Charlene F Estrada
email: cestrada@jhu.edu

Dimitri A Sverjensky

Manuel Pelletier

Angélina Razafitianamaharavo

Robert M Hazen

Interaction between L-aspartate and the brucite [Mg(OH) 2 ]-water interface

The interaction of biomolecules at the mineral-water interface could have played a prominent role in the emergence of more complex organic species in life's origins. Serpentinite-hosted hydrothermal vents may have acted as a suitable environment for this process to occur, although little is known about biomolecule-mineral interactions in this system. We used batch adsorption experiments and surface complexation modeling to study the interaction of L-aspartate onto a thermodynamically stable product of serpentinization, brucite [Mg(OH) 2 ], over a wide range of initial aspartate concentrations at four ionic strengths governed by [Mg 2+ ] and [Ca 2+ ]. We observed that up to 1.0 µmol of aspartate adsorbed per m 2 of brucite at pH~10.2 and low Mg 2+ concentrations (0.7x10 -3 M), but surface adsorption decreased at high Mg 2+ concentrations (5.8x10 -3 M). At high Ca 2+ concentrations (4.0x10 -3 M), aspartate surface adsorption doubled (to 2.0 µmol•m -2 ), with Ca 2+ adsorption at 29.6 µmol•m -2 . We used the extended triple-layer model (ETLM) to construct a quantitative thermodynamic model of the adsorption data. We proposed three surface reactions involving the adsorption of aspartate (HAsp -) and/or Ca 2+ onto brucite: 2>SOH + H + + HAsp -= >SOH 2 + >SAsp -+ H 2 O, >SOH + HAsp -+ Ca 2+ = >SO -_Ca(HAsp) + + H + , and >SOH + Ca 2+ + 2H 2 O = >SOH 2 +

_ Ca(OH) 2 + H + . We used the ETLM to predict that brucite particle surface charge becomes more negative with increasing [Mg 2+ ], creating an unfavorable electrostatic environment for a negativelycharged aspartate molecule to adsorb. In contrast, our addition of Ca 2+ to the system resulted in Ca 2+ adsorption and development of positive surface charge. Our prediction of surface speciation of aspartate on brucite with Ca 2+ revealed that the calcium-aspartate complex is the predominant surface aspartate species, which suggests that the increase in aspartate adsorption with Ca 2+ is primarily driven by calcium adsorption. The cooperative effect of Ca 2+ and the inhibitive effect of Mg 2+ on aspartate adsorption onto brucite indicate that serpentinite-hosted hydrothermal fluids provide an ideal environment for these interactions to take place.

Introduction

The origin of life on early Earth was a geochemical sequence of emergent steps involving increasing complexity [START_REF] Hazen | Genesis: The Scientific Quest for Life's Origin[END_REF]. Among the first of these steps was the synthesis of prebiotic organic molecules in the midst of the Archean atmosphere, ocean, and lithologies. The emergence of simple molecules such as amino acids and sugars may have occurred under a variety of plausible Archean environments [START_REF] Ponnamperuma | Possible abiogenic origin of some naturally occurring hydrocarbons[END_REF][START_REF] Deamer | Amphiphilic Components of the Murchison Carbonaceous Chondrite -Surface-Properties and Membrane Formation[END_REF][START_REF] Hennet | Abiotic synthesis of amino-acids under hydrothermal conditions and the origin of life -a perpetual phenomenon[END_REF][START_REF] Holm | Hydrothermal simulation experiments as a tool for studies of the origin of life on earth and other terrestrial planets: A review[END_REF][START_REF] Jalbout | Sugar synthesis from a gas-phase formose reaction[END_REF][START_REF] Cleaves | A reassessment of prebiotic organic synthesis in neutral planetary atmospheres[END_REF][START_REF] Kim | Synthesis of carbohydrates in mineral-guided prebiotic cycles[END_REF]. Far less is known about the selection, concentration, and selforganization of these biomolecules into macromolecular systems from dilute solutions.

Mineral surfaces may provide the means by which simple biomolecules self-organize.

The mineral-water interface is known to concentrate biomolecules through adsorption [START_REF] Jonsson | Attachment of L-glutamate to rutile (α-TiO 2 ): A potentiometric, adsorption, and surface complexation Study[END_REF][START_REF] Jonsson | Adsorption of L-aspartate to rutile (α-TiO 2 ): Experimental and theoretical surface complexation studies[END_REF][START_REF] Cleaves | Mineral-organic interfacial processes: Potential roles in the origins of life[END_REF]. Mineral surfaces change significantly with shifts in pH owing to surface protonation reactions. Accordingly, mineral surfaces may have potentially played a key role in the origin of life, whereby the mineral-water interface provided sites for the selection, concentration, and self-organization of biomolecules [START_REF] Goldschmidt | Geochemical aspects of the origin of complex organic molecules on the Earth, as precursors to organic life[END_REF][START_REF] Hazen | Presidential address to the Mineralogical Society of America, Salt Lake City, October 18, 2005: Mineral surfaces and the prebiotic selection and organization of biomolecules[END_REF][START_REF] Cleaves | Mineral-organic interfacial processes: Potential roles in the origins of life[END_REF].

Hydrothermal vent systems have been discussed as plausible environments for the origin of life by providing templates for macromolecular assembly [START_REF] Baross | Submarine hydrothermal vents and associated gradient environments as sites for the origin and evolution of life[END_REF][START_REF] Shock | The potential for abiotic organic synthesis and biosynthesis at seafloor hydrothermal systems[END_REF][START_REF] Sleep | Serpentinite and the dawn of life[END_REF]. The disequilibria established by mixing hot, hydrothermal fluids (<350 ºC) with the overlying cold seawater (2 ºC) may drive the formation of some prebiotic molecules [START_REF] Shock | Organic synthesis during fluid mixing in hydrothermal systems[END_REF][START_REF] Shock | The potential for abiotic organic synthesis and biosynthesis at seafloor hydrothermal systems[END_REF]. A different type of hydrothermal system known as the Lost City hydrothermal field was discovered off the Mid-Ocean Ridge Axis (Kelley et al., 2001). The Lost City hydrothermal field belongs to a class of hydrothermal systems that undergo serpentinization, which involves the hydration of magnesium-rich olivine to serpentine and ferro-brucite [START_REF] Bach | Unraveling the sequence of serpentinization reactions: Petrography, mineral chemistry, and petrophysics of serpentinites from MAR 15°N (ODP Leg 209, Site 1274)[END_REF], according to the reaction: Mg 1.8 Fe 0.2 SiO 4 + 3H 2 O Mg 2.85 Fe 0.15 Si 2 O 5 (OH) 4 + Mg 0.75 Fe 0.25 (OH) 2

(1)

Serpentinite-hosted hydrothermal vents such as the Lost City hydrothermal field release fluids that contain up to 19x10 -3 M and 4x10 -3 M of H 2 and CH 4 , respectively [START_REF] Kelley | A serpentinite-hosted ecosystem: the Lost City hydrothermal field[END_REF][START_REF] Proskurowski | Low temperature volatile production at the Lost City Hydrothermal Field, evidence from a hydrogen stable isotope geothermometer[END_REF]. The mixing of these hydrothermal fluids with seawater creates a strong redox gradient that may facilitate the formation of prebiotic molecules [START_REF] Holm | Alkaline fluid circulation in ultramafic rocks and formation of nucleotide constituents: a hypothesis[END_REF][START_REF] Shock | The potential for abiotic organic synthesis and biosynthesis at seafloor hydrothermal systems[END_REF]. Furthermore, greenstone sequences discovered at the Isua Formation (3.8 Ga) and the Pilbara Formation (3.5 Ga) suggest that serpentinite-hosted hydrothermal activity may have been present on early Earth [START_REF] Dymek | Petrogenesis of ultramafic metamorphic rocks from the 3800 Ma Isua Supracrustal Belt, West Greenland[END_REF][START_REF] Van Kranendonk | Review: secular tectonic evolution of Archean continental crust: Interplay between horizontal and vertical processes in the formation of the Pilbara Craton, Australia[END_REF][START_REF] Shibuya | Highly alkaline, hightemperature hydrothermal fluids in the early Archean ocean[END_REF]. These localities and the presence of Archean komatiites provide evidence that the oceanic crust on early Earth was more ultramafic compared to today's mafic, basalt-hosted seafloor [START_REF] Herzberg | Thermal history of the Earth and its petrological expression[END_REF][START_REF] Van Kranendonk | Two types of Archean continental crust: Plume and plate tectonics on early Earth[END_REF].

Depending on the prevalence of the ultramafic host rock, serpentinite-hosted hydrothermal fields may have been prolific on the Archean seafloor prior to the emergence of the first cellular lifeform at 3.48 Ga [START_REF] Noffke | Microbially induced sedimentary structures recording an ancient ecosystem in the ca. 3.48 billion-year-old Dresser Formation, Pilbara, Western Australia[END_REF].

Ferro-brucite [Mg 0.75 Fe 0.25 (OH) 2 )] is a thermodynamically stable mineral of the serpentinization reaction in Eq. ( 1). The ferrous iron in ferro-brucite controls the amount of H 2(aq)

produced in the hydrothermal field as magnetite is subsequently precipitated:

(Mg x Fe y )(OH) 2 (Mg x Fe y-3z )(OH) 2 + zFe 3 O 4 + zH 2(aq) + z2H 2 O (2)

As this reaction proceeds to the right, the amount of H 2(aq) flowing through the system becomes limited, and the brucite in the serpentinite-hosted hydrothermal field approaches the magnesium endmember [START_REF] Bach | Unraveling the sequence of serpentinization reactions: Petrography, mineral chemistry, and petrophysics of serpentinites from MAR 15°N (ODP Leg 209, Site 1274)[END_REF][START_REF] Mccollom | Thermodynamic constraints on hydrogen generation during serpentinization of ultramafic rocks[END_REF]. Holm and coworkers (2006;[START_REF] Holm | The significance of Mg in prebiotic geochemistry[END_REF] have suggested that magnesium plays a role in stabilizing prebiotic biomolecules such as proteins and nucleic acids. As the primary constituent of brucite, magnesium may promote the formation of more complex molecules at the mineral-water interface within a serpentinite-hosted hydrothermal system.

