Alice Briole

Abou Mati

Molecular rotors in haemoglobin and bovine serum albumin proteins

Molecular rotors are fluorescent viscosity probes and their response in simple fluids is known to be a Förster-Hoffman power law, allowing the viscosity of the medium to be quantified by its fluorescence intensity. They are attractive probes in biological media, usually consisting of proteins, but how does a molecular rotor behave in a protein solution ? The response of the DASPI molecular rotor is compared in two globular protein solutions of similar size, haemoglobin (Hb) and bovine serum albumin, one absorbent, the other not. In absorbent Hb, a model validated by experiments in triangular geometry allows to correct the absorbing effect and to compare the rotor response in both proteins. With concomitant microrheology measurements, we investigate the relation between the DASPI fluorescence intensity and solution viscosity. In protein solutions, we show that viscosity is no longer the parameter determining the rotor response in contrast to simple fluids. Varying the viscosity by concentration or temperature is not equivalent, and the Förster-Hoffmann power laws do not apply when the solution concentration varies. We show that the concentration regime of the protein solution, semi-dilute or concentrated, determines the sensitivity of the rotor to its environment.

Introduction

Molecular rotors are fluorescent molecules, now well-established as viscosity probes. After photoexcitation, their relaxation occurs either by fluorescent radiation or by non radiative intramolecular rotation. In a highly constrained environment, the predominant decay pathway is radiative, which leads to a large increase in the fluorescence quantum yield. In simple fluids, it was demonstrated that their quantum yield φ increases with the fluid viscosity η according to the Förster-Hoffmann equation [START_REF] Forster | Die viskositatsabhangigkeit der fluoreszenzquantenausbeuten einiger farbstoffsysteme[END_REF][START_REF] Law | Fluorescence probe for microenvironments: anomalous viscosity dependence of the fluorescence quantum yield of p-n,n-dialkylaminobenzylidenemalononitrile in 1-alkanols[END_REF][START_REF] Iwaki | Antibodies for fluorescent molecular rotors[END_REF][START_REF] Loutfy | Effect of viscosity and temperature on torsional relaxation of molecular rotors[END_REF][START_REF] Kung | Microviscosity measurements of phospholipid bilayers using fluorescent dyes that undergo torsional relaxation[END_REF][START_REF] Haidekker | Effects of solvent polarity and solvent viscosity on the fluorescent properties of molecular rotors and related probes[END_REF][START_REF] Wang | Characterization of 2-phenylbenzo[g]quinoxaline derivatives as viscosity-sensitive fluorescent probes[END_REF][START_REF] Haidekker | Environment-sensitive behavior of fluorescent molecular rotors[END_REF] :

log φ = C + x log η (1)
where C and x are solvent-and dye-dependent constants. The exponent is a constant of x = 2/3 in the derivation of the Förster and Hoffmann model [START_REF] Forster | Die viskositatsabhangigkeit der fluoreszenzquantenausbeuten einiger farbstoffsysteme[END_REF] , but it can be variable according to the free-volume theory by Loutfy et al. [START_REF] Loutfy | Effect of viscosity and temperature on torsional relaxation of molecular rotors[END_REF] . This relationship (1) has been extensively investigated and validated in a wide range of viscosities, in both polar and non polar fluids [START_REF] Kung | Microviscosity measurements of phospholipid bilayers using fluorescent dyes that undergo torsional relaxation[END_REF][START_REF] Haidekker | Effects of solvent polarity and solvent viscosity on the fluorescent properties of molecular rotors and related probes[END_REF][START_REF] Haidekker | Environment-sensitive behavior of fluorescent molecular rotors[END_REF][START_REF] Haidekker | Dyes with segmental mobility: molecular rotors[END_REF] .

Molecular rotors have proven their value in a variety of applications such as the real-time monitoring of aggregation and polymerization processes (PMMA, chain entanglement of macromolecules) [START_REF] Loutfy | Effect of polymer chain tacticity on the fluorescence of molecular rotors[END_REF][START_REF] Zhu | Application of molecular rotors to the determination of the molecular weight dependence of viscosity in polymer melts[END_REF] , investigation of phospholipid bilayers and cell membranes [START_REF] Kung | Microviscosity measurements of phospholipid bilayers using fluorescent dyes that undergo torsional relaxation[END_REF][START_REF] Furuno | A fluorescent molecular rotor probes the kinetic process of degranulation of mast cells[END_REF][START_REF] Viriot | Molecular rotors as fluorescent probes for biological studies[END_REF][START_REF] Haidekker | Fluid shear stress increases membrane fluidity in endothelial cells: a study with dcvj fluorescence[END_REF] . Recent studies have focused on the development of new fluorescent probes with specific properties for imaging biological materials: low toxicity, good stability, high sensitivity to small variations in microviscosity or specific localisation in biological media [START_REF] Ma | A minireview of viscosity-sensitive fluorescent probes: design and biological applications[END_REF][START_REF] Miao | Functionalized bodipys as fluorescent molecular rotors for viscosity detection[END_REF][START_REF] Lee | Fluorescent molecular rotors for viscosity sensors[END_REF][START_REF] Zhou | Molecular rotors as fluorescent viscosity sensors: molecular design, polarity sensitivity, dipole moments changes, screening solvents, and deactivation channel of the excited states[END_REF] . BODIPY fluorophores are particularly interesting in this context as they have good photophysical properties and can easily be functionalized [START_REF] Miao | Functionalized bodipys as fluorescent molecular rotors for viscosity detection[END_REF] . In addition, numerous studies have focused on the use of molecular rotors in proteins to study the effects of aggregation and protein conformational changes [START_REF] Haidekker | Effects of solvent polarity and solvent viscosity on the fluorescent properties of molecular rotors and related probes[END_REF][START_REF] Hawe | Fluorescent molecular rotors as dyes to characterize polysorbate-containing igg formulations[END_REF][START_REF] Kung | Fluorescent molecular rotors: a new class of probes for tubulin structure and assembly[END_REF][START_REF] Sawada | Fluorescent rotors and their applications to the study of gf transformation of actin[END_REF][START_REF] Kubankova | Probing supramolecular protein assembly using covalently attached fluorescent molecular rotors[END_REF][START_REF] Thompson | Molecular rotors provide insights into microscopic structural changes during protein aggregation[END_REF][START_REF] Bai | Illuminating protein phase separation: Reviewing aggregation-induced emission, fluorescent molecular rotor and solvatochromic fluorophore based probes[END_REF] or to detect proteins in living cells and specific biomolecular interactions [START_REF] Goh | Molecular rotors as conditionally fluorescent labels for rapid detection of biomolecular interactions[END_REF][START_REF] Yu | Protein sensing in living cells by molecular rotor-based fluorescence-switchable chemical probes[END_REF][START_REF] Gatzogiannis | Mapping protein-specific micro-environments in live cells by fluorescence lifetime imaging of a hybrid genetic-chemical molecular rotor tag[END_REF] .

Recently, we have demonstrated the utility of the DASPI molecular rotor in the assessment of the intracellular viscosity of red blood cells as a function of temperature [START_REF] Briole | Molecular rotors as intracellular probes of red blood cell stiffness[END_REF] , paving the way for applications in the diagnosis of red blood cell pathologies. DASPI is well adapted to the characterisation of haemoglobin (Hb), the major component protein of the red blood cell, as its fluorescence excitation and emission spectrum interfere little with the fluorescence spectrum of Hb. Although positioned in the region of absorbance minima, between 550 -600 nm [START_REF] Liu | Specific absorption spectra of hemoglobin at different po 2 levels: potential noninvasive method to detect po 2 in tissues[END_REF] , the emission signal by the rotor is still subject to a low absorbance of Hb, which may affect the interpretation of this emission signal in terms of rheological properties. More generally, compared to simple fluids, protein solutions are complex because of the structure of the proteins themselves and the resulting assembly in solution. At the molecular rotor scale, complex interactions with proteins, such as binding [START_REF] Iwaki | Antibodies for fluorescent molecular rotors[END_REF][START_REF] Kubankova | Probing supramolecular protein assembly using covalently attached fluorescent molecular rotors[END_REF] , localisation to a specific area [START_REF] Ma | A minireview of viscosity-sensitive fluorescent probes: design and biological applications[END_REF][START_REF] Miao | Functionalized bodipys as fluorescent molecular rotors for viscosity detection[END_REF] , are possible and may affect its response. Given the diversity and complexity of proteins, the determination of rotor response will require extensive studies, taking into account the specificity of each rotor-protein pair.

