Andreas Rutz

Chandan K Das

Andrea Fasano

Jan Jaenecke

Shanika Yadav

Ulf-Peter Apfel

Vera Engelbrecht

Vincent Fourmond

Christophe Léger

Lars V Schäfer

Thomas Happe

Increasing the O 2 Resistance of the [FeFe]-Hydrogenase CbA5H through Enhanced Protein Flexibility

Keywords: Metalloenzymes, [FeFe]-hydrogenase, spectroscopy, protein film voltammetry, molecular dynamics

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

[FeFe]-hydrogenases catalyze the reversible oxidation and production of hydrogen at high rates. 1,[START_REF] Kleinhaus | Maturation and Reactivity of Enzymatic Systems and Overview of Biomimetic Models[END_REF] These redox enzymes use a unique active center, the so-called "H-cluster", which consists of two sub-clusters. The cubane subcluster, [4Fe]H, is a standard [4Fe-4S]-cluster ligated by four cysteine ligands to the protein backbone. One of the cysteine ligands also bridges the [4Fe]H cluster and the binuclear FeS cluster, [2Fe]H, which is additionally coordinated by two CN -and three CO ligands. [START_REF] Peters | X-Ray Crystal Structure of the Fe-Only Hydrogenase (CpI) from Clostridium Pasteurianum to 1.8 Angstrom Resolution[END_REF][START_REF] Nicolet | Desulfovibrio Desulfuricans Iron Hydrogenase: The Structure Shows Unusual Coordination to an Active Site Fe Binuclear Center[END_REF] Both iron atoms, Fep and Fed (the subscripts p and d refer to "proximal" and "distal" with respect to the cubane subcluster), are connected via an azadithiolate bridge (ADT), which plays an important role during the catalytic hydrogen turnover. [START_REF] Peters | X-Ray Crystal Structure of the Fe-Only Hydrogenase (CpI) from Clostridium Pasteurianum to 1.8 Angstrom Resolution[END_REF][START_REF] Nicolet | Desulfovibrio Desulfuricans Iron Hydrogenase: The Structure Shows Unusual Coordination to an Active Site Fe Binuclear Center[END_REF][START_REF] Silakov | 14N HYSCORE Investigation of the H-Cluster of [FeFe] Hydrogenase: Evidence for a Nitrogen in the Dithiol Bridge[END_REF][START_REF] Rodríguez-Maciá | Intercluster Redox Coupling Influences Protonation at the H-Cluster in [FeFe] Hydrogenases[END_REF] The vacant site at Fed is involved in hydrogen oxidation/evolution and is prone to the binding of various inhibitors (O2, CO, SH). [START_REF] Kubas | Mechanism of O2 Diffusion and Reduction in FeFe Hydrogenases[END_REF][START_REF] Baffert | Hydrogen-Activating Enzymes: Activity Does Not Correlate with Oxygen Sensitivity[END_REF][START_REF] Rodríguez-Maciá | Caught in the Hinact: Crystal Structure and Spectroscopy Reveal a Sulfur Bound to the Active Site of an O2-Stable State of [FeFe] Hydrogenase[END_REF][START_REF] Rodríguez-Maciá | Sulfide Protects [FeFe] Hydrogenases from O 2[END_REF][START_REF] Wait | Formaldehyde -A Rapid and Reversible Inhibitor of Hydrogen Production by [FeFe]-Hydrogenases[END_REF][START_REF] Greco | Structural Insights into the Active-Ready Form of [FeFe]-Hydrogenase and Mechanistic Details of Its Inhibition by Carbon Monoxide[END_REF][START_REF] Stripp | How Oxygen Attacks [FeFe] Hydrogenases from Photosynthetic Organisms[END_REF][START_REF] Goldet | Electrochemical Kinetic Investigations of the Reactions of [FeFe]-Hydrogenases with Carbon Monoxide and Oxygen: Comparing the Importance of Gas Tunnels and Active-Site Electronic/Redox Effects[END_REF] In contrast to industrial platinum-based hydrogen production catalysts, [FeFe]-hydrogenases rely on earth abundant metals such as iron and can be considered as biological blueprints for the design of synthetic catalysts. [START_REF] Jones | Direct Comparison of the Electrocatalytic Oxidation of Hydrogen by an Enzyme and a Platinum Catalyst[END_REF][START_REF] Esmieu | From Protein Engineering to Artificial Enzymes-Biological and Biomimetic Approaches towards Sustainable Hydrogen Production[END_REF][START_REF] Rauchfuss | Diiron Azadithiolates as Models for the [FeFe]-Hydrogenase Active Site and Paradigm for the Role of the Second Coordination Sphere[END_REF][START_REF] Ding | Interplay of Hemilability and Redox Activity in Models of Hydrogenase Active Sites[END_REF] However, their catalytic performance is limited by a high O2-sensitivity. The binding of oxygen to the vacant coordination site is coupled to further protonation and reduction steps that eventually lead to the formation of reactive oxygen species (ROS), which subsequently results in an irreversible destruction of the active site. [START_REF] Kubas | Mechanism of O2 Diffusion and Reduction in FeFe Hydrogenases[END_REF][START_REF] Baffert | Hydrogen-Activating Enzymes: Activity Does Not Correlate with Oxygen Sensitivity[END_REF][START_REF] Mebs | Hydrogen and Oxygen Trapping at the H-Cluster of [FeFe]-Hydrogenase Revealed by Site-Selective Spectroscopy and QM/MM Calculations[END_REF][START_REF] Bruska | Regioselectivity of H Cluster Oxidation[END_REF][START_REF] Swanson | FeFe]-Hydrogenase Oxygen Inactivation Is Initiated at the H Cluster 2Fe Subcluster[END_REF][START_REF] Esselborn | Loss of Specific Active-Site Iron Atoms in Oxygen-Exposed [FeFe]-Hydrogenase Determined by Detailed X-Ray Structure Analyses[END_REF] Note that in standard hydrogenases, the destruction of the enzyme by O2 is mainly irreversible, but a partial reactivation, resulting from the reduction of O2 at the active site, can be detected after short exposure to O2. [START_REF] Kubas | Mechanism of O2 Diffusion and Reduction in FeFe Hydrogenases[END_REF][START_REF] Orain | Electrochemical Measurements of the Kinetics of Inhibition of Two FeFe Hydrogenases by O2 Demonstrate That the Reaction Is Partly Reversible[END_REF] Computational and experimental studies suggested that O2-binding leads either to the decomposition of the [2Fe]H subsite, retaining an intact [4Fe]H [START_REF] Swanson | FeFe]-Hydrogenase Oxygen Inactivation Is Initiated at the H Cluster 2Fe Subcluster[END_REF] or ROS (O2 -, OOH -) diffusion initiates the decomposition at the [4Fe]H. [START_REF] Stripp | How Oxygen Attacks [FeFe] Hydrogenases from Photosynthetic Organisms[END_REF]24 However, an in crystallo study could demonstrate that both pathways can coexist and are highly dependent on the electron supply. [START_REF] Esselborn | Loss of Specific Active-Site Iron Atoms in Oxygen-Exposed [FeFe]-Hydrogenase Determined by Detailed X-Ray Structure Analyses[END_REF] The enzyme CbA5H from the bacterium Clostridium beijerinckii is so far the only characterized enzyme, which tolerates prolonged exposure to O2, by reversibly switching between the active Hox state to the inactive but O2-protected Hinact state. [START_REF] Morra | Oxygen Stability in the New [FeFe]-Hydrogenase from Clostridium Beijerinckii SM10 (CbA5H)[END_REF][START_REF] Corrigan | Investigation of the Unusual Ability of the [FeFe] Hydrogenase from Clostridium Beijerinckii to Access an O2-Protected State[END_REF] The Hinact state was originally identified in DdH from Desulfovibrio desulfuricans and provided an irreversible protection against O2, albeit only limited to the first reductive reactivation. [START_REF] Goldet | Electrochemical Kinetic Investigations of the Reactions of [FeFe]-Hydrogenases with Carbon Monoxide and Oxygen: Comparing the Importance of Gas Tunnels and Active-Site Electronic/Redox Effects[END_REF][START_REF] Roseboom | The Active Site of the [FeFe]-Hydrogenase from Desulfovibrio Desulfuricans. II. Redox Properties, Light Sensitivity and CO-Ligand Exchange as Observed by Infrared Spectroscopy[END_REF][START_REF] Glick | P. and properties of the periplasmic hydrogenase from D. desulfuricans. C. J. M. 26:1214-12[END_REF] Studies by Rodríguez-Maciá et al., could provide evidence that this effect is attributed to the binding of exogenous sulfide under oxidizing conditions. [START_REF] Rodríguez-Maciá | Caught in the Hinact: Crystal Structure and Spectroscopy Reveal a Sulfur Bound to the Active Site of an O2-Stable State of [FeFe] Hydrogenase[END_REF] Sulfide treatment to other [FeFe]-hydrogenases could reproduce this inactivation, enabling effective protection against O2 prior to the first reactivation. [START_REF] Rodríguez-Maciá | Sulfide Protects [FeFe] Hydrogenases from O 2[END_REF][START_REF] Felbek | Mechanism of Hydrogen Sulfide-Dependent Inhibition of FeFe Hydrogenase[END_REF] In contrast to that, CbA5H possesses an intrinsic protection mechanism towards O2, independent of exogenous sulfide, which is governed by the coordination of an adjacent cysteine residue (C367). Upon oxidizing conditions, C367 can coordinate to Fed and thus prevent the binding of O2 and the subsequent destruction of the active site. [START_REF] Morra | Oxygen Stability in the New [FeFe]-Hydrogenase from Clostridium Beijerinckii SM10 (CbA5H)[END_REF][START_REF] Corrigan | Investigation of the Unusual Ability of the [FeFe] Hydrogenase from Clostridium Beijerinckii to Access an O2-Protected State[END_REF][START_REF] Winkler | A Safety Cap Protects Hydrogenase from Oxygen Attack[END_REF] It has been shown that various residues are crucial for the movement of the cysteine residue and, based on spectroscopic and kinetic data, we proposed a detailed model for the conformational change of the "TSC" peptide loop that relocates the conserved cysteine close enough to Fed to allow coordination. A structural comparison of CbA5H and the standard [FeFe]-hydrogenase CpI from Clostridium pasteurianum unveiled a complex interplay of different residues which prevents the coordination of the cysteine residue in conventional [FeFe]-hydrogenases. Substituting these amino acids with analogues of CpI resulted in slower conformational changes and more O2-sensitive CbA5H variants. In the WT enzyme, the reductive reactivation is limited to a few cycles of O2-exposure and reductive reactivation: a fraction of the enzyme is irreversibly degraded in each reversible conversion from active (A) to inactive (I) form, as observed in independent investigations of CbA5H. [START_REF] Corrigan | Investigation of the Unusual Ability of the [FeFe] Hydrogenase from Clostridium Beijerinckii to Access an O2-Protected State[END_REF] In this work, we show that methionine 382, an amino acid positioned more than 18 Å away from the active site (see Figure 1A) is an important structural determinant of the O2 resistance of CbA5H. Due to the inherent properties of methionine residues, M382 anchors the protein framework and stabilizes a particular configuration of the peptide chain. A substitution of this residue results in structural changes within the protein, which increase the flexibility of a loop (termed "Loop A") adjacent to the TSC-loop. By combining site-directed mutagenesis, IR spectroscopy, molecular dynamics simulations and electrochemical kinetic studies, we show that the residue at position 382 remotely controls the active site chemistry of CbA5H and that its substitution towards and glutamic acid accelerates the conformational changes and renders the enzyme more resistant to oxygen.