Previous studies of brucite surface chemistry have focused on its precipitation and dissolution kinetics [START_REF] Hostetler | The stability and surface energy of brucite in water at 25 degrees C[END_REF][START_REF] Schott | Electrokinetic studies of magnesium hydroxide[END_REF][START_REF] Jordan | Dissolution rates and activation energy for dissolution of brucite (001): A new method based on the microtopography of crystal surfaces[END_REF][START_REF] Pokrovsky | Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control[END_REF][START_REF] Pokrovsky | Kinetics of brucite dissolution at 25°C in the presence of organic and inorganic ligands and divalent metals[END_REF][START_REF] Kudoh | Dissolution of brucite on the (001) surface at neutral pH: In situ atomic force microscopy observations[END_REF]. Nevertheless, few studies exist on the adsorption of organic species onto the brucite surface over a wide range of conditions. Pokrovsky and coworkers (2005) have studied the effect of oxalate, citrate, glycine, xylose, and catechol on brucite dissolution and precipitation. These biomolecules affected brucite dissolution at concentrations greater than 1x10 -2 M and at neutral to weakly alkaline pH conditions. Citrate adsorbed in amounts as high as 0.4 µmol•m -2 , and it and the other biomolecules may have attached onto the brucite surface as an inner-sphere species [START_REF] Pokrovsky | Kinetics of brucite dissolution at 25°C in the presence of organic and inorganic ligands and divalent metals[END_REF]. Pokrovsky and coworkers (2005) also observed that concentrations of at least 1x10 -2 M Ca 2+ increase the brucite dissolution rate at pH= 4.9, and they assumed that calcium might adsorb onto brucite as a bidentate or monodentate mononuclear surface species.

In this investigation, we characterized the adsorption of the amino acid L-aspartate (C 4 H 7 NO 4 ) onto powdered brucite. Aspartate is a polar amino acid with three protonation sites:

two carboxyl groups and one amine group. Hennet and coworkers (1992) synthesized aspartate under mineral-buffered, simulated hydrothermal conditions. The adsorption of aspartate has been previously well-characterized on rutile [START_REF] Giacomelli | Aspartic acid adsorption onto TiO 2 particles surface. Experimental data and model calculations[END_REF][START_REF] Roddick-Lanzilotta | An in situ Infrared spectroscopic study of glutamic acid and of aspartic acid adsorbed on TiO 2 : Implications for the biocompatibility of titanium[END_REF][START_REF] Jonsson | Adsorption of L-aspartate to rutile (α-TiO 2 ): Experimental and theoretical surface complexation studies[END_REF], calcite [START_REF] Hazen | Selective adsorption of L-and D-amino acids on calcite: Implications for biochemical homochirality[END_REF], kaolinite [START_REF] Ikhsan | Adsorption of aspartic acid on kaolinite[END_REF], and alumina [START_REF] Greiner | Adsorption of L-glutamic acid and L-aspartic acid to γ-Al 2 O 3[END_REF]. However, there are no studies on the adsorption of aspartate on brucite under the effect of variable divalent cation concentration, molecular concentration, and/or pH conditions.

The aim of this study is to evaluate the potential role that minerals within serpentinitehosted hydrothermal fields play in concentrating and selecting prebiotic molecules from a dilute aqueous environment. In this framework, we characterized the extent and possible importance of this interaction with a combination of batch adsorption experiments at 25 ºC and 1 bar and surface complexation modeling. Furthermore, we investigated the effects that common dissolved ions, including Mg 2+ and Ca 2+ , have on the interaction between aspartate and the brucite-water interface so that we may predict mineral surface reactions in plausible prebiotic aqueous environments.

Materials and Methods

Brucite Synthesis

We synthesized a microcrystalline brucite powder with a precipitation method previously reported by Henrist and coworkers (2003) and Lu and coworkers (2004). With 18.2 MΩcm Milli-Q water (Millipore), we prepared a 2.0 M MgCl 2 solution (99.99 % Alfa Aesar dry ampoules under Ar gas) and a solution containing 2.0 M NH 4 OH (Sigma-Aldrich, 25 wt. % solution). We added the MgCl 2 dropwise to the NH 4 OH solution at a rate of approximately 2.5 mL•min -1 using a graduated buret while we kept the latter solution vigorously stirred at a constant temperature of 45 ± 3 ºC. Lu and colleagues (2004) occurred during the addition of MgCl 2 to NH 4 OH. After brucite precipitated, we set the sealed reaction vessel aside to cool at room temperature for 3 days. We thoroughly washed the soluble NH 4 Cl byproduct from the precipitate with Milli-Q water. We then dried the precipitate on a

Corning PC-420D hot plate at 135 ºC for 1 hour.

Hydrothermal Treatment

Henrist and coworkers (2003) and Lu and colleagues (2004) observed that the crystallinity and morphology of synthetic brucite improved when it was sealed with water in a reaction vessel heated above 100 ºC over an extended period of time. We carried out a hydrothermal aging treatment on our synthetic brucite by sealing an aqueous suspension of the synthetic brucite in Milli-Q water within a PTFE-lined stainless steel reaction vessel (Col-Int-Tech). We heated the precipitate in a furnace at 150 ºC for 3 days, and after cooling the brucitewater solution to room temperature, we dried the powder at 135 ºC with a hotplate. We then stored the hydrothermally-treated brucite powder in a glass vial under an Ar gas atmosphere at room temperature.

SEM imaging (JEOL 8500F) revealed that the untreated brucite has a crystal habit characterized by rosettes of rough, circular, and oblong platelets (Fig. 1a), whereas the hydrothermally-treated brucite is distinguished by clusters of lamellar, hexagonal platelets (Fig. 1b). Additionally, the powder XRD (Bruker D2 Phaser) pattern of the hydrothermally-treated brucite demonstrates higher intensity peaks in the case of reflection (001) and reduced intensity for the (100), ( 101) and ( 111) reflections (Fig. 2). This pattern is consistent with powder XRD patterns collected under ambient conditions that have been archived at the International Centre for Diffraction Data (http://icdd.com). Our SEM and powder XRD observations may be interpreted as evidence that the hydrothermal treatment process enhanced the crystallinity in the basal direction by reducing terraces and kink sites and improving hexagonal morphology.

Brucite Specific Surface Area

We characterized the surface area of the synthetic brucite powder with the multi-point BET N 2 adsorption method (Micromeritics, Norcross, GA, USA) to obtain a specific surface area of 17.6 ± 0.1 m 2 •g -1 . A high proportion of this measured surface area most likely represents the prominent (001) basal surface, although the distribution between the basal and lateral (edge)

surfaces cannot be determined with the classical N 2 gas adsorption method. This distinction is important because previous adsorption studies involving mineral surfaces similar to brucite, such as gibbsite, geothite, illite, and kaolinite, conclude that only the lateral surfaces are active in the protonation and deprotonation reactions that lead to surface adsorption [START_REF] Prélot | Morphology and surface heterogeneities in synthetic goethites[END_REF][START_REF] Sayed-Hassan | AFM and lowpressure argon adsorption analysis of geometrical properties of phyllosilicates[END_REF][START_REF] Liu | Understanding surface acidity of gibbsite with first principles molecular dynamics simulations[END_REF]. If the lateral surfaces primarily adsorb aspartate, it is necessary to determine the surface area specific to these edge surfaces.

We assayed the edge-specific surface area (ESA) with low-pressure Ar gas adsorption at the Laboratoire Interdisciplinaire des Environnements Continentaux (Vandoeuvre les Nancy, France). Consistent basal-and edge-specific surface areas were previously obtained with this technique for several lamellar minerals including talc, kaolinite, illite, lamellar silica, saponite, and smectite clays (Villiéras et al., 2002;[START_REF] Michot | Assessment of surface energetic heterogeneity of synthetic Na-saponites. The role of layer charge[END_REF][START_REF] Eypert-Blaison | Surface heterogeneity of kanemite, magadiite and kenyaite: a high-resolution gas adsorption study[END_REF][START_REF] Tournassat | Nanomorphology of montmorillonite particles: Estimation of the clay edge sorption site density by low-pressure gas adsorption and AFM observations[END_REF][START_REF] Sayed-Hassan | Role of exchangeable cations on geometrical and energetic surface heterogeneity of kaolinites[END_REF][START_REF] Sayed-Hassan | AFM and lowpressure argon adsorption analysis of geometrical properties of phyllosilicates[END_REF][START_REF] Perronnet | Towards a link between the energetic heterogeneities of the edge faces of smectites and their stability in the context of metallic corrosion[END_REF]. Other types of minerals have also been investigated with this method, including goethite, anatase, and manganese dioxide [START_REF] Prélot | Morphology and surface heterogeneities in synthetic goethites[END_REF][START_REF] Stevanovic | Evidences for the relationship between surface structure and reactivity of goethite nanoparticles based on advanced molecular-probe methods[END_REF][START_REF] Ahmad | Influence of morphology and crystallinity on surface reactivity of nanosized anatase TiO 2 studied by adsorption techniques. 1. The use of gaseous molecular probes[END_REF].

We determined a total surface area of 19.8 ± 0.2 m 2 •g -1 with low-pressure Ar gas adsorption, which is comparable to the BET determined by N 2 gas (17.6 ± 0.1 m 2 •g -1 ). Using the methods detailed in previous studies [START_REF] Villiéras | Texture and surface energetic heterogeneity of solids from modeling of low pressure gas adsorption isotherms[END_REF]Villiéras et al., 1997;Villiéras et al., 2002;[START_REF] Tournassat | Nanomorphology of montmorillonite particles: Estimation of the clay edge sorption site density by low-pressure gas adsorption and AFM observations[END_REF][START_REF] Sayed-Hassan | AFM and lowpressure argon adsorption analysis of geometrical properties of phyllosilicates[END_REF], we have estimated that 89.5 % of the surface area can be represented by basal brucite surfaces, whereas 10.5 % are represented by lateral brucite surfaces (see Appendix A). We adopted a basal surface area of 15.7 m 2 •g -1 and a lateral surface area of 1.9 m 2 •g -1 by assuming that the total surface area was 17.6 m 2 •g -1 . We tested these surface areas by deriving the brucite particle thickness (t) and length (l) with the equations

l ൌ ସ .ୗ ౢ (4) and t ൌ ଶ .ୗ ౘ (5)
where ρ is the density of brucite (2.39 g•cm -3 ) and S l and S b are the lateral and basal surface areas, respectively. We calculated an average brucite plate length of 0.9 µm and thickness of 53 nm, which were consistent with the dimensions we observed with SEM (l= 0.1 to 1 µm and t= 30 to 50 nm, see Fig. 1b). We therefore consider 1.9 m 2 •g -1 to accurately represent the ESA of the lateral surface of our brucite sample.