In this perspective, we study the capacity of the molecular rotor DASPI to characterize the viscosity of two protein solutions, bovine serum albumin (BSA) and Hb. The two globular proteins have a similar molecular weight around 65kDa, and at the absorption and emission wavelengths of DASPI, Hb is optically absorbent whereas BSA is not. We propose a correction model for the absorbance of Hb, based on Beer Lambert's law, which will be used to compare the rotor response in the two proteins. The correction model is detailed and validated in the Appendix, in a geometry of increasing thickness that allows the probing of increasing absorbance levels. The viscosity of the protein solutions, measured by microrheology, is varied either by concentration (section 3.1) or by temperature (section 3.2). Microrheology and rotor fluorescence measurements were carried out concomitantly in the protein solutions. With concentration, the signal emitted by the rotor follows a master curve, which saturates at high viscosity. It does not follow a Förster-Hoffmann law. With temperature, on the other hand, we measure Förster-Hoffmann power laws, with a parameter C that depends on the concentration of the solution. Varying the concentration or temperature is therefore not equivalent in protein solutions, unlike what is measured in simple fluids with C independent on temperature [START_REF] Briole | Molecular rotors as intracellular probes of red blood cell stiffness[END_REF][START_REF] Howell | Intrinsic and extrinsic temperature-dependency of viscosity-sensitive fluorescent molecular rotors[END_REF] and concentration. This highlights that viscosity is not the predominant factor of the rotor response in proteins. The concentration regime of the protein solution, semi-dilute or concentrated, determines the sensitivity of the rotor to its environment and must be considered.

Materials and Methods

Preparation of protein solutions

Human haemoglobin from red blood cells The Hb (molar mass 64 kDa [START_REF] Haney | Purification and chemical modifications of hemoglobin in developing hemoglobin based oxygen carriers[END_REF] ) was extracted from human red blood cells. Blood samples were obtained from healthy donors and provided by the Etablissement Français du Sang (EFS Rhône-Alpes). The red blood cells were washed three times in PBS buffer. After a final centrifugation at 1200 × g for 10 min, all supernatant was removed. The RBC pellet was exposed to 3 freeze-thaw cycles (from -80 • C to 37 • C) to lyse the RBC membranes. Membrane residues were then extracted by adding of CCl 4 to the lysate (1/3 of the volume), followed by strong agitation and ultra-centrifugation at 10000 × g for 15 min. From this stock Hb solution, phosphate-buffered saline (PBS) was used for dilution. The concentration of the stock solution was carried out using 300 000 MWCO Vivaspin 2 Centrifugal Concentrators (Sartorius) by centrifugation at 4500 × g and 37 • C for 30mn. The concentration of Hb solutions was varied between 2g/dL and 42g/dL and measured by colorimetry with a MAK 115 Hb Assay Kit (Sigma-Aldrich).

Bovine serum albumin solutions BSA solutions (molar mass 66 kDa) were prepared by diluting lyophilized BSA powder (Sigma-Aldrich) in PBS (phosphate buffered saline, 1X, pH=7.4). The BSA concentration of the solutions, ranging from 1g/dL to 54g/dL, was measured by colorimetry with the Bradford Comassie Blue test (Sigma-Aldrich).

Measurement geometries: standard and triangular

Microrheology and fluorescence measurements were performed together on the same sample containing the protein solution, Hb or BSA. The solutions were placed in a standard geometry, consisting of a glass slide and a coverslip separated by a 250 µm thick spacer (see Figure 5a in Appendix A). For the Hb solutions, a triangular geometry was also used, which gives access to several levels of absorbance of the solution. In this case, the Hb solution is placed between two coverslips separated by a 250 µm high spacer on one side, creating an increasing thickness from 0 to 250 µm across the chamber (see Figure 5b in Appendix A).

Particle tracking microrheology

The viscosity of the protein solutions was measured using particle tracking microrheology. This technique consists of investigating the Brownian motion of microscopic probe particles embedded in the fluid to deduce its rheological properties [START_REF] Waigh | Advances in the microrheology of complex fluids[END_REF] . Typically, microrheology experiments are performed on small volumes of the order of 1µL. This is of interest in biological samples where tiny volumes can be probed, such as recently insect secretion with 10 pL of liquid [START_REF] Abou | Extensive collection of femtolitre pad secretion droplets in the beetle leptinotarsa decemlineata allows nanolitre microrheology[END_REF] . Another important aspect in complex fluids is to be able to probe the spatial heterogeneity of the fluid by comparing the response of different probe beads at different locations in the sample [START_REF] Colin | Spatially heterogeneous dynamics in a thermosensitive soft suspension before and after the glass transition[END_REF] .

Calibrated Polystyrene beads (0.994 µm in diameter) were dispersed in the solutions to be studied at a low volume fraction of less than 1%. The thermal motion of the tracer beads was recorded for 20 s at 100 Hz with a fast sCMOS camera (OrcaFlash4.0 v2+, Hamamatsu Photonics France) mounted on a Leica DMI 8 (Leica Microsystems GmbH, Germany) inverted bright-field microscope at 100X magnification (oil immersion objective, NA = 1.3, depth of field: ∼ 200 nm). The sample temperature was controlled with an objective heater using immersion oil in contact with the sample (Bioptechs Inc., USA) to within ±0.1 • C. A custom image analysis software allowed to track the x and y positions of any beads close to the objective focus plane. For reliable analysis, special attention was brought to record only beads far from the surfaces of the glass slides in the standard or triangle geometries.

For each tracer bead i, the time-averaged mean-squared displacement was calculated according to < ∆r 2 i (t) >=< (x i (t +t ′ )x i (t ′ )) 2 + (y i (t + t ′ )y i (t ′ )) 2 > t ′ . For a homogeneous sample, which is the case for our protein solutions at any concentration, the MSD is then averaged over all the beads to determine the ensemble-averaged MSD, ⟨∆r 2 (t)⟩. In case where the MSD grows linearly with time t, which is the signature of a viscous fluid (without an elastic component), a diffusion coefficient D is determined according to < ∆r 2 (t) >= 4Dt (in two dimensions). The viscosity η can then be estimated with the Stokes-Einstein relation, D = kT /6πRη, with R the diameter of the bead and kT the thermal energy [START_REF] Einstein | Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen[END_REF] .

Fluorescence microscopy

Measurements of the DASPI molecular rotor response in protein solutions were performed by fluorescence microscopy (Leica DMI 8, Leica Microsystems GmbH, Germany) with excitation between 460 -500 nm and detection between 565 -625 nm at 100X magnification in the standard geometry and at 63X magnification in the triangular geometry. Images were recorded with the fast sCMOS camera (OrcaFlash4.0 v2+, Hamamatsu Photonics France). Intensity measurements of the fluorescence level of the images were performed using ImageJ software (ImageJ, Rasband, W.S., ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA, https://imagej.nih.gov/ij/, 1997-2018). Left: Fluorescence intensity of the DASPI molecular rotor (in arbitrary units, a.u.) as a function of solution viscosity, in BSA and Hb, in the standard geometry at temperature T = 25°C. The rotor concentration is adjusted to 0.1, 0.01 and 1 mM in BSA and 1 mM in Hb. In BSA solutions, the rotor response increases with increasing viscosity. In contrast, in Hb solutions, the rotor signal decreases with increasing solution viscosity, due to the increase in solution absorbance with concentration. Right: Intensity -viscosity response of DASPI molecular rotor at 1 mM concentration in Hb solutions: raw data (solid symbols) and absorbance-corrected data (empty symbols). The margins of error are of the order of magnitude of the marker size in both directions: 5% for viscosity measurements and 7% for intensity measurements.