Experimental Section

Site directed mutagenesis. QuikChange PCR was used to generate hydrogenase genes with different codons according to the protocol described earlier. [START_REF] Zheng | An Efficient One-Step Site-Directed and Site-Saturation Mutagenesis Protocol[END_REF] Expression plasmids were amplified by using mismatch primers (Table SI). Products were treated with endonucleases DpnI and transformed into E. coli strain DH5α by using heatshock method. All DNA constructs were subsequently verified via sequencing.

Expression and purification: E. coli strain BL21 (DE3) ΔiscR was transformed with expression plasmid pET21b containing the codon optimized CBA5H gene (NCBI GenBank: KX147468.1) and was used to express apo CbA5H (lacking the [2FeH] subcluster). [START_REF] Akhtar | Deletion of IscR Stimulates Recombinant Clostridial Fe-Fe Hydrogenase Activity and H2-Accumulation in Escherichia Coli BL21(DE3)[END_REF] Expression and purification was conducted under strictly anaerobic conditions as described previously. [START_REF] Kuchenreuther | High-Yield Expression of Heterologous [FeFe] Hydrogenases in Escherichia Coli[END_REF] Affinity chromatography was performed used Strep Tacting High-capacity resin (IBA GmBH). Protein concentration was determined by Bradford assay [START_REF] Bradford | A Rapid and Sensitive Method for the Quantitation of Microgram Quantities of Protein Utilizing the Principle of Protein-Dye Binding[END_REF] and purity was verified by SDS-PAGE (polyacrylamide gel electrophoresis). [START_REF] Laemmli | Cleavage of Structural Proteins during the Assembly of the Head of Bacteriophage T4[END_REF] Proteins were stored at -80 °C in 100 mM Tris-HCl buffer pH 8 with 2 mM sodium dithionite (NaDT).

In vitro maturation: Apo proteins were incubated on ice for 1 hour with a 10-fold molar excess of the artificially synthesized [START_REF] Li | Iron Carbonyl Sulfides, Formaldehyde, and Amines Condense to Give the Proposed Azadithiolate Cofactor of the Fe-Only Hydrogenases[END_REF] in order to reconstitute active protein as described earlier. [START_REF] Esselborn | Spontaneous Activation of [FeFe]-Hydrogenases by an Inorganic [2Fe] Active Site Mimic[END_REF] Holo proteins and excess [2Fe]H were separated by size exclusion chromatography (NAP 5 column, GE healthcare).

[2Fe]H cofactor mimic ([2Fe2[µ-(SCH2)2NH](CN)2(CO)4] 2-)

Enzyme activity assay (H2 production) with multiple inactivation cycles: H2 production activity

was assayed with 10 mM methyl viologen (MV) as electron mediator, 200 mM NaDT as electron donor and 400 ng holo-enzyme in 100 mM potassium phosphate buffer (K2HPO4/KH2PO4) at pH 6.8.

The reaction mixture was degassed with 100 % argon and incubated for 20 min at 37 °C in a sealed 8 ml glass vessel. The amount of H2 was determined by gas chromatography. The inactivation was performed by incubating the enzyme solution for 15 min under an atmosphere of air, on ice, making sure the solution is aerated. After the first inactivation and prior to every further inactivation with air, the solution was treated for 20 min with 100 % H2 in order to ensure full activation. All protein solutions were prepared in the absence of NaDT. After each inactivation, aliquots were taken for subsequent standard in vitro assays as described before. Each measurement was performed in triple determination with three technical replicates.

Protein film electrochemistry. Cyclic voltammetry and the amperometry experiments employed

to elucidate the kinetics of the conformational change leading to Hinact-formation were carried out https://pubs.acs.org/doi/10.1021/acscatal.2c04031 in a JACOMEX glovebox filled with N2 in a thermostated (T = 5 °C) electrochemical cell with two compartments. The main compartment contained the rotating working electrode (pyrolytic graphite edge, 3 mm diameter, typical rotation rate 3000 rpm, mounted on a Pine MSR rotator) and the counter electrode (a platinum wire) as well as the inlet of H2. The main compartment was filled with a mixed buffered solution (consisting of 5 mM of each MES, HEPES, sodium acetate, TAPS, and CHES and 0.1 M NaCl). The main compartment was connected via a Luggin capillary to a second compartment, containing the calomel reference electrode in 0.1 M NaCl. All potentials are quoted with respect to the standard hydrogen electrode, calculated using ESHE = Ecalomel + 0.241 V. To prepare the protein films, the pyrolytic graphite "edge" (PGE) rotating disc working electrode was polished with an aqueous alumina slurry (Buehler, 1 μm), rinsed, then painted with 0.5 μl of an enzyme solution (~ 5 mg/mL in 100 mM Tris-HCl, pH 8 with 2 mM NaDT) and let dry for 2 min. The measured catalytic currents were between 1-and 10 μA, so that mass transport towards the rotating electrode was not limiting. [START_REF] Merrouch | Reliable Estimation of the Kinetic Parameters of Redox Enzymes by Taking into Account Mass Transport towards Rotating Electrodes in Protein Film Voltammetry Experiments[END_REF] (CVs and chronoamperometric experiments were recorded with the program GPES and analyzed with the open source program QSoas. [START_REF] Fourmond | QSoas: A Versatile Software for Data Analysis[END_REF] Chronoamperometric experiments were started and ended at a potential 30 mV below the H + /H2 equilibrium potential (pH 7: -0.459 V vs SHE) to ensure complete activation of the enzyme film. The intermediate steps at oxidative potential were of 100 mV amplitude. Before analyzing the changes in H2-oxidation current, we subtracted the background capacitive current recorded in a control experiment without enzyme.

ATR-FTIR spectroscopy. Attenuated total reflectance fourier transform spectroscopy was performed on a Bruker Tensor II spectrometer (Bruker Optik, Germany), equipped with a 9 reflection ZnSe/Si crystal (Microm ATR Vision, Czitek). All measurements were conducted under anoxic conditions (1.5 % H2, 98.5 % N2) at 25 °C. The FTIR spectra were recorded from 4000 -1000 cm -1 with a resolution of 2 cm -1 . The protein film was dried with a H2 gas stream for around 10 minutes and re-humidified with an aerosol by purging a buffer containing compartment.

Molecular Dynamics Simulations. All molecular dynamics (MD) simulations were performed with

GROMACS version 2021.4. [START_REF] Abraham | High Performance Molecular Simulations through Multi-Level Parallelism from Laptops to Supercomputers[END_REF] The structure of the H-domain was taken from the previously reported crystal structure of WT CbA5H captured in the Hinact state (PDB ID 6TTL). [START_REF] Winkler | A Safety Cap Protects Hydrogenase from Oxygen Attack[END_REF] The M382E variant structure was generated by replacing the M382 side-chain in 6TTL. The CHARMM36 force field was employed for the protein together with the CHARMM-specific TIP3P water model. The force field parameters for the H-cluster and other Fe-S clusters were taken from the work of Chang et al. and McCullagh et al. [START_REF] Chang | Density Functional Theory Calculation of Bonding and Charge Parameters for Molecular Dynamics Studies on [FeFe] Hydrogenases[END_REF][START_REF] Mccullagh | Unraveling the Role of the Protein Environment for[END_REF] The Hox state was simulated, with the C367 side-chain protonated (-SH). The protein structures were solvated in dodecahedron-shaped periodic simulation boxes filled with 13206 water molecules and sodium ions to neutralize the systems. Prior to the MD simulations, the systems were energy-minimized, followed by stepwise equilibration for 2.7 ns, during which harmonic position restraints were applied to different sets of atoms. In the first NVT equilibration phase (0.2 ns), position restraints with force constants of 1000 kJ/mol/nm 2 were applied to all nonhydrogen atoms of the protein and the Fe-S clusters. Subsequently, the second equilibration phase was continued for another 2.5 ns in the NpT ensemble. During the initial 0.5 ns of this second equilibration phase, the position restraints were still applied to all non-hydrogen atoms of the protein and the Fe-S clusters. During the final 2.0 ns, the position restraints were only applied to all nonhydrogen atoms of the protein backbone. The MD simulations were conducted withing periodic boundary conditions in the NpT ensemble at constant temperature of 300 K and 1 bar pressure, by coupling to the velocity rescaling thermostat of Bussi and coworkers and weak coupling barostat, respectively. [START_REF] Bussi | Canonical Sampling through Velocity Rescaling[END_REF][START_REF] Berendsen | Molecular Dynamics with Coupling to an External Bath[END_REF] The Coulomb and Lennard-Jones interactions were described with a buffered Verlet pair list with a 1.2 nm cutoff, with the forces smoothly switched to zero between 1.0 nm and 1.2 nm. [START_REF] Páll | A Flexible Algorithm for Calculating Pair Interactions on SIMD Architectures[END_REF] Long-range electrostatic interactions were treated with the particle mesh Ewald (PME) method with 0.12 nm grid spacing. [START_REF] Darden | Particle Mesh Ewald: An N•log(N) Method for Ewald Sums in Large Systems[END_REF] The LINCS and SETTLE constraint algorithms were employed to constrain all protein bonds involving H-atoms and internal degrees of freedom of water molecules, respectively, allowing to integrate the equations of motion with 2 fs time steps. [START_REF] Hess | A Parallel Linear Constraint Solver for Molecular Simulation[END_REF][START_REF] Miyamoto | Settle: An Analytical Version of the SHAKE and RATTLE Algorithm for Rigid Water Models[END_REF] Finally, starting with the equilibrated systems, two 1500 ns production MD simulations for each of the two different systems (WT enzyme, M382E) were carried out in the NpT ensemble, initiated with different random seeds to generate the initial atomic velocities from a Maxwell distribution at 300 K.