Batch Adsorption Experiments

In a single batch sample, we added between 2 and 300 µM aspartate to 10.0 ± 0.5 g•L -1 brucite in a 15 mL sterile Falcon tube. The pH of each sample (10.2 to 10.3 without added

MgCl 2 ) was strongly buffered by the brucite powder. We studied four ionic strengths that resulted from the dissolution of Mg 2+ from brucite and our addition of either MgCl 2 or CaCl 2 to the aqueous phase. We conducted low-Mg 2+ , high-Mg 2+ , low-Ca 2+ , and high-Ca 2+ experiments, which we describe in Table 1.

We conducted preliminary adsorption experiments over multiple periods of time and determined that aspartate adsorption on brucite reaches a steady state within 16 hours. In this study, we placed the batch samples on a test tube rotator at 40 rpm (25 ± 1 ºC, 1 bar) for 22 hours to ensure that the brucite-aspartate suspensions had reached a steady state. We then measured the pH of the brucite-aspartate suspensions with a combination glass electrode (Thermo-Electron Orion 8103BNUWP) that we calibrated prior to the experiment with NIST-standardized buffers that referred to pH values of 4, 7, and 10 (Fischer Scientific). As we obtained pH measurements, we flushed each sample with Ar gas to avoid contamination by CO 2 . We centrifuged the samples for 10 minutes with a relative centrifugal force of 1073g. In each sample, we then separated the liquid supernatant from the solid brucite.

We analyzed the concentration of the aspartate, Mg 2+ and Ca 2+ in the supernatant with ion chromatography (IC). We used a Dionex ICS-5000 DP dual pump system equipped with an AminoPac10 column, IonPac CS12A column, and Chromeleon 6.8 software (Dionex Corporation, Sunnyvale, CA, USA). We analyzed the samples in triplicate and determined the mean concentration of aspartate remaining in the liquid supernatant within ±1 standard error (σM

Γ ୟୢୱ ൌ ሾଡ଼ሿ బ ିሾଡ଼ሿ ౧ େ ౩ ౩ (6)
in which [X] 0 is the initial concentration of aspartate or Ca 2+ , [X] eq is the concentration of aspartate or Ca 2+ remaining in the liquid supernatant, C s is the solid concentration, and A s is the edge-specific surface area of brucite. We report Γ ads as an isotherm as a function of [X] eq .

Surface Complexation Modeling Approach

We modeled the data from our batch adsorption experiments with the extended triplelayer model or ETLM [START_REF] Sverjensky | Theoretical prediction of single-site surface-protonation equilibrium constants for oxides and silicates in water[END_REF][START_REF] Sahai | Solvation and electrostatic model for specific electrolyte adsorption[END_REF][START_REF] Sverjensky | Standard states for the activities of mineral surface sites and species[END_REF][START_REF] Sverjensky | Prediction of surface charge on oxides in salt solutions: Revisions for 1:1 (M+L-) electrolytes[END_REF][START_REF] Sverjensky | A predictive model (ETLM) for As(III) adsorption and surface speciation on oxides consistent with spectroscopic data[END_REF]. Unlike other solid-water interface models, the ETLM includes the electrical work resulting from the release of water dipoles during inner-sphere adsorption. We iteratively fit the adsorption data in a manner described in previous studies [START_REF] Bahri | Adsorption and surface complexation study of L-DOPA on rutile (α-TiO 2 ) in NaCl solutions[END_REF][START_REF] Jonsson | Attachment of L-glutamate to rutile (α-TiO 2 ): A potentiometric, adsorption, and surface complexation Study[END_REF] and obtained reaction stoichiometries that represent our best fit to the adsorption data. When it has been possible to test such surface complexation modeling with spectroscopy and quantum chemical modeling [START_REF] Parikh | Evaluating glutamate and aspartate binding mechanisms to rutile (α-TiO 2 ) via ATR-FTIR spectroscopy and quantum chemical calculations[END_REF][START_REF] Lee | Speciation of L-DOPA on nanorutile as a function of pH and surface coverage using surface-enhanced Raman spectroscopy (SERS)[END_REF], there has been excellent

agreement as to the nature of the adsorbed species. We carried out calculations for the ETLM with the computer code GEOSURF [START_REF] Sahai | GEOSURF: A computer program for modeling adsorption on mineral surfaces from aqueous solution[END_REF]. We estimated a pH PZC = 10.5 from measurements of the pH after only aspartate or water had been added to brucite during our batch adsorption experiments. We previously calculated speciation reactions involving aqueous aspartate and found them to be consistent with those determined with potentiometric titrations [START_REF] Robertis | Salt effects on the protonation of Lhistidine and L-aspartic acid: A complex formation model[END_REF][START_REF] Jonsson | Adsorption of L-aspartate to rutile (α-TiO 2 ): Experimental and theoretical surface complexation studies[END_REF]. We obtained both protonation and electrolyte adsorption parameters for the brucite surface from a regression of surface titration data measured by [START_REF] Pokrovsky | Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control[END_REF]. As illustrated by Fig. 3, we fit these data with the ETLM using parameters that were derived from a constant capacitance model (C= 500 µF•cm -2 ), where pH PZC = 11.0, site density (N s )= 10 sites•nm -2 , and BET surface area (A s )= 9.2 m 2 •g -1 were reported for the titration study at 1.0x10 -2 M NaCl and 1.0 M NaCl. We recalculated the protonation and electrolyte adsorption parameters for our estimated pH PZC , lateral A s , and N s using the methods detailed by [START_REF] Sverjensky | Standard states for the activities of mineral surface sites and species[END_REF]2005). These parameters are displayed in Table 2.

Site densities can be estimated from the number of broken bonds at the surface, and these estimations are usually consistent with measurements by tritium exchange experiments [START_REF] Koretsky | A model of surface site types on oxide and silicate minerals based on crystal chemistry; implications for site types and densities, multi-site adsorption, surface infrared spectroscopy, and dissolution kinetics[END_REF]. Accordingly, we calculated site densities for the lateral brucite surfaces (100), ( 010), ( 110), and ( 111) by examining the broken bonds of each idealized surface with the program CrystalMaker (Palmer, 2009). We estimated a minimum possible site density of 9.7 sites•nm -2 and a maximum possible site density of 20.0 sites•nm -2 (Table 3). However, to fit both the Ca 2+ and aspartate adsorption data we observed for the low-Ca 2+ and high-Ca 2+ experiments, we required a site density of 38 sites•nm -2 . This value is greater than what we estimated for the idealized surfaces, but it is consistent with site densities estimated (40.8 sites•nm -2 ) and measured (36 sites•nm -2 ) on periclase [MgO], a mineral that is structurally similar to brucite and may well be covered by a thin layer of brucite in water [START_REF] Anderson | Interaction of water with the magnesium oxide surface[END_REF][START_REF] Koretsky | A model of surface site types on oxide and silicate minerals based on crystal chemistry; implications for site types and densities, multi-site adsorption, surface infrared spectroscopy, and dissolution kinetics[END_REF]. We can also use our measurements of aspartate and Ca 2+ adsorption to estimate site density (e.g., 1.0 µmol•m -2 = 0.6 sites•nm -2 ). However, due to possible intermolecular forces between surface species, it may be unlikely that every active site within one nm 2 would interact with Ca 2+ or aspartate. It may also be possible that surface imperfections primarily caused by the dissolution of Mg 2+ from brucite in the aqueous phase explain why it is necessary for us to adopt a higher site density. Our estimated site density of 38 sites•nm -2 could be tested by future adsorption studies involving a variety of chemically different ions as probes of the surface.

With the parameters we established in Table 2, we carried out iterative fits of the adsorption data to establish the stoichiometry of surface reactions that could account for the data.

We collected surface adsorption data at four ionic strengths with different dissolved ions present and a variable pH range; thus, we thoroughly tested our surface complexation model to permit the selection of a unique set of surface reactions that successfully predict the adsorption of aspartate and Ca 2+ onto brucite.

Results and Discussion

Aspartate Adsorption onto Brucite at Low Mg 2+ Concentrations

The adsorption isotherm in Fig. 4 shows the surface adsorption of aspartate on brucite as a function of the remaining aspartate concentration in the aqueous phase ([Asp] eq ) when low concentrations of Mg 2+ dissolved from the surface. We report all aspartate adsorption data in As previously discussed, we assumed that only the lateral brucite surfaces were active in adsorption reactions; however, we were unable to distinguish whether there was one lateral surface that more predominantly adsorbed aspartate. Our crystallographic examination of the idealized lateral surfaces (100), ( 110), (111), and (010) revealed two distinct terminations on the three-coordinated brucite hydroxyl group: a geminal site (>Mg(OH) 2 ) with two bonds broken and a bridging site (>MgOH) with a single bond broken at the surface. We could not determine whether aspartate attached at a geminal or bridging reaction site with the ETLM because our proposed surface reactions in Table 2 resulted in the same amount of electrical work at both sites.

Therefore to avoid ambiguity, we display surface reactions occurring at the (100) brucite plane as an example surface only, and henceforth regard the neutral brucite surface as ">SOH".

