed line. Reprinted with permission from Mitochondrion (Krammer et al. 2014) with slight modification.

Fig. 2 .

 2 Fig. 2. Net charge of plant VDAC proteins. Data were obtained from a set of 80 gene sequences encoding putative VDAC proteins retrieved from full sequenced genomes of representatives of 16 different plant genus (https://phytozome.jgi). These VDAC proteins contain from 274 to 280 amino acids and have theoretical isoelectric point (pI) consistent with the data found for VDAC in 2D-PAGE. The number attached to the symbol indicates the number of sequences with the specified net charge with an average value of 3.5 ± 2.3 (mean ± S.D.).

Mis en forme : Français (Belgique)

Within the chapter we will follow the proposition of the Nomenclature Committee on Cell Death(Galluzzi et al.

2015).

The affinity for glucose is 1-3 orders of magnitude higher than that of other sugars.

Acknowledgments

FH is a Research Director at the F.R.S.-FNRS (Belgium)


D Lanzarotto
email: damiano.lanzarotto@supergrid-institute.com

P B Steckler

K Vershinin

F Morel

Open-Delta SBC: a New Converter Topology with Low Number of Sub-Modules for MV applications

Keywords: converter», «AC-DC converter», «DC-AC converter», «Volume reduction», «Modular

Multilevel Converters (MMC)»

Introduction

It is well established nowadays that high voltage direct current (HVDC) technology represents the most advantageous technical solution to problems such as long-distance energy transmission, asynchronous AC systems interconnection, interconnection of different regions requiring submarine and underground cables and transmission of offshore wind power to shore [START_REF] Bahrman | The ABCs of HVDC transmission technologies[END_REF][START_REF] Bresesti | HVDC connection of offshore wind farms to the transmission system[END_REF]. In particular, the installation of HVDC lines is rapidly expanding in Europe and China. This is driven by the possibility of interconnecting large renewable energy sources located far away from where the main loads are [START_REF] Qin | Study on the development and reliability of HVDC transmission systems in China[END_REF][START_REF] Xie | Reliability-oriented networking planning for meshed VSC-HVDC grids[END_REF][START_REF] Orths | The European North seas countries' offshore grid initiative-The way forward[END_REF]. The modular multilevel converter (MMC) represents the standard in terms of converter choice for recent HVDC applications mainly because its advantages compared to line-commuted converters (LCC): capability of realizing an independent P/Q control and small footprint due to the absence of any filter requirements. In addition, its modularity allows the use of low voltage building blocks to create high voltage stacks instead of using hundreds of high frequency switches connected in series. However, if compared to the traditional two-level voltage source converter (VSC), the MMC with half-bridge (HB) sub-modules (SM) requires twice the number of switches for the same output voltage [START_REF] Ghat | The hybrid-legs bridge converter: A flexible and compact VSC-HVDC topology[END_REF] and a large overall converter capacitance leading to higher footprint and costs. To address the issues mentioned above, researchers have been proposing new hybrid converter topologies with the aim of combining the advantages of the two-level VSC and the modular technology in a single architecture. Many solutions have been proposed following this line of research. The most significant ones consist of: the alternate arm converter (AAC) [START_REF] Merlin | The extended overlap alternate arm converter: A voltage-source converter with DC fault ride-through capability and a compact design[END_REF][START_REF] Merlin | The alternate arm converter: A new hybrid multilevel converter with dc-fault blocking capability[END_REF], the series bridge converter (SBC) [START_REF] Diez | Control and experimental validation of the series bridge modular multilevel converter for HVDC applications[END_REF][START_REF] Farr | The series bridge converter (SBC): AC faults[END_REF], the hybrid series converter (HSC) [START_REF] Patro | Hybrid series converter: a dc fault tolerant HVDC converter with wide operating range[END_REF] and the H-bridge hybrid multilevel converter [START_REF] Ghat | A new H-bridge hybrid modular converter (HBHMC) for HVDC application: operating modes, control, and voltage balancing[END_REF]. Similar reasons to the ones that led to a rapid expansion of HVDC applications have recently started to drive the development of new medium voltage direct current (MVDC) concepts for power distribution [START_REF] Métayer | Break-even distance for MVDC electricity networks according to power loss criteria[END_REF][START_REF]Electricity Network Innovation Competition[END_REF] with slightly different requirements (range of dc voltage and power of course, but also shape of required PQ domain). For applications with dc voltage of several tens of kV, MMC is an attractive solution thanks the converter modularity and low switching losses (if compared to two or three-level VSCs). Also, the know-how and technology transfer from the HVDC world allows a rapid growing of the number of applications of MMCs in MV domain. However, the above-mentioned weaknesses of MMCs in HVDC applications also arise MVDC then pushing research on alternative modular converters. The goal of this paper is therefore to propose and analyze a new converter topology has the advantage of a reduced number of SMs in MVDC applications.