Because the starting structures of the Hox states were built from the Hinact crystal structure, the initial 200 ns of each simulation were considered to be equilibration and discarded in the analyses.

Results and Discussion

We focus on the position of methionine 382, which is located in a bridging position between Helix A and Loop A, close to the TSC-loop (Figure 1B). The crystal structure of CbA5H suggests that M382 forms hydrophobic contacts with residues L549 and I552 (Figure 1B, inset), which might coordinate the peptide chain. Methionine residues often stabilize protein structures by forming hydrophobic interactions with nearby residues. [START_REF] Heiby | Methionine in a Protein Hydrophobic Core Drives Tight Interactions Required for Assembly of Spider Silk[END_REF][START_REF] Aledo | Methionine in Proteins: The Cinderella of the Proteinogenic Amino Acids[END_REF] The highly flexible side chain with the unique properties of the thioether sulfur render this amino acid as highly versatile. [START_REF] Heiby | Methionine in a Protein Hydrophobic Core Drives Tight Interactions Required for Assembly of Spider Silk[END_REF][START_REF] Ravi | FTIR Markers of Methionine Oxidation for Early Detection of Oxidized Protein Therapeutics[END_REF][START_REF] Yashiro | Studies as a Function of PH Using X-and Q-Band Time-Resolved Electron Paramagnetic Resonance Spectroscopy[END_REF][START_REF] Kudryavtseva | Hydrogen Peroxide for Disulfide Bridge Formation in Methionine-Containing Peptides[END_REF] It was proposed that methionines form tighter van der Waals contacts than other hydrophobic side chains, which provides a natural anchor point in the protein environment. [START_REF] Gellman | On the Role of Methionine Residues in the Sequence-Independent Recognition of Nonpolar Protein Surfaces[END_REF] The replacement of a methionine can abolish such interactions and therefore may increase the flexibility of peptide chains. [START_REF] Heiby | Methionine in a Protein Hydrophobic Core Drives Tight Interactions Required for Assembly of Spider Silk[END_REF] We aimed to alter the protein structure at this position by replacing M382 and studying the influence of the mutation on the conformational dynamics and on the (in)activation mechanism.

Enhanced O2 stability of the M382E variant

We replaced M382 with glutamic acid, isoleucine, and alanine. The M382A variant did not exhibit measurable activity, while the isoleucine exchange maintained high catalytic performance. The exchange of methionine to glutamic acid (M382E) resulted in an H2-production activity of about 50-60 % compared to the CbA5H WT protein. We investigated the stability of the variant M382E after repeated cycles of exposure to air and H2 using methyl viologen based H2-production assays.

Figure 2. H2 production activities after aerobic inactivation of CbA5H

WT and M382E. Normalized activity measurements of three independent measurements after cycles of air exposure (15 min at 4°C). After every inactivation step the protein solution was reactivated under 100 % H2 atmosphere for 20 min. Individual data sets are summarized in Figure S3 and Supplementary table S2.

The results in Figure 2 show a decrease in activity after each exposure to air for the WT and the variant. The observed decay of CbA5H WT activity is in agreement with earlier reports (∼40 % after the 1 st exposure, ∼75 % after the 2 nd exposure 26 ). However, the relative decrease in activity is smaller for the M382E variant and indicates an improved protection, which might be associated with the easier or faster coordination of the C367 side chain to the distal Fe.

Influence of the M382E substitution on the catalytic cycle

We examined the protein variants using FTIR spectroscopy to assess the extent of incorporation of the [2Fe]H subsite into the protein and to monitor catalytic relevant redox states. We observed a reduced H-cluster occupancy in the M382E variant which is consistent with the reduced activity https://pubs.acs.org/doi/10.1021/acscatal.2c04031 (see SI Figure S4). The difference spectrum in Figure 3 A shows that the treatment of the WT enzyme with a hydrogen saturated aerosol led to the accumulation of the bands at 1893 cm -1 , 1916 cm - 1 , 2040 cm -1 and 2075 cm -1 , which are assigned to the HredH + state with minor contributions of Hhyd and Hox. The HredH + state features a reduced [2Fe]H and a proton bound to the ADT bridge. [START_REF] Katz | Vibrational Spectroscopy Reveals the Initial Steps of Biological Hydrogen Evolution[END_REF][START_REF] Sommer | Proton Coupled Electronic Rearrangement within the H-Cluster as an Essential Step in the Catalytic Cycle of [FeFe] Hydrogenases[END_REF] A one-electron reduction leads to the formation of the HsredH + state which enables the subsequent formation of the Hhyd state, featuring a terminal hydride species bound to Fed. [START_REF] Winkler | Accumulating the Hydride State in the Catalytic Cycle of [FeFe]-Hydrogenases[END_REF] In contrast to that we could observe that the spectrum of the M382E variant exhibited a significant contribution of the Hhyd state (2091 cm -1 , 2083 cm -1 , 1979 cm -1 , 1963 cm -1 and 1855 cm -1 ) after prolonged exposure to hydrogen (Figure 3). variants or under acidic conditions in a combination with an atmosphere of H2. [START_REF] Winkler | Accumulating the Hydride State in the Catalytic Cycle of [FeFe]-Hydrogenases[END_REF] The accumulation of Hhyd in the M382E variant might suggest a conformational change of the native proton transfer pathway. This notion is supported by our MD simulations (see below), which show that in the M382E variant, residue S387, which is a key residue in the native proton transfer pathway (PTP), is dislocated and no longer participates in an H-bond network with E341 and E344, which would be required for efficient proton transfer along this pathway (Figure S5). We speculate that the enhanced spatial freedom influences the protonation dynamics of the H-cluster, hence providing a reasonable explanation for the Hhyd accumulation in M382E. Previous studies could report a similar observation for proton transfer deficient CpI variants, which exhibited an increased population of the hydride bound state. [START_REF] Winkler | Accumulating the Hydride State in the Catalytic Cycle of [FeFe]-Hydrogenases[END_REF][START_REF] Duan | Crystallographic and Spectroscopic Assignment of the Proton Transfer Pathway in [FeFe]-Hydrogenases[END_REF] Additionally, it could be shown that an impaired protonation of O2 - species due an interrupted PTP prevent the formation of mobile ROS and reduces the degradation of the H-cluster. [START_REF] Mebs | Hydrogen and Oxygen Trapping at the H-Cluster of [FeFe]-Hydrogenase Revealed by Site-Selective Spectroscopy and QM/MM Calculations[END_REF] The structural deviations in the PTP of the variant M382E and the resulting presence of a terminal bound hydride might support the resistance towards oxygen. The subsequent exposure of the enzymes to air led to the formation of the O2 protected Hinact state (2107 cm -1 , 2080 cm -1 , 2011 cm -1 , 1991 cm -1 and 1840 cm -1 ).

The M382E substitution changes the conformational dynamics of the protein

To understand how the mutation at site 382 modulates the conformational ensembles of CbA5H, we carried out all-atom MD simulations of the WT enzyme and the M382E variant. The simulations were started from the H ox state, which corresponds to the A 1 state (see below). The MD simulations were based on the X-ray crystal structure of CbA5H from C. beijerinckii (PDB code 6TTL). The atomic coordinates of the M382E variant were generated from the crystal structure by replacing the M382 side chain.

Figure 4A-C show that in the M382E variant Loop A undergoes structural changes, which also affect the vicinity of the TSC-loop. This conformational change is triggered by solvation forces, which displace the charged E382 side chain from the hydrophobic environment in which M382 is located in the WT protein, such that E382 becomes fully hydrated by moving away from the helix bearing the hydrophobic contact-forming residue L549 (Figure 4B-D). This conformational change goes along with a pronounced increase of the structural flexibility in this region (see RMSF profile showing the fluctuations of the residues in Figure 4E). Besides residue S387 of the PTP, this part of the peptide chain bears a residue that is relevant for the positioning of C367 near Fed (P386) and may influence the kinetics of the cysteine coordination to Fed. These observations are in line with our previous results, which suggested that at least three distinct positions (L364, P386, and A561) are crucial for the conformational change. [START_REF] Winkler | A Safety Cap Protects Hydrogenase from Oxygen Attack[END_REF] To further investigate the link between the structural dynamics and the inactivation kinetics, we employed protein film electrochemistry.

Position M382 influences anaerobic inactivation

Protein film electrochemistry (PFE) was used to examine the kinetics of the conformational changes that lead to reversible inactivation in CbA5H WT and the variant, using the method described https://pubs.acs.org/doi/10.1021/acscatal.2c04031 earlier. [START_REF] Winkler | A Safety Cap Protects Hydrogenase from Oxygen Attack[END_REF] The activity of the enzyme adsorbed onto a graphite electrode is measured as a current following sweeps or steps of the applied potential, which trigger its (in)activation. All electrochemical experiments were performed at 5°C to minimize film loss. Figure 5 compares the cyclic voltammograms (CVs) of the WT protein and the M382E variant (see Figure S7 for the M382I variant and Figure S8 for the effect of varying the scan rate). See SI Figure S7 for the comparison between the data obtained with CbA5H and M382I variant. Note that in protein film voltammetry the magnitude of the signal cannot be interpreted because it depends on the unknow enzyme coverage. Only the shape of the signal matters, and therefore the potential chosen for the normalization of the current is arbitrary. See SI Figure S6 A for the raw (non-normalized) data plotted in this figure .      In both cases, a negative current reveals H2 production at low potential and H2 oxidation is seen as a positive current at high potential. The current response is dependent on the direction of the sweep (the CVs show a very pronounced hysteresis). The H2 oxidation current decreases at low potential (positive of the H + /H2 Nernst potential) due to oxidative inactivation and the enzymes reactivate during the reductive sweep. These processes are slow on the voltametric time scale, hence the hysteresis. The high potential inactivation observed with CbA5H differs from that observed with https://pubs.acs.org/doi/10.1021/acscatal.2c04031 standard hydrogenases: it occurs at much lower potential than that of standard hydrogenases and it is not due to the presence of chloride anions in the buffer (Figure S9 in reference 30 for the WT, and SI Figure S9 for the M382E mutant). S10). Three rate constants are potential independent and shown with dark orange, orange and yellow circles (kinact, k1 and k-1, respectively) for the WT protein, and in gray, slate gray and dark gray (kinact, k1 and k-1, respectively) for the M382E mutant. k-1 is ill-defined (cannot be accurately determined) and was set to the same value for both enzymes. The values of kreact are shown as red and black circles for the WT enzyme and for the mutant, respectively. The WT data are replotted from ref. 30.