Results

Molecular rotor response with concentration

Absorbance correction and intensity-viscosity master curve in protein solutions

The response of the DASPI molecular rotor was studied in BSA and Hb protein solutions of increasing viscosity as a result of increasing concentration. Figure 1 -(left) shows the fluorescence intensity of the rotor as a function of solution viscosity. In BSA solutions, the intensity emitted by the rotor increases overall with increasing viscosity, whereas it decreases with increasing viscosity in Hb solutions, due to the increase in absorbance of the solution with increasing concentration. In Figure 1 -(right), the intensity emitted by the rotor in Hb solutions has been corrected for the absorbing term (see Appendix A for details), and the corrected and uncorrected signal from the rotor are displayed. With the correction, the signal from the rotor in Hb increases with viscosity as in the case in BSA, and two rotor response regimes -low and high viscosity -are detectable on the intensity-viscosity curves.

As the emitted intensity is a quantity expressed in arbitrary units, the BSA and Hb curves were matched at the same level, to reveal a master curve reflecting the rotor response in our protein solutions (Figure 2). At low viscosity, the emitted intensity increases sharply according to a power-law, log I = C + b log η, with an exponent b = 3.4 greater than 2/3 measured in simple fluids, indicating a high sensitivity of the rotor to the protein environment. At high viscosity, the rotor response reaches a plateau, giving evidence of a lack of sensitivity to viscosity in this second regime. Without doubt, in these protein solutions, the rotor does not respond according to a Förster-Hoffmann power-law over the entire viscosity range as observed in simple fluids [START_REF] Haidekker | Environment-sensitive behavior of fluorescent molecular rotors[END_REF][START_REF] Briole | Molecular rotors as intracellular probes of red blood cell stiffness[END_REF] .

Response of the molecular rotor in the semi-dilute and concentrated regime

In this section, we compare the response of the two probes -fluorescence intensity for the molecular rotor and viscosity for the Brownian beads -as a function of the concentration of the protein solutions (Figure 3). Each probe interacts with the surrounding medium at its own scale, sub-nanometric for the rotor and micrometric for the Brownian bead. We first describe the response of the Brownian beads, i.e. the viscosity-concentration curves. The viscosity of both BSA and Hb solutions increases slowly at low concentration and then quite drastically at higher concentration, reminiscent of the characteristic signature of hard-sphere colloids [START_REF] Cheng | Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions[END_REF][START_REF] Krieger | Rheological studies on sterically stabilized model dispersions of uniform colloidal spheres : Ii. steady-shear viscosity[END_REF][START_REF] De Kruif | Hard sphere colloidal dispersions : viscosity as a function of shear rate and volume fraction[END_REF] , widely used in globular proteins to account for this drastic increase [START_REF] Parker | The nonequilibrium phase and glass transition behavior of betalactoglobulin[END_REF][START_REF] Brownsey | The glass transition behavior of the globular protein bovine serum albumin[END_REF][START_REF] Sharma | Rheology of globular proteins: apparent yield stress, high shear rate viscosity and interfacial viscoelasticity of bovine serum albumin solutions[END_REF][START_REF] Foffi | Hard sphere-like glass transition in eye lens α-crystallin solutions[END_REF][START_REF] Garting | Optical microrheology of protein solutions using tailored nanoparticles[END_REF][START_REF] Josephson | Particle tracking microrheology of protein solutions[END_REF][START_REF] Tu | Microrheological detection of protein unfolding[END_REF] . Although the comparison between globular proteins (with anisotropic 3D structure, polydispersity, surface charges and anisotropic interactions) and hard spheres is questionable, especially at high concentrations [START_REF] Sarangapani | The limitations of an exclusively colloidal view of protein solution hydrodynamics and rheology[END_REF][START_REF] Stradner | Potential and limits of a colloid approach to protein solutions[END_REF] , this allows the radius of the globular protein to be estimated at low concentration with an Einstein-Batchelor model [START_REF] Batchelor | The effect of brownian motion on the bulk stress in a suspension of spherical particles[END_REF] . This model describes the viscosity of hard-sphere suspensions in the semi-dilute regime (volume fraction less than Φ ∼ 0.2) where only the interactions between two particles are taken into account. At higher volume fractions, we enter the concentrated regime where empirical equations of the Mooney [START_REF] Mooney | The viscosity of a concentrated suspensions of spherical particles[END_REF] or Krieger & Dougherty 50 type are used to describe the drastic viscosity increase. At low concentration below 12g/dL, the radii of the BSA and Hb proteins could be estimated to be 3.3 ± 0.2 nm and 3.6 ± 0.2 nm respectively, in accordance with the literature on the subject [START_REF] Tu | Microrheological detection of protein unfolding[END_REF][START_REF] Jachimska | Characterization of globular protein solutions by dynamic light scattering, electrophoretic mobility, and viscosity measurements[END_REF][START_REF] Stadler | Hemoglobin dynamics in red blood cells: correlation to body temperature[END_REF][START_REF] Digel | Body temperature-related structural transitions of monotremal and human hemoglobin[END_REF][START_REF] Arosio | Static and dynamic light scattering approach to the hydration of hemoglobin and its supertetramers in the presence of osmolites[END_REF] . We verify a posteriori by assimilating the protein to a sphere of the radius found experimentally that this limit concentration, 12g/dL, corresponds to volume fractions, Φ ∼ 16% in BSA and Φ ∼ 22% in Hb, consistent with the boundary between the semi-dilute and concentrated regimes in hard spheres.

We now analyse the rotor response with the protein concentration. We observe two power-law regimes with a higher exponent at low concentration (1.1 in BSA and 0.8 in Hb) than at high concentration (0.6 in BSA and Hb). The cross-over between the two regimes is observed for c BSA = 10.4g/dL (Φ ≃ 14%) in BSA and c Hb = 11g/dL (Φ ≃ 20%) in Hb, close to the upper limit of the semi-dilute regime probed in microrheology. This highlights a decrease in rotor sensitivity beyond the semi-dilute regime, which suggests a sensitivity of the rotor to its environment and a screening of its response with crowding.

From the curves in Figure 3, we can see that each probe detects the boundary between the semi-dilute and concentrated regimes. The fact that the Brownian beads and the rotor do not probe the protein solutions at the same scale explains why the semi-dilute regime is not exactly seen at the same concentration by both types of probes. In Hb solutions, the intensity emitted by the rotor was corrected for the absorbance term. Empty markers are used for solutions where only the viscosity has been measured. The DASPI concentration is set at 0.1 mM in BSA and 1mM in Hb. The black solid curve on the viscosity curves correspond to the Einstein-Batchelor model describing the semi-dilute regime of hard sphere suspensions, and allows the radius of each globular protein and the extent of the semi-dilute regime to be estimated. The rotor response shows two power-law regimes, at high (exponent 0.6 in BSA and Hb) and low (exponent 1.1 in BSA and 0.8 in Hb) concentration (red solid and dotted lines). Each probe, Brownian bead and rotor, although probing at different scales, seems to detect the transition from the semi-dilute to concentrated regime.

Molecular rotor response with temperature

In the previous sections, the viscosity of the protein solutions was varied with concentration. Here we vary the temperature -18°C, 25°C, 30°C, 37°C and 43°C -at a fixed concentration, which induces a variation in viscosity of up to 30%. Figure 4-(a,b) represents the fluorescence response of DASPI with temperature variations, plotted as a function of the viscosity, in protein solutions of different concentrations. The rotor fluorescence signal increases with viscosity and depends on the concentration of the protein solution. The intensity-viscosity curves are plotted at the same origin (Figure 4-(c,d)) and all data are adjusted to a Förster-Hoffmann power law I/I 43 • C = C (η/η 43 • C ) x . Exponents x = 0.7 ± 0.2 in BSA and x = 0.9 ± 0.2 in Hb are found, they are close to those predicted for simple fluids x = 0.7 [START_REF] Haidekker | Effects of solvent polarity and solvent viscosity on the fluorescent properties of molecular rotors and related probes[END_REF][START_REF] Haidekker | Environment-sensitive behavior of fluorescent molecular rotors[END_REF] . With the determined and fixed x values, the parameter C is found to decrease sharply at high concentration (insets in Figure 4-(c,d)). Therefore, for a given viscosity value in Figure 4-(a,b), there may be different rotor intensities, depending on the concentration of the solution, highlighting that viscosity is not the relevant parameter to describe the rotor response in protein solutions. The concentration of the solution determines the response of the rotor through the parameter C, which again suggests that the response of the rotor depends on the crowding of the environment.

