Frederic Harb

Bernard Tinland

Toward electrophoretic separation of membrane proteins in supported n-bilayers

Keywords: Electrophoresis, Membrane, Mobility, Proteins, Separation

Membrane proteins are key constituents of the proteome of cells but are poorly characterized, mainly because they are difficult to solubilize. Proteome analysis involves separating proteins as a preliminary step towards their characterization. Currently, the most common method is "solubilizing" them with sophisticated detergent and lipid mixtures for later separation via, for instance, sodium dodecyl sulfate polyacrylamide gel electrophoresis. However, this later step induces loss of 3D structure (denaturation). Migration in a medium that mimics the cell membrane should therefore be more appropriate. Here, we present a successful electrophoretic separation of a mixture first of two and then of three different membrane objects in supported nbilayers. These "objects" are composed of membrane proteins Sulfide Quinone Reductase and α-Hemolysin. Sulfide Quinone Reductase forms an object from three monomers together and selfinserts into the upper leaflet. α-Hemolysin inserts as a spanning heptamer into a bilayer or can build stable dimers of α-Hemolysin heptamers under certain conditions. By appropriately adjusting pH it proved possible to move them in different ways. This work holds promise for separating membrane proteins without losing their 3D structure, thus their bioactivity, within a lipidic environment that is closer to physiological conditions and for building drug/diagnostic platforms.

Introduction

Membrane proteins play an important role in biological processes. Located at the boundary surface between the inside and the outside of the cell, they play many roles, acting as a gate in active/passive transport of ions/molecules through membranes and thereby ensuring reception/transmission of signals, modeling and adhesion, intercellular recognition, extracellular matrix binding, enzymatic activity, etc. Although they constitute roughly 30% of the proteome of a mammalian cell, i.e. close to 30 000 proteins, only 1040 (≈ 3.5 %) 3D structures are known 1 . Yet membrane proteins represent 50% of pharmaceutical targets, knowledge of 3D structure being crucial to researchers seeking to design better-targeted drugs. This lack of characterization stems from issues with purifying, crystallizing and functionally reconstituting membrane proteins. The main reason is that they are extremely difficult to handle in a water environment without denaturing them. In practice, a mixture of detergents and lipids must be used to stabilize the 3D structure. In addition, the environment is very difficult to reproduce in a fully biomimetic manner, and can wind up being completely different, for example with a separation method like SDS-PAGE. In that case, because of denaturing conditions, the 3D structure is completely lost. As a successful alternative, methods like Blue Native and Clear Native PAGE [START_REF] Schagger | Blue native electrophoresis for isolation of membrane protein complexes in enzymatically active form[END_REF][START_REF] Schagger | Analysis of molecular masses and oligomeric states of protein complexes by blue native electrophoresis and isolation of membrane protein complexes by two-dimensional native electrophoresis[END_REF][4][START_REF] Wittig | High resolution clear native electrophoresis for in-gel functional assays and fluorescence studies of membrane protein complexes[END_REF][START_REF] Burré | Non-classical 2-D electrophoresis[END_REF] involve one-step isolation of membrane proteins using nonionic detergents such as dodecyl maltoside, Triton X-100 or digitonin under conditions enabling to solubilize biological membranes. By carefully selecting and adjusting the detergent and its concentration, it is possible to create conditions that are not harmful to the membrane proteins or the complexes, owing to the presence of some of the lipids from the solubilized membranes. Then, separated bands can be excised and run in another dimension for final separation with various denaturing techniques (SDS-PAGE, doubled SDS-PAGE and IEF/SDS 3D PAGE).

Pioneering work has been done to apply electrophoresis to achieve biomolecule separation in model membrane. The authors showed that both the electrophoretic and electroosmotic forces could be altered independently of one another and then can be used to precisely control the movement of membrane bound species [START_REF] Monson | Supported Bilayer Electrophoresis under Controlled Buffer Conditions[END_REF] . Later they developed electrophoretic-electroosmotic focusing of membrane-bound proteins in SLB containing charged lipids [START_REF] Liu | Protein Separation by Electrophoretic-Electroosmotic Focusing on Supported Lipid Bilayers[END_REF] . Some years ago, another strategy was used [START_REF] Babu | Interaction landscape of membrane-protein complexes in Saccharomyces cerevisiae[END_REF] . In this work, the authors were able to report progress in the knowledge of membrane proteins, by identifying complexes playing vital biological roles in Saccharomyces cerevisiae. They identified complexes with 1590 putative integral, extrinsic and lipid-anchored membrane proteins using tandem affinity purification and mass spectrometry.

More recently, Okamoto et al. separated for the first time two membrane pore-forming proteins in multilayer lipid membranes at one pH [START_REF] Okamoto | Electrophoretic separation method for membrane pore-forming proteins in multilayer lipid membranes[END_REF] . Embedding the membrane proteins in a medium which partially mimics their natural environment meant that they could be separated without denaturation. Bao et al have reported a 25-fold increased concentration of trans-membrane protein-proteorhodopsin incorporated into supported lipid bilayers using electric fields [START_REF] Bao | Controlling transmembrane protein concentration and orientation in supported lipid bilayers[END_REF] .

In the field of separating membrane proteins, another interesting technique was developed by the Fredrik Höök's group. They demonstrated affinity capturing and local enrichment of membrane proteins by using a fluid lipid bilayer as the mobile phase. Specific membrane-protein capturing and enrichment was accomplished by moving with a hydrodynamic flow the membrane protein inserted in a supported bilayer over a capture region [START_REF] Gunnarsson | Affinity Capturing and Surface Enrichment of a Membrane Protein Embedded in a continuous Supported Lipid Bilayer[END_REF] . An alternative to this method consists in targeting the desired membrane protein contained in proteoliposome with nanoparticles. Then proteoliposomes are merged into a continuous supported bilayer. Through the extended nanoparticle tag, a weak hydrodynamic force could be applied, inducing directed in-membrane movement of targeted membrane protein exclusively. This enabled selective thousand-fold enrichment of the targeted membrane protein while preserving a natural lipid environment [START_REF] Lundgren | Affinity Purification and Single-Molecule Analysis of Integral Membrane Proteins from Crude Cell-Membrane Preparations[END_REF] We propose here to carry out electrophoretic separation of a mixture of two objects at differing pHs in differing lipidic systems (different chemical nature and number of bilayers) and then to separate a mixture of three objects: the two previous objects plus a dimer of one of them. These objects are composed of membrane proteins Sulfide Quinone Reductase (SQR) or α-Hemolysin (α-HL), model proteins easily handled in aqueous solution before insertion. Sulfide Quinone Reductase forms an object from three monomers together with some detergent and self-inserts into the upper leaflet of the bilayer. α-Hemolysin inserts as a spanning heptamer into the bilayer or can build stable dimers of α-Hemolysin heptamers under certain conditions. In previous papers [START_REF] Harb | Beyond Saffman-Delbruck approximation: a new regime for 2D diffusion of α-hemolysin complexes in supported lipid bilayer[END_REF][START_REF] Harb | Electric migration of α-hemolysin in supported n-bilayers: a model for transmembrane protein microelectrophoresis[END_REF][START_REF] Harb | Insertion and selfdiffusion of a monotopic protein, the Aquifex aeolicus sulfide quinone reductase, in supported lipid bilayers[END_REF][START_REF] Harb | Electrophoretic mobility of a monotopic membrane protein inserted into the top of supported lipid bilayers[END_REF] we measured some physico-chemical properties (diffusion coefficient, electrophoretic mobility, and charge) of these two different objects alone, taken as models in such an environment. Sulfide Quinone Reductase (SQR) and α-Hemolysin (α-HL) were chosen because they are very different: one is monotopic (inserts in one leaflet); the other is transmembrane (spans the two leaflets). This increases the probability that they will have different electrophoretic mobilities. Another reason is that they are easy to handle because soluble as monomers in aqueous solution which auto-assemble and then self-insert into the bilayer. About α-HL and its ability to form multimers, this method shows that it could be a way for separation of multimeric ion channels.

We use supported phospholipidic n-bilayers of two different lipids with n which can be set to 1, 2 or ≅ 35. The method was "learning when walking »: i) building one single bilayer (n=1) with a Langmuir-Blodgett trough leads to a well-defined basic system; ii) a double bilayer (n=2) provides another test system; iii) a multibilayer (n ≅ 35), very easy to build by simply rehydrating a desiccated film, will be useful for quick applications. It is a third system to test reproducibility of results and might improve membrane protein loading capacities for what we hope will become routine separation.