The inactivation of CbA5H WT disappears when C367 is replaced with aspartate and was therefore related to the formation of the Hinact state. [START_REF] Winkler | A Safety Cap Protects Hydrogenase from Oxygen Attack[END_REF] Figure 5 shows that the (in)activation of the variant is more pronounced. The kinetics of the transformation is easily assessed by interpreting potential steps experiments such as those in Figure 6B, where the electrode potential is repeatedly stepped up and down, and the current response is analyzed using a kinetic model. Note in this figure that the change in current following the potential steps is faster for the variant than the WT. The previously established kinetic model 30 considers three distinct species (A1, A2 and I, Figure 7), and accounts for the biphasic kinetic traces that are observed in chronoamperometry experiments. "A1" and "A2" are active forms of the enzyme, "I" is an inactive form, the "Hinact state", in which cysteine C367 is coordinated to the distal iron, competing with hydrogen binding and thus preventing turnover. The potential-independent rate constants k1 and k-1 describe the conversion between A1 and A2. Due to the slow transition between these two forms (1/(k1 + k-1) ≈ 10 s), we proposed that this step is associated with a conformational change. The final coordination of the cysteine ligand itself occurs during the transformation of A2 to I and the bond is labile (1/(kinact + kreact) ≈ 1 s) due to the relatively long distance of 3.1 Å. Note that the inactive state is formed upon anaerobic or aerobic oxidation and provides effective protection against O2. Hence the faster the inactivation, the more resistant the enzyme. This correlation has already been observed in our previous work, although the mutants examined therein were slower to inactivation and thus less O 2 resistant. [START_REF] Winkler | A Safety Cap Protects Hydrogenase from Oxygen Attack[END_REF] The second step https://pubs.acs.org/doi/10.1021/acscatal.2c04031

involves the transfer of one proton and one electron, but the analysis of the data shows that only the backward rate constant kreact is potential dependent (see reference 30 and Figure 6). We analyzed a number of chronoamperometric traces such as those in Figure 6B (see SI figure S10) to measure the rate constants of interconversion between the active and inactive forms of the enzymes under various conditions of electrode potential. The results are shown in Figure 6D for the WT protein and the M382E variant (see S12 for the M382I variant). The results in Table 1 show that the M382E mutation has no significant effect on the k1/k-1 transition (note that, as mentioned in our previous work, k-1 cannot be accurately determined and was fixed to the WT protein value in all fitting procedures), but it increases the rate constants kinact and kreact, about 5.5-fold, respectively, leaving the ratio unchanged. The 5.5-fold acceleration corresponds to a 4 kJ/mol decrease in activation energy of step 2. Together with the increased structural flexibility observed in the MD simulations (see above) this provides a reasonable explanation why C367 coordinates faster to Fed in the M382E variant than in the WT. The dynamic conversion between the different states (A1/2 ↔ Hinact) determines the efficiency of the inactivation mechanism of CbA5H. Our study illustrates how the replacement of a residue is associated with an increased local flexibility of Loop A, which directly affects the TSC loop and thus the catalytic properties of the enzyme.

Table 1. Values of k1, k-1, kreact, kinact for CbA5H

WT and M382E. Measured at pH7, 5°C. All rate constants are potential independent, except kreact which is given here at E = -199 mV vs SHE. The value of k-1 is the least well-defined in the fitting procedure (as observed previously [START_REF] Winkler | A Safety Cap Protects Hydrogenase from Oxygen Attack[END_REF] ), and was fixed to the WT. The WT data are taken from ref. 30.

It is reported that local perturbations can affect protein dynamics over large distances (> 25 Å) [START_REF] Boehr | A Distal Mutation Perturbs Dynamic Amino Acid Networks in Dihydrofolate Reductase[END_REF] with implications on different biological processes. [START_REF] Tang | Long-Range Correlation in Protein Dynamics: Confirmation by[END_REF][START_REF] Henzler-Wildman | Dynamic Personalities of Proteins[END_REF] Loops, which are structural relevant elements for protein stability, 62,63 specificity, [START_REF] Gunasekaran | Triggering Loops and Enzyme Function: Identification of Loops That Trigger and Modulate Movements[END_REF] and protein-protein interactions [START_REF] Herbert | Molecular Mechanism of SSR128129E, an Extracellularly Acting, Small-Molecule, Allosteric Inhibitor of Fgf Receptor Signaling[END_REF] , often facilitate allosteric communication 66 and catalysis. [START_REF] Malabanan | A Role for Flexible Loops in Enzyme Catalysis[END_REF] Detailed studies of various enzyme provide important insights into the role of protein dynamics in catalysis. In enzymes such as protein tyrosine phosphatase, a wide range of conformational changes can be observed, and loop flexibility can be significantly affected by the sequence composition. [START_REF] Crean | Loop Dynamics and Enzyme Catalysis in Protein Tyrosine Phosphatases[END_REF][START_REF] Hammes-Schiffer | Relating Protein Motion to Catalysis[END_REF][START_REF] Moise | B Chimera Shows the Importance of the WPD-Loop Sequence to the Activity, Structure, and Dynamics of Protein Tyrosine Phosphatases[END_REF] Similar loop dynamics were studied in E.coli dihydrofolate reductase EcDHFR, showing that two dynamically coupled loops play a critical role in controlling protein dynamics and function. [START_REF] Boehr | A Distal Mutation Perturbs Dynamic Amino Acid Networks in Dihydrofolate Reductase[END_REF] Experimental and computational work suggested a dynamic network that includes residues that remotely control catalysis and dynamic fluctuations of the loops. [START_REF] Boehr | A Distal Mutation Perturbs Dynamic Amino Acid Networks in Dihydrofolate Reductase[END_REF][START_REF] Wang | Coordinated Effects of Distal Mutations on Environmentally Coupled Tunneling in Dihydrofolate Reductase[END_REF] On the other hand, allosteric effects are rarely reported for metalloproteins. For the FeS protein family mitoNEET, conformational changes of a loop 20 Å away from the metal center showed to affect the properties of the metal center. [START_REF] Baxter | Allosteric Control in a Metalloprotein Dramatically Alters Function[END_REF] Our observations in the [FeFe]hydrogenase CbA5H complement several previous studies, showing that coupled networks of amino acids exist in proteins and that distant effects can influence active site events.

k1 (s -1 ) k-1 (s -1 ) kinact (s -1 ) kreact (s -

Conclusions

Up Supplementary Table S3. Values of k1, k-1, kreact, kinact for CbA5HWT and variants. Measured at pH7, 5°C. All rate constants are potential independent, except kreact which is given here at E = -199 mV. The value of k-1 is the least well-defined in the fitting procedure (as observed previously 1 ) and was fixed to the WT value in this analysis. The WT data are replotted from ref. (1).

Protein film electrochemistry

30

 30

Figure 1 .

 1 Figure 1. Structural overview of the [FeFe]-hydrogenase CbA5H WT . A) X-ray structure of CbA5H air (PDB: 6TTL) shown as cartoon. H-cluster and accessory FeS clusters are depicted as spheres. Residue M382 is represented as stick in red. B) Structural alignment of CpI (PDB: 4XDC, yellow) and CbA5H air (light blue). H-cluster and residues that are expected to influence the loop flexibility are depicted as sticks and highlighted in red. Inset shows residues that are in close vicinity to M382 as sticks.

Figure 3 .

 3 Figure 3. IR-frequencies of CbA5H WT and M382E. A) ATR-FTIR difference spectra of CbA5H WT and M382E (200-500 µM, 0.1 M potassium phosphate buffer, pH 7) after 100 % H2 gassing and after treatment with air. Blue (Hinact), red (HredH + ), purple (Hhyd), grey (Hox). B) Relative band intensities of WT protein and variant in respect to the relative absorbance spectra.

Figure 4 .

 4 Figure 4. MD simulations of CbA5H WT and M382E. A) Cartoon representation of CbA5H showing WT protein in orange and M382E variant in grey. H-cluster and residues C367, M382 (CbA5H WT ) and E382 (M382E variant) are shown as sticks. Loop A is shown in thick and the TSC-loop is indicated by a box. B) Structural overlay of representative snapshots from the MD simulations of WT and M382E variant. Distances between Cα atoms of residues 382 and 549 are indicated by dashed lines. C) Histogram of the distance between Cα atoms of residues 382 and 549 in CbA5H WT and M382E variant. D) Number of water molecules around residue 382 in CbA5H WT and variant. A water molecule were counted if its O-atom was within 0.5 nm of any atom of residue 382. E) RMSF plot depicting the fluctuations of the residues in WT and M382E. The TSC-loop and Loop A are highlighted with grey boxes. Standard [FeFe]-hydrogenases accumulate this intermediate usually in proton transfer deficient

Figure 5 .

 5 Figure 5. Cyclic voltammograms showing the anaerobic (in)activation of CbA5H (orange) and the M382E variant (gray) under conditions of direct electron transfer with a rotating disc pyrolytic graphite edge electrode (pH 7, 5°C, 1 bar H2, scan rate 20mV/s, electrode rotation rate 3000 rpm).See SI FigureS7for the comparison between the data obtained with CbA5H and M382I variant. Note that in protein film voltammetry the magnitude of the signal cannot be interpreted because it depends on the unknow enzyme coverage. Only the shape of the signal matters, and therefore the potential chosen for the normalization of the current is arbitrary. See SI FigureS6A for the raw (non-normalized) data plotted in this figure.

Figure 6 .

 6 Figure 6. Potential steps experiments used to quantify the anaerobic inactivation kinetics of the CbA5H WT and the M382E variant. See SI Figure S11-12 for the comparison between the data obtained with CbA5H and the M382I variant. A) an example of potential steps applied to the electrode onto which the enzymes are adsorbed (pH 7, 5°C, 1 bar H2, 3000 rpm). B) the current responses (orange: WT, gray: M382E) to the potential steps in panel A. The best fit of the model is described earlier and is shown in dashed green. 30 C) residual of the fit. D) the four rate constants determined by fitting the model to a series of chronoamperograms obtained with different potential steps (see SI FigureS10). Three rate constants are potential independent and shown with dark orange, orange and yellow circles (kinact, k1 and k-1, respectively) for the WT protein, and in gray, slate gray and dark gray (kinact, k1 and k-1, respectively) for the M382E mutant. k-1 is ill-defined (cannot be accurately determined) and was set to the same value for both enzymes. The values of kreact are shown as red and black circles for the WT enzyme and for the mutant, respectively. The WT data are replotted from ref.30.