Discussion and conclusion

We study the signal emitted by a molecular rotor, DASPI, in two protein solutions, BSA and Hb, and show that its response with viscosity differs when varying concentration or temperature. The two globular proteins are the same size, and one is absorbent while the other is not. We propose a simple model based on Beer Lambert's law, that takes into account the configuration of our set-up and allows to correct for the effect of Hb absorbance. The correction term depends on the Hb concentration c Hb and the chamber height L via a screening length L e = 50 -200 µm which is a characteristic length of absorbance (see Appendix A). With the correction, the rotor signal in the absorbing Hb and in the non-absorbing BSA can thus be compared.

Let us recall some results obtained in simple fluids with the molecular rotor DASPI. In glycerol and ethylene glycol solutions, we measured its response with viscosity by concentration or temperature variation. With concentration variation, the DASPI fluorescence intensity follows a Förster-Hoffmann power-law over 1.5 -2 decades of viscosity, with a parameter C depending on the fluid-rotor couple and the rotor concentration [START_REF] Briole | Molecular rotors as intracellular probes of red blood cell stiffness[END_REF] . We measured that C does not depend on the the solution concentration, and that the viscosity is the only parameter that determines the quantum yield of the rotor. This has already been described extensively in previous studies where the Förster-Hoffmann power-law relationship between quantum yield and viscosity was measured over more than three orders of magnitude of the solvent viscosity [START_REF] Haidekker | Environment-sensitive behavior of fluorescent molecular rotors[END_REF][START_REF] Haidekker | Molecular rotors-fluorescent biosensors for viscosity and flow[END_REF] . By temperature variation, we measured that the rotor signal follows the same Förster-Hoffmann power-law as by varying the concentration, corresponding For each concentration, the temperature variation induces a viscosity variation. The data in Hb solutions are corrected for the absorbance term. The intensity-viscosity curves are plotted at the same origin and fitted with Förster-Hoffmann power laws of exponent 0.7 ± 0.2 in BSA (bottom left) and 0.9 ± 0.2 in Hb (bottom right). The margins of error are 5% for viscosity measurements and 7% for intensity measurements but are not shown here to simplify reading.

to the same parameter C in both cases. This result was also confirmed in previous studies where C could be assumed to be independent of temperature because the Förster-Hoffmann relationship reproduces the variations in intensity measured by temperature-induced viscosity variations [START_REF] Howell | Intrinsic and extrinsic temperature-dependency of viscosity-sensitive fluorescent molecular rotors[END_REF] . In simple fluids, varying the temperature or concentration is therefore equivalent, and the viscosity was shown to be the predominant parameter that determines the rotor response [START_REF] Haidekker | Environment-sensitive behavior of fluorescent molecular rotors[END_REF][START_REF] Haidekker | Fluid shear stress increases membrane fluidity in endothelial cells: a study with dcvj fluorescence[END_REF] .

In protein solutions however, we show that varying the viscosity with concentration or temperature is not equivalent for the rotor. When the viscosity is varied with concentration in BSA and Hb, the fluorescence intensity of the rotor increases sharply at low concentration and reaches a plateau at high concentration. The intensity -viscosity curves follow a master curve combining the results obtained in the two protein solutions, and cannot be described by a Förster-Hoffmann power law. With concomitant microrheology mesurements, we show that the plateau is reached in the concentrated regime of the protein solution, beyond the semi-dilute regime, which is a first indication that the crowding of its environment has an influence on the rotor response. By varying the viscosity through temperature, we find Förster-Hoffmann power laws, I = Cη x , with the viscosity exponent x = 0.7 -0.9 close to that measured in simple fluids. A major new feature in protein solutions is that the parameter C now depends on the concentration of the solution, unlike simple fluids, and decreases sharply beyond the semi-dilute protein regime.

Because temperature and viscosity effects cannot be decoupled in this experiment, it cannot be excluded that the rotor response is influenced by temperature variation. Nevertheless, we have previously shown in PBS or in simple fluids [START_REF] Briole | Molecular rotors as intracellular probes of red blood cell stiffness[END_REF] that when the viscosity is modified by temperature, the dominant parameter governing the DASPI signal is the viscosity of the medium. This suggests that temperature has little influence on the DASPI signal and validates our findings that concentration is the parameter to be considered in the rotor response.

In Figure 3, the Brownian bead response is used to define the boundary between the semi-dilute and concentrated regimes of the proteins. The boundary between the two regimes is quite visual. Typically, in the semi-dilute regime, an Einstein-Batchelor model can be applied to the viscosity and allows the protein size to be determined, and in the concentrated regime, the viscosity increases drastically with concentration. The rotor also shows different responses in the two regimes, with lower sensitivity in the concentrated regime. This highlights that the rotor response is determined by the crowding of the surrounding proteins.

Let us estimate the ratio rotor per protein to have an idea of the rotor environment in Figure 1. Given the experimental conditions, the number of molecules of BSA is 1.7 -respectively 17 and 170 -per molecule of DASPI at the crossover point (11 g/dL), when the rotor concentration is 1mM -respectively 0.1mM and 0.01mM. At the end of the plateau regime (49 g/dL), we have 7.6 molecules of BSA -respectively 76 and 760 -for 1 molecule of DASPI , when the rotor concentration is 1mMrespectively 0.1mM and 0.01mM. The very low concentration of the rotor relative to BSA suggests that the rotor response is dominated by surrounding protein crowding rather than specific rotor-protein interactions. This is consistent with the fact that it depends on the concentration regime of the protein solution, semi-dilute or concentrated.

A similar intensity-viscosity curve -increase then plateau -was measured with the CCVJ rotor in antibody solutions [START_REF] Iwaki | Antibodies for fluorescent molecular rotors[END_REF] . The dramatic increase in fluorescence intensity at low antibody concentration prior to the plateau was attributed to the binding of CCVJ to the antibody. In comparison, in our BSA solutions in Figure 1, the threshold between the increase regime and the plateau remains the same by varying the concentration of DASPI. This seems to exclude the hypothesis of a binding of the rotor to the BSA protein since one would expect a shift to a lower concentration as the rotor concentration increases.

In conclusion, in these protein solutions, the viscosity is not the parameter to be taken into account in the response of the rotor DASPI, the concentration appears to be a determining factor. At low rotor concentration compared to protein, which is the case in our experiments, the rotor signal is sensitive to the crowding of the protein solution and shows different responses in the semi-dilute and concentrated regimes. At a fixed concentration or given environment crowding, the rotor follows a Förster-Hoffmann power law with varying viscosity, I = Cη x with C depending on the protein concentration in the solution. When the crowding varies, the intensity-viscosity curve deviates from the Förster-Hoffmann power law. This must be taken into account when using rotors in biofluids or complex fluids where the environment is complex at the rotor scale. Further research will probably shed light on the mechanisms of rotor-protein interaction in order to use these rotors quantitatively in biofluids.