We used the ETLM to carry out a series of iterative calculations to establish possible surface reactions for the aspartate. We proposed a surface reaction represented by the stoichiometry

2>SOH + H + + HAsp -= >SOH 2 + >SAsp -+ H 2 O (7)
This reaction resulted in a close fit to the adsorption data, within analytical uncertainties, as illustrated by Fig. 4. We subsequently interpreted this surface reaction as involving a bidentate mononuclear, or "leaning" configuration with two points of attachment (one that is hydrogenbonded and one that is inner-sphere) onto the brucite surface. A possible schematic illustration of the "leaning" surface species is shown in Fig. 5. Pokrovsky and coworkers (2005) also concluded that it was likely that biomolecules attached onto brucite through an inner-sphere attachment.

Our observed range of aspartate adsorption on the brucite surface is consistent with the citrate adsorption (0.4 µmol•m -2 ) measurements by Pokrovsky and colleagues (2005). Furthermore, we previously measured similar amounts of aspartate adsorption (1 µmol•m -2 ) on rutile [TiO 2 ], and our calculations with the ETLM also predicted an inner-sphere attachment of the aspartate molecule at the mineral-water interface [START_REF] Jonsson | Adsorption of L-aspartate to rutile (α-TiO 2 ): Experimental and theoretical surface complexation studies[END_REF].

The reaction in Eq. ( 7) corresponds to the equilibrium constant

* K வୗୌ మ శ வୗୱ୮ ష ൌ ୟ ಭోౄ మ శ ಭఽ౩౦ ష ୟ ಭౄ మ ో ୟ మ ಭೄೀಹ ୟ ౄఽ౩౦ ష ୟ ౄ శ 10 ూಠ ౨,7 మ.యబయ (8)
where the superscript "*" indicates the reaction is expressed relative to the >SOH surface, and "0" refers to a hypothetical 1.0 molal standard state [START_REF] Sverjensky | Standard states for the activities of mineral surface sites and species[END_REF]. The value ∆ψ r,7 represents the electrical work involved in Eq. ( 7). The electrical work includes a contribution from the movement of water dipoles off the brucite surface according to ∆ψ r= -n H2O (ψ 0 -ψ β ), where n H2O are the number of water molecules on the right-hand side of the reaction. In Eq. ( 7), n H2O = 1, which resulted in ∆ψ r,7 = ψ 0 -ψ β .

Aspartate Adsorption onto Brucite at High Mg 2+ Concentrations

When brucite is immersed in water, the surface dissolves in aqueous solution according to

Mg(OH) 2 + 2H + = Mg 2+ + 2H 2 O (9)
where the equilibrium constant of Eq. ( 9) is

logK ൌ ୟ మశ ୟ ౄ శ మ ( 10
)
We calculated equilibrium constants of logK=17.3 ± 0.01 and logK= 17.3 ± 0.06 for batch experiments in which we added only water or aqueous aspartate, respectively, to our synthetic brucite powder. These equilibrium constants are consistent with Pokrovsky and Schott's measured value of logK=17.6 ± 0.5 for a ground, natural sample of brucite. We calculated the steady-state activity ratio from the activity coefficient of Mg 2+ with GEOSURF and our measured pH values from the batch adsorption experiments. We observed that the activity ratio in Eq. ( 10) did not change as a function of pH (Fig. 6). Therefore, we assumed that brucite was in equilibrium with the aqueous phase during our batch adsorption experiments. If brucite was in equilibrium with the aqueous phase, we estimated that our addition of MgCl 2 to an aspartate batch experiment would decrease solution pH while maintaining the equilibrium constant. We therefore calculated the activity ratio with data from the high-Mg 2+ experiment. As we predicted, pH decreased (pH= 9.9 ± 0.1), and the average activity ratio of logK= 17.2 ± 0.04 was consistent within the range of uncertainty of the logK we calculated for the low-Mg 2+ experiment.

The adsorption isotherm in Fig. 7 shows aspartate adsorption on brucite at high Mg 2+

concentrations along with data from the low-Mg 2+ experiment. We had no indication from our IC analysis that the MgCl 2 we added adsorbed onto the brucite surface. Aspartate adsorption at high Mg 2+ concentrations was between 1.7x10 -2 and 0.6 µmol•m -2 . In comparison with adsorption data we obtained under low Mg 2+ concentrations, Γ ads decreased by a factor of about 1.5.

Using the ETLM and the surface reaction proposed in Eq. ( 7), we predicted adsorption of aspartate for the high-Mg 2+ data at pH= 9.9. As shown in Fig. 8, there is close agreement between the curve predicted by the "leaning" aspartate species from Eq. ( 7) and our data at two distinct Mg 2+ concentrations. This fit lends support to our use of the surface reaction in Eq. ( 7).

We also tested and dismissed dozens of other surface reactions with the ETLM. For instance, we considered the reaction stoichiometry

3>SOH + HAsp -+ H + = 2(>S)>SOHAsp + 2H 2 O (11)
which resulted in an excellent fit to the adsorption data at low Mg 2+ concentrations. However, this reaction also predicted substantially higher amounts of aspartate adsorption (up to 3.5 µmol•m -2 ) at high Mg 2+ concentrations. This strong disagreement with the experimental data led us to dismiss this surface reaction. Through this process of elimination, we determined that only the surface reaction in Eq. ( 11) could predict aspartate adsorption at both Mg 2+ concentrations.

According to the reaction in Eq. ( 7), Asp 2-attaches onto brucite. However, when the pH decreased from 10.2 in the low-Mg 2+ experiment to 9.9 in the high-Mg 2+ experiment, the abundance of the doubly-deprotonated aspartate species (pKa=10.01) decreased in the aqueous phase. Therefore, the decrease in pH may have caused a decrease in aspartate adsorption.

Aspartate Adsorption onto Brucite in the Presence of Ca 2+

The adsorption isotherms in Fig. 8 illustrate aspartate adsorption onto brucite in the presence of low and high Ca 2+ concentrations. The low-Ca 2+ and high-Ca 2+ experiments were conducted at a pH of 10.2 ± 0.02 and 10.2 ± 0.05, respectively. We observed that surface adsorption increased with Ca 2+ concentration, where Γ ads was between 4.3x10 -2 and 1.8 µmol•m -2

for the low-Ca 2+ experiment and between 0.1 and 2.1 µmol•m -2 for the high-Ca 2+ experiment.

The range of Γ ads in the high-Ca 2+ experiment corresponded to between 56.4 and 17.1 % aspartate adsorption, respectively.

Aspartate surface adsorption was significantly greater in the presence of Ca 2+ compared with the low-Mg 2+ experiment (see Fig. 4). In particular, when aspartate adsorbed onto brucite at high Ca 2+ concentrations, Γ ads increased two-fold. In addition to this increase in aspartate adsorption, we observed that a significant amount of Ca 2+ adsorbed onto brucite as illustrated in Fig. 9. The amount of Ca 2+ surface adsorption averaged 21.6 ± 1.8 µmol•m -2 (41.8 %) for the low-Ca 2+ experiment and 29.6 ± 2.3 µmol•m -2 (14.4 %) for the high-Ca 2+ experiment. We report all calcium adsorption data in Table 5.

We developed a model of the surface adsorption of aspartate and Ca 2+ by iteratively fitting the adsorption data. We discovered that in addition to the surface reaction in Eq. ( 7), two surface reactions involving Ca 2+ were needed to fit the experimental data. The first surface reaction involved the formation of a calcium-aspartate complex >SOH + HAsp -+ Ca 2+ = >SO -_CaHAsp + + H + (12) that may attach as a monodentate outer-sphere species on brucite. Franchi and colleagues (2003) observed enhanced adsorption of nucleic acids on the clay minerals montmorillonite and kaolinite in the presence of Ca 2+ . The authors suggested a configuration involving calciumnucleic acid complexes where the Ca 2+ ion would act as a "bridge" between the nucleic acid and the clay-water interface [START_REF] Franchi | Cations as mediators of the adsorption of nucleic acids on clay surfaces in prebiotic environments[END_REF]. We estimated a similar configuration of our predicted calcium-aspartate species at the brucite surface in Fig. 10a. We proposed that the calcium-aspartate species adsorbs in addition to the "leaning" aspartate species (Fig. 5). The equilibrium constant of the surface reaction in Eq. ( 12) is

* K வୗ ష _େୟሺୌୱ୮ሻ శ ൌ ୟ ಭో ష _ሺౄఽ౩౦ሻ శୟ ౄ శ ୟ ಭೄೀಹ ୟ ౄఽ౩౦ ష ୟ ి మశ 10 ూಠ ౨,12 మ.యబయ (13)
where the value ∆ψ r,12 = -ψ 0 + ψ β .

The second reaction we proposed required the adsorption of a hydrated calcium complex

>SOH + Ca 2+ + 2H 2 O = >SOH 2 + _ Ca(OH) 2 + H + (14)
that can be interpreted as a monodentate outer-sphere surface species as illustrated in Fig. 10b.

The equilibrium constant of the surface reaction in Eq. ( 14) is

* K வୗୌ మ శ _େୟሺୌሻ మ ൌ ୟ ಭోౄ మ శ _ిሺోౄሻ మ ୟ ౄ శ ୟ ಭೄೀಹ ୟ ి మశ ୟ ౄ మ ో మ 10 ూಠ ౨,14 మ.యబయ (15)
where ∆ψ r,14 = ψ 0 .

Our proposed species differs from the prediction by Pokrovsky and coworkers (2005) that Ca 2+ may be attaching onto brucite as a monodentate or bidentate inner-sphere species. We tested surface reactions containing these species with the ETLM. However, they failed to adequately fit the Ca 2+ and aspartate adsorption data. For example, the reaction stoichiometry

>SOH + Ca 2+ + H 2 O = >SOHCaOH + + H + (16a)
which we can alternatively express as

>SOH + Ca 2+ + H 2 O = >SCaOH 2 + + H + (16b)
might result in a monodentate inner-sphere calcium species at the brucite surface. This reaction underestimated the amount of Ca 2+ adsorption for the high-Ca 2+ experiment by approximately 5.7 µmol•m -2 . Furthermore, the addition of this surface reaction in combination with Eqs. ( 7) and ( 12) suppressed the amount of aspartate adsorption to less than 0.1 µmol•m -2 at both Ca 2+ concentrations. We therefore could not consider Eq. ( 16) as a surface reaction representing Ca 2+ adsorption onto brucite.