Starting with a mixture of known objects, conditions can be chosen so as to immobilize either one or the other object, move them in opposite directions, etc. Later, starting with an unknown mixture, after a screening of the pHs, separating conditions can be chosen in accordance with each situation. Furthermore, these systems can be used as a drug or diagnostic platform, once proteins have been separated.

Results and Discussion

Characterization of the different systems

Because lipids of our SLBs have phosphatidylcholine head groups, saturated aliphatic backbones, and because diffusion coefficients, mobilities, quantitative analysis of protein incorporation have been measured in the fluid phase, there is no difference between them going from a system to another. This was expected and there is no reason to observe different behaviour under electric field as reported [START_REF] Eggenberger | Fluid surface coatings for solid-state nanopores: comparison of phospholipid bilayers and archaea-inspired lipid monolayers[END_REF][START_REF] Yusko | Controlling the translocation of proteins through nanopores with bioinspired fluid walls[END_REF] , perhaps due to the confined geometry.

The different systems of our study are summarized in Table 1.

Mixture of two objects

For the mixture of the two objects, we used different membrane models and as shown in the table 1, we incubated both SQR and α-HL in a single bilayer of DMPC, a multibilayer of DMPC and a multibilayer of EggPC. After incubation of SQR over a single bilayer of DMPC, the support was placed under a fluorescence microscope and a density of 426 spots/mm² was observed. After incubation of α-HL and washing, the spot density observed for α-HL was 177 spots/mm². The order of magnitude of the spots densities was reproducible whatever the system.

Mixture of three objects

We did this experiment on a double bilayer of DMPC as indicated in the table 1. As an illustration of what was described in the previous paragraph, we observed 392/mm 2 spots versus 426 spots/mm 2 (mixture of 2) for SQR, a reproducibility of insertion to that of the protein alone, which saturated at around 400 spots/mm 2 in [16]. There was the same trend for α-HL with 182 spots/mm 2 versus 177 spots/mm 2 (mixture of 2) and ≈180 spots/mm² for the protein alone [START_REF] Harb | Beyond Saffman-Delbruck approximation: a new regime for 2D diffusion of α-hemolysin complexes in supported lipid bilayer[END_REF] . For the dimer of heptameric α-HL, we found 130 spots/mm², which is in good agreement with the 139 spots/mm² obtained after 24 h incubation [START_REF] Harb | Insertion and selfdiffusion of a monotopic protein, the Aquifex aeolicus sulfide quinone reductase, in supported lipid bilayers[END_REF] . Number of spots varied from one experiment to another by around 5 %.

In addition, these reproducible densities shed light upon the mechanism of dimer formation: the dimers are built independently, their formation does not consist in dimerization of already-inserted heptameric α-HL.

Identification of objects

Fluorescence intensity in arbitrary unit (a.u)

In previous work [START_REF] Harb | Beyond Saffman-Delbruck approximation: a new regime for 2D diffusion of α-hemolysin complexes in supported lipid bilayer[END_REF][START_REF] Harb | Electric migration of α-hemolysin in supported n-bilayers: a model for transmembrane protein microelectrophoresis[END_REF][START_REF] Harb | Insertion and selfdiffusion of a monotopic protein, the Aquifex aeolicus sulfide quinone reductase, in supported lipid bilayers[END_REF][START_REF] Harb | Electrophoretic mobility of a monotopic membrane protein inserted into the top of supported lipid bilayers[END_REF] , we observed an average intensity close to 38 arbitrary unit (a.u.) for trimeric SQR and heptameric α-HL. The same intensity was observed here, corresponding to the label content of each object. For the dimer of heptameric α-HL alone, the average intensity was ≈ 70 a.u, roughly twice the previous intensity, as expected.

In the mixture of two objects, we observed spots having an average intensity of 38 a.u. In the mixture of three objects, we observed spots having the same intensity and spots having an average intensity of 67-70 a.u, indicating the presence of the three objects.

Differentiation between SQR and α-HL

For both mixtures (2 or 3 objects):  SQR was incubated first, then videoed and analyzed. Recording free particle trajectories with our video setup, and treating them with Image J developed by the MOSAIC GROUP at ETH Zurich [25], we determined diffusion coefficients D of SQR at zero electric field (with the plugin), finding values of D in good agreement with previous reports [START_REF] Harb | Insertion and selfdiffusion of a monotopic protein, the Aquifex aeolicus sulfide quinone reductase, in supported lipid bilayers[END_REF] .  Next, α-HL was incubated. Then, we put the electric field on and observed two populations: each had its own mobility, similar to when it was measured on protein alone [START_REF] Harb | Beyond Saffman-Delbruck approximation: a new regime for 2D diffusion of α-hemolysin complexes in supported lipid bilayer[END_REF][START_REF] Harb | Electric migration of α-hemolysin in supported n-bilayers: a model for transmembrane protein microelectrophoresis[END_REF] . This enabled us to distinguish SQR from α-HL.  No video measurements of diffusion coefficients were performed for α-HL but total spot density was observed to have increased, indicating that SQR and α-HL were now inserted in the same bilayer.  Each determination (fluorescence intensity and electrophoretic mobility) on each video was carried out on 10 spots at least. Using these determinations, we obtained a position pattern for a given object that was then used, in a sort of feedback loop, to selectively color the spots on the figures of the article (SQR in red, α-HL in blue) for easier discrimination.

Relevant pHs for protein separation

We wished to visualize, and thus to predict, which pH(s) could be used to separate the objects. Our previous studies [START_REF] Harb | Electric migration of α-hemolysin in supported n-bilayers: a model for transmembrane protein microelectrophoresis[END_REF][START_REF] Harb | Electrophoretic mobility of a monotopic membrane protein inserted into the top of supported lipid bilayers[END_REF] provided data on how electrophoretic mobility of each protein depends on pH, enabling us to draw Figure 1 to compare them. That is what was observed. To help visualize the differing behaviors, in addition to the videos (Supplementary Information S1-S5) a series of snapshots is presented in figures 2-3. SQR objects are colored red, α-HL objects blue, and dimer α-HL objects yellow, as are the arrows illustrating their motion.

Separation of two objects (trimeric SQR + heptameric α-HL)

At pH 7.2, both proteins have mobility, but in opposite directions since they have opposite charges (see fig. 1). The complete sequence is shown in video 1 (Supplementary information S1). They frequently appear to simply go their own way, ignoring the existence of other species. However, there are some situations where two different objects approach each other closely enough to collide, with potentially varying results. The question is: will they join together and stop migrating? Or will they migrate as one object with a mobility that is derived from their opposite mobilities?

We were able to capture these particular situations (bottom/left and top/right, yellow ellipses in video 1). We focus on one of these events from the movie, detailed in figure 2: we extracted some snapshots, time interval 2.3 s to 6.8 s, from video 1 (Supplementary information S1). In the movie, the objects start to bump into each other at first, bounce, and finally manage to find a way to glide past each other before following separate paths. The striking feature is that, even though they have opposite charges, they do not stick to each other. This is a very interesting result since it proves that, even with opposite charges, separation is still possible. This is one of the key points that such a platform could perform the separation for multiple biomolecules. We suggest that they do not stick to each other because each object is surrounded by a belt of bound lipids. This is supported by previous studies which have established that the folding, structure and function of membrane proteins are influenced by their lipid environments and that lipids can bind to specific sites [START_REF] Laganowsky | Membrane proteins bind lipids selectively to modulate their structure and[END_REF][START_REF] De Vlugt | Identifying lipids tightly bound to an integral membrane protein[END_REF] The complete sequence at pH 9.2 is shown in video 2 (Supplementary information S2). As figure 1 shows, the difference in mobility is maximal, meaning that this is the pH at which separation is fastest and most efficient for this system. At this pH, all objects have a negative charge and race toward the positive electrode as shown by the red (for SQR) and blue (for α-HL) arrows. SQR migrates faster (µ SQR = 2.2x10 -4 cm 2 /V. s) than α-HL (µ α-HL = 6x10 -5 cm 2 /V. s), the mobilities being the same as when the proteins were alone. SQR either overtakes α-HL easily while migrating when they are in distinct lanes or may overtake by changing lanes when SQR catches up with α-HL on the same trajectory (see yellow ellipse on video 2 around t =13 s). Again, we observe no sticking to each other or overcrowding that would prevent separation. A histogram of distribution of measured electrophoretic mobility including the number of individual proteins tracked (SQRdifferent red-and αHl -different blue-) at pH 9.2 is provided in figure 3. This distribution results from the analysis of 3 experiments carried out at 3 different places on the same sample (around 60 spots followed). Beyond natural dispersion of a measure, this distribution can come from variation of the label content of the objects (two dyes on a monomer or two labeled monomers in an object). The overall variation is for each mobility is close to 10 %. At pH 6.8, the SQR is motionless, while the α-HL moves toward the negative electrode (see video 3-Supplementary information S3). At this pH, α-HL (blue spots) has a positive charge whereas SQR (red spots) has reached its pI (isoelectric point) [START_REF] Harb | Electric migration of α-hemolysin in supported n-bilayers: a model for transmembrane protein microelectrophoresis[END_REF][START_REF] Harb | Electrophoretic mobility of a monotopic membrane protein inserted into the top of supported lipid bilayers[END_REF] . We measured the mobility of α-HL, and found µ = -1.9 x10 -5 cm 2 /V. s alike when it was alone [START_REF] Harb | Electric migration of α-hemolysin in supported n-bilayers: a model for transmembrane protein microelectrophoresis[END_REF] . The next experiment is intended to reverse roles for SQR and α-HL. At pH = 8.3, α-HL reached its pI and SQR had a net negative charge.