Figure 7 .

 7 Figure 7. AAI model for the reversible conversion between active and inactive forms of CbA5H WT . Structural alignment of CpI (A1, light blue) and CbA5Hair (Hinact: red). Three main states are identified 30 , the active species A1, a 2 nd active species A2 after conformational change of the TSC-loop (central panel), and the inactive species Hinact, where C367 is coordinated to Fed. Arrows indicate the rate constants k1, k-1, kinact, kreact.

  to now, two independent Hinact forming protection mechanisms are known in [FeFe]-hydrogenases, both of which rely on the protective function of the thiol groups that are coordinated to the vacant site of the H-cluster. While the initially described sulfide dependent inactivation is enabled due to the presence of sulfide in sulphate reducing microorganism like D. desulfuricans, CbA5H developed an intriguing inactivation mechanism on the basis of a flexible cysteine side chain that can coordinate to the H-cluster. Both examples represent a convergent mechanism to resist O2 and may result as a consequence of their ecological niche. This work demonstrates how individual amino acid exchanges can influence the catalytic properties of enzymes, even though they are located far away from the active site. Using site directed mutagenesis we investigate how local changes in the protein network can alter the dynamic interplay of the protein environment and fine tune the intrinsic O2-tolerance of CbA5H. Our results contribute to the understanding of long-range effects and their modulation of dynamical conformational changes with respect to the prominent O2-protection mechanism of CbA5H. With these findings we aim to provide new mechanistic insights into the development of advanced hydrogen catalysts for biotechnological purposes.

Figure S4 .

 S4 Figure S4. IR-frequencies of CbA5HWT and hydrogenase variants. A) ATR-FTIR absorbance spectra of CbA5H WT , M382I, M382E (200-500 µM, 0.1 M potassium phosphate buffer, pH 7) with 100 % H2 gassing and after treatment with air depicting the accumulation of Hinact. Blue (Hinact), red (HredH + ), purple (Hhyd), grey (Hox). Spectra were normalized to amide band II.

Figure S6 :Figure S7 :

 S6S7 Figure S6: Cyclic voltammogram traces of CbA5H (orange) and the variant M382E (gray). A) raw B) normalized cyclic voltammograms of CbA5H WT and the variant M382E. Conditions: 5ºC; pH 7; 3000 rpm; 20 mV/s

Figure S9 .

 S9 Figure S9. The anaerobic inactivation of M382E CbA5H is not due to chloride inhibition. The figure shows two consecutive scans at 20 mV/s recorded with the same film. The black trace has been recorded into a buffer containing 0.1M Na2SO4 as supporting electrolyte, instead of NaCl. Between the two CVs, 0.1 M NaCl was introduced in the cell (the injection at -0.5V is seen as a spike). The second scan (gray) has been recorded in the presence of 0.1M NaCl. See also fig S9 in ref (1), which demonstrates the absence of effect of chloride on the voltammetry of CbA5H WT

Figure

  Figure S11 chronoamperograms performed with the mutant M382I, to measure the rate constants plotted in figure S12D At every potential step, inactivation and reactivation occur more slowly than the respective experiments with the variant M382E, which is consistent with the slower rate constants plotted in figure S12D.

Figure S12 :

 S12 Figure S12: Potential steps experiments used to quantify the anaerobic inactivation kinetics of CbA5H and the M382I variant. Panel A: an example of potential steps applied to the RD PGE electrode onto which the enzymes are adsorbed. Panel B: the current responses (orange: WT, gray: M382I) to the potential steps in panel A. The best fit of the model is described earlier and is shown in dashed green. 1 Panel C: residual of the fit. Panel D: the four rate constants determined by fitting the model to a series of chronoamperograms obtained with different potential steps. Three rate constants are potential independent and shown with darkorange, orange and yellow circles (kinact, k1 and k-1, respectively) for the WT, and in gray, slate gray and darkgray (kinact, k1 and k-1, respectively) for the mutant. k-1 is ill-defined and set to the same value for both enzymes. The values of kreact are shown as red and black circles for the WT enzyme and for the mutant, respectively. Experimental conditions: T=5°C, pH 7, 3000 rpm. The WT data are replotted from ref. (1).

1 ) kinact/ kreact

	CbA5H WT	0.061	0.016	0.42	0.17	2.5
	M382E	0.096	0.016	2.45	0.81	3.0

  Increasing the O 2 resistance of the [FeFe]-hydrogenase CbA5H through enhanced protein flexibilityAndreas Rutz 1 , Chandan K. Das 2 , Andrea Fasano 3 , Jan Jaenecke 1 † , Shanika Yadav 4 , Ulf-Peter Apfel 4,5 , Vera Engelbrecht 1 , Vincent Fourmond 3 , Christophe Léger 3 , Lars V. Schäfer 2 , Thomas

		https://pubs.acs.org/doi/10.1021/acscatal.2c04031
	Supplementary table S2: H2 production activity measurements after aerobic inactivation and reactivation of
	CbA5H WT variant and M382E
	ATR-FTIR spectroscopy	μmol H2 × min-1 × mg
	A	average	standard deviation		average	standard deviation
		3827,7	350,1		2394,6	20,7
	WT as is	(100 %)	(9 %)	M382E as is	(100 %)	(1 %)
		2803,3	87,0		2223,8	215,7
	WT -1	(72 %)	(2 %)	M382E-1	(92 %)	(9 %)
		1227,0	309,7		910,3	21,0
	WT -2	(32 %)	(8 %)	M382E-2	(38 %)	(1 %)
		636,8	36,1		671,6	5,7
	WT -3	(17 %)	(1 %)	M382E-3	(28 %)	(0,2 %)
	Happe 1* WT-4	214,6 (6 %)	19,0 (0,5 %)	M382E-4	279,9 (12 %)	19,1 (1 %)
			μmol H2 × min-1 × mg
	B	average	standard deviation		average	standard deviation
		4418,4	206,0		1700,3	3,1
	WT as is	(100 %)	(5 %)	M382E as is	(100 %)	(0,2 %)
		2501,3	267,5		1409,2	5,9
	WT -1	(57 %)	(6 %)	M382E-1	(83 %)	(0,3 %)
		1789,3	66,1		1153,3	30,0
	WT -2	(41 %)	(1,5 %)	M382E-2	(68 %)	(2 %)
		1416,9	99,7		887,9	23,7
	WT -3	32 %)	(2 %)	M382E-3	(52 %)	(1 %)
		405,0	40,2		270,4	2,6
	WT-4	(9 %)	(1 %)	M382E-4	(16 %)	(0,2 %)
		166,5	26,4		222,2	58,9
	WT-5	(4 %)	(1 %)	M382E-5	(13 %)	(3 %)
			μmol H2 × min-1 × mg
	C	average	standard deviation		average	standard deviation
		3940,0	393,9		2935,9	82,5
	WT as is	(100 %)	(10 %)	M382E as is	(100 %)	(3 %)
		2561,4	107,4		2756,5	17,5
	WT -1	(65 %)	(3 %)	M382E-1	(94 %)	(1 %)
		998,3	207,7		1786,9	147,3
	WT -2	(25 %)	(5 %)	M382E-2	(61 %)	(5 %)
		721,6	104,3		1122,3	62,8
	WT -3	(18 %)	(3 %)	M382E-3	(38 %)	(2 %)
		372,0	26,5		530,0	84,2
	WT-4	(9 %)	(1 %)	M382E-4	(18 %)	(3 %)
		186,3	25,7		499,0	69,5
	WT-5	(5 %)	(1 %)	M382E-5	(17 %)	(2 %)

k1 (s -1 ) k-1 (s -1 ) kinact (s -1 ) kreact (s -1 ) kinact/ kreact

	CbA5H WT	0.061	0.016	0.42	0.17	2.5
	M382I	0.062	0.016	0.59	0.20	3
	M382E	0.096	0.016	2.45	0.81

https://pubs.acs.org/doi/10.1021/acscatal.2c04031

Photobiotechnology, Department of Plant Biochemistry, Ruhr-Universität Bochum, 44801 Bochum, Germany.

Theoretical Chemistry, Ruhr-Universität Bochum, 44801 Bochum, Germany.

Laboratoire de Bioénergétique et Ingénierie des Protéines, CNRS, Aix-Marseille Université, Institut de Microbiologie de la Méditerranée, 13009 Marseille, France.

Inorganic Chemistry Ι, Department of Chemistry and Biochemistry, Ruhr-Universität Bochum 44801 Bochum, Germany.

Fraunhofer UMSICHT, 46047 Oberhausen, Germany. *Correspondence to: thomas.happe@rub.de

ACKNOWLEDGMENT This project received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 801459 -FP-RESOMUS and was funded by the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy -EXC 2033 -390677874 -RESOLV, the CNRS and Aix Marseille University. T.H. thanks the Volkswagen Stiftung (Az 98621) and the DFG for funding (HA 2555/10-1 & AP242/12-1). We thank the Studienstiftung des deutschen Volkes for supporting A.R. S.Y. thanks the DAAD for funding. We thank Christina Felbek for her help with the electrochemical measurements. ABBREVIATIONS ADT, azadithiolate; FeS, iron-sulfur; ATR-FTIR, Attenuated total reflectance fourier transform infrared; IR, Infrared; NaDT, sodium dithionite; MV, methyl viologen; CVs, cyclic voltammograms; [2Fe]H, ([2Fe2[µ-(SCH2)2NH](CN)2(CO)4] 2-); PFE, Protein film electrochemistry; https://pubs.acs.org/doi/10.1021/acscatal.2c04031

Figure S3: H2 production activities after aerobic inactivation of CbA5H WT and M382E. Normalized activity measurements after cycles of air exposure. After every inactivation step the protein solution was reactivated under 100 % H2 atmosphere for 20 min. https://pubs.acs.org/doi/10.1021/acscatal.2c04031

AUTHOR INFORMATION

Corresponding Author thomas.happe@rub.de https://pubs.acs.org/doi/10.1021/acscatal.2c04031

Notes

The authors declare no competing financial interest. https://pubs.acs.org/doi/10.1021/acscatal.2c04031


Axel Muller

Metod Saniga

Alain Giorgetti

Henri De Boutray

Frédéric Holweck

Computer-assisted enumeration and classification of multi-qubit doilies

teaching and research institutions in France or abroad, or from public or private research centers.