We combined the surface reactions in Eqs. ( 7), ( 12), and ( 14) to fit the aspartate adsorption data at low and high Ca 2+ concentrations (Fig. 9). The calculated curve for the low-Ca 2+ experimental data fit within analytical uncertainty. Although in overall agreement with the isotherm shape, the curve calculated at high Ca 2+ concentrations is a bit low compared with all of the data points except for the highest surface coverage, but is consistent with the data within ±2.5 σM, or approximately 7 % uncertainty.

We predicted curves for Ca 2+ adsorption as a function of initial aspartate concentration,

[Asp] 0 . As shown in Fig. 9, there are two data points from the high-Ca 2+ experiment that are elevated above the predicted curve. However, we determined that the average predicted surface adsorption of Ca 2+ was 28.1 µmol•m -2 , which is well within the analytical uncertainty of the average experimental surface adsorption of Ca 2+ , 29.6 ± 2.3 µmol•m -2 . Therefore, our prediction of Ca 2+ surface adsorption is in acceptable agreement with the data collected at low and high Ca 2+ concentrations. We thus regard the surface reactions proposed by Eqs. ( 7), ( 12), and ( 14) as sufficiently characterizing the aspartate-brucite and Ca 2+ -brucite adsorption systems with respect to different ionic strengths, pH conditions, divalent cation concentrations and initial aspartate concentrations.

Prediction of Brucite Particle Surface Charge

The significant increase in aspartate adsorption with Ca 2+ and its decrease with MgCl 2 addition suggest that the particle surface charge of brucite shifted relative to the experimental conditions we investigated (Table 1). We therefore calculated the particle surface charge by predicting the ζ-potential of the brucite surface with the ETLM as a function of [Asp] 0 for each type of batch experiment. In these calculations, we assumed that the ζ-potential was equal to the potential at the start of the diffuse layer (Ψ d ) in the ETLM. As shown in Fig. 11, we predicted that ζ-potential was neutral to slightly negative for the low-Mg 2+ experiment, and it decreased with increasing [Mg 2+ ]. This could be a result of decreased pH with added MgCl 2 , which may directly affect the brucite surface charge. Moreover, we did not observe Mg 2+ adsorption on brucite, although we added MgCl 2 to the system. In Eq. ( 7), we also predicted the doublydeprotonated aspartate molecule, Asp 2-, adsorbed onto brucite. A decrease in surface particle charge could create an unfavorable electrostatic environment for Asp 2-to adsorb onto brucite, which reflects our observation of decreased aspartate adsorption with added MgCl 2 . In Fig. 11, we modeled a reversal of the ζ-potential with Ca 2+ . This calculation of positive particle surface charge reflects the ETLM reactions in Eqs. ( 12) and ( 14) where calcium adsorbs onto the brucite surface resulting in a net positive surface charge.

The cooperative calcium-aspartate complex, CaHAsp + , may have enabled the aspartate molecule to adsorb in greater amounts. We predicted the distribution of the two adsorbing aspartate species in Eqs. ( 7) and ( 12) with the ETLM at both low and high Ca 2+ concentrations as a function of [Asp] 0 in Fig. 12. At both Ca 2+ concentrations, we observed that the calciumaspartate outer-sphere species overwhelmingly predominates, whereas very little of the surface adsorption can be represented by the "leaning" aspartate species. This result may provide evidence that the formation of a calcium-aspartate complex enhances the adsorption of aspartate.

We predicted that a calcium-aspartate surface species forms at the brucite-water interface (Eq. 12). We predicted the distribution of aqueous aspartate species that can be represented by calcium-aspartate complexes (Fig. 13), and we determined that up to 25.8 % and 6.5 % of aqueous aspartate species are represented by CaAsp 0 at high Ca 2+ and low Ca 2+ concentrations, respectively. This prediction indicates that the calcium-aspartate aqueous complex could easily form during our batch adsorption experiments. Whereas CaAsp 0 predominates in aqueous solution, CaHAsp + does not exceed 0.5 % at low Ca 2+ concentrations and 2 % at high Ca 2+

concentrations. Nevertheless, we predicted that the CaHAsp + species predominates as a surface species, which illustrates the tendency for the mineral-water interface to adsorb organic species that may not always predominate in bulk water [START_REF] Geiger | Second Harmonic Generation, Sum Frequency Generation, and χ (3): Dissecting environmental interfaces with a nonlinear optical swiss army knife[END_REF][START_REF] Malin | Free energy relationships in the electric double layer and alkali earth speciation at the fused silica/water interface[END_REF].

It is possible that because aspartate is a polar, negatively-charged amino acid, it may readily form a cooperative complex with calcium that leads to advantageous surface adsorption on brucite. A similar amino acid, such as glutamate (C 5 H 9 NO 4 ), may also form a complex with Ca 2+ and follow a similar pattern of increased surface adsorption. Likewise, Ca 2+ may not strongly bond to a positively-charged amino acid, such as lysine (C 6 H 14 N 2 O 2 ), and competitively adsorb with the amino acid on the brucite surface. Whether Ca 2+ may either cooperatively or competitively affect the surface adsorption of a particular biomolecule onto brucite is worth future investigation.

Prediction of Aspartate Adsorption in Lost City Fluids

We propose that an ideal natural environment for aspartate to adsorb onto brucite would have elevated concentrations of Ca 2+ and little or no Mg 2+ present. Serpentinite-hosted hydrothermal systems provide such an environment with brucite and possibly other biomolecules such as aspartate (Kelley et al., 2001;[START_REF] Shock | The potential for abiotic organic synthesis and biosynthesis at seafloor hydrothermal systems[END_REF]. Kelley and coworkers (2002) report that vent fluids at the Lost City hydrothermal field have high concentrations of Ca 2+

(23.3x10 -3 M) relative to a 0 M Mg 2+ endmember composition over a pH range between 9.0 and 9.8. We invoked the surface reactions in Eqs. ( 7), ( 12), and ( 14) with the major ion (Na + , Cl -, Ca 2+ and SO 4 2-

) concentrations reported by Kelley and coworkers (2002) to predict the surface adsorption of aspartate on brucite in Lost City vent fluids at 25 ºC and 1 bar. We predicted surface adsorption at pH values of 9.8 and 10.2. We found that surface adsorption steadily increases with a decrease in pH. For instance, we predicted that surface adsorption at a pH of 9.8 is approximately double the adsorption at a pH of 10.2 at a wide range (2-300 µM) of aspartate concentrations. Although some of the aspartate concentrations in our predictions might exceed prebiotically-plausible concentrations of amino acids at hydrothermal vents, our model could possibly predict changes in amino acid adsorption as pH fluctuates as a consequence of an evolving hydrothermal system.

Our predictions for aspartate adsorption in the presence of the Lost City vent fluids are at ambient conditions. However, it is possible that the ETLM predictions could be extrapolated to higher temperatures in future studies if experiments are conducted under more plausible hydrothermal temperatures and pressures. It also may be that vent fluids in a Lost City-type hydrothermal field may mix with cold seawater to approximate ambient temperatures. This lowtemperature environment may hold an ideal Ca 2+ /Mg 2+ ratio that could promote favorable aspartate adsorption onto brucite. Therefore, the results we both observed and predicted in this study appear to be highly relevant for natural serpentinite-hosted hydrothermal systems. Within this plausible prebiotic environment we have observed a cooperative surface adsorption effect between Ca 2+ and aspartate on brucite. Our combination of batch adsorption data and surface complexation modeling contributes to a fundamental understanding of the role of the brucitewater interface in the emergence of complex biochemistry and the geochemical origin of life. High-Mg 2+ 0.6x10 -3 5.2x10 -3 N/A 17.4x10 -3

Low-Ca 2+ 0.9x10 -3 N/A 1.0x10 -3 5.8x10 -3

High-Ca 2+ 1.0x10 -3 N/A 4.0x10 -3 15.2x10 -3

Table

Table 2. Aqueous aspartate properties a , characteristics of brucite b , and ETLM parameters for proton, electrolyte, and aspartate surface adsorption. [START_REF] Robertis | Salt effects on the protonation of Lhistidine and L-aspartic acid: A complex formation model[END_REF][START_REF] Jonsson | Adsorption of L-aspartate to rutile (α-TiO 2 ): Experimental and theoretical surface complexation studies[END_REF] b Brucite properties are N s = 38 sites•nm -2 , A s = 1.9 m 2 •g -1 , C 1 = 190 µF•cm -2 , C 2 = 190 µF•cm -2 , pH PPZC = 10.5, ∆pK θ n =2.08, logK θ 1= 9.46, logK θ 2 = 11.54, log θ K Na += -9.14 log θ Cl -= 11.66 c Equilibrium constants relative to site occupancy standard states can be written relative to charged surface sites calculated using the equations:

logK வௌைு మ శ வୗୱ୮ ష = log * K வௌைு మ శ வୗୱ୮ ష + log(N s A s C s )/100 ; logK வୗ ష _େୟୌୱ୮ శ = log * K வୗ ష _େୟୌୱ୮ శ + log(N s A s )/100 ; logK வௌைு మ శ __େୟሺୌሻ మ = log * K வௌைு మ శ __େୟሺୌሻ మ
+ log(N s A s )/100, where N s is site density, A s is BET edge surface area m 2 •g -1 , and C s is solid concentration g•L -1 . Table 3. A summary of site densities calculated from idealized lateral brucite surfaces using the estimation procedures described by Koretsky and coworkers (1998), where a broken bond at a surface is considered one site per unit area. We estimated multiple site densities for every possible termination of the surfaces (100), ( 010), (110), and (111). 2 where aspartate attaches onto brucite as bidentate mononuclear, or "leaning" species. Red spheres represent oxygen, yellow spheres are magnesium, tan spheres are hydrogen, black spheres are carbon, and pale blue spheres are nitrogen atoms.