The SQR moves toward the positive electrode (see video 4-Supplementary information S4) but the α-HL is immobile. We measured the mobility of SQR, finding a value of 1.0 x10 -4 cm 2 /V. s, alike when it was alone [START_REF] Harb | Electrophoretic mobility of a monotopic membrane protein inserted into the top of supported lipid bilayers[END_REF] .

All these scenarios at differing pHs will lead to the separation of the proteins.

Separation of three objects (trimeric SQR + heptameric α-HL+ di-heptameric α-HL)

As a final experiment, we prepared a mixture of three objects: trimeric SQR, heptameric α-HL and dimer of heptameric α-HL. We constructed a system composed of a double bilayer into which we inserted these three objects, as described in the Materials and Methods section. The experiment was run at pH 9.2, where all objects are negatively charged. They race each other toward the positive electrode (video 5-Supplementary information S5). In this video, the different objects have different shades of gray (trimeric SQR and heptameric α-HL: light gray; the dimer of heptameric α-HL: brilliant gray). In figure 4, as illustration of video 5, trimeric SQR and heptameric α-HL are shown in their usual color, red and blue respectively, and the third object, the dimer, is in yellow (same color code for the arrows). Circles/ellipses illustrate situations where the three objects (red, blue and yellow) are close at the beginning and where distances between them increase with time. The fastest is SQR and the slowest is the dimer. Each object has its mobility value, determined during previous work on protein alone. This experiment shows again that it is possible to electrophoretically separate a mixture of membrane proteins in supported lipid bilayers in a short time and with a fairly low electric field.

All the mobilities recorded during these experiments are presented in table 2.

Conclusion

This work provides new insights into the feasibility of an electrophoretic separation of membrane proteins in single, double and multi supported bilayers that can be routinely used starting from a cell or a cell lysate. This separation occurs at low electric field. Beyond separation to establish 3D structure of individual membrane proteins, thus keeping their bioactivity, these systems can be use as test platform for drug or diagnostic. It reveals that SQR remains immobile (when at its pI) while α-HL can migrate alone or vice versa, which is achieved by suitably adjusting the pH of the buffer.

We also demonstrated that when proteins are charged (mixture of two or three objects), separation is feasible due to the differing mobility that results from their differing structures and charges. If the proteins interact while migrating, they do not stick together, probably due to the existence of bound lipids which act as a bumper, avoid each other and continue migrating. This is a very interesting result since even in these situations, separation occurs. Compared to standard electrophoretic methods, we observed clear separation of the three objects in substantially shorter distances (microns) and times (seconds), and with a weak field (3V/cm). We hope to generalize to other membrane proteins after solving the next challenge which is to insert an unknown membrane protein mixture from living systems into the supported multibilayer. We suggest two methods as potentially feasible: direct fusion of cells on an already-present supported bilayer or healing an intentionally-created scratch in a multibilayer with a low-detergent solubilized biological membrane. In addition, this multibilayer system, easy to build using rehydration of a dried lipid film, could increase membrane protein loading capacities.

Materials and Methods

Sample

Supports

The slides used as supports were 2.5x 2.5 cm², either mica cleaved on both sides just before use (JBG-Metafix, France) to support the double bilayer or glass (Marienfield, cut edges, France) to support the single bilayer or the multibilayer. They were cleaned by immersion for 10 min in freshly prepared alcoholic NaOH, then thoroughly rinsed with ultra-pure water and sonicated 3 times for 5 min in ultra-pure water.

Lipids

All lipids were purchased from Avanti Polar Lipids (Coger, France) and used without further purification. Supported single and double bilayers were prepared using 1,2-dimyristoyl-snglycero-3-phosphocholine (DMPC, Mw 734 g•mol -1 ). Supported multibilayers were prepared using either DMPC or L-α-phosphatidylcholine (EggPC, Mw 770 g•mol -1 ).

The single bilayer and double bilayer of DMPC were built using the Langmuir-Blodgett transfer technique (for details, see [22]). Lipid molecules solubilized in chloroform (∼1 mg/ml) were deposited on the water subphase (18 MΩcm, MilliQ, 15 °C) of a Langmuir trough (KSV Minitrough 361 mm × 74 mm, Finland), equilibrated for 10 minutes to allow complete solvent evaporation and then compressed to 30 mN/m. Transfer ratios were close to 1.

For the double bilayer on mica, the fourth monolayer, closing the second bilayer, was transferred using the Langmuir-Schaefer (LS) technique. Transfer ratios were close to 1 for the first three monolayers and 0.8 for the fourth monolayer.

The multibilayer was formed via the lipid film hydration method. 20 μL of lipids (either DMPC or EggPC) in chloroform (1mg/mL) were first desiccated under vacuum for 1 h on a glass slide.

Then the slide was positioned in our incubation cell (a Teflon™ cylinder embedded in steel, 1 cm diameter) and the film was rehydrated at room temperature with ultrapure water (18 MΩ•cm, MilliQ) for 30 min. Obtaining a multibilayer can be difficult. Several articles detail how Multilamellar Vesicles (MLV) can be produced via rehydration of dry lipidic film. We noticed that it usually involves supplying energy to the system, for instance through strong agitation or electric fields. Failing this, the outermost bilayer of a rehydrated DOPC film will spontaneously peel off (possibly bilayer by bilayer). However, it is also reported that peeling does not occur when starting from DPPC in gel phase [START_REF] Hishida | Hydration process of multi-stacked phospholipid bilayers to form giant vesicles[END_REF] . More recently, Relat-Gobena et al [START_REF] Relat-Goberna | The Nanomechanics of Lipid Multibilayer Stacks Exhibits Complex Dynamics[END_REF] carried out AFM experiments on supported rehydrated multibilayer stacks in buffer solution. Keeping the same buffer without rinsing, they avoided turbulences and thus detachment of the lipid stacks.

In our system, we obtain a supported multibilayer and this is ensured by the following:

-Removal, washing and addition to the Teflon cell were performed very gently and along the wall of the cell, to minimize turbulence.

-Working in pure water on glass increases electrostatic interactions because of the low ionic strength. This helps stabilize the rehydrated multibilayer at the glass surface.

-Qualitatively, under the microscope, the sample appeared flat: there was no need to adjust the z direction to remain in focus, and no sign of the existence of slowly "swimming" MLVs.

Additionally, the electrophoretic mobilities of our objects were analogous when measured in single or double bilayers. Experiments were performed in replicate reproducibly in all systems (at least twice, sometimes more).

Assuming a lipid head molecular area [START_REF] Kukol | Lipid Models for United-Atom Molecular Dynamics Simulations of Proteins[END_REF] of 0.63 nm², given the amount of dried lipids (20 μL from a solution 1mg/mL) and the area exposed to rehydration (a circle 1 cm in diameter), we estimated a number of bilayers close to ≈ 35 in the multibilayer.

Supported Lipidic Bilayers (SLB) were kept under water throughout the experiment and used directly after preparation.