A ANNEX : Molecular rotor in haemoglobin: correction of absorbance

The influence of Hb absorbance on the rotor fluorescence signal was corrected using a model based on the Beer-Lambert law, valid for Hb concentrations close to physiological concentrations [START_REF] Friebel | Determination of the complex refractive index of highly concentrated hemoglobin solutions using transmittance and reflectance measurements[END_REF] . We propose a theoretical expression for the intensity emitted by the rotor in a Hb solution placed in a standard measurement geometry of height L, under an inverted microscope (section A.1). This expression is validated experimentally using a triangular geometry of increasing height between 0 and L. This geometry allows us to probe the rotor response by increasing the height of the Hb solution and thus its degree of absorbance (section A.2). We propose with this model a corrective term for the absorbance of the Hb solution involving a screening length. The corrected intensity is proportional to the quantum yield of the DASPI molecules in the solution, and will be compared to the signal in non-absorbing proteins in section 3.1.1.

A.1 Measured intensity in the standard geometry

We consider here a Hb solution containing molecular rotors, observed under an inverted microscope in a standard measurement geometry represented in figure 5a, between a microscope slide and a coverslip separated by a spacer of height L. The molecular rotor is excited at a wavelength λ exc and re-emits at a wavelength λ em . The aim of this paragraph is to quantify the fluorescence intensity emitted by the molecular rotors and measured on the camera, I meas , by considering the absorbance of the surrounding Hb solution. Let us consider a beam of excitation light of wavelength λ exc and intensity I 0 coming initially from the microscope objective in the inverted configuration. We assume that this beam is cylindrical with a cross-section S. According to the Beer-Lambert law [START_REF] Valeur | Molecular Fluorescence: Principles and Applications[END_REF] , a volume element dV = S • dz of the fluid at height z receives an excitation intensity I exc (z) lower than I 0 due to the absorbance of the solution over the height z :

I exc (z) = I 0 • 10 -ε exc •z•c Hb
I em (z) = I exc (z) • Φ • dN
This emitted light still has once again to pass through a height z of hemoglobin, before being measured at the camera as I meas , inducing a new Beer-Lambert correction term 10 -ε em •z•c Hb with ε em = ε em (λ em ) the molar extinction coefficient of Hb at the rotor emission wavelength. Since the camera collects the intensity coming from each volume element between z = 0 and z = L, we obtain for the measured intensity :

I mes (L) = L 0 I em (z) • 10 -ε em •z•c Hb dz = L 0 I 0 • Φ • N a • c DASPI • S • 10 -(ε exc +ε em )•z•c Hb • dz
which is also written :

I meas (L) = P • (1 -10 -L/L e ) (2)
with

L e = 1 c Hb • (ε exc + ε em ) ; P = I 0 • N a • c DASPI • S • Φ ln(10) • L e (3)
L e is interpreted as a screening length above which the DASPI molecules will receive no signal (white dots in Figure 5b) due to the high absorbance of the fluid below, and P as the plateau value that the fluorescence signal reaches for a fluid thickness L e or more. In the limit where L e tends to infinity (L/L e → 0), corresponding to the absence of screening by the absorbing molecules, the measured intensity in equation 2 is written to first order: lim

L/L e →0 I meas (L) = P/L e • L • ln(10) = I 0 N a • c DASPI • S • L • Φ (4)
which is proportional to the quantum yield Φ and corresponds to the intensity measured in a non-absorbing limit. Our model was tested in a triangular geometry shown in figure 5b, consisting of a container of increasing thickness. In this geometry, Hb in trapped between two coverslips separated on one side by a L = 250µm high spacer. For a solution of Hb of given concentration, the intensity I meas (h) can be measured for layers of Hb of height h between 0 ≤ h ≤ L, moving along the longitudinal axis of the container.

Figure 6a shows the fluorescence intensity evaluated for different heights h, in Hb solutions of concentration c Hb = 5, 12, 20, 28, 42g/dL covering the range of interest. At all Hb concentrations, the fluorescence intensity could be fitted with excellent agreement using equation 2, with two parameters L e and P. This experimentally demonstrates the existence of a screening length L e above which a plateau value P for the fluorescence intensity emitted by the rotor is reached.

Figure 6b now shows the screening length L e extracted from I meas using equation 2, as a function of the Hb concentration c Hb . The graph also shows the theoretical range for L e using equation 3, by varying ε exc between 2, 67 • 10 6 m -1 •M -1 and 3, 03•10 6 m -1 •M -1 and ε em between 1, 03•10 6 m -1 •M -1 and 1, 85•10 6 m -1 •M -1 . The ε-values were measured from absorbance spectra of diluted Hb (Varian Cary 50 UV-Vis spectrophotometer -Agilent) with uncertainties due to the width of the wavelength range selected by the fluorescence device: excitation 460 -500 nm, detection 565 -625 nm. The theoretical predicions (red band) for L e (c Hb ) in Figure 6b show excellent agreement with the experimental data.

Our model (equations 2 and 3) is in excellent agreement with experimental data for I meas and L e , obtained in the triangular geometry. We propose to consider the quantity P/L e as an intensity corrected for the influence of absorbance because it is directly proportional to the quantum yield Φ of the molecular rotors, as it is the case in non-absorbing limit (equation 4). We thus define the corrected fluorescence intensity as :

This correction involves two parameters to be known, the screening length L e related to the Hb concentration c Hb with equation 3, and the chamber height L. This correction will be used in the section 3.1.1 to compare the response of the rotor in absorbing and non-absorbing protein solution.

Figure 1 .

 1 Figure 1.Left: Fluorescence intensity of the DASPI molecular rotor (in arbitrary units, a.u.) as a function of solution viscosity, in BSA and Hb, in the standard geometry at temperature T = 25°C. The rotor concentration is adjusted to 0.1, 0.01 and 1 mM in BSA and 1 mM in Hb. In BSA solutions, the rotor response increases with increasing viscosity. In contrast, in Hb solutions, the rotor signal decreases with increasing solution viscosity, due to the increase in solution absorbance with concentration. Right: Intensity -viscosity response of DASPI molecular rotor at 1 mM concentration in Hb solutions: raw data (solid symbols) and absorbance-corrected data (empty symbols). The margins of error are of the order of magnitude of the marker size in both directions: 5% for viscosity measurements and 7% for intensity measurements.

Figure 2 .

 2 Figure 2.Master curve of the rotor response in BSA and Hb protein solutions of increasing viscosity, at temperature T = 25°C. The rotor signal in Hb solutions is corrected for the absorbance of Hb. Two regimes are visible: at low viscosity, the rotor signal increases strongly with viscosity, while at high viscosity, the rotor signal saturates and reaches a plateau. The first regime was fitted by a power-law log I = C + b log η with C = 4.1 • 10 3 and b = 3.4 (red solid line) and the second by a constant value I = 2.5 • 10 4 in arbitrary units (red dotted line). We do not observe a Förster-Hoffmann power-law over the entire viscosity range as in simple fluids. At low viscosities where a power law behaviour is measured, note that the exponent b is larger than the 2/3 expected for a Förster-Hoffmann relation.

Figure 3 .

 3 Figure 3. Viscosity measured by microrheology and fluorescence intensity measured by the DASPI rotor, in solutions of BSA(left) and Hb (right) of increasing concentration, at temperature T = 25°C. In Hb solutions, the intensity emitted by the rotor was corrected for the absorbance term. Empty markers are used for solutions where only the viscosity has been measured. The DASPI concentration is set at 0.1 mM in BSA and 1mM in Hb. The black solid curve on the viscosity curves correspond to the Einstein-Batchelor model describing the semi-dilute regime of hard sphere suspensions, and allows the radius of each globular protein and the extent of the semi-dilute regime to be estimated. The rotor response shows two power-law regimes, at high (exponent 0.6 in BSA and Hb) and low (exponent 1.1 in BSA and 0.8 in Hb) concentration (red solid and dotted lines). Each probe, Brownian bead and rotor, although probing at different scales, seems to detect the transition from the semi-dilute to concentrated regime.

Figure 4 .

 4 Figure 4. Intensity -viscosity curves by temperature variation in BSA (top left) and Hb (top right). The rotor fluorescence signal is measured at different protein concentrations.For each concentration, the temperature variation induces a viscosity variation. The data in Hb solutions are corrected for the absorbance term. The intensity-viscosity curves are plotted at the same origin and fitted with Förster-Hoffmann power laws of exponent 0.7 ± 0.2 in BSA (bottom left) and 0.9 ± 0.2 in Hb (bottom right). The margins of error are 5% for viscosity measurements and 7% for intensity measurements but are not shown here to simplify reading.