Fig. 6. Equilibrium constant for Eq. ( 10), or log(a Mg2+ /a H+ ) 2 , as a function of solution pH for low-Mg 2+ , water, and high-Mg 2+ experiments. The vertical error bars are ±1 standard deviation of each dataset. 2 as a function of initial aspartate concentration for the low-Mg 2+ (red), high-Mg 2+ (blue), low-Ca 2+ (purple), and high-Ca 2+ (green) experiments.

Fig. 12. The predicted surface speciation of aspartate on brucite as a function of initial aspartate concentration for the (a) low-Ca 2+ and (b) high-Ca 2+ experiments. The "leaning" and outer-sphere species refer to Fig. 5 and Fig. 10a and reaction stoichiometries in Eqs. ( 7) and ( 11), respectively. Dashed curves represent the individual species and the solid curve represents the total aspartate adsorption.

Fig. 1 .

 1 Fig. 1. SEM image of synthetic brucite (a) before hydrothermal treatment where oblong platelets are clustered in rosettes and (b) after hydrothermal treatment where platelets are hexagonal and in lamellar clusters (scale= 1 µM).

FigureFig. 2 .

 2 Figure

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig.3. Surface titration data for brucite at 25 ºC determined by[START_REF] Pokrovsky | Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control[END_REF] as function of solution pH at 1.0 M NaCl (red) and 1.0 x10 -2 M NaCl (blue). Dashed curves are modeled fits to the experimental data using the ETLM and the initial parameters logK 1 = 10.0, logK 2 = 12.0, logK * Na + = -9.6, logK * Cl -= -12.2, A s = 9.2 m 2 •g -1 , and N s = 10 sites•nm -2 .

Fig. 7 .Fig. 8 .Fig. 9 .Fig. 10 .

 78910 Fig. 7. Adsorption of aspartate onto brucite as a function of aspartate concentration remaining in solution for the low-Mg 2+ (red) and high-Mg 2+ (blue) experiments. Dashed curves represent the modeled fits to the experimental data calculated with the parameters in Table2. Symbols represent experimental data that are the average of a triplicate run and horizontal and vertical error bars are ±1 standard error from the average

Fig. 13 .

 13 Fig.13. The predicted distribution (%) of the aspartate aqueous species that can be represented by calcium-aspartate complexes, including CaH 2 Asp 2+ , CaHAsp + , and CaAsp 0 as a function of initial aspartate concentration in the presence for the a) low-Ca 2+ and b) high-Ca 2+ experiments.

Fig. 14 .

 14 Fig. 14. Predicted aspartate surface adsorption on brucite as a function of aspartate concentration remaining in solution in the presence of Lost City-type fluids at 25 ºC and 1 bar. Aspartate surface adsorption is calculated with the parameters in Table 2 in the presence of [Na + ]=0.49 M, [Cl -]= 0.55 M, [Ca 2+ ]= 23.3x10 -3 M, and [SO 42-]= 12.9x10 -3 M at a pH of 9.8[START_REF] Kelley | Volcanoes, fluids, and life at mid-ocean ridge spreading centers[END_REF] and a pH of 10.2.

Table 4 .

 4 Aspartate surface adsorption (Γ ads ) at a pH of 10.3 ± 0.1 increased steadily as a function of[Asp] eq . The error in Fig.4is ±1 σM of each Γ ads and [Asp] eq value. Aspartate surface adsorption was between 8.4x10 -2 and 1.0 µmol•m -2 . This range of Γ ads corresponds to 16.4 to 3.6 % of the initial aspartate added, where the percentage of adsorbed aspartate decreases with increasing Γ ads . As a consequence, the reported error substantially increases with Γ ads and [Asp] eq .

Table 1 .

 1 Description of the low-Mg 2+ , high-Mg 2+ , low-Ca 2+ , and high-Ca 2+ experiments. Dissolved Mg 2+ concentrations from brucite are present in each experiment in addition to added MgCl 2 and CaCl 2 . All concentrations are expressed in mol/L.

	Experiment Low-Mg 2+	Dissolved Mg 2+ 0.7x10 -3	Added MgCl 2 N/A	Added CaCl 2 N/A	Ionic Strength 2.1x10 -3

Table 4a .

 4a Aspartate surface adsorption data observed for the low-Mg 2+ and high-Mg 2+ batch experiments.

	Batch Experiment	[Asp] aq (µM)	Γ Γ Γ Γ ads (µmol•m -2 )	% Ads
	Low Mg 2+	4.5	0.03	10.2
		17.6	0.14	12.9
		37.3	0.16	7.8
		45.8	0.24	9.0
		70.0	0.28	7.4
		110.7	0.52	8.3
		134.7	0.85	10.8
		188.2	0.70	6.7
		1.9	0.01	3.6
		8.5	0.08	16.4
		27.3	0.15	11.6
		52.1	0.43	13.8
		77.4	0.43	9.8
		87.4	0.40	8.5
		99.2	0.57	10.3
		277.4	1.00	8.1
	High Mg 2+	4.8	0.02	4.0
		9.8	0.02	4.5
		18.3	0.09	9.4
		46.1	0.20	8.1
		70.4	0.23	6.1
		95.0	0.34	6.6
		144.5	0.42	3.8
		190.4	0.52	5.0
		53.6	0.28	9.5
		36.4	0.16	7.7
		28.1	0.08	5.5
		238.4	0.63	4.3
		116.0	0.19	2.5
		79.8	0.27	5.4

Table 4b .

 4b Aspartate surface adsorption data observed for the low-Ca 2+ and high-Ca 2+ batch experiments.

	Batch Experiment	[Asp] aq (µM)	Γ Γ Γ Γ ads (µmol•m -2 )	% Ads
	Low Ca 2+	217.2	1.77	13.6
		127.2	1.20	15.3
		84.6	0.76	14.9
		61.1	0.71	18.8
		40.4	0.48	19.3
		20.3	0.25	18.8
		7.9	0.11	21.5
		4.2	0.04	17.3
	High Ca 2+	90.4	1.50	24.8
		208.0	2.10	17.1
		115.9	1.73	22.8
		73.2	1.36	26.6
		51.9	1.19	30.9
		33.6	0.86	32.8
		13.4	0.59	46.4
		4.4	0.29	56.4
		2.4	0.13	52.7

Table 5 .

 5 Ca 2+ surface adsorption data observed for the low-Ca 2+ and high-Ca 2+ batch experiments.

	Batch Experiment	[Ca 2+ ] (µM)	Γ Γ Γ Γ ads (µmol•m -2 )	% Ads
	Low Ca 2+	614.1	21.88	40.7
		591.2	23.25	42.9
		605.0	22.21	41.6
		586.2	22.32	43.4

Acknowledgements

We would like to thank Cécile Feuillie, Namhey Lee, Alyssa K. Adcock, Timothy Strobel, Dionysis Foustoukos, Paul Goldey, John Armstrong, Adrian Villegas-Jimenez, Stephen Hodge and Steven Coley for their invaluable expertise and advice throughout this project. We thank the National Science Foundation, the NASA Astrobiology Institute, the Deep Carbon Observatory, Johns Hopkins University, and the Carnegie Institution for Science for support of this research.

 Villiéras F., Michot L. J., Bardot F., Cases J. M., François M. and Rudziński W. (1997)


Arnaud Zalta

Jen-Cheng Hou

Monique Thonnat

Fabrice Bartolomei

Benjamin Morillon

Aileen Mcgonigal
email: aileen.mcgonigal@univ-amu.fr

Neural correlates of rhythmic rocking in prefrontal seizures

Keywords: Seizure, Semiology, Oscillations, Rocking, Phase amplitude coupling, Delta, gamma

Objectives. -Rhythmic body rocking movements may occur in prefrontal epileptic seizures. Here, we compare quantified time-evolving frequency of stereotyped rocking with signal analysis of intracerebral electroencephalographic data. Methods. -In a single patient, prefrontal seizures with rhythmic anteroposterior body rocking recorded on stereoelectroencephalography (SEEG) were analyzed using fast Fourier transform, time-frequency decomposition and phase amplitude coupling, with regards to quantified video data. Comparison was made with seizures without rocking in the same patient, as well as resting state data.

Results. -Rocking movements in the delta (∼1 Hz) range began a few seconds after SEEG onset of low voltage fast discharge. During rocking movements: (1) presence of a peak of delta band activity was visible in bipolar montage, with maximal power in epileptogenic zone and corresponding to mean rocking frequency; (2) correlation, using phase amplitude coupling, was shown between the phase of this delta activity and high-gamma power in the epileptogenic zone and the anterior cingulate region. Conclusions. -Here, delta range rhythmic body rocking was associated with cortical delta oscillatory activity and phase-coupled high-gamma energy. These results suggest a neural signature during expression of motor semiology incorporating both temporal features associated with rhythmic movements and spatial features of seizure discharge.

Introduction

Complex rhythmic movements seen in some epileptic seizures involve automatic motor behaviors such as chewing or pedaling movements [START_REF] Tassinari | Central pattern generators for a common semiology in fronto-limbic seizures and in parasomnias. A neuroethologic approach[END_REF]. Such behaviors may be associated not only with epileptic seizures but also with sleep disorders [START_REF] Laganière | Disturbed nighttime sleep in children and adults with rhythmic movement disorder[END_REF] or other neurological conditions [START_REF] Goldman | Stereotypies in autism: a video demonstration of their clinical variability[END_REF], and have been conceptualized as being associated with central pattern generators [START_REF] Tassinari | Central pattern generators for a common semiology in fronto-limbic seizures and in parasomnias. A neuroethologic approach[END_REF] likely involving subcortical circuitry [START_REF] Aupy | Cortico-striatal synchronization in human focal seizures[END_REF][START_REF] Mcgonigal | Semiology and epileptic networks[END_REF]. When occurring in the context of a seizure, these more complex patterns are generally not concomitant with a focal seizure discharge confined to a single brain region but rather emerge when several connected structures within associative cortex are involved by early propagation of seizure discharge [START_REF] Aupy | Insulo-opercular cortex gener-ates oroalimentary automatisms in temporal seizures[END_REF][START_REF] Bartolomei | Defining epileptogenic networks: contribution of SEEG and signal analysis[END_REF][START_REF] Chauvel | Emergence of semiology in epileptic seizures[END_REF][START_REF] Mcgonigal | Semiology and epileptic networks[END_REF]. Not only anatomical constraints but also the temporal characteristics of the seizure discharge (e.g. rhythmicity, frequency, time-lag, coherence between structures) influence clinical expression [START_REF] Bartolomei | Defining epileptogenic networks: contribution of SEEG and signal analysis[END_REF][START_REF] Chauvel | Emergence of semiology in epileptic seizures[END_REF][START_REF] Mcgonigal | Semiology and epileptic networks[END_REF].