Proteins

α-Hemolysin (α-HL), extracted from Staphylococcus aureus, was purchased from Sigma Aldrich Inc and used without further purification.

Sulfide Quinone Reductase (SQR) was extracted from A. aeolicus membrane with dodecyl-β-D-Maltoside (DDM) and purified as previously described [START_REF] Prunetti | New functional sulfide oxidase-oxygen reductase supercomplex in the membrane of the hyperthermophilic bacterium Aquifex aeolicus[END_REF] . Following purification, SQR was dialyzed against 50 mM HEPES buffer pH 7.2, 0.1% DDM using Vivaspin ultrafiltration spin columns (Sartorius stedim), concentrated at about 2 mg/ml and stored at -20 °C.

Protein Labeling

We labelled the proteins using a kit from Molecular Probes (Invitrogen) to covalently link Alexafluor™ 488 fluorescent dye to the protein [START_REF]Alexa Fluor® 488 Protein Labeling Kit (A10235[END_REF] . Alexa Fluor® dyes are reactive molecules used After purification, the solution containing the labelled protein was mixed with the proper amount of a solution of the same protein unlabelled, to reach a final solution of α-HL with 1/7 labelled monomer and a solution of SQR with 1/3 labelled monomer. This rather low-labelled monomer content rules out any disturbance of the insertion mechanism of the protein and of the dynamics of the final object. Final aliquots of protein (0.2 µM) in Phosphate Buffer (PB) 20mM and NaCl 100 mM pH 7 were stored at -18 °C before use (with DDM in the case of SQR). We used the same label Alexa Fluor® 488 for both proteins because our camera is black and white, we have acquired the skill of the labelling process and our optical setups are designed for blue excitation and green emission.

Protein Insertion

SQR inserts as a trimeric integral monotopic (lipid-anchored in only one leaflet) membrane protein at the end of the process 28-29 and we define it as the first object.

Incubated over a fluid bilayer, α-HL monomers in solution assemble as heptameric pre-pores at the surface of the bilayer, turning into transmembrane (spanning) heptameric pores [START_REF] Harshman | Staphylococcal alpha-toxin: a study of membrane penetration and pore formation[END_REF][START_REF] Bhakdil | Alpha-toxin of Staphylococcus aureus[END_REF] . We define it as the second object.

Incubating α-HL over a lipid bilayer consisting of a mixture of fluid/gel regions (half transition)

promotes the formation of dimers of α-HL heptameric pores [START_REF] Harb | Beyond Saffman-Delbruck approximation: a new regime for 2D diffusion of α-hemolysin complexes in supported lipid bilayer[END_REF] , we define it as the third object of our protein mixture.

The composition of the aliquots leads on average to one fluorescent label per object (the heptameric pore for α-HL and the SQR trimer for SQR) and to two fluorescent labels per dimer of heptameric α-HL.

Preparing a system containing a mixture of 2 objects: trimeric SQR and single heptameric α-HL

The volume over a slide with the bilayer (or multibilayer) positioned in our incubation cell was 1 ml. First, 700 µl of water were removed, leaving the bilayer under the remaining 300 µl, and 300 µl of an SQR aliquot were added. This final volume of 600 µl of protein (SQR 0.1 µM in PB 10mM NaCl 100 mM, pH 7.2) was incubated for 12 hours at 33 °C (bilayer in the fluid phase), after which 300 µl of the supernatant were discarded and the excess of SQR was gently removed by adding and pipetting 500 µl of distilled water 10 times.

The sample was returned to the incubation cell and again immersed under 1 ml of distilled water, 700 µl of which were removed again. Then 300 µl of an aliquot of α-HL were added to the incubation cell following the same protocol (12 hours at 33 °C).

Preparing a system containing a mixture of 3 objects: SQR, single heptameric α-HL, and dimer of heptameric α-HL

The incubation was carried out over a DMPC double bilayer. The first two steps were as described above for the mixture of two objects. Formation of dimers of heptameric α-HL depends on temperature and time. To obtain inserted dimers of heptameric α-HL, the solution was brought back to 22 °C, a temperature where gel and fluid lipid regions coexist and which is thus conducive to the formation of dimers of heptameric α-HL. An extra 12 hours of incubation was carried out, which added to the initial 12 h incubation of α-HL gave a total of 24 hours, found to be optimal to obtain a large number of dimers 14 .

Systems

The temperature used to measure electrophoretic mobilities was 35 °C for all systems, a temperature where bilayers are fluid. For a given species, for a given pH, all mobilities were identical whatever the system (single bilayer, double bilayer, and multibilayer, composed of EggPC or DMPC) and identical to the value measured on the object when alone and not in a mixture.

Videomicroscopy

Cell

The sample (supported bilayer + inserted proteins) was transferred underwater in a thermostated electrophoretic cell (see [15] and Supplementary information S1).

Video

An inverted fluorescence microscope (Leica) and a camera (Hamamatsu C2400-77: 768 x 494 pixels, 30 MHz) equipped with a fluorescence intensifier suitable for fluorescence imaging (magnification x 400) were used to carry out protein velocity measurements. Videos of migration of proteins under electric field (3V/cm) at different pHs are available in the Supplementary information files S1-S5 (video 1 to 5). As illustrations, series of snapshots extracted from videos at different times are shown in the Results and Discussion section (figures 2-3). Briefly, every time after applying the electric field during 20 s to record one experiment, we flush the cell with fresh buffer to remove electrolysis products, moved to another place over the sample. The setup is ready to record a new experiment.

Electrophoretic mobility

The resulting effective mobility of an object (µ eff ) is the sum of several contributions [11]: µ eff = µ E + µ lipid + µ EOF (eq. #1)

We showed that changing the sign of the protein by changing the pH reversed the direction of its migration. We also showed that the pI of the proteins was unchanged by the presence of Alexa Fluor® 488. Both arguments mean that the contribution of the charge of the dye to the total charge of the object is negligible. Therefore, µ E is the mobility of the charged object, depending on its charge and its size. Because phosphatidylcholine groups are globally neutral, µ lipid is also negligible. Lastly, the contribution of electroosmosis (EOF) is also negligible due to the ionic strength and the "coating of the surface by the bilayers as reported by Monson et al [START_REF] Monson | Supported Bilayer Electrophoresis under Controlled Buffer Conditions[END_REF] .

We thus get:

µ eff = µ E (eq. #2)
We obtain the mobility of the object directly by simply dividing its velocity by the field value.

Drift velocity measurements were performed as described in Harb et al. [START_REF] Harb | Electric migration of α-hemolysin in supported n-bilayers: a model for transmembrane protein microelectrophoresis[END_REF] . Briefly, the velocity of at least 10 spots measured on three different locations in the bilayer from each sample was obtained by dividing distance traveled by the objects by time. Reproducibility was within 10 %. The primary source of error was the measurement of the displacement, due to the resolution of the microscope (± 1µm).

Acknowledgment

We are grateful to Dr. Marianne Guiral and Dr. Marie-Therese Guidici-Orticoni (Bioenergetics and protein engineering lab, CNRS-AMU) for the kind gift of SQR and for valuable comments.

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ABBREVIATIONS

DMPC, 1,2-dimyristoyl-sn-glycero-3-phosphocholine; EggPC, L-α-phosphatidylcholine (Egg, Chicken); SLB, Supported Lipidic Bilayer; SQR, Sulfide Quinone Reductase, α-HL, Alpha

Hemolysin.

T

  SQR & α-HL) then 22 °C to obtain α-HL dimers --------------

Figure 1 :

 1 Figure 1: Electrophoretic mobility of trimeric SQR alone (open red circles) and heptameric α-HL alone (full blue circles) as a function of pH (the error bar is ± 10%).

  8 and 8.3 (SQR and α-HL, respectively): one object should be immobile because the pH corresponds to its pI;

Figure 2 :

 2 Figure 2: Zoom on SQR (red) bumping into α-HL (blue) inserted in EggPC supported multibilayer at pH = 7.2 under a 3 V/cm electric field with the time interval 2.3 s to 6.8 s extracted from video 1 (S1). Scale bar: 50 µm.

