Geochemical Complexity in Terrestrial Hot Spring Fields: Implications for the Origin of Life

2.1.1. Temperature, pH, and conductivity

Water temperature, pH, and conductivity were measured at each location. Temperature and pH were measured using a WTW 330i meter and probe (Xylem Analytics, Weiheim, Germany). Conductivity was measured using a YSI 30 conductivity meter and probe (YSI Inc., Yellow Springs, OH). Both instruments were calibrated and checked daily against standard solutions.

2.1.2. Water sample collection

Water samples were collected using a 140-mL acid-washed syringe (3-day soak in 10% TraceMetal Grade HNO₃ followed by a triple rinse using 18.2 MΩ/cm deionized water). The syringe was acid-washed to leach out any trace element contaminants from within the plastic. At the field site, prior to sample collection, the syringe was then rinsed three times using the hot spring water. During sampling, the syringe was slowly filled to exclude air bubbles. Water samples were dispensed into two glass cuvettes, prerinsed with sample water, for spectrophotometric analysis of silica (SiO₂), sulfide (S²⁻), and ferrous iron (Fe²⁺) (see Section 2.1.3). The remaining water was filtered through 25 mm 0.2 μm polyethersulfone syringe filters (VWR International, Radnor, PA) to sterilize and remove particulates, and then dispensed into new polypropylene centrifuge tubes (VWR) for different analyses: 10 mL was dispensed into a 15 mL centrifuge tube for spectrophotometric analyses of nitrate and ammonia (see Section 2.1.3); anion samples were filtered into a 15-mL centrifuge tube for ion chromatography. Samples for analysis with an induced coupled plasma mass spectrometer (ICP-MS) and an induced coupled plasma emission spectrometer (ICP-OES) were filtered into a 15-mL acid-washed centrifuge tube (3 days in 10% TraceMetal Grade HNO₃ (Fisher Scientific, Hampton, NH) followed by triple rinsing with 18.2 MΩ/cm deionized water). These samples were acidified using 400 μL OmniTrace Ultra™ concentrated HNO₃ (EMD Millipore, Billerica, MA) after each field day. Then, 2 mL of the sample was filtered into a 2-mL microcentrifuge tube for D/H and δ¹⁸O analysis. Samples for dissolved inorganic carbon (DIC) were filtered into a three-way stopcock/needle/5-mL gas-tight syringe and then injected into a He-purge Labco Exetainers^® (Labco Limited, Lampeter, UK) with excess He removed following the addition of 4 mL of sample. Then, 40 mL of the sample for dissolved organic carbon (DOC) was filtered into a sterilized 50-mL centrifuge tube, which was then flash frozen on dry ice in the field and kept frozen until analysis. All samples (except those flash frozen) were kept cool with water ice during fieldwork and then kept at 4°C in the dark until analysis. Prior to analyses, 1 mL of H₃PO₄ was added to each DIC sample.

2.1.3. Spectrophotometric measurements

Total dissolved silica, sulfide, and ferrous iron (Fe²⁺) were measured on site using a DR1900 portable spectrophotometer (Hach Company, Loveland, CO). Dissolved silica values should be treated as qualitative estimates, as higher temperatures and interferences from other aqueous species are known to affect the colorimetric chemical reaction involved with the Hach methods (unpublished data). After each field day, nitrate and ammonia were also measured using the portable spectrophotometer via powder pillows upon return to the laboratory to minimize interferences from temperature and interfering chemical species (e.g., sulfide).

2.2.1. Elemental analysis

Anion samples were measured using a Thermo Scientific Dionex ICS 5000 + ion chromatography system. Cations were measured using a Thermo Scientific iCAP 6000 series ICP-OES. Trace element analysis was carried out using a Thermo Scientific X Series 2 ICP-MS. All anion, cation, and trace element analyses were carried out by the Quantitative Bio-element Imaging Center (QBIC) at Northwestern University.

2.2.2. Carbon concentration and isotopes

Samples for DIC and DOC were analyzed by the Stable Isotope Facility (SIF) at the University of California, Davis using a GasBench II system interfaced to a Delta V Plus isotope ratio mass spectrometer (IR-MS) (Thermo Scientific, Bremen, Germany) for concentration and δ¹³C signal, with raw delta values converted to final values with the use of standards provided at the SIF (lithium carbonate, δ¹³C = −46.6‰ and a deep seawater, δ¹³C = +0.8‰) calibrated against standards NBS-19 and L-SVEC. DOC analyses for concentration and ¹³C isotopic signal were carried out using an OI Analytical AURORA Model 1030 TOC Analyzer (College Station, TX). The ratio of ¹³C/¹²C of the sample or standard is reported in comparison to that of the Vienna Pee Dee Belemnite (VPDB) standard and calculated using the equation:

δ C = C 13 / C 12 sample C 13 / C 12 standard - 1 13 × 1000 %

2.2.3. Water isotopes (oxygen and hydrogen)

Water δ¹⁸O and D/H ratios were analyzed using method 2017 A on a Picarro L2130-i Cavity Ringdown Spectrometer with a Vaporization Module Autosampler. Analyses were calibrated using Picarro standards (ZERO, δ¹⁸O = 0.3‰ and D/H = 1.8‰; MID, δ¹⁸O = −20.6 ‰ and D/H = −159.0 ‰; and DEPL, δ¹⁸O = −29.6‰ and D/H = −235.0‰, all vs. Vienna standard mean ocean water (VSMOW)) and checked against an internal lab standard (MLPS rainwater). δ¹⁸O D/H isotopic values are reported as are carbon stable isotopes, analyzed at the Gibson Hydrogeochemistry Laboratory, University of Minnesota.

2.4.1. X-ray diffraction analysis

A set of 68 sediment samples was analyzed by powder X-ray diffraction (XRD) to identify the major mineralogical phases and determine the proportion of minerals. Approximately 1–2 g of each sediment sample was air-dried and pulverized into powder using an agate mortar and pestle, cleaned with ethanol between each sample. A PANalytical Empryrean diffractometer was operated for sample analysis at 45 kV and 40 mA with CuKα radiation (λα1 = 1.54060 Å; λα2 = 1.54443 Å). Diffraction patterns were collected from 5 to 70° 2ϴ with a 0.02° step size, a 1° fixed divergence slit, and an integrated dwell time of 70–100 s/step. Highscore Plus software was utilized for data processing, with mineral identification based on comparison of analyzed sample diffraction patterns to reference materials in the Crystallography Open Database (COD) (Gražulis et al., 2020), and to perform Rietveld analyses to quantify mineral proportions. X-ray amorphous mineraloid proportions were calculated using the procedure described by Rowe et al. (2012). The relative proportions of amorphous and crystalline components were quantified using a series of XRD standards created from mixtures of glass and mineral (quartz, plagioclase feldspar, alkali feldspar) powders (0%–100% crystallinity in 10% increments).

2.4.2. Sediment geochemistry analysis

Geochemical analyses of sediment samples were performed at the Pheasant Memorial Laboratory, Institute for Planetary Materials (PML), Okayama University (Misasa, Japan) following the procedures utilized in Yokoyama et al. (1999), Makishima and Nakamura (2001, 2006), Makishima et al. (2002), Lu et al. (2007), and Nakamura et al. (2022).

Sediment samples were transferred into new 15 mL Falcon tubes and centrifuged at 3000 rpm for 5 min. The resulting fluid supernatant was removed using a single-use plastic syringe and placed into a polypropylene container. One-half of the sediment separate was scooped into an alcohol-cleaned Teflon container and then immersed in deionized milli-Q water (USQ; Nakamura et al., 2022) and centrifuged at 3500 rpm for 3 min, with the supernatant removed by pipetting. This procedure for separating the sample supernatant was repeated three times. Each sample was then dried in the Teflon container that was placed on a hot plate in a clean-evaporator at ∼90°C for 24 h and then homogenized using a heat-sterilized silicon nitride mortar and pestle.

Trace, major, and minor elements were determined by induced coupled plasma mass spectrometry with a quadrupole analyzer using a Thermo Fisher Scientific iCAP TQ and by induced coupled plasma sector field mass spectrometry using a Thermo Fisher Scientific ELEMENT XR, respectively, in duplicate, with relative differences generally less than 5%, although Ni, Cu, Zn, In, and Ba showed relative differences >10%. These variations were not systematic across samples (i.e., which would indicate variation dependence on concentration or measured signal intensity), which indicates sample heterogeneity. For Sb, samples were redecomposed with only an Sb spike and analyzed independently. Sulfur and Cr concentrations were determined simultaneously by isotope dilution with S and Cr spikes.

4.1.1. Geochemical variability from subsurface processes

EP1 is clear, has a pH = 6.09, is 73.8°C, has a Cl⁻ concentration of 141 µmol/L, 0.622 mmol/L SO₄²⁻, 208.63 µmol/L sulfide, DIC = 177.19 µg C/mL, δ¹⁸O_VSMOW = 8.83 ‰, and a D/H_VSMOW = 4.61‰ (Table 1). In contrast, EP2 is dark, has pH = 5.92, and Cl