The doily is the unique triangle-free self-dual finite geometry composed of 15 points and 15 lines, with three points on a line and, dually, three lines through a point.

This talk [MSG + 22a] is about doilies labeled with N -qubit observables, to be called N -qubit doilies or multi-qubit doilies, that are related to Kochen-Specker operator-based proofs of quantum contextuality. We describe an algorithm for the enumeration of all N -qubit doilies, for any N ≥ 2, and an optimized C implementation of this algorithm. We also present several classification criteria of N -qubit doilies, that are their types of observables, their linear or quadratic nature and their configurations of negative lines. As the numbers of N -qubit doilies increase rapidly with N , the enumeration program can in practice only be executed for small numbers of qubits. We use it to classify N -qubit doilies for 1 N = 4 and N = 5, according to these criteria. We thus produce precise tables for the number of doilies in each category. Before this work, the classification was only known for N = 3 [START_REF] Saniga | Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank[END_REF]. The presented results are published in [MSG + 22b].

  hal.science/hal-03932840Submitted on 10 Jan 2023

Acknowledgments

This work is supported by Agence Nationale de la Recherche -Plan France 2030 -EPiQ project (ANR-22-PETQ-0007), the EIPHI Graduate School (contract ANR-17-EURE-0002), and the Slovak VEGA Grant Agency, Project # 2/0004/20.


Cosimo Lucci
email: cosimo.lucci@unifi.it

Niccolo Baldanzini

Pedro Huertas Leyva

Simone Piantini

Giovanni Savino

Thomas Lich

Jan Schumacher

Claire Naude

Adrien Canu

Christophe Perrin

Niccolò Baldanzini

Thierry Serre

Defining suitable parameters for safe and effective deployment of a motorcycle Pre-Crash Braking system: findings from field testing and crash simulations

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Methods

First, a field test program involving 51 common riders as participants on two test vehicles was executed to assess the feasibility of different levels of autonomous braking intervention. The system was tested in the speed range of 30-50 km/h while performing typical manoeuvres including straight riding and lane change. Second, 60 crash cases sourced from two different in-depth databases from Italy and France were reconstructed using two different 2D simulation software, to test various obstacle detection system requirements and evaluate the potential safety benefits of the PCB intervention.

Results

In both straight-line and lane change manoeuvres, autonomous braking intervention reaching decelerations up to 5 m/s 2 with fade-in jerk up to 20 m/s 3 for a duration of approx. 1 s were considered manageable on both test vehicles by participants. Overall, the system intervention was tested more than 900 times with no loss of control. The crash simulation analysis indicated that a field of view of 80° and a detection range of 30m or higher can be adequate to effectively identify obstacles and trigger PCB. Tangible safety benefits were found to be achievable with several combinations of the analysed design parameters.

Introduction

This study presents the results of the collaborative research performed within the framework of the European Commission-founded project PIONEERS, whose general objective was to improve the safety of Powered-Two-Wheelers (PTWs) users through an innovative integrated approach to rider protection, based on personal protective equipment and onboard active safety systems.

Within the project, one of the cores of research was Pre-Crash Braking (PCB), being one of the most promising technologies among onboard safety systems in development for PTWs [START_REF] Terranova | Applicability Assessment of Active Safety Systems for otorcycles Using Population-Based Crash Data : Cross-Country Comparison among Australia , Italy , and USA[END_REF]. PCB provides the functionalities of Motorcycle Autonomous Emergency Braking (MAEB) in pre-crash conditions, delivering an autonomous braking action intended to reduce the pre-crash speed of the host PTW immediately before the crash. Such technology showed a positive effect on other road vehicles such as trucks and passenger cars [START_REF] Fildes | Effectiveness of low speed autonomous emergency braking in real-world rear-end crashes[END_REF].

The working parameters of PCB, intended as braking parameters, which define the performance of the precrash autonomous braking action, and obstacle detection requirements, which define the performance of obstacle detection tools required for effectively detect opponent vehicles or objects and trigger the PCB at the proper timing, are the key for safe and effective implementation of PCB on PTWs. As indicated in studies on passengers' cars, different parameters can provide different results in terms of impact speed reduction and injury mitigation [START_REF] V. Graci | Quantitative characterization of AEB pulses across the modern fleet[END_REF].

In order to explore suitable parameters for PCB intervention, early studies employed mainly two approaches: field tests to evaluate rider stability during the deployment of Automatic Braking (AB), and crash simulations to estimate PCB potential benefits for injury mitigation [START_REF] Savino | Active safety systems for powered two-wheelers: A systematic review[END_REF]. Studies focusing on field testing started in 2010 with professional riders and with a PTW equipped with a laser-scanner and producing automatic decelerations in correspondence with a target obstacle [START_REF] Giovannini | Analysis of the minimum swerving distance for the development of a motorcycle autonomous braking system[END_REF]. Further research was performed testing AB with common riders as participants and decelerations up to 2 m/s 2 deployed unexpectedly via remote control [START_REF] Savino | Exploratory field trial of motorcycle autonomous emergency braking (MAEB): Considerations on the acceptability of unexpected automatic decelerations[END_REF], and again, with professional riders in lane-change riding scenarios [START_REF] Merkel | imits of Autonomous Emergency Brake Systems for Powered Two-Wheelers -an Expert Study[END_REF]. Crash simulations were also employed to develop decision logic to trigger PCB interventions [START_REF] Savino | Triggering algorithm based on inevitable collision states for autonomous emergency braking (AEB) in motorcycle-to-car crashes[END_REF], and to explore its potential benefits on crashes [START_REF] Savino | A robust estimation of the effects of motorcycle autonomous emergency braking (MAEB) based on in-depth crashes in Australia[END_REF], [START_REF] Savino | Can Experienced iders Benefit from an Autonomous Emergency Braking System ?[END_REF].

In order to make PCB a mature technology to be introduced on standard vehicles, further research is required to define safe and reliable working parameters. Some preliminary studies which analysed its effectiveness, suggested that the parameters of intervention field-tested so far may not be sufficient to reduce the likelihood of sustaining serious injuries in case of crashes [START_REF] Piantini | Potential head injury mitigation of -AEB in real-world motorcycle crashes[END_REF]. In addition, the current technological development of obstacle recognition tools fostered by the introduction of Autonomous Emergency Braking for passenger cars and research for Autonomous Driving, offered in the last few years new reliable tools for obstacle detection, which could pave the way to an effective triggering of PCB.

The goal of this study is to identify suitable parameters of intervention and technical requirements for obstacle detection tools for a safe and effective application of PCB. We performed field tests with two prototype vehicles and participants to assess the acceptability of the PCB among end-users and the controllability of the vehicle with different sets of braking parameters, while computer simulations were used to evaluate PCB effects and its efficacy in reducing impact speed with a broader set of braking parameters and obstacle detection requirements.

Methods

This study combines two different methodologies -Field testing and Crash modelling-with the common goal of identifying suitable parameters for safe and effective deployment of Pre-Crash Braking system on Powered-Two-Wheelers (see Figure 1). In this section both the methodologies and the sets of PCB working parameters tested in field testing and simulations will be presented.

Field test methods

Field tests were performed on two different test vehicles provided with Automatic Braking (AB) devices capable of activating braking without rider action. Both vehicles (a sport-touring motorcycle and a two-front wheels scooter, from now on called Multistrada and MP3 respectively) were employed to test the intervention of AB in straight-line and lane-change manoeuvre.

The AB test procedure was developed based on previous studies based on pilot testing and literature review carried out by the authors [START_REF] Lucci | Investigating the feasibility of Motorcycle Autonomous Emergency Braking (MAEB): design criteria for new experiments to field test automatic braking[END_REF]. The AB interventions were tested at different velocities ranging from 30 km/h to 60 km/h (depending on the requested manoeuvres).

The participants were recruited among active riders with two years or 10000 km of riding experience and aged between 20 and 65. The advertisement for the participants' recruitment was disseminated through the university web page, social media, flyers and biker groups.

This study obtained ethical approval from the Ethics Committee of the University of Florence (Written opinion N. 46, 20/03/2019).

Test procedure and AB parameters

Participants tested the intervention of the AB system by riding with one of the two test vehicles along the test track: the AB activations were manually triggered by one investigator via remote control [START_REF] Lucci | emote controlled braking actuation for motorcycle safety system development[END_REF]. The AB was triggered only when the PTW was in precise spots of the track while the participants were performing the specific manoeuvres.

For the Multistrada, the test included two phases with a nominal deceleration of respectively 3 m/s 2 and 5 m/s 2 and fade-in jerk of 15 m/s 3 tested in four manoeuvres (straight-line, lane-change, slalom, and curve). For the MP3, as for the Multistrada, the test included two phases with a nominal deceleration of respectively 3 m/s 2 and 5 m/s 2 and fade-in jerk of 15 m/s 3 , tested in two manoeuvres (straight-line and lane-change). The test with MP3, after the above-mentioned phases, also included two other phases with fade-in jerk up to 25 m/s 3 . The participants were not aware of the timing of AB intervention nor the exact position within the test track: this aimed to obtain AB events that were as unexpected for the rider as possible while keeping a low learning effect. Overall, the AB was deployed in the different manoeuvres with an average frequency of one activation every 100 s of riding and with a pseudo-random order. Full details of the test procedure were presented in [START_REF] Lucci | Autonomous Emergency Braking system for Powered-Two-Wheelers: testing end-user acceptability of unexpected automated braking events deployed pre-crash trajectories[END_REF].

Test vehicles

The first test vehicle was a Ducati Multistrada 1260S, a sport-touring motorcycle equipped with Motorcycle Stability Control (MSC), combined braking and semi-active suspensions. The vehicle was provided with outriggers to prevent the vehicle from lateral fall (see Figure 2 -left), since the intervention of AB in lateral manoeuvres such as cornering and slalom was also tested with this vehicle, but it will not be presented in this paper. The second vehicle was a Piaggio MP3 500, a two-front-wheel scooter provided with Antilock Braking System (ABS) (see Figure 2

Data recording

A similar data acquisition system was employed on both vehicles to collect data from the PTWs' CAN-Bus (throttle, brake action, steering angle, vehicle tri-axis acceleration and gyro), from an Inertial Measurement Unit (IMU) attached to the back of the participants to record the chest movement during the tests, and from an internal tri-axes accelerometer and GPS receiver. Both test vehicles were also equipped with action cameras to record the driver's body and monitor his/her behaviour during the AB. In order to collect subjective data, questionnaires were adopted to ask participants their opinion on the test, the AB system tested and the controllability of the vehicle during the AB activation in the different manoeuvres.