Figure 3 :

 3 Figure 3: Distribution of measured electrophoretic mobility as a function of the number of individual objects tracked (distributions in nuances of blue for αHl and in nuances of red for SQR)

Figure 4 :

 4 Figure 4: Images of fluorescent SQR (red), α-HL (blue) and dimeric α-HL (yellow) electrophoretic migration recorded at 0 s, 10 s and 20 s extracted from video 5 (S5). The vertical red dotted line is an arbitrary reference line to highlight the position change of objects. Scale bar: 50 µm.

  to add a fluorescent label to the primary amines (R-NH2) of proteins. It provides the combination of water solubility and pH insensitivity between pH 4 and 10 for compatibility in diverse biological environments. We used Alexa Fluor® 488 TFP (tetrafluorophenyl) ester because TFP esters are less susceptible to spontaneous hydrolysis during conjugation reactions. The initial concentration of the protein was 0.4 mg/ml in PBS 1x (with DDM in the case of SQR), the reaction time was 15 min for α-HL and 40 min for SQR. This yields an average labelling of 0.2 mole Alexa 488/mole protein.

Table 1 :

 1 Systems, pH and incubation temperature in different supported lipidic bilayer systems

			DMPC	DMPC	DMPC	EggPC
	Mixture Conditions
			single bilayer	double bilayer	Multibilayer	Multibilayer
	of 2	pH	6.8; 8.3; 9.2	-------	6.8; 8.3; 9.2	6.8; 7.2; 8.3; 9.2
	Objects Incubation

Table 2 :

 2 Mobilities µ of the different objects as a function of pH and x, the number of species present in the mixture. Values of µ: ± 10%.

	Mobility (10 -5 cm²/V.s) of		SQR			αHL		dimer-αHl
	System with x	x= 1	x=2	x=3	x= 1	x=2	x=3	x=1	x=3
	species	(alone)	(+	(+	(alone)	(+SQR)	(+	(alone)	(+
			αHL)	αHL,			SQR,		SQR,
	pH			dimer)			dimer)		αHL)
	5.2-5.5	-20.6	-	-	-8.2	-	-	-	-
	6.4	-6.0	-	-	-	-	-	-	-
	6.8 (pI of SQR)	0	0	-		-1.9	-	-	-
	7.2	1.6	1.6	-	-1.9	-2.1	-	-1,0	-
	8.3 (pI of αHL)	9.9	10.0	-	0	0	-	-	-
	9.2	22.0	22.2	21.8	5.8	6.0	6.1	-	1.9

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We thank Aix-Marseille University for financial support to Frederic Harb and Marjorie Sweetko for English language editing. We thank Dr. Mathilde Lepoitevin for careful rereading.

The authors have declared no conflict of interest.

Supporting Information.

S1 to S5: Video 1 to 5 (.avi file) S6: Schematic diagram of the video/electrophoretic cell and its description. Protocol to make videos (text and diagram, pdf)

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AUTHOR INFORMATION

Corresponding Author

*: To whom correspondence should be addressed: tinland@cinam.univ-mrs.fr

Author Contributions


Claire Bénit-Gbaffou

Ananya Roy

Informal practices of the state in urban governance Views from Southern African cities Unpacking state practices in city-making, in conversations with Ananya Roy

a conversation with

cities, on the other. "Governability" is a fuzzy but useful concept that refers both to the capacity of the state to steer society, and to the capacity or inclination of societies to comply or to resist being governed. Although the two are linked, we focus here on the first meaning (state's ability to steer society), as we are attempting to direct an analytical gaze towards the state and its practices. "Governmentality" on the other hand is a more classic, Foucauldian concept that we understand here as the ways in which governable subjects are produced through the internalisation of urban policies' dominant visions and norms. These two ways of interrogating state practices correspond to two threads in Roy's work. Although not using the term "governability", she explicitly questions "why India cannot plan its cities" (Roy 2009a), building on previous work excavating the role of the state in framing urban informality (2003,2005). In other work [START_REF] Roy | Civic governmentality: the politics of inclusion in Beirut and Mumbai[END_REF], she analyses the ambiguities of "civic governmentality" and how the politics of cooperation of NGOs in India and Lebanon are caught between dynamics of genuine empowerment, the perhaps necessary pragmatism of constrained negotiations, and a problematic contribution to the manufacture of consent amongst the poor in the city. In so doing, she coins two concepts that were relevant for this collection. The one is the "politics of un-mapping", a deliberate confusion maintained by the state around the status of ownership of urban land, enabling the state to retain flexibility in its future intervention and engage in land speculation. The second, related but broader concept, is "informality as an idiom of urbanisation" [START_REF] Roy | Urban informality: toward an epistemology of planning[END_REF](Roy , 2009a) ) which politicises informality as a purposeful modality of state's practice in governing cities, thus innovatively applying the concept of informality to the state itself. This overview frames the papers' engagements with these concepts and questions: Governability and Governmentality, The Politics of Un-mapping, and the Question of Intentionality. It ends by consolidating a reflection, based on the collection, that contributes to emerging debates on Informal Practices of the State.

Governability and governmentality

Governability and governmentality could be seen as contrasting but complementary ways of analysing power in cities, in this case specifically the role and place of "the state". This echoes Clarence [START_REF] Stone | Power, Reform, and Urban Regime Analysis[END_REF] suggestion to study the "power to" in addition to the more traditional "power over". By this, he means that in order to understand who governs cities, we need to not only interrogate domination, influence, coalitions and contentions (power over), as is done classically, but also comprehend what is produced in the city through these relationships -what directions and shapes are given to cities, if any (power to act). Governability considers the productive dimension of power, in contrast to governmentality which focuses on the ways in which power travels, is incorporated, naturalised and diffused in multiple sites. All papers in this collection question the importance and limitations of the state's ability to shape cities, in relation to public housing delivery, street trading regulation, informal settlement management or urban land release. Some papers focus more directly on the issue of governability, in particular looking at processes through which "the state" constructs its policy instruments.

The collection concentrates on unpacking "the state" through its practices. The state is understood in the broad sense, as government and a vast array of public and semi-public agencies; as a multilevelled, multi-departments, multi-layered entity that is complexified by both decentralisation and neoliberalisation dynamics. We argue however that it cannot be understood solely in terms of diversity, centrifugal forces, heterogeneity and arbitrariness; and that the tensions we explore in this issue (sometimes under the concept of informality) emerge precisely from constant attempts by diverse state agents and units to construct direction, unity, consistency and control amongst its diverse arms, units and agencies.

Bénit-Gbaffou interrogates states' abilities to govern contemporary cities. In a sector often described as ungovernable, the regulation of street trading in city centres, she asks what produces this ungovernability. The state's incapacity to govern the sector manifests in its practical (but failing) attempts to limit street trading in congested urban centres, and in its claimed (but limited) endeavours to support micro-enterprise by recognising its permanence and social, if not economic, utility. Using the case of Johannesburg, she contests easy explanations of "policy-implementation gaps", where well-intended policies are betrayed by their implementation challenges. Instead, observing continuity in municipal practice in the form of two decades of repression against street trading, and analysing internal processes framing its policy instruments, Bénit-Gbaffou shows how the state has manufactured its own incapacity to govern, hiding behind a progressive but superficial public policy to continue a self-defeating politics of repression, one that is embedded in institutions, budgets, tools and officials targets.

Charlton describes an impressive South African state machinery, in terms of policy, budget, multilevelled administration, established to deliver mass public housing as promise by the ANC coming to power in 1994, and its relative efficiency in delivering on this to low-income citizens. This narrative of success in state intervention is however disturbed by beneficiaries' uses of their houses, deviating from policy intentions. Charlton is interested in what officials make of this variation between state intent and beneficiaries' use, and shows how they oscillate between criminalisation and understanding, but mostly how state institutions fail to measure, acknowledge or reflect on the phenomenon that could question the framing, and possibly the legitimacy, of existing policy. Charlton interrogates the lack of reform of this programme, indicating that the state's acknowledging existing beneficiaries' practices and the reasons for them, and attempting to adapt its policy accordingly, could compromise its capacity to act. The state is understood as not having the technical, administrative and financial capacity to directly accommodate complex social dynamics that reflect more fundamental socio-economic conditions, and limits its investigation of these in line with what it can achieve.