Figure 5 .

 5 Figure 5. (a) Standard geometry : the Hb solution is trapped between a microscope slide and a coverslip separated by a 250µm thick spacer. The incident beam intensity is I 0 and I exc (z), I em (z), I meas (L) are described in the text. (b) Triangle geometry : the Hb solution is trapped between two coverslips separated by a 250µm high spacer positioned on one side, creating a triangle geometry. Above a screening length L e the molecules no longer receive an excitation signal due to the absorbance of the Hb below. The DASPI molecules in solution are represented by yellow and white dots. The yellow dots are those that receive an excitation signal, and the white ones are those that do not.

  with c Hb the concentration of the Hb solution and ε exc = ε exc (λ exc ) the molar extinction coefficient of Hb at the exciting wavelength. This volume element contains dN = N a • c DASPI • dV DASPI molecules whose fluorescence emitting signal is proportional to the excitation intensity I exc (z) and to their quantum yield Φ. The intensity emitted by the molecular rotors in this volume element, at wavelength λ em , is written :

Figure 6 .

 6 Figure 6. Model validation. (a) Fluorescence intensity I meas (h) of the DASPI rotor at concentration c = 1 mM, measured in the triangular geometry (coloured dots) for different Hb concentrations bewteen 5g/dL≤ c Hb ≤ 42g/dL along with data fits with equation 2 (coloured dotted lines). (b) Screening length L e obtained by fitting I meas (h) with the model equation 2 as a function of Hb concentration : theoretical and experimental values.

I( 5 )

 5 corr (L, c Hb ) = P L e = I 0 • N a • c DASPI • S ln(10) • Φ By rewriting the above expression with equations 2 and 3, the expression for the corrected intensity is obtained from the measured intensity I meas (L), with a corrective term: I corr (L, c Hb ) = 1 L e (c Hb ) • 1 -10 -L/L e (c Hb ) • I meas (L)

A.3 Data accessibility

Datasets for all experiments reported in this paper are available on FigShare (doi: 10.6084/m9.figshare.21512124 58 ).

A.4 Author contribution A.B. performed experiments. A. B. and B. A. consulted together on the interpretation of results and the preparation of the manuscript.

A.5 Declaration of Interests

The authors declare no competing interests.

A.6 Acknowledgements

The authors would like to thank Marc Durand and Olivia du Roure for the fruitful discussions.


Adeline Kerner
email: kerner@mnhn.fr

Archaeocyatha, a computer-aided identification of genera

Keywords: Xper2, knowledge base, standardized characters, interactive identification key

An online service is proposed for recognition of the genera of a Cambrian fossil group, the Archaeocyatha, using Xper 2 . It stores, edits and publishes the descriptive data compiled in the available documentation and provides a free access key. Why Archaeocyatha? They are well studied by an international cooperation, so avoiding most of the problems of an abundant and contradictory nomenclature as well as quarrels about the taxonomic rank of the taxa. Any geologist finding new Cambrian faunas may use this easy tool to help the identification of the collected material. The archaeocyath knowledge base comprises: 307 valid genera, their Cambrian stratigraphical and geographical distribution. Each genus is defined by figures of the type-specimen and 120 descriptors, each one comprising definition, pictures and character states. If an incomplete specimen cannot be identified at the genus level using traditional diagnosis, identification can be obtained with the free access key. Xper 2 offers tools to analyze geographic and systematic data of the knowledge base, to create lists of taxa for local faunal revisions, and to compare relationships between genera of the same taxonomic rank. The knowledge base is interactive and could be modified and improved at any moment. This work is permanently up to date and in progress.

Foreword

Establishing a data base, generally extended to a knowledge base, is currently one of the necessary steps for systematic identification of recent or fossil specimens. It could be also applied to researches on biodiversity, ecology, and spatial and temporal distribution. Xper 2 is a management system for storage and editing descriptive data (knowledge base). Knowledge bases on various taxonomic groups are already available. Comparison of descriptions, export of data and interactive identification are operational [START_REF] Ung | Xper2: introducing e-taxonomy[END_REF]. This system and associated tools is the software used for the present study devoted to the Archaeocyatha, a Cambrian fossil group. The resulting free interactive identification key offers specialists and nonspecialists a tool that is easy to use (Kerner et al., 2011a(Kerner et al., , 2011b)).

Why Archaeocyatha? Reasons for establishing a knowledge base on Archaeocyatha

First studies of a recently discovered group

The group seems an ideal candidate for establishing a knowledge base. Their range is limited in time, mainly early Cambrian to the end of late Cambrian (i.e. Cambrian stages two to nine according to the International Stratigraphic Chart), and in space, as components of reefs in inter-tropical zones [START_REF] Debrenne | Répartition paléogéographique des archéocyathes et délimitation des zones intertropicales au Cambrien inferieur[END_REF][START_REF] Debrenne | Lower Cambrian archaeocyathan bioconstructions[END_REF][START_REF] Gandin | Distribution of the archaeocyathcalcimicrobial bioconstructions on the Early Cambrian shelves[END_REF]. Archaeocyatha were discovered only in the midnineteenth century [START_REF] Bayfield | On the Junction of the Transition and Primary Rocks of Canada and Labrador[END_REF], whereas many other fossil groups were known for a longer period, in some cases since the eighteenth century, and consequently, were independently studied by numerous authors in different languages using their own descriptive terms, thus making further standardization very complex. On the contrary, the first studies on archaeocyaths concerned more their putative affinities with other known groups (corals, sponges, protozoans, even sphenophytes, [START_REF] Debrenne | Irregular Archaeocyaths: morphology, ontogeny, systematics, biostratigraphy, palaeoecology -Archéocyathes irréguliers: morphologie, ontogénie, systématique, biostratigraphie, paléoécologie[END_REF] than detailed descriptions of specimens. The first regional monograph was written by Bornemann on Sardinian fossils [START_REF] Bornemann | Über die Fortsetzung seiner Untersuchungen cambrischer Archaeocyathus-Formen und verwandter Organismen von der Insel Sardinien[END_REF][START_REF] Bornemann | Die Versteinerungen des Cambrischen Schichtensystems der Insel Sardinien, nebst vergleichenden Untersuchungen über analogue Vorkomnisse aus anderen Ländern[END_REF]. He described and figured four new genera and 31 new species while only nine species were previously known from worldwide. He established a new subdivision "Archaeocyathinae" and named the group "Archaeocyatha" a class among Coelenterata. He was the first author to publish high-quality photographs rather than ink drawings. The second monograph, published by [START_REF] Taylor | The Archaeocyathinae from the Cambrian of South Australia: with an account of the morphology and affinities of the whole class[END_REF], dealt with Australian faunas. He described 31 new species distributed among 12 genera (six of which were new). He established the first higher subdivision in archaeocyathan systematics by the allocation of the 15 known genera into five families, based on differences in intervallar structures. He was also the first to recognize their distinctiveness in considering Archaeocyatha as an independent group, intermediate between Porifera and Coelenterata and of the same taxonomic rank. Progressively, discoveries took place around the world [START_REF] Debrenne | Irregular Archaeocyaths: morphology, ontogeny, systematics, biostratigraphy, palaeoecology -Archéocyathes irréguliers: morphologie, ontogénie, systématique, biostratigraphie, paléoécologie[END_REF]. The real start of modern researches took place around 1930. Two schools were in competition, the Eastern school led by A.G. Vologdin and his team in Moscow, and the Western school led by V.J. Okulitch in Vancouver, and associated with the Bedfords in Australia. Okulitch's systematics is based on ontogenetic stages [START_REF] Okulitch | North American Pleospongia[END_REF]. He proposed a new class of Porifera, the Pleospongea, divided into three subclasses according to the number of walls and the structure of the central cavity. This classification was not accepted by other specialists because parallel researches in the USSR by the Eastern school came to a more coherent pattern based on abundant and well preserved material. In the fifties about 400 species of archaeocyaths had been described, of which over 230 were due to the studies on material from the former USSR, (Siberian Platform, Altay-Sayan, Tuva, Urals, Kazakhstan) and Mongolia. For the Eastern school, archaeocyaths are divided into two classes Regularia and Irregularia on the basis of morphological differences of the secondary calcareous skeleton and ontogenetic stages, [START_REF] Vologdin | Arkheotsiaty i rezul'taty ikh izucheniya v SSSR [Archaeocyaths and the results of their study in the USSR[END_REF] and considered as an independent phylum, Archaeocyatha [START_REF] Vologdin | Morfologiya pravil'nykh arkheotsiat [Morphology of regular archaeocyaths[END_REF]. [START_REF] Okulitch | Archaeocyatha and Porifera[END_REF] accepted the concept of an independent phylum and the name Archaeocyatha instead of Pleospongea (being too evocative of sponges), and slightly modified previous systematics by establishing seven orders including three classes (previously subclasses): (1) one wall, central cavity empty; (2) two walls; (3) central cavity full. He distinguished among others Metacyathida and Ajacicyathida equivalent to the Russian subdivisions.