The paper is organized as follows. Section 1 deals with the description of the new converter topology, the strategies to balance the internal energy and its characteristic equations. Section 2 presents assumptions made to carry out the converter sizing, defines the key performance indicators (KPIs) and gives the sizing results themselves. Finally section 3 illustrates the comparison between the proposed topology and the MMC in a typical MVDC application.

Open-Delta SBC

General Description

The proposed converter (Figure 1) has been proposed in [START_REF] Steckler | PATENT APPLICATION: Convertisseur de tension AC/DC triphasé comprenant uniquement deux modules de conversion électrique[END_REF] and is named "open-delta SBC". This new topology consists of two phase-legs, or phase elements (PEs), similar to the ones found in conventional SBC, but there are only two single-phase transformers connected in open delta configuration. Each phase leg consists of a main Hbridge (MHB) and two stacks of SMs: Series Full Bridge (SFB) and Chain Link (CL). A SM stack is simply a series connection of a certain number of SMs which can be of the half-bridge (HB) or full-bridge (FB) type as shown in Figure 2. In particular, in this paper the SFB is a stack composed by HB and FB SMs while the CL in only composed by HB SMs. The voltage created by the stack is given instant by instant by the number of capacitors that are inserted in the circuit and it is characterized by the typical "staircase" profile. In order to create a symmetric and balanced load/generator from the grid standpoint, currents and voltages have to be properly controlled by both phase elements (PE1 and PE2 in Figure 1) as detailed in the following section. In order to form a symmetric and balanced three-phase system, the open-delta current and voltage vector diagram must be the one of Figure 3 [15], In particular, the converter control must always ensure that:

1 2 Ga Gb Gb Gc v e e v e e            (1)
where the voltage drop due to the transformer leakage inductance and resistance is neglected. By satisfying (1) we obtain a 3-phase symmetric system, i.e.:

1 2 a c i i i i           (2)
Hence, satisfying (2) in the normal operation implies that the two phases of the converter absorb currents which are always of the same amplitude and have a 60 degrees angle difference. Alternatively, if needed, currents with an inverse component can be created. It appears clear that the two phases carry the same amount of active power only when the reactive power is zero (i.e. when φ=0).

Figure 3 Open-delta connection voltage and current phasor diagram

Given the presence of SM stacks in the converter, the energy balance management issue acquires great importance. As a matter of fact, controlling and maintaining constant the average energy stored in the SM capacitors is crucial for converters with modular elements.

The basis , in Eq. ( 3) and

=

are used in the following in order to carry out calculations in per unit (pu).

,max , b DC b DC V V I I   (3)
It can be easily verified that with reference to Figure 1 active and reactive powers in phase elements can be written as in Eq (4) where and are the active and reactive power absorbed from the grid in per unit (pu), , , and are the active and reactive power flowing through phase 1 and 2 respectively, as shown in Figure 1.

1 1 2 2 3 3 3 3 3 3 3 3 , , , 6 6 6 6
AC AC AC AC p q p q p q p q p q p q          (4)

Energy management

Energy management of the converter and individual stacks is an essential aspect of modular multilevel converters.