Body rocking occurs fairly rarely in prefrontal seizures [START_REF] Bonini | Frontal lobe seizures: from clinical semiology to localization[END_REF][START_REF] Jobst | Intractable seizures of frontal lobe origin: clinical characteristics, localizing signs, and results of surgery[END_REF][START_REF] Rheims | Analysis of clinical patterns and underlying epileptogenic zones of hypermotor seizures[END_REF] and is observed in various other physiological and pathological contexts including autistic spectrum disorder (ASD) [START_REF] Liss | Sensory and attention abnormalities in autistic spectrum disorders[END_REF]. However, neural correlates of rhythmic body rocking in humans are unknown.

We previously reported video quantification of anteroposterior rhythmic rocking [START_REF] Hou | Rhythmic rocking stereotypies in frontal lobe seizures: a quantified video study[END_REF] as a stereotyped expression of frontal seizure semiology [START_REF] Bonini | Frontal lobe seizures: from clinical semiology to localization[END_REF][START_REF] Hou | Rhythmic rocking stereotypies in frontal lobe seizures: a quantified video study[END_REF][START_REF] Mcgonigal | Prefrontal seizures manifesting as motor stereotypies[END_REF]. Here, we investigate neural correlates during the period of rocking, in a patient recorded on SEEG. We wished to evaluate whether rhythmic neural activity could be evidenced in relation to the rhythmic body movements, and to describe the temporo-spatial relation between seizure-and body rocking-based activities.

Methods

Clinical case

A 32-year-old right-handed woman presented pharmacoresistant frontal lobe epilepsy from the age of 18 years. Seizures consisted of abrupt onset of stereotyped hyperkinetic motor behavior characterized by rhythmic antero-posterior truncal rocking movements, during which the patient was unresponsive. Neuroimaging was normal. Following non-invasive presurgical investigations, SEEG was performed, during which habitual seizures with rocking were recorded. The patient also presented some seizures without body rocking, characterized by hyperkinetic behavior mainly of lower limbs while she remained lying on the bed (considered ''control seizures'' for the present study). All seizures had similar pattern on seizure onset on SEEG. As previously reported, automated video analysis allowed characterization of the rhythmic body movements [START_REF] Hou | Rhythmic rocking stereotypies in frontal lobe seizures: a quantified video study[END_REF] and showed mean rocking frequency that varied between 0.48 and 1.01 Hz across all seizures for this patient (Patient 1, Seizures 2 and 4 in the previous study [START_REF] Hou | Rhythmic rocking stereotypies in frontal lobe seizures: a quantified video study[END_REF]). SEEG exploration in 2005 consisted of 7 orthogonally implanted electrodes, with 6 exploring right premotor and prefrontal structures (see Fig. 1) and one contralateral electrode in left prefrontal cortex. Analysis of SEEG data, including quantification of seizure onset with the Epileptogenicity Index [START_REF] Bartolomei | Epileptogenicity of brain structures in human temporal lobe epilepsy: a quantified study from intracerebral EEG[END_REF] showed initial organization of seizures (epileptogenic zone, EZ) predominantly involving right dor-solateral prefrontal cortex (see Fig. 1); however, early involvement of contralateral dorsolateral prefrontal cortex was also noted, as well as rapid spread of tonic discharge to mesial regions including anterior cingulate and pre-supplementary motor area (pre-SMA). To complement visual analysis, the Epileptogenicity Index [START_REF] Bartolomei | Epileptogenicity of brain structures in human temporal lobe epilepsy: a quantified study from intracerebral EEG[END_REF] was applied to quantify seizure onset. This is a semi-automatic method of quantifying fast activity at seizure onset, incorporating measures of rapidity of discharge and earliness of appearance. This showed maximal values in lateral contacts of CR and FD (thus, predominantly right dorsolateral prefrontal cortex) (Fig. 1A). Semiology onset occurred around 2 s after discharge onset, at which time slower rhythmic activity was visible. Subsequent to SEEG exploration, cortectomy including right superior and middle frontal gyri was performed. Histopathology showed non-specific gliosis. The patient had satisfactory surgical outcome at 10 years (ILAE class 2).

SEEG signal analysis

A total of 4 seizures were analyzed from the beginning to the end of the semiology corresponding to clinical seizures (two with rocking, called ''seizures 1 and 2 ; two without rocking, called ''control seizures (seizures 3 and 4)'' ) as well as resting background activity without pathological neural or clinical activity (baseline period), within the same patient. Methodology consisted of several steps:

(1) Preprocessing. Data analysis was performed with Brainstorm [START_REF] Tadel | Brainstorm: a user-friendly application for MEG/EEG analysis[END_REF] and Matlab (The Mathworks). SEEG data associated with four seizures (two seizures associated with rhythmic body rocking, called seizure 1 and 2 here; also, two control seizures without rocking, called seizure 3 and 4), as determined by a clinician were selected. Four baseline epochs, of similar durations to the four seizures, but corresponding to a data segment from the interictal period while the patient was at rest, each obtained the same day as the corresponding seizure, were also selected. Channels that presented significant artefact during the seizures were discarded after visual inspection of the signal. We estimated the focal neural activity between two channels by applying a bipolar montage on the remaining neighboring channels. Of note, all the analyses were done on all the implanted electrodes to investigate the dynamic of the neural network suspected to be involved in the seizure. (2) Fast Fourier transform (FFT). A fast Fourier transform was applied to the coordinates of the head movements extracted from the quantified video [START_REF] Grinenko | A fingerprint of the epileptogenic zone in human epilepsies[END_REF] and to the neural data to estimate their respective power spectrum in the delta range (0.5-4 Hz). (3) Estimation of high-gamma power. A time-frequency decomposition of the neural signal was performed between 60 and 150 Hz in logarithmic scale, by applying a time-frequency wavelet transform, using a family of complex Morlet wavelets [central frequency of 1 Hz, time resolution (FWMH) of 3 s; hence, three cycles].

We then estimated high-gamma power in decimal logarithmic units (in dB), and applied a grand-average, across frequencies and time, to obtain a global estimate of high-gamma activity for the seizure and baseline epochs. (4) Phase-amplitude coupling (Pac). In order to investigate the inter-dependence between delta and high-gamma oscillations, we estimated the phase-amplitude crossfrequency coupling between the phase of the neural signal corresponding to the body rocking movement (∼1 Hz) and the high-gamma amplitude [START_REF] Aru | Untangling cross-frequency coupling in neuroscience[END_REF][START_REF] Özkurt | A critical note on the definition of phase-amplitude cross-frequency coupling[END_REF], following the method described in Özkurt and Schnitzler [START_REF] Özkurt | A critical note on the definition of phase-amplitude cross-frequency coupling[END_REF].

This estimates co-fluctuations between low and high frequency neural signals and quantifies the amount of high-gamma activity modulated in phase with the body rocking movement. The same procedure was applied to seizure and baseline epochs. periods. We then combined the two seizures of similar nature (i.e. associated with rhythmic body rocking or not) by multiplying their respective indexes, per channel (i.e., per contact). This allowed us to highlight the channels for which neural activity was high relative to baseline during Seizures 1 and 2. We also applied the same method to the two control (non-rocking) Seizures 3 and 4. (6) Statistical procedure. Paired t tests, Bonferroni corrected with a factor 4, were performed at the level of individual electrode contacts (bipolar montage) between seizure and baseline epochs.

Results

Body rocking movement and the neural signal for the two seizures present a strong similarity (Fig. 1 B,C) supported by the computation of power spectrum which revealed the modal frequency of the body rocking movement (Fig. 2 A) and neural activity in the delta range (Fig. 2 B) -1 Hz for seizure 1 and 0.9 Hz for seizure 2. Using bipolar montage, we extracted the neural power at the peak frequency and contrasted it from baseline periods (Fig. 2C). Across the two seizures (Fig. 2D), external contacts of FP, CR and FD' electrodes (exploring right and left dorsolateral prefrontal cortex) emerged. The first two captured neural activity situated in the EZ, while FD' is situated in the early propagation zone.

We next investigated the relationship between body rhythmic movements and high-gamma neural activity (60-150 Hz), which best approximates multi-unit activity [START_REF] Parvizi | Promises and limitations of human intracranial electroencephalography[END_REF]. We computed the phase-amplitude coupling (PAC) between the phase of the delta (∼1 Hz) activity and the amplitude of the high-gamma activity on the bipolar montage data contrasted to baseline periods (Fig. 3A). We show an overall increase of delta-gamma coupling during seizures (paired t tests against zero: t (80) = 7.99 and t (80) = 15.9 for seizures 1 and 2 respectively; all p < 0.01). Combining the coupling strength of the two seizures (relative to baseline; see Methods; Fig. 3B) we observed a maximal coupling in in the dorsolateral prefrontal cortex corresponding to EZ (where a large delta activity was observed) and in the motor cingulate region (BA24; CC electrode).