Archaeocyatha: an international field of research

From the mid-1950s, I.T. Zhuravleva (Novosibirsk, USSR) began to exchange regular correspondence with F. Debrenne (Paris, France), despite the language barrier. From 1970 onwards, Debrenne was the guest of the All Soviet Union of Paleontologists periodic meetings and then became the link between the two research worlds even during this Cold War time. Since then, Russian and Western specialists have engaged in active cooperation that still continues today. Zhuravleva was at the origin of all modern researches. She proposed a firmer basis for the definition of Regulares and Irregulares, and emended the names Regularia and Irregularia to avoid confusion with the major subdivisions of Echinoidea and Cystoidea [START_REF] Zhuravleva | K poznaniyu arkheotsiat Sibiri [Toward knowledge of the archaeocyaths of Siberia[END_REF]. She established the basis of modern systematics by applying the ontogenetic principle [START_REF] Zhuravleva | Arkheotsiaty Sibirskoy Platformy [Archaeocyaths of the Siberian Platform[END_REF] (Fig. 1), studying the order of appearance and complication of skeletal structures. She demonstrated that the intervallar elements have hierarchic primacy over the outer wall structures, which in turn have primacy over the inner wall structures. Debrenne, working on North African-West European faunas [START_REF] Debrenne | Archaeocyatha. Contribution à l'étude des faunes cambriennes du Maroc, de Sardaigne et de France[END_REF], and Hill on Antarctic faunas [START_REF] Hill | Archaeocyatha from Antarctica and a review of the phylum[END_REF][START_REF] Hill | Archaeocyatha[END_REF] Ontogeny of archaeocyaths, stages of growth. 1: form with taeniae, 2: form with hexagonal radial tubes (syringes), 3: form with taeniae and tabulae, 4: form with pectinate tabulae, 5: form without tabulae, 6: form with tabulae. C iw: inner wall with canals, C ow: outer wall with canals, C Ta: convex tabulae, IW: inner wall, L: hexagonal loculi, MT: multiperforate tabulae, OW: outer wall, P Ta: porous tabulae, Pe Ta : pectinate tabulae, RR: radial rods, S: septa, Sp : spine, Sp T: spinose taeniae, T: taeniae, V: vesicular tissue. (Zhuravleva, 1960, modified). Growth patterns in various groups of Porifera and allied organisms (Debrenne & Zhuravlev, 1994, modified).

except some prescient zoologists who persisted in including them in Porifera, estimated that Archaeocyatha were a type of primitive organism convergent to many groups without dominant affinities. The position of archaeocyaths was definitively settled by the discovery of Recent calcified sponges in submarine caves. In this environment, Vacelet found a chambered demosponge with a massive calcareous skeleton devoid of spicules, described as Neocoelia (now Vaceletia) crypta [START_REF] Vacelet | Une nouvelle relique du Secondaire: un représentant actuel des Eponges fossiles Sphinctozoaires[END_REF]Picket, 1982). The absence of spicules is no longer a necessary character to define a sponge. [START_REF] Debrenne | Archaeocyatha: is the sponge model consistent with their structural organization?[END_REF] demonstrated that the sponge model is consistent with the structural organization of archaeocyaths, a proposal accepted by [START_REF] Pickett | Vaceletia, a living archaeocyathid[END_REF] and [START_REF] Kruse | Are archaeocyaths sponges, or are sponges archaeocyaths? In The Evolution of a late Precambrian-early Palaeozoic rift complex: the Adelaide Geosyncline[END_REF] (Fig. 2). Immune reactions, asexual reproduction, cells interpreted as crypt cells suggest probable affinities with demosponges [START_REF] Debrenne | Archaeocyathan affinities: how deep can we go into the systematic affiliation of an extinct group[END_REF]. In Systema Porifera , a Guide to the Classification of Sponges [START_REF] Hooper | Systema Porifera: a guide to the classification of sponges[END_REF], [START_REF] Debrenne | Class Archaeocyatha Bornemann, 1884. Bibliography of Class Archaeocyatha[END_REF] updated the diagnoses of genera published by [START_REF] Debrenne | Regular archaeocyaths: morphology, systematic, biostratigraphy, palaeogeography, biological affinities -Archéocyathes réguliers: morphologie, systématique, biostratigraphie, paléogéographie, affinités biologiques[END_REF] and [START_REF] Debrenne | Irregular Archaeocyaths: morphology, ontogeny, systematics, biostratigraphy, palaeoecology -Archéocyathes irréguliers: morphologie, ontogénie, systématique, biostratigraphie, paléoécologie[END_REF]: every valid genus is defined by a short synonymy, its type species, its holotype, its definition, age, and stratigraphic and geographic distribution. A hierarchical set of keys is provided, based on the principles established by [START_REF] Zhuravleva | Arkheotsiaty Sibirskoy Platformy [Archaeocyaths of the Siberian Platform[END_REF]. This work was used to establish the present knowledge base on Archaeocyatha.

Sources for the knowledge base

Since 1960s, the genus has become a taxonomic category whose definition has achieved general consensus among specialists. It is based on variations of skeletal elements, particularly within designated categories of wall construction, and presence or absence of supplementary elements. [START_REF] Rozanov | Zakonomernosti morfologicheskoy evolyutsii arkheotsiat i voprosy yarusnogo raschleneniya nizhnego kembriya [Regularities in the morphological evolution of archaeocyaths and problems of Lower Cambrian stage division[END_REF], applying Vavilov's Principle (repetition of the same limited set of features = homologous series in variation, [START_REF] Vavilov | The law of homologous series in variation[END_REF], found homological series at the genus level in Archaeocyatha, permitting the establishment of classification based on homological variability. This is one of the first attempts at an identification key. The increasing number of genera between 1975 and 1990 reflects regional discoveries worldwide. Unfortunately, the splitting of taxa based on minor variations of the same morphological element led to inflation, and subsequent intensive revision was necessary to determine the systematic value of skeletal variations, and to list invalid names corresponding to incomplete or poorly preserved specimens, or to lost types, when no topotypes could be found. The different skeletal structures have been typified and their variations carefully defined to result in a clear systematization and the recognition of junior synonyms. Consequently, the number of genera in the whole group was drastically reduced from 587 before 1989 to 298 in 1992. This simplification allowed a better knowledge of the group and better application to paleogeographic reconstructions, biostratigraphic zonations and correlations [START_REF] Debrenne | Regular archaeocyaths: morphology, systematic, biostratigraphy, palaeogeography, biological affinities -Archéocyathes réguliers: morphologie, systématique, biostratigraphie, paléogéographie, affinités biologiques[END_REF][START_REF] Debrenne | Irregular Archaeocyaths: morphology, ontogeny, systematics, biostratigraphy, palaeoecology -Archéocyathes irréguliers: morphologie, ontogénie, systématique, biostratigraphie, paléoécologie[END_REF]. Debrenne, Zhuravlev and Kruse completed the research on genera: every valid genus is defined by a short synonymy, its type species, its holotype, its definition, age, stratigraphic and geographic distribution. This work, together with unpublished documents compiled for the Treatise of Invertebrate Paleontology (in press), are the sources used for the present computerization of Archaeocyatha.