For individual stacks, voltage and current waveforms observed shall result in zero power variation across fundamental cycle. For initial analysis of the topology presented in this paper, we assume that appropriate control system is designed and ignore discrete nature of the voltage across the stack. Therefore, we can use analytical expressions for voltage and current across different elements of the converter.

There is a number of different ways how the converter can operate. In this paper, we propose the following operation strategy for the converter which is based on the minimizing of the circulating current, which is normally linked to the stack oversizing. In order to do so, the CL1 and CL2 voltage are chosen to be time-constant equal to and . Considering that DC current is the same in both phase elements and = and = , and can be expressed as:

      1 2 1 2 3 3 3 3 , 6 6 AC AC DC DC p p p q p q v v p p p p (5)
In general, ≠ and and have to adapt to converter set point while their sum always has to be equal to . It is easy to verify from ( 5) that one has = = 0.5 at cos( ) = 1, whereas for cos( ) = 0.95 one obtains = 0.5 ± 10% and = 0.5 ∓ 10%. Making the converter operate at lower power factors would further increase the max and determining a disadvantageous sizing. This is one of the reasons why the proposed converter is analyzed for MVDC applications, where the minimum cos( ) is fixed to a certain value close to one (typically in the range 0.9-0.95) [START_REF]Electricity Network Innovation Competition[END_REF] leading to a cone-shaped domain in the PQ plane.

By choosing the phase element DC voltage according to [START_REF] Orths | The European North seas countries' offshore grid initiative-The way forward[END_REF], the overall energy of each phase element is balanced, therefore if the SFB energy is balanced then CL energy will also be balanced.

Equation [START_REF] Orths | The European North seas countries' offshore grid initiative-The way forward[END_REF] describes the CL steady state voltage and current (without loss of generality only the CL1 is considered).

      1 1 1 1 CL DC CL SFB DC v t v i t i t i         (6)
By eliminating any harmonic voltage injection (i.e. by choosing that = and = ), the only way to control the energy stored in the SFB is through the control of the average value of the SFB current. This can be obtained by the selection of an appropriate instant at which the MHB rectifies the transformer secondary side current and voltage. This particular instant depends on the operating condition, and it can be measured by an angle quantifying its delay from the voltage zero crossing instant. The rectifying action above described is depicted in Figure 4. The part on the left of the figure shows the typical voltage and current waveforms of the MHB in the well-known SBC, where the voltage is rectified at its zero crossing.

Figure 4 MHB average current control

The part on the right on the other hand shows that the voltage is rectified at an angle measured from the zero crossing. Thanks to this technique the average value of the SFB current can be controlled. Considering PE1 only without the loss of generality voltage and current in SFB can be expressed as:

      1 1 1 1 2 ''sin sin 2 ''sin sin 6 in SFB v V ωt sign ωt α π i I ωt φ sign ωt α                       (7)
 

1 1 1 1 1 1 1 SFB in DC SFB AC DC SFB p v v i p v i     (8)
where is the instantaneous power flowing into the SFB. Therefore, by averaging (8) over the period:

  1 1 1 1 1 1 0 1 , T pu SFB SFB AC DC SFB P p dt P v i φ α T     (9)
where is the active power flowing into PE1 and ( , ) is the mean value of the SFB current which depends on and . Thus, in order to always maintain the SFB in energy balance, i.e. = 0, the following relation must always hold:

1 1 1 pu AC SFB DC P i v  (10)
It is important to remark that the MHB voltage rectified with angle ≠ 0 becomes negative (see Figure 4), thus, a slight constructive modification has to be applied on the MHB itself in order to ne able to sustain it. Therefore, a certain amount of switches able to block a certain negative voltage are added as shown in Figure 5. In particular, it can be easily shown that the amount of the negative voltage to block depends on the minimum power factor (cos( )) for which the converter has to be designed to operate (the lower the cos( ) the higher is the absolute value of the negative voltage). For instance, with a minimal power factor of 0.95, the maximal negative voltage is roughly 25% of the maximal positive voltage. Thus, the number of the additional necessary switches in the MHB can be calculated. Limiting the power factor to a minimum value allows to not oversize the MHB for the reason explained above, the CL for reasons that can be found in equation ( 5) and consequently the SFB. This is another reason for the limitation of the converter work points in a cone-shaped PQ plane (MVDC applications) as already mentioned above.