Crash simulation methods

The second step of this study employed computer simulations to reconstruct real-world crashes and assess the potential benefits of PCB applied with different parameters of intervention. The simulations were designed to cover a broad range of PCB parameters, including those tested in the field test campaign. Also, different levels of performance for the obstacle recognition tools supposed to trigger PCB were analysed.

Crash data source

Crash cases for simulation were extracted from two different in-depth road crash databases: the InSAFE database from the University of Florence (UNIFI), which collects crashes from the Florence metropolitan area, Italy [START_REF] Piantini | Advanced accident research system based on a medical and engineering data in the metropolitan area of Florence[END_REF], and the EDA database from the University Gustave Eiffel (UGE), which collects crashes from both rural and urban roads in France [START_REF] Canu | Interest of in-depth investigation for studying the relation between speed and accident risk[END_REF]. In total sixty cases were employed, thirty from each database, extracted and reconstructed based on the detailed description of the crash collected in the database, including for example road configuration, marks documented in the crash scenario, damage to vehicles, injuries of riders, and police reports. Overall, crashes included in the study involved mainly L3 PTWs (77%) and 23% of L1 PTWs only. They occurred mainly at intersections (70%), while only 22% were in straight-line and 8% in curves. The distribution of the crash configuration among the two databases was slightly different: the InSAFE dataset collected more Head-to-side (T-bone) crashes (56%), while in the EDA database 50% of cases were Head-on crashes (see Table 1 -for the detailed definition of the crash configurations see [START_REF] Piantini | Assessment of the effect of otorcycle Autonomous Emergency Braking (MAEB) based on real-world crashes[END_REF]). A lower proportion of Head-to-rear and Sideswipe crashes were included in both databases.

Crash reconstruction tools

Crash reconstructions were performed on two different 2D simulation tools developed by UNIFI and UGE based on previous studies on PCB [START_REF] Savino | A robust estimation of the effects of motorcycle autonomous emergency braking (MAEB) based on in-depth crashes in Australia[END_REF]. Among the 60 cases included in the study, 20 were simulated in both crash simulation tools (10 from each database), to compare results from the two different software. Each crash case was first reconstructed in the virtual environment and validated using all the information collected in the database (e.g., comparing the impact speed at the crash and the incidence of the two vehicles involved in simulations with detailed data from crash investigators). Then, the intervention of PCB with different parameters was simulated (see the following section). The effect of PCB was measured in terms of Impact Speed Reduction (ISR), as the difference between the impact speed without and with PCB.

PCB tested parameters

Crash simulations were employed to assess the influence on PCB effectiveness of five parameters, three related to the automatic braking system (Triggering Strategy, Deceleration and Fade-in Jerk), and two related to the obstacle recognition system (Field of View and Range). See Table 2 for full details about the ranges and the incremental steps used for simulations.

The Triggering Strategy defines the timing of deploying PCB based on the detection of the inevitable collision state: the time in which the crash between the PTW and the opponent vehicle/object becomes unavoidable.

Based on different thresholds of deceleration in longitudinal and lateral directions achievable by the PTW, it is possible to define different triggering strategies. These correspond to a different time to collision at which the PCB is triggered. Full details of the definition of triggering strategies are presented in [START_REF] Savino | Inevitable Collision States for otorcycle-to-Car Collision Scenarios[END_REF]. For this study, three triggering strategies (called "Conservative", "Standard" and "Progressive") were simulated in both crash simulation software. In order to have a more realistic PCB behaviour, the software employed by UGE added to PCB simulation a constraint on times to collision with the realistic values of 0.6 s (Conservative), 0.8 s (Standard) and 1 s (Progressive).

Three values of PCB Deceleration were employed in crash simulations: two of these values (respectively, m/s² and 5 m/s²) were devised by field tests performed with participants (see section 2.1.1), while the highest value of deceleration (7 m/s²) was tested to assess what could be the potential benefits of PCB with decelerations even higher than those currently field-tested with participants. Similarly to deceleration, the two levels of Fade-in Jerk tested with participants were also employed in simulations.

The Field of View represents half of the width in degrees of the detection zone of the obstacle recognition system. Combining its value with the Range, we can define the obstacle recognition cone in which an opponent vehicle or object can be recognised by the system (see Figure 3). This defines the timing when the other vehicle is detected by embedded sensors on the PTW and therefore PCB can be triggered. The Range is the maximum distance at which the PCB can detect an opponent vehicle/object. For both parameters, a wide range of values was tested in simulations, based on the state-of-the-art radar technology. It is evident that state-of-the-art sensor devices are capable to have a wider range. However, to limit simulation time, for PCB with progressive triggering strategy the range does not extend 90 m. The wide number of parameters tested allowed us to assess the influence of each parameter on PCB performance (see section 3.2.1). However, 450 different combinations of PCB parameters tested did not allow us to obtain a realistic assessment of the expected benefits provided by the system. Three combinations of parameters were therefore selected to analyse the potential effectiveness of PCB considering a pessimistic (low efficiency), an average, and an optimistic (high efficiency) implementation of parameters. The sets of parameters selected for the three configurations are displayed in Table 3.

Based on results from field testing (see section 3.1.4), for the PCB deceleration, the more conservative setting (3 m/s²) was selected for the pessimistic configuration while for the average and progressive configurations the deceleration of 5 m/s² was chosen. Similarly, the fade-in jerk was set to 15 m/s 3 for the pessimistic configuration and 25 m/s 3 for both the average and optimistic configurations. Deceleration (m/s²)

3 5 5
Fade-in jerk (m/s 3 ) 15 [START_REF] Ucci | otorcycle Autonomous Emergency Braking (MAEB) employed as enhanced braking: estimating the potential for injury reduction using real-world crash modeling[END_REF] 25

Range (m) 30 30 30

Field of View (°)

+/-15 +/-45 +/-45 3 Results

Field test results

The results of the field-testing activity will be presented in this section: actual PCB working parameters fieldtested for both test vehicles will be related to their feasibility in different riding conditions and acceptability among users.

Test participants

Overall, 51 participants (10 women, 41 men) were included in this study, testing only one of the two vehicles. Thirty-one participants tested AB on the Multistrada, while 20 on the MP3. Participants were selected based on their main usage of PTWs: the majority of participants who tested AB on Multistrada were mainly leisure riders while participants selected to test the AB intervention on the MP3 were mostly commuters. The age of participants ranged from 21 to 59 years, and they were characterized by different levels of education and a broad range of riding experience. For further details on the sample of participants included in the study please see [START_REF] Lucci | Autonomous Emergency Braking system for Powered-Two-Wheelers: testing end-user acceptability of unexpected automated braking events deployed pre-crash trajectories[END_REF].

Tested Automatic Braking intervention and manoeuvres

Table 4 reports a summary of the AB-tested intervention for the two test vehicles in the two manoeuvres considered in this study: straight-line riding and lane change reproducing an avoidance action (see Figure 4). Due to weather conditions, not all the participants were involved in testing the AB in all the manoeuvres and with all the levels of intervention planned in the test protocol.

Overall, the AB was tested with the Multistrada almost 250 times in straight line and lane change, whereas considering also the trials in different conditions and manoeuvres more than 500 AB tested interventions were recorded. With the MP3 the AB intervention was tested approx. 290 times the same manoeuvres.

For the Multistrada, the AB was deployed at two different levels of nominal deceleration (respectively 3 m/s 2 and 5 m/s 2 ), and with a fade-in jerk level of 15 m/s 3 . These nominal values were also measured after testing. Similarly, for the MP3 the two values of deceleration (3 m/s 2 and 5 m/s 2 ) were measured in the trials, while the two levels of fade-in jerk (respectively 15 m/s 3 and 25 m/s 3 ) set for the test resulted in a wide distribution of values of fade-in jerk, with peaks reaching up to 30 m/s 3 .

The AB duration for both vehicles was approx. 1 s (respectively, 1.08 s and 0.97 s for Multistrada and MP3), while the riding speed at AB trigger ranged from 37 to 45 km/h.

PCB intervention during avoidance action

Being the feasibility of PCB intervention when the rider is performing lateral maneuvers one of the main open issues when assessing its safety and applicability, an in-depth analysis of PCB intervention during lane-change maneuver reproducing avoidance action was performed [START_REF] Ucci | Field testing the applicability of motorcycle autonomous emergency braking (MAEB) during pre-crash avoidance manoeuvre[END_REF].

Vehicle dynamics in the lane change manoeuvre with and without automatic braking were compared (see Figure 5): minor effects were found on vehicle dynamics -except for those produced by the automatic brakingwhich never questioned the controllability of the vehicle. For both vehicles, participants were always able to manoeuvre the lane change by avoiding the virtual obstacle without executing other actions or braking. Due to the automatic deceleration and lower speed, minor differences in the vehicle lean were reported. No loss of control was reported by the participants in the questionnaire nor recorded by cameras.

Users' acceptability of 5 m/s 2 PCB deceleration

At the end of the test, the participants assessed the Automatic Braking system based on the conditions they experimented. Even if after testing the AB there were few negative opinions about it, for both test vehicles all the participants managed to complete the whole test without asking to interrupt the trials due to the intervention of the AB or other reasons. Moreover, no potentially dangerous situations were created by the intervention of the AB or the participants' behaviour.

The perception of the intensity of AB intervention in terms of braking deceleration and fade-in jerk is displayed in Figure 6 for both test vehicles.

Crash simulation results

The results of the crash simulation activity will be presented in this section: first, the influence of different PCB working parameters on Impact speed Reduction will be presented, second, the effect of three different sets of PCB parameters (an optimistic, average, and pessimistic configuration) will be compared.

Influence of PCB parameters

A total of 60 crash cases (half from the InSafe database and half from the EDA database) were employed to assess the influence of PCB working parameters such as triggering timing, braking deceleration and the fadein jerk. The same set of 60 cases was also used to simulate the effect of obstacle recognition parameters such as Field of View (FOV) and Range.

In order to assess the influence of each parameter, simulations were performed employing a standard set of parameters (Standard triggering, Deceleration = 5 m/s 2 , Fade-in jerk = 25 m/s 3 , Field of View = 40°, and Range = 30 m), and by varying only one parameter at a time.