Archaeocyatha, a free-access knowledge base: http:// www.infosyslab.fr/archaeocyatha

When one opens this knowledge base for the first time the screens appear rather complex and inaccessible for the novice, but its use is more intuitive than it appears. We outline below how to work with and obtain an identification.

Identification tools

Traditionally, an identification paper key is used to identify a specimen. This type of key has a fixed sequence of questions. When the user has answered each question without doubt, an identification is obtained. In the case of archaeocyaths, the identification key is named a natural key, because the asked questions follow the classical systematic classification. In conventional determination, if one structure is missing, no complete identification can be obtained. In such cases a more flexible tool is required. The free access key offers several possibilities (Fig. 3 and Tab. 1). The archaeocyathan interactive key belongs to latter type. It is included in a three-part website: (1) introduction to Archaeocyatha, their role in the Cambrian system, their morphology and a list of references; (2) general remarks about the knowledge base and some exports: list of genera and their detail sheets, list of descriptors, list of groups of descriptors and knowledge base properties; (3) the interactive key and its tools: user guide, matching terminology and glossary.

Knowledge base construction

Standardization seems to be unnecessary after the important revisions quoted above. Nevertheless when definitions have been added to the knowledge base some difficulties appear. So a standardization step is required even for this group.

Firstly, terms already present in the base are examined and questioned: are they homogeneous and/or are they synonymous? A single term may correspond to different

Natural key (single access keys)

Free access key

Information reduction

Identification speed

Complex statements (and, or...)

Question-answer style

Difficulty of choosing next decision

Doubt managment

Resources required for construction

High

Depends on the creators of the key structures, i.e. spine, a skeletal element close to bracts or tiny skeletal elements dividing pores to form an additional sheath. For a traditional determination there is no confusion but, for computer identification, the terms must be distinguished and standardized; the term spine is attributed to a structure equivalent to small bracts and protrusion leading to pore subdivision. Besides, some traditional terms included several concepts: anthoid pore contains information on pore shape and arrangement. Next, each character and its states have been reexamined and broken down into basic descriptors. Only terms corresponding to one concept are retained while similar concepts are regrouped.

Incomplete specimens managment

Only characters with taxonomic interest are present in previous diagnoses, but for computer-aided identification it is necessary to find other descriptive terms even without taxonomic importance, for instance external shape, solitary or colonial forms and so on. New terms are thus added.

Thin sections are absolutely necessary to study archaeocyathan skeletal structures. The resulting observations may correspond to primary morphological structures or to distorted observations because of the orientation of the sections. Descriptors have to be sorted by the type of section (Fig. 4).

Knowledge base conformation

When the standardization is complete, an adapted terminology is adopted. For specialists accustomed to the traditional terminology, a table explains the correspondence between ancient terms and computerized ones (Fig. 5). The taxonomic description module comprises 307 genera with systematics information and figures of type specimens. It is composed of 120 descriptors: 85 on morphology, 8 on stratigraphic and geographic distribution, 27 on traditional classification. Each descriptor has several states and descriptors and states are defined and illustrated (Fig. 6A).

User guide to the knowledge base

Successive steps of identification

To identify a specimen, it is necessary to follow several steps. The first is the choice of an adequate descriptor; the second, the choice of the states; the third, the confirmation of your choice. When this part is completed, the description is submitted and the process is repeated until the identification is obtained (Fig. 6B). At any time, it is possible to know how many states are different between the described specimen and each discarded genus and to check the differences (in red) on the detailed sheet of the discarded genus. At the end a detailed sheet appears with information on the classification, the genus type species, with figure of the type specimen and the complete description of the identified genus.

Tools

Moreover, other tools may help in the choice of the different steps described above. For example, it is possible to sort descriptors in alphabetical order, to display or conceal miniature pictures of descriptors, states and genera and eventually to reset the button and begin a new identification.

Descriptors may be sorted by special tools: the filter and the discrimination power. The filters reduce the list of descriptors to one special domain, for instance, by type of skeletal structure (outer or inner wall, intervallum), by other information (stratigraphy, geography, classification) or by orientation of the sections (transverse, longitudinal, oblique…). The second possibility is sorting descriptors by discrimination power. There are three possible sorting methods: Xper original sorting, Sokal and Michener sorting and Jaccard sorting.

The descriptors that discriminate more genera are placed at the top of the list. This order has to be examined with a critical mind as the first descriptor could be difficult to define or might not be morphological data. To be as precise as possible for the description of the studied specimen, logical operators (or, and, not, nor…) allow to improve the description or to raise doubt. For example, if external plates are observed they may be scales or annuli then OR is used (doubt); if these two structures are present in the same specimen then AND is used (qualification). Several genera are compared by opening the window "comparison" on the data sheet. Descriptive data are represented in a table of taxa (row) and times descriptors (columns). This last tool permits to conclude an identification or to find the characteristics of different taxonomic ranks.

Conclusions

This knowledge base is either used as an identification genera key or as a special motor for different domains of archaeocyathan research, for instance, faunal geographic and stratigraphic distributions. The knowledge base is interactive and can be modified and sophisticated at any moment. This work is permanently up to date and in progress: a future stage is to include paleoecological data.

  Figure1.Ontogeny of archaeocyaths, stages of growth. 1: form with taeniae, 2: form with hexagonal radial tubes (syringes), 3: form with taeniae and tabulae, 4: form with pectinate tabulae, 5: form without tabulae, 6: form with tabulae. C iw: inner wall with canals, C ow: outer wall with canals, C Ta: convex tabulae, IW: inner wall, L: hexagonal loculi, MT: multiperforate tabulae, OW: outer wall, P Ta: porous tabulae, Pe Ta : pectinate tabulae, RR: radial rods, S: septa, Sp : spine, Sp T: spinose taeniae, T: taeniae, V: vesicular tissue.(Zhuravleva, 1960, modified).

Figure 2 .

 2 Figure 2. Archaeocyath growth patterns. A: Archaeocyath skeleton (Debrenne, 1964, modified) B:Growth patterns in various groups of Porifera and allied organisms(Debrenne & Zhuravlev, 1994, modified).

Figure 3 .

 3 Figure 3. Archaeocyaths traditional key follow the classification: a natural identification keys.

Figure 5 .

 5 Figure 4. Different orientation of sections illustrated as in the knowledge base. A: Transverse section. B: Longitudinal section. C: Oblique section. D: Example of tangential section of tabulae.

Figure 6 .

 6 Figure 6. Knowledge base interfaces. A: Taxonomic description module with the 307 genera described with 120 descriptors. B: Interactive identification module: left: list of available descriptors and their states; middle: definitions above and images below, and right: list of remaining taxa above and list of discarded taxa below.

Table 1 .

 1 Comparison of two identification methods: natural key and free access key[START_REF] Hagedorn | Types of identification keys[END_REF].

		None (complete information is optimal)
		Depends on user's background
		knowledge; may exceed average
	Yes but not recommended for polytomous keys	No
	Possible for simple statements	Implicit in character state or value choice
	None	Often high for beginners
	Difficult: all alternative paths must be followed to the end	Easy
	Identification is possible but taxonomic rank is higher	Easy
	Low for first draft.	High investment until
	Good keys require high expertise	first version can be tested

Acknowledgements

I am grateful to Françoise Debrenne for introducing me to archaeocyaths and for supporting my studies over the last years. Pr. Régine Vignes-Lebbe is warmly thanked for comments during the standardization step of characters. I also acknowledge the review effort of Dr P.D. Kruse and Dr E. Moreno Eiris. And I want to thank the Centre National de la Recherche Scientifique (CNRS) for funding of my PhD thesis.