Converter Steady State First Harmonic Equations

Summing up, the converter equations in p.u. for the MHB, the CL and the SFB can be expressed as: Please note that energy unit is time because it is calculated as Joules/Watts, i.e. it is normalized by .

      1 1 1 1 1 sin sin 2 sin sin 6 in v pu in v R ωt sign ωt α MHB π i I ωt φ sign ωt α                            (11)   1 1 1 1 3 3 6 2 sin sin 6 CL pu CL p q v p CL π i I ωt φ sign ωt α p                          (12) 1 1 1 1 1 1 SFB in CL SFB in v v v SFB i i         (

Sizing results comparison with the MMC

Study case presentation

It is well described in [START_REF] Evans | Cost-performance framework for the assessment of Modular Multilevel Converter in HVDC transmission applications[END_REF] how the interest in a particular converter configuration depends mainly on the converter cost, size and efficiency. It is therefore important to identify parameters able to suitably represent those aspects, consequently, the following key performance indicators (KPIs) are considered here:  Transformer winding number and transformer sizing power: these parameters are related to the cost and volume of the transformers.  Switch total sizing power ( ): it is related to the "quantity of silicon" (voltage to withstand by semiconductors and current passing through them) and therefore related to the converter cost. The total switch sizing power associated to one stack is defined by equation [START_REF]Electricity Network Innovation Competition[END_REF].

, , max max stack pu stack pu stack stack SW SW S N V I  (14)
Where is the stack switch number and:

        , ,
I i t I V v V   (15)
The total converter switch sizing power is obtained by summing the sizing power associated to each stack.



Stored Energy: this parameter quantifies the energy stored in the converter which is mainly due to SM capacitors which represents the major part of the SM volume. Therefore, this parameter is linked to the to the converter volume.



Semiconductor switch total sizing power: This is related to the "quantity of silicon" (voltage the semiconductors must withstand and the current passing through them), and therefore is related to the converter cost. In simple terms, it represents the sum of the sizing power of all the switches.  Sub-module number: it is related to the number of interconnexions between submodules and mechanical assemblies, the number of capacitor voltages to measure, number of discharge circuits (and number of by-pass circuits depending on the manufacturer's technical choices). It is then related to the converter cost.  Sub-module cell capacitance: it is mainly related to the SM size (which is an important information on the ability to handle it during the construction phase and during replacing operations of faulty SMs). It is also related to the energy stored in an individual sub-module which is a constraint for the devices in the fault courant path in case of SM internal short-circuit. The calculation of the SM capacitance is conducted following the approach described in [START_REF] Merlin | Cell capacitor sizing in modular multilevel converters and hybrid topologies[END_REF].



Arm inductor number: it is linked to the converter volume and footprint.

Those KPIs are calculated for the MMC (which represent the state-of-the-art topology) and the open-delta SBC proposed here. The numerical values of the main parameters are listed in table 1 [START_REF] Lanzarotto | Rapid Evaluation Method for Modular Converter Topologies[END_REF]. Thanks to the equations ( 11), ( 12) and ( 13) all the proposed KPIs can be evaluated for the most critical operating point. For each indicator, the lowest value, the better. Each separate type of KPI is normalized with respect to the maximum of the two to show a relative comparison between the topologies. The notation in the label text corresponding to each KPI: "1→x", means that 1 corresponds to the specified x value. The stored energy unit is time because it is calculated as Joules/Watts, i.e. it is normalized by .

Based on the data presented in Figure 10 it can be seen that open-delta SBC does not have a distinct advantage of the standard configuration of HB MMC. Open-delta SBC has half the number of SM compared to MMC but these submodules are bigger (have larger capacitors and higher switch rated current). Although open delta SBC has slightly lower stored energy it shows much higher semiconductor sizing power.