Butcher analyses the spatial and sectoral limits of state intervention, interrogating the governability of the abundant mining land that bisects Johannesburg. She studies the dominant mining company as a quasi-state that has captured most of the capacity to govern this strategic metropolitan asset, through the power of both superficial and subterranean land titles and monopolistic spatial knowledge. The state, in this instance the municipality, appears hollowed-out, its planning documents directly influenced by the mining company's objectives prior even to public comment. It appears incapable of steering how land should be used, especially in the short periods where municipal objectives do not coincide with the company's. In contrast, the company is able to manipulate this land asset on a long-term basis, playing on variations in mining technologies, gold price, housing markets and to some extent only, constraints imposed by the policy environment. It is definitely easier to manage an urban space as a business, than it is to govern it as a city. This highlights by default that state (in)capacity to steer urban spaces might be less technical than political: unlike businesses, states have to hold together the needs to frame, maintain and update technical capacity, but also to respond to multiple accountabilities, and to drive planning objectives that are publicised and contested.

Rubin analyses the limits of state's capacity to govern, in relation to the messy and fluid urban dynamics of informal settlements and urban growth. There, shifting and contested state objectives, fragmented and diverging positions, between repression, tolerance and development, added to the technical complexities of engaging with informal local politics (embedded in in-situ upgrading and community engagement processes), create uncertainty amongst state officials. The state's attempts to govern these areas involve at times acknowledging, incorporating, and even adopting locallyframed instruments of regulation: informal land registers, locally-crafted criteria for housing allocation. In other cases, it means delegating its governing powers for the tasks that it cannot openly or directly perform: containing settlement growth, possibly through community violence; constructing a local administration, potentially through forms of local extortion. In terms of governability, this practices and instruments depicted reflect the limits of state capacity, but also paradoxically the extension of the state's realm of intervention [START_REF] Hibou | La « décharge », nouvel interventionnisme[END_REF]. In terms of governmentality, Rubin shows how the state both learns from and adopts categories framed by civil society, and how civil society groups mimic state instruments to govern local spaces. Governmentality operates in both directions, even though the power to eradicate, evict or ignore remains predominantly in the hands of the state.

Buire is more interested in governmentality. She interrogates state power in producing the city, through practices of "slum clearance" twinned with public housing construction in urban peripheries by focusing on "the state-in-society" in Luanda. Her paper examines how the state penetrates everyday and intimate lives -through party branches, social surveillance and the promise of clientelistic access to resources, rather than reticulated administration or consistent public intervention. Buire shows how, although elusive, the state remains powerfully present through the dominant party it is intertwined with, manufacturing consent amongst its actual or would-be local clientele.

"A politics of un-mapping" -state knowledge and the capacity to govern

Four of the papers in the collection engage with the issue of state knowledge in its relation to state power: but this engagement is less in terms of social control and governmentality, than in terms of governability, capacity to act. Here Roy's concept of "un-mapping" is productive. This concept is framed in the specific context of Kolkata's urban peripheries and their uncertain, blurred and opaque land legal and institutional status. Roy argues that this uncertainty is deliberately maintained by the state, to facilitate flexibility in its interventions, and possibly forms of land speculation. Through this concept of "unmapping", Roy contests the Foucauldian understandings of the knowledge-power nexus, where knowledge is the condition and instrument for the state exerting control over populations and spaces. Roy contends on the contrary that the lack of knowledge, purposefully produced and reproduced, can be a powerful instrument of state power (Roy 2009a). But she adds that this lack of knowledge is simultaneously the state's demise, as this legal uncertainty is also the basis for a multiplicity of particular private claims to emerge as soon as state intervention crystallises, de facto impeding, delaying or blocking its projects.

Butcher explicitly engages with Roy's concept, as the mining company's power relies on spatial knowledge and a monopoly on "mapping", built on land ownership but also technical expertise: mapping mining land requires an understanding of the underground, and not only the superficially visible environment. Her argument would seem to run contrary to Roy, in line with Foucaultmapping equates to power, and the state's incapacity to get, record, archive knowledge on mining land ipso facto deprives it of the capacity to act. Reversely, mining companies owning spatial knowledge (embodied through maps) are in a dominant position to strategise, resist state's or civil society's claims and effectively decide on land release, retention or development. This power is not absolute: reality resists, broader environmental dynamics affect the underground beyond the company's control. But this knowledge is constitutive of the capacity to govern.

Rubin argues that the state is limited in its intervention due to its lack of knowledge of informal settlements population, movements and transactions. This lack of knowledge has been partly manufactured by the state's own approaches towards informal settlements, unmapped as unwanted, ignored, categorised as temporary and therefore not worthy of attention. Hence local officials rely on locally-crafted registers, verbal or informal recognition by key local leaders, constructing rather messy but at least existing forms of knowledge on which to base their intervention. Here too, even in more complex ways, knowledge (in the form of registration and mapping) is the condition for intervention, an instrument of control (of population growth in particular) but also of distribution of benefits (access to formal housing, title deed, infrastructure and services).

Bénit-Gbaffou and Charlton, on the other hand, examine the linkages between knowledge and power in line with Roy's contention -state's deliberate ignorance of information or data, in order to act. This argument was broadened by [START_REF] Breckenridge | Will to Know: The Rise and Fall of African Civil Registration in Twentieth-Century South Africa[END_REF], showing, contrary to Foucault's nexus of knowledge as power, how population registration under apartheid was linked to the granting of social benefits, and therefore how groups excluded from (segregationist) welfare states were also excluded from these registration efforts. What Breckenridge terms "no will to know," in reference to a state content with containment and indirect rule and not needing to keep a thorough register of excluded groups, Bénit-Gbaffou reframes as "will not to know": deliberate resistance to hearing, seeing, counting and recording certain facts, groups or areas. In the case of street traders in Johannesburg, the state's politics of un-mapping is understood as the refusal of the state to take responsibility for unauthorised traders, whose existence is denied. It is also a form of disempowerment of such traders, not aware of their own mass, as shown a contrario by the politics of enumeration from below (illustrated in Roy 2009b), where pavement dwellers' self-driven census provide them with self-awareness and local expertise that proved empowering in negotiations with the state.

Charlton's case of the state "not seeing" why housing beneficiary practices deviate from that intended by the state shows a less malevolent intent. In her argument, integrating unemployment complexities, urban movements, shifting households and livelihood strategies into the housing policy is too demanding, given the state's already stretched administrative capacities to steer a housing programme that remains seen as globally of benefit to the poor. As argued by [START_REF] Ferguson | The Uses of Neoliberalism[END_REF], complex policy instruments may appear just in theory but less so in practice, as states are unable to implement them. Ignorance as the condition for the state's continued ability to act; selective knowledge as enabling a constrained intervention [START_REF] Scott | Seeing like a state. How certain schemes to improve the human condition have failed[END_REF]; deeper knowledge as paralysing intervention, are paradoxical conclusions of her interrogation.

The vexed question of intentionality

The provocation from Roy's work that inspired the most debate in this collection is the question of state's intentionality, or purposive use of informal practices to achieve specific objectives. Adding to the debate is the fact that Roy's case studies mostly depict the state as malevolent, developing neoliberal, oppressive, possibly corrupt and certainly speculative objectives, using planning flexibility in sinister ways (2009a, 2009b). In the Southern African context, we aimed at conceptualising state intentionality in a wider variety of directions.

The authors grappled with the choice of a concept to describe purposefulness, that does not personify the state as a unified and individual agent. Concepts abound in this respect, none of which was entirely convincing to the authors, especially as they are often framed by analysts viewing the state from the outside (from its margins, its effects, its representations), rather than from the inside. Neo-marxist approaches look for conflicting interests, attributed to groups and institutions. Liberal approaches emphasise rational choice or constructed and shifting preferences. Foucauldian perspectives excavate state rationalities through studies of their policy instruments, flirting with the not-so-clear concept of strategies without agency. Policy and public administration studies conceptualise policy objectives, that they increasingly understand as complex processes marked by a variety of agendas, again possibly framed in terms of interests, preferences or rationalities. The papers in this collection adopt one or the other approach to discuss whether informal practices of the state are purposefully framed and used by state agents, or if they are the arbitrary outcome of complex processes.