Finally, we computed the overall high-gamma power relative to baseline to investigate whether the previous result was specific to a high-gamma activity locked to body rhythmic movements. We observed an overall larger high-Fig. 3 A. Phase-amplitude coupling (PAC), computed between the phase of delta (∼1 Hz) activity and high-gamma (60-150 Hz) amplitude, extracted from bipolar montage data and normalized to baseline, for seizures 1 (left) and 2 (right). B. Spatial distribution of PAC combined across the two seizures. Same convention as Fig. 2C. Power of high gamma activity (60-150 Hz), in decibel (dB), extracted from the bipolar montage data and normalized to baseline, for seizures 1 (left) and 2 (right). D. Spatial distribution of high-gamma power combined across the two seizures (in dB 2 ). Same convention as Fig. 2. Each line or point corresponds to one contact.

gamma activity during seizures (paired t tests against zero: t (80) = 26.4 and t (80) = 25.3 for seizures 1 and 2 respectively; all p < 0.01; Fig. 3C). Combining the profile of response of the two seizures (Fig. 3D) we observed a maximal response in the most medial contacts of electrode CR, also situated in the early propagation zone, but in anterior cingulate gyrus (BA32), a region not reported in the previous analyses. These results indicate selective coupling between delta and high gamma activity that is not merely related to non-specific global increase in gamma activity in these locations.

We applied the same analysis pipeline used for rhythmic body rocking seizures on two control seizures from the same patient (Seizures 3 and 4). They were characterized by hyperkinetic motor behavior but did not present the body rocking movement semiology of the other seizures. As expected, we did not find a selective pattern of lowfrequency activity in the neural time-course (Fig. 4A) or in the power spectrum (Fig. 4B). In particular, the power spectrum of bipolar montage data at 1 Hz was not different in these control seizures than baseline activity (paired t tests against zero : t (82) = -3.4, p < 0.01 and t (82) = -0.99, p > 0.05 for seizures 3 and 4 respectively; Fig. 4C-D). No significant delta-high gamma phase-amplitude coupling was observed neither (paired t tests against zero: t (82) = -1.21 and t (82) = 0.62 for seizures 3 and 4 respectively; all p > 0.05; Fig. 5A-B), confirming the selectivity of the neural activity locked to the rhythmic body rocking described previously. Finally, we observed the presence of significant high-gamma activity in the two control seizures compared to baseline (paired t tests against zero: t (82) = -11.2 and t (82) = 14.5 for seizures 3 and 4 respectively; all p < 0.01; Fig. 5C) in BA32 region as previously observed (Fig. 5D).

Discussion

To our knowledge, this is the first study analyzing neural correlates of rhythmic body rocking during epileptic seizures, associating quantified video and intracerebral EEG data. Here, we describe two main characteristics of cortical activity associated with rhythmic body rocking semiology, compared to seizures without rocking movements and to interictal rest periods. First, using fast Fourier transform analysis (FFT), a peak of delta band activity, maximal in EZ and early propagation zones, was observed during rhythmic body ictal rocking, corresponding to quantified rocking frequency. Secondly, using phase-amplitude coupling [START_REF] Aru | Untangling cross-frequency coupling in neuroscience[END_REF], the phase of the clear delta peak was correlated with highgamma (60-150 Hz) activity, in EZ and propagation zones including motor cingulate regions. Thus, as well as bringing additional evidence of the tight relation between seizure onset and propagation zones in both temporal and spatial aspects [START_REF] Grinenko | A fingerprint of the epileptogenic zone in human epilepsies[END_REF], our data highlight a clear temporal relation between cortical activity and rhythmicity of motor clinical expression.

A limitation here, apart from the small number of data (due to rarity of SEEG recording of this clinical pattern), is the possibility of an artefactual cause for the delta activity, notably movement artefact from the rhythmic rocking being transmitted via the SEEG cable, suggested by the similarity of amplitude across electrode contacts. However, we investigated this possibility by using a bipolar montage, considered to produce spatial filtering, thus minimizing artefact from a common source [START_REF] Bonmassar | Motion and ballistocardiogram artifact removal for interleaved recording of EEG and EPs during MRI[END_REF]; the same delta band peak persisted in these conditions. While head movement would be more likely to introduce artefact in contacts close to the skull [START_REF] Jerbi | bral EEG: dissociating neural from ocular muscle activity[END_REF][START_REF] Mcgonigal | Postictal stereo-EEG changes following bilateral tonic-clonic seizures[END_REF] and in a widespread distribution, maximal delta activity was observed in seizure onset and propagation zones, which included deeper cerebral contacts far from electrode skull entry points; the topographical distribution of this effect thus also tends to argue against an artefactual cause. Non-rocking seizures in the same patient were characterized by hyperkinetic, non-rhythmic body and leg movements; these showed similar seizure onset pattern but were not associated with visible 1HZ activity on the SEEG trace during semiological expression.

We also investigated the dynamics of high-gamma activity, typically the predominant frequency range in neocortical seizures [START_REF] Bartolomei | Defining epileptogenic networks: contribution of SEEG and signal analysis[END_REF][START_REF] Weiss | Seizure localization using ictal phase-locked high gamma A retrospective surgical outcome study[END_REF]. High gamma band activity closely approximates multi-unit activity [START_REF] Parvizi | Promises and limitations of human intracranial electroencephalography[END_REF] and cannot be induced by cable movements. In all seizures (with (Fig. 3) and without (Fig. 5C-D) body rocking semiology), high-gamma activity was maximally present in the anterior cingulate gyrus (BA32), possibly related to its important role here in seizure propagation.

We next evidenced a correlation between the phase of delta band peak and the amplitude of high-gamma oscillations selectively during the periods of rhythmic rocking. This effect was particularly marked within electrode contacts in the EZ. Additionally, strong delta-high gamma coupling was observed in the electrode exploring the BA24 section of the cingulate gyrus. This portion of the cingulate has a major role within the motor system, notably in terms of motor coordination and selection [START_REF] Devinsky | Contributions of anterior cingulate cortex to behaviour[END_REF][START_REF] Morecraft | Cingulofrontal interactions and the cingulate motor areas[END_REF].

One possible explanation of the topographical distribution of our results could reflect the usual evolution of the seizure discharge as it spreads to cingulate motor regions. This could have a role in driving rocking behavior for example by induction of multi-unit activity by delta activity, leading to activation or disinhibition of an intrinsic neural oscillator [START_REF] Marder | Central pattern generators and the control of rhythmic movements[END_REF], perhaps involving the striatal connections of the anterior cingulate [START_REF] Devinsky | Contributions of anterior cingulate cortex to behaviour[END_REF].

Established models of epilepsy networks based on signal analysis from intracerebral EEG data have shown that, during seizures, connections between neural groups in different anatomical structures are abnormally selected and facilitated [START_REF] Bartolomei | Defining epileptogenic networks: contribution of SEEG and signal analysis[END_REF][START_REF] Wendling | Interpretation of interdependencies in epileptic signals using a macroscopic physiological model of the EEG[END_REF]. In studying these relations between neural activities, most work to date on epilepsy networks has focused on the period of seizure onset [START_REF] Wendling | Epileptic fast intracerebral EEG activity: evidence for spatial decorrelation at seizure onset[END_REF] works have investigated links to putative mechanisms of semiological production [START_REF] Mcgonigal | Semiology and epileptic networks[END_REF]. While firm conclusions cannot be drawn from the present work due to small number of data, our results suggest that correlating quantified ictal movement patterns with quantified cerebral data is feasible. Study of a larger data set could help to shed light on underlying pathophysiology of complex ictal behaviors.

Fig. 1 A

 1 Fig. 1 A. SEEG trace of a typical seizure characterized by rocking. Semiological onset occurred 2 s after onset of low voltage fast activity (blue arrow). Lower right inset shows schematic representation of SEEG electrodes in the right hemisphere. Six orthogonal electrodes explored right frontal lobe, reaching medial structures. There is also one contralateral electrode FD', symmetric with FD (not shown in figure). The red oval represents the zone maximally involved by seizure onset (electrodes FP, CR, FD) and the yellow oval represents the zone of seizure propagation (electrodes SA, PM and CC). The top right inset shows a map of the Epileptogenicity Index [4] (see text for explanation) for this seizure, which shows maximal values at seizure onset in the external contacts of FD and CR. B, C : Selected clinical semiology and neural time courses of seizures 1 (left) and 2 (right). B. Amplitude of body rocking movement extracted from video. C. Amplitude of neural signal for bipolar montage data (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

( 5 )Fig. 2

 52 Fig.2Power spectra (in volts for neural signal; arbitrary units for body rocking movement) of (A) body rocking movements and (B) of neural activity from bipolar montage data for each contact, for seizures 1 (left) and 2 (right). C. Delta (∼1 Hz) power during seizures relative to baseline, extracted from the bipolar montage data; paired t tests against zero (Bonferroni corrected with a factor 4): t (80) = 5.83 and t (80) = 7.96 for seizures 1 and 2 respectively; all p < 0.01. D. Spatial distribution of delta power combined across the two seizures (in volt 2 ). Contacts are plotted for each electrode following a medio-lateral gradient (from medial to lateral: 1-14). Each line or point corresponds to one contact.

Fig. 4 A

 4 Fig. 4 A. Neural time courses of the two control seizures 3 (left) and 4 (right), without body rocking movement semiology. Amplitude of neural signals for bipolar montage data. B. Power spectra of neural activity from bipolar montage data for the two control seizures. C. Delta (∼1 Hz) power during control seizures relative to baseline, extracted from the bipolar montage data. D. Spatial distribution of delta power combined across the two control seizures (in volt 2 ). Same convention as in Fig. 2. Each line or point corresponds to one contact.

Fig. 5 A

 5 Fig. 5 A. Phase-amplitude coupling (PAC), computed between the phase of delta (∼1 Hz) activity and high-gamma (60-150 Hz) amplitude, extracted from bipolar montage data and normalized to baseline, for the two control seizures. B. Spatial distribution of PAC combined across the two seizures. Same convention as Fig. 2C. Power of high gamma activity (60-150 Hz), in decibel (dB), extracted from the bipolar montage data and normalized to baseline, for the two control seizures. D. Spatial distribution of highgamma power combined across the two control seizures (in dB 2 ). Same convention as Fig. 2. Each line or point corresponds to one contact.

Acknowledgements

This paper has been carried out within the Federation Hospitalo-Universitaire (FHU) EPINEXT thanks to the support of the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the Ïnvestissements d'Avenir French Government program managed by the French National Research Agency (ANR). The authors wish to thank Christian Bénar, Jean-Michel Badier and other members of the Dynamap team, INS, Aix-Marseille University, for helpful discussion.

Conflicts of interest

None.