An improvement in the trade off can be achieved for open-delta SBC if the "DC fault blocking capability" is required by application. In the scope of this paper, we consider DC fault blocking capability is an ability of the converter to stay connected to AC grid under existence of the DC pole to pole fault. Indeed, for the MMC, at least 50% of the HB SMs must be replaced by FB SMs for the converter to block DC short-circuits [START_REF] Steckler | Contribution à la conversion AC/DC en Haute Tension[END_REF]. With reference to for the open-delta SBC, as soon as the fault is detected, the switches in SMs (CLs and SFBs) can be blocked (all IGBTs in SMs controlled to be in off-state, letting only diodes as possible paths for the current) and two strategies can be adopted in order to block the DC fault current. Given the particular structure of the MHB (see Figure 5), it can be designed so that = . Indeed, if the number of diodes pointing downward is the same as the number of diodes pointing upward the DC fault current can be blocked without applying an overvoltage to those devices and their IGBT in parallel. 2. The MHB can be controlled to reproduce the behavior of a diode rectifier when the DC fault occurs (in particular, only the IGBT blocking the negative voltage must be controlled). In this case the SFB voltage ( , ) must be high enough to oppose the MHB output voltage ( , ) so that the DC current can be taken to zero.

Let us consider the second option. The necessary amount of SFB voltage can be obtained as follows:

1 2 1 2 SFB SFB in in V V V V    (16)
Assuming = = and = = , then:

, 2 '' SFB SM FB cell in N V V V   (17)
,

SFB v SM FB pu cell R N V  (18)
Thanks to [START_REF] Merlin | Cell capacitor sizing in modular multilevel converters and hybrid topologies[END_REF] and to the values chosen in Table 1, one has that , ≥ 11. Since already = 5, then 6 HB SMs must be replaced by FB SMs for each SFB. This means that in total * 100 ≅ 34% of the HB SMs must be replaced by FB SMs. Therefore, requiring the DC blocking capability from the open-delta SBC affects less its sizing than the MMC, where at least 50% of SMs must be replaced.

Conclusion

A new converter topology for MVDC applications is investigated. Converter structure principles of operations and energy balancing are briefly described. A set of KPIs are defined and used to assess the advantages and drawbacks of the proposed converter when compared to the MMC for an application case. Results show that the new topology is characterized by a significantly lower SM number with respect to the MMC. It can lead to an advantageous solution from complexity, cost and footprint points of view. Moreover, if the converter is required to able to block faults on the DC side, less switches should be added than in the MMC case.

Figure 1 Figure 2

 12 Figure 1 Open-delta SBC topology

Figure 5

 5 Figure 5 Additional IGBTs and diodes allowing the MHB to operate with negative

  13) where = √2 / in which is the rms value of the secondary side voltage of the transformer and = . Voltage, current and stack energy waveforms are shown in the following figures for a particular operating point.

Figure 6 SFB

 6 Figure 6 SFB Voltage (left) and current (right) and waveforms for = 1, ( ) = 0.95 and = 0.7

Figure 7 SFB 1 . 7 Figure 8

 7178 Figure 7 SFB 1 Energy Variation (left) and SFB 2 Energy Variation (right) for = 1, ( ) = 0.95 and = 0.7

Figure 11 DC

 11 Figure 11 DC short-circuit current path in the open-delta SBC 1.Given the particular structure of the MHB (see Figure5), it can be designed so that = . Indeed, if the number of diodes pointing downward is the same as the number of diodes pointing upward the DC fault current can be blocked without applying an overvoltage to those devices and their IGBT in parallel. 2. The MHB can be controlled to reproduce the behavior of a diode rectifier when the DC fault occurs (in particular, only the IGBT blocking the negative voltage must be controlled). In this case the SFB voltage ( , ) must be high enough to oppose the MHB output voltage ( , ) so that the DC current can be taken to zero.

Table 1

 1 Numerical values of the main parameters

	Name	Symbol	Value
	Rated DC power	,	30
	DC voltage		54
	P.u. Secondary Voltage		0.7
	Minimum cos( )	cos( )	0.95
	Rated SM voltage	,	3.6
	Max stack relative voltage variation		±10%
	Result comparison