Triggering

Setting all the other parameters to the standard value and varying only the triggering strategy, median reductions in impact speed of 5 km/h (conservative), 7.5 km/h (standard) and 12 km/h (progressive) were obtained (see Figure 7).

Deceleration

The PCB deceleration turn out to provide the highest influence on impact speed reduction: comparing ISR produced by 3, 5 and 7 m/s² PCB deceleration, the median speed reduction obtained by PCB intervention was, respectively, 2.5 km/h, 7.5 km/h and 9 km/h, using the standard setting for the other parameters (see Figure 8).

Fade-in jerk

Regarding the fade-in jerk, its influence on ISR among the two levels tested in the simulations was found to be limited (about 1 km/h) among the 60 cases (Figure 9). A median impact speed reduction of 6 km/h was estimated for a Fade-in jerk of 15 m/s 3 using standard values for all the other parameters, while 7 km/h ISR was obtained for a Fade-in jerk of 25 m/s 3 .

Field of View

Figure 10 shows influence of the Field of View employing the standard set of parameters. With a FOV of 10° (on either side of the longitudinal axis of the PTW, i.e., 20° of total aperture), the detection was zero in at least half the cases. At 25° FOV, the median impact speed reduction was 4 km/h, at 40° it was 7.5 km/h while beyond 40° the ISR gain was very limited.

Range

Due to limitations in the simulation tools, the influence of the Range on ISR was analyzed by employing only 40 cases simulated by Univ. Eiffel: 30 cases from EDA and 10 from InSafe. The influence of the Range was however very limited: using the standard set of parameters, only a small difference between a range of 30 m and a range of 45 m was found (ISR increase of 0.2 km/h), while beyond 45 no increase of ISR was measured. Also using a different set of parameters (defined as "optimistic" -see section 2.2.3), the difference between the Range of 30 m and 40 m was limited (an increase of the average ISR of 0.4 km/h).

Realistic PCB configurations

From the large number of parameters considered in this study for the analysis of PCB effects, three realistic combinations of parameters were selected to represent typical system effects assuming a pessimistic (low efficiency), average, and optimistic approach (high efficiency). Considering all 60 simulated crashes in the three configurations, median reductions in impact speeds of 0.0 km/h, 7.4 km/h and 11.6 km/h were obtained (see Figure 11 -left). In 15 crash cases, the PCB was not triggered with any of the three configurations, or its intervention did not produce any effect (e.g., in cases in which the opposing vehicle was not detected in time, or the rider is manually braking with a higher deceleration than that produced by PCB). Excluding these cases, and therefore selecting crashes in which PCB is applied effectively, the median ISR was, respectively, 2.8 km/h, 10.7 km/h and 15.1 km/h for the three PCB parameter configurations (see Figure 11 -right). In 8 crash cases, at least one of the three configurations prevented the crash. The identification of suitable working parameters is the key to the future introduction of Pre-Crash Braking (PCB) on standard Powered-Two-Wheelers (PTWs). This study, results of the EC-founded PIONEERS project, merged two different approaches, field testing in the real world with common users as participants and crash simulations, to identify a set of appropriate parameters which can make PCB safe and effective in reducing injuries to PTW users.

The field tests campaign, which involved 51 participants and two different test vehicles, aimed to assess the feasibility and acceptability of PCB in the real world for a broad range of working conditions and parameters, which were never been tried before [START_REF] Marra | The future of the Autonomous Emergency Braking for Powered-Two-Wheelers: field testing end-users' acceptability in realistic riding manoeuvres[END_REF]. The sample size of participants employed for field testing was the widest so far in the field research concerning autonomous braking (PCB and MAEB). The system intervention was tested more than 1000 times on the two different types of vehicles with different parameters and manoeuvres. All the participants completed the experiment and agreed to test the intervention of the AB unexpectedly in the conditions proposed by the investigators and no dangerous situation occurred in the context of the deployment of AB. The sample of participants was characterized by a wide range of ages, sex, riding experience and motivations for riding. However, despite this large sample and the wide variability, the participants involved in this study may not be completely representative of all PTW user populations. They expressed generally a positive opinion about the system tested in both test vehicles, as the controllability of the PTWs was never at risk. Participants were always able to execute the avoidance manoeuvres, even with the highest level of PCB deceleration. The subjective assessment [START_REF] Ucci | The acceptance of Autonomous Emergency Braking System for Motorcycle: results before and after testing[END_REF] and objective data analysis performed based on these tests [START_REF] Ucci | Field testing the applicability of motorcycle autonomous emergency braking (MAEB) during pre-crash avoidance manoeuvre[END_REF]- [START_REF] Ucci | The acceptance of Autonomous Emergency Braking System for Motorcycle: results before and after testing[END_REF], [START_REF] Cassese | Analysis of the rider's body movement during the intervention of the Autonomous Emergency Braking system for otorcycles ( AEB)[END_REF] indicated the applicability and feasibility of PCB with 3 m/s 2 and 5 m/s 2 of deceleration and up to 20 m/s 3 of fade-in jerk, for interventions of up to 1 s duration.

The computer simulation approach was applied to sixty real-world crashes sourced from the InSafe and EDA databases, which were employed to estimate the effects of PCB and explore the influence of different sets of working parameters on its efficacy. Using two different simulation tools developed by the University of Florence and the University Gustave Eiffel, crashes were kinematically reconstructed and the PTW impact speed reduction provided by PCB was used as a reference for its efficacy, being strictly related to injury reduction [START_REF] Ding | otorcyclist injury risk as a function of reallife crash speed and other contributing factors[END_REF]. A large number of parameters were considered in the analysis concerning the autonomous braking performance (deceleration, fade-in jerk, and triggering) and obstacle recognition tools performance (field of view and range). This allowed for a comprehensive assessment of the influence of each parameter on impact speed and the identification of three realistic combinations of PCB system settings. Deceleration and triggering were found to be the most important parameters to maximize the effects of PCB, while a Field of View of the obstacle detection system equal to or higher than 45° (so overall 90° of view) was found not to be beneficial to increase PCB capabilities to detect obstacles. The three realistic sets of parameters representing respectively, pessimistic, average and optimistic conditions for PCB parameters provided median impact speeds reductions of, respectively, 0 km/h, 7.4 km/h and 11.6 km/h. These values, which are affected by different riding conditions and manual braking actions of the rider, are in line with studies focusing on different traffic environments and are potentially capable to mitigate injuries and fatalities [START_REF] Ucci | otorcycle Autonomous Emergency Braking (MAEB) employed as enhanced braking: estimating the potential for injury reduction using real-world crash modeling[END_REF].

This study identified the influence of the key working parameters of Pre-Crash Braking, one of the most promising technologies to enhance the safety of PTW users, on its effectiveness in terms of braking action and obstacle recognition. These results can be employed by manufacturers and researchers to tune the braking intervention, design the detection system and develop the triggering algorithms and therefore further develop Autonomous Braking for PTWs, towards its introduction on standard vehicles. Also, the combined approach of field-testing computer simulation developed for this study can be a reference for future studies aiming at the development of new active safety systems for PTWs.

Figure 1 -

 1 Figure 1 -Methodological approach employed for this study

  -right).

Figure 2 -

 2 Figure 2 -Test vehicles: Ducati Multistrada 1260 (left) and Piaggio MP3 500 (right)

Figure 3 -

 3 Figure 3 -Crash simulation tools employed for the study by UNIFI (left) and UGE (right)

Figure 4 -

 4 Figure 4 -AB activation in the two manoeuvres: 1) Multistrada in straight-line, 2) Multistrada in lane-change, 3) MP3 in straight-line, and 4) MP3 in lane-change.

Figure 5 -

 5 Figure 5 -Comparison of acceleration (blue) and vehicle lean (green) between a lane change with (solid) and without (dotted) AB. Left -3 m/s 2 AB intervention on Multistrada; Right -5 m/s 2 AB intervention on MP3

Figure 6 -

 6 Figure 6 -Perception of AB intervention for Multistrada (left) and MP3 Scooter (right)

Figure 7 -

 7 Figure 7 -Influence of the Triggering in PCB simulation Figure 8 -Influence of the Deceleration in PCB simulation

Figure 9 -Figure 10 -

 910 Figure 9 -Influence of the Fade-In Jerk in PCB

Figure 11 -

 11 Figure 11 -Impact speed reductions for the three realistic PCB configurations considered (Left: all 60 cases -Right: 45 cases with PCB really triggered)

Table 1 -

 1 Crash Configuration distribution of 60 cases among the two databases

	Crash Configuration	InSAFE	EDA	Total
	Head-on
		5 (16.7%)	15 (50.0%)	20 (33.3%)
	Head-to-rear
		3 (10.0%)	2 (6.7%)	5 (8.3%)
	Head-to-side
		17 (56.7%)	7 (23.3%)	24 (40.0%)

Sideswipe 5 (16.7%) 6 (20.0%) 11 (18.3%) Total 30 (100.0%) 30 (100.0%) 60 (100.0%)

Table 2 -

 2 PCB Parameters variation

	Parameter	Range	Incremental step
	Triggering strategy	[conservative, standard, progressive]	-
	Deceleration	[3 m/s² -7 m/s²]	2 m/s²
	Fade-in Jerk	[15 m/s 3 -25 m/s 3 ]	-
	Field 0f View	+/-[10°-70°]	15°
	Range	[30 m -90 m]	15 m

* NOTE: this value represents half of the whole FOV of the detection cone

Table 3 -

 3 Sets of parameters for the three PCB realistic configurations

	Parameter	Pessimistic	Average	Optimistic
	Triggering strategy	Conservative	Standard	Progressive

Table 4 -

 4 Summary of AB tested interventions

	Test Vehicle	Participa nts	Manoeuvre	Nominal decelera tion [m/s 2 ]	N° of PCB activation s	Initial Speed [km/h] Mean SD Mean SD Mean SD Mean SD Event Deceleration Fade-in jerk duration [s] [m/s 2 ] [m/s 3 ]
			Straight-line	3	63	47.6 4.7 1.07 0.03 2.9 0.3 15.
	Ducati Multistrada	31

Acknowledgement

The authors would like to acknowledge Ducati Motor Holding SPA and Piaggio & C. SPA for their support in this project.

Funding

This paper is part of a project that has received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement N° 769054, project PIONEERS (Protective Innovations Of New Equipment for Enhanced Rider Safety).

Disclosure statement: All authors have read and agreed to the submitted version of the manuscript. The authors declare no conflict of interest.