The state is crossed by multiple rationalities, interests and objectives, and in particular internally: between multiple levels of the state, diverse departments and units, different professional and political positions within them (Charlton, Bénit-Gbaffou, this issue). Yet, state interventions often appear more bluntly, consistent and continuous, powerful in their effects and intentions, to the victims of eviction or beneficiaries of welfare (Bénit-Gbaffou, Buire, Charlton this issue). How to understand together the messiness of state's internal policy processes, and the experienced continuities in state's interventions in the city? And how to account for persisting internal contradictions in state's policies: why are they allowed to endure, why are they not resolved? Charlton explains how state officials are able to ignore the contradiction between policy vision and implementation realities: out of the fear that confronting these would paralyse state intervention; because of their confidence in the overall developmental effects of a policy that delivers (housing and political support); and based on the absence of any vigorous contestation of the programme on the basis of this gap. There is indeed no opposition from below, as it might be more efficient for beneficiaries to rely on state laisser-faire than to overtly confront the hand that feeds. Opposition from above is equally limited: the housing policy is too central in the ANC post-apartheid vision to be challenged, even if the National treasury starts questioning whether this is the best use of public resources. State officials ignore the contradiction because they can. Sticking to the policy as it is, ignoring its shortcomings, is rewarding politically and development-wise. They persist in their actions in spite of the contradictions they are aware of. They might respond to it through informal practices on the ground, and this grey area certainly opens a space for corruption. But officials do not seem to use the contradiction as an "idiom of urbanisation", to fulfil collective objectives, developmental or speculative.

Rubin analyses how state officials on the ground purposefully use informal practices, to respond to the practical needs of their jobs, of the social and urban realities they are mandated to deal with. The discretion they use (in line with Lipsky 1971), intentionally, is sometimes oppressive, reflective of prejudices and preferences, engaging in patronage networks for personal benefit, using manipulation to sedate social opposition. But Rubin argues that discretion can also be pragmatic and developmental, embedded in participatory practices, innovatively aimed at problem-solving.

Buire, from the study of the history of the residential trajectory of a household in Luanda, shows how state control is internalised through a vast, opaque and elusive social control network that becomes integrated in the intimacy of family spaces. Even if this consent functions as a form of "remote control", she contests any notion of state calculation in the way this process operates. She rather explores how this consent is essential to the reproduction of hegemony [START_REF] Hibou | Anatomie politique de la domination[END_REF], and argues that its pervasiveness is far more difficult to confront than a direct or overt state intention.

Bénit-Gbaffou similarly contests that the contradiction between progressive street trading policy and repressive practices has been crafted purposefully. However, this contradiction proves functional for certain interests within the state: shielding the state's dominant objective of restricting street trade from the public gaze limits collective debate and mobilisation, especially from traders' organisations. This usefulness might explain the limited interest for the state to resolve its internal contradictions. Furthermore, like in Roy's account, the contradictions that are used (even if not purposefully framed) to facilitate state action simultaneously produce ungovernability: unresolved policy reform leads to criminalising both traders and officials, consolidating space for informal and illegal arrangements between them.

"Informality as idiom of urbanisation" -interrogating state practices as informal

Roy's framing of informality [START_REF] Roy | Urban informality: toward an epistemology of planning[END_REF] shows that it is essentially a political construct, dependent on how legislation defines the boundaries between formal and informal: its contours can shift at the stroke of a pen. She further coins informality as "an idiom of urbanisation", referring to the deliberate use by the state of informality to govern the city (Roy 2009a). Roy does however not elaborate much on what informality is used by the state, and how it is used, beyond her mention of "un-mapping", the deliberate production and reproduction of legal and institutional uncertainty on land status. Furthermore, she looks at the issue mostly from outside the state, from the effects of its choices, policies and practices. She comments on the absence of a map, the blurriness of land status, the lack of state response, the shifting planning regulations issued, that she encounters during the process of research. In the same line, she deducts rather than observes the purposeful use of informality by the state, inferring it from its strategic usefulness and economic profitability.

Taking "informal practices of the state" seriously

The study of informality in relation to state practices is not new. It has been theorised mostly around the state-society porous borders (in literature on governance, clientelism, lobbying and corruption, or on street level bureaucracy). An array of scholars has explored the "grey area" surrounding state intervention, but t the state is seldom their primary object of enquiry. For instance, Auyero is interested in the construction of domination by the state over the subalterns -he writes about "the gray zone" to describe the obscure relations linking state officials and its police apparatus, social movements and criminal elements, in violent public interventions [START_REF] Auyero | Routine Politics and Violence in Argentina. The Gray Zone of State Power[END_REF]) -but he does not further unpack state practices, nor does he go "beyond the counter" when he analyses the politics of waiting (Auyero 2010a), or beyond the patron when he unpacks the dynamics of clientelism [START_REF] Auyero | From the Client's Point(s) of View": How Poor People Perceive and Evaluate Political Clientelism[END_REF]) -the state he invokes remains a black box, one of "visible fists, clandestine kicks and invisible elbows" (Auyero 2010b). [START_REF] Lund | Twilight Institutions: Public Authority and Local Politics in Africa[END_REF] crafts the concept of "twilight institutions" to refer to the multiplication of non-state institutions that parallel, mimic and compete with the state in performing social regulatory functions; but similarly, he does not expand on what this does to state institutions and practices. [START_REF] Yiftachel | Critical theory and 'gray space': Mobilization of the colonized[END_REF] coins the term "gray spaces" to characterise areas and groups living in limbo, in a permanent state of uncertainty, under the threat of eviction; a theme further developed by [START_REF] Chatterjee | The Politics of the Governed: Reflections on Popular Politics in Most of the World[END_REF] under the concept of "political society", referring to a specific mode of relationship (uncertain, temporary, clientelistic) between state institutions and informal population groups. Chatterjee does mention the world of petty bureaucrats and local politicians, in direct contact with informal urban groups, but does not explore beyond this "margin" of the state [START_REF] Das | Anthropology in the margins of the state[END_REF]). This theme is further explored by [START_REF] Benjamin | Urban land transformation for pro-poor economies[END_REF], who observes the "politics by stealth" exerted by "porous bureaucracies" in Indian cities, often at the interface between civil society and junior politicians and bureaucrats; but also, interestingly through the contradictory interplay between local and regional state institutions. Similar to Roy, McFarlane (2012) suggests considering the informal as above all a practice (interrelated to the formal), but unlike her, he does not refer specifically to the state as the agent of such practices. Te Lintelo ( 2017) is one of the few authors explicitly using informality to describe state practices, but (as do Yiftachel and Chatterjee), he tends to limit it to the management of urban informality. He proposes three types of "informal state practices" (te Lintelo, 2017: 85-86), ranging from ad hoc street bureaucrats' discretion (a la Lipsky), the production of "policy short circuits" to directly contradict existing legislation (a la Roy), and the laisser-faire, tolerance or even reproduction of informal settlements and activities through temporary (turning permanent) arrangements, as a way to manage urban poverty (a la Chatterjee). There is a growing interest for rethinking the state through the concept of informality, as announced in the concluding sections of recent publications on urban governance [START_REF] Boudreau | Global Urban Politics: Informalization of the State[END_REF][START_REF] Davis | Informality and state theory: Some concluding remarks[END_REF][START_REF] Morelle | L'informalité politique en ville. 8 chercheurs et 9 villes face aux modes de gouvernement urbain[END_REF] or on the state (Radnitz 2011). This interest is often, actually, inspired by Roy's work. The present collection contributes to this emerging field of study, by offering a conceptualisation of "informal practices of the state", debating its usefulness and limitations, and proposing a typology of such practices.

To further unpack what informal practices of the state might entail, it is important to distinguish informality from illegality. Informality, unlike illegality (breaking the law), refers to a "grey area" where there is no clarity on a course of action from state officials' perspective. State officials may understand that some urban dweller's practices cannot comply with legislation, at least not immediately, that such practices have a degree of social legitimacy that could even be defining "the norm" as they become dominant in urban spaces, and that state capacity and will to act upon such practices might be lacking for a variety of reasons. It is from this perspective that some informal activities and spaces can be legalised or formalised, tacitly accepted and tolerated [START_REF] Yiftachel | Critical theory and 'gray space': Mobilization of the colonized[END_REF][START_REF] Roy | Strangely Familiar: Planning and the Worlds of Insurgence and Informality[END_REF]), encouraged and reproduced [START_REF] Chatterjee | The Politics of the Governed: Reflections on Popular Politics in Most of the World[END_REF][START_REF] Benjamin | Urban land transformation for pro-poor economies[END_REF]). This understanding builds both flexibility and uncertainty into state officials' practices. Indeed, informal practices always take place in a gap, a contradiction, a tension (a "grey area") between different rules and norms. It is partly this "problem of gap" that Olivier de Sardan (2015) makes the central issue of his reflection on state practices. For him, there is always a "gap" between what is expected from state officials and what is observed in reality. He usefully proposed the term of "practical norms" as opposed to "official" ones, encouraging us to look for a multiplicity of norms shaping state officials' practices: official and practical but also social, political and professional norms. The body of work he leads mostly looks at state-society interface to understand these gaps and the contradictory or multiple norms that explain the gap. We suggest that, beyond state-society interface, the quest for such multiple norms is also useful to characterise state internals processes.

All papers in the collection deal with contradictions or tensions in state practices when governing the city: synchronic (Bénit-Gbaffou, Charlton) or diachronic (Buire, Butcher); pertaining to several levels or components of the state (Charlton), different departments or branches of government (Bénit-Gbaffou), or inscribed as contradictory norms in individual officials' practices (Charlton, Rubin); perceived as contradictory by urban dwellers (Buire, Bénit-Gbaffou, Rubin, Butcher), or by officials themselves (Charlton, Rubin). Few authors however explicitly use the term "informal practices of the state", beyond un-mapping (Butcher, Bénit-Gbaffou) and local arrangements at the interface between state and groups (Bénit-Gbaffou). It is Rubin who most directly engages with the term, proposing a typology of informal state practices. Analysing state officials' practical acknowledgement of community-based instruments for local regulation (that are replacing, complementing or expanding ill-adapted official instruments), she distinguishes three types of informal state practices. The first ("negotiability") acknowledges the validity of informal land and population registers and transactions, paralleling impractical or outdated official ones. The second ("porosity") is officials' direct use of the informal registers, in the absence of existing official instruments to that effect. The third ("exceptionality") refers to the adoption of instruments (e.g. categories of beneficiaries) that run contrary to existing policy requirements, but have local legitimacy and practical efficiency.

Towards a typology of informal state practices

Reflecting back on the collection of papers, the wide array of practices of the state they depict and invoke, explicitly or not, as informal, and confronting them to existing literature starting to frame what "informal state practices" might mean, we wish to propose, as an opening for discussion and further research, a typology of informal state practices.

To do so, we frame a definition of 'informal practices of the state' that is narrower perhaps than what its loose usage might have come to draw. Looking for informal practices of the state means examining the 'grey area' of uncertainty and indeterminacy of officials' practices, and this can be done in two main directions, connected but often contrasted as belonging to different theoretical and disciplinary traditions. On the one hand, it is about focusing on officials' practices: analysing how they navigate this grey area, how they choose a course of action, how they determine their own practices -finding patterns (Olivier de Sardan 2015), but also possibly paralysis, fluidity or arbitrariness [START_REF] Gupta | Red Tape: Bureaucracy, Structural Violence, and Poverty in India[END_REF]. On the other hand, it is about examining the politics of policy instruments [START_REF] Lascoumes | Introduction: Understanding Public Policy through Its Instruments-From the Nature of Instruments to the Sociology of Public Policy Instrumentation[END_REF], to better unpack the multiple and contradictory norms that generate this grey area in which officials find themselves --what these norms are, where they are located institutionally and instrumentally, and what incentives or sanctions are attached to their adoption or breach.

We distinguish here between six different meanings and modalities of such grey areas, zones of uncertainty that trigger informal state practices: (1) Framing exceptionality, (2) Navigating policy contradiction, (3) Manufacturing uncertainty, (4) Playing on porosity, (5) Delegating public mandate / Developing a politics of mediation, (6) Engaging in co-production.

Framing exceptionality -Informal state practices as the state acting outside its own legislation: suspending it (in time or in space), or acting in breach of its own legislation (purposefully or not). This is the main type outlined by Roy (2009a), by te Lintelo (2017), illustrated by Rubin and Bénit-Gbaffou (this issue).

Navigating policy contradiction -Informal state practices resulting from multiple and contradictory policy instruments and directions, for reasons such as the sedimentation of successive documents in time (Bierschenck 2010); the lack of coordination between different levels of the state [START_REF] Benjamin | Urban land transformation for pro-poor economies[END_REF]; different departmental priorities and their related professional norms, and misalignment between policy instruments and policy guidelines (Bénit-Gbaffou, this issue).

Manufacturing Uncertainty -Informal state practices exploiting a gap, confusion or opacity in knowledge, as framed by Roy's "un-mapping" (2009a) and Breckenridge's "no will to know" (2012). This gap in knowledge has several drivers, from the quest for simplification and legibility of reality in order to act [START_REF] Scott | Seeing like a state. How certain schemes to improve the human condition have failed[END_REF] to some extent Charlton this issue), the choice of ignorance as a way to keep flexibility in state intervention (Roy 2009a), the abdication of responsibility through denied recognition of specific marginalised groups (Bénit-Gbaffou, this issue), and the delegation of knowledge and operation to the private sector (Butcher, this issue) or to specific social groups (Buire, Rubin, this issue).

Playing on porosity -Informal state practices arising from state agents' different identities, positions, and networks straddling state and society [START_REF] Benjamin | Urban land transformation for pro-poor economies[END_REF][START_REF] Stone | Power, Reform, and Urban Regime Analysis[END_REF][START_REF] Bawa | Where is the state? How is the state? Accessing Water and the State in Mumbai and Johannesburg[END_REF][START_REF] Te Lintelo | Enrolling a goddess for Delhi's street vendors: The micro-politics of policy implementation shaping urban (in)formality[END_REF]Rubin, this issue). Multiple identities not only explain specific official behaviours (sympathy or interest in accommodating non-compliant urban practices), but also might assist the state in relating to social groups, in particular in the case of contentious politics. This porosity can also be problematic, leading to undemocratic state capture by opaque party and business interests [START_REF] Olver | How To Steal A City: The Battle For Nelson Mandela Bay. An inside account[END_REF].

Delegating public mandate, developing a politics of mediation -Informal state practices as delegating (explicitly or not, voluntarily or not) core public functions to non-state agents and institutions, formal and informal (Lund 1996, Cuvi et al. forthcoming). This delegation has profound effects on the state's capacity to act, opening a gap between strategic direction and operational capacity and knowledge (Butcher, this issue), as highlighted above. However, it also sometimes allows the state to expand the realm of its intervention at limited cost, as a form of indirect rule [START_REF] Hibou | La « décharge », nouvel interventionnisme[END_REF]): enabling it to enter spaces or groups it had limited purchasing power in through the brokerage of local leaders and groups (Rubin, Buire, this issue); through the indirect recruitment or co-option of additional administrative, technical or political capacity (Rubin, Roy this issue); or through the use of modes of interventions that its own policies or legal requirements would interdict (e.g. community violence as delegated means to regulate settlement growth: Rubin, this issue).

Engaging in co-production -Informal state practices as flexibly and incrementally co-produced with non-state agents, as theorised by [START_REF] Ostrom | Crossing the great divide: Coproduction, synergy, and development[END_REF], who defines co-production of urban services as a process in which state officials depart from their mandates and job description, and frame their intervention in complement with that of local communities (or other partners). This dimension is best illustrated by Rubin (this issue), although it talks to the limit of the notion of "informal practice of the state": how relevant is it to frame such flexibility in state practices as "informal", if this flexibility is inscribed into the official process of incremental and participatory engagement with communities?

Conclusion

Collectively, on the basis of Roy's inspiring work, the papers extend and deepen engagement around informality of the state, conceptualised in an Indian urban context, then applied and debated in a Southern African urban context. The differences emerging, as Roy's concepts and approaches travel, serve to underline differentiated state capacities, institutional and political histories, and various insertions into globally-funded programmes. They also might highlight different relationships between academia and the state.

The recent character of the liberation moment in South Africa has to some extent opened up the State to researchers' gaze, based on the penetration of anti-apartheid activists in various levels of the State in the post-apartheid era, aiming at reforming institutions, policies and practices to better society, often in close conversations with supportive academics. Those activists-turned-officials or politicians, driving progressive change in cities from the state rather than from the street, could be called "activists in the state", following Clavel's "Activists in City Hall" (2010). One may find an equivalent opening in Brazil under Lula, where a significant number of social movement activists became government officials, and have opened to sharing with researchers their experience in driving policy and social change from this institutional position [START_REF] Abers | Institutional Activism: Mobilizing for Women's Health from Inside the Brazilian Bureaucracy[END_REF]. Such opening of the state to the researcher's gaze is highly uneven, obviously biased, restricted to selected sections of the state, and possibly short-lived. But it assists in complexifying our understanding of state intervention in the city beyond a sinister and malevolent one, as is dominant in most literature studying the state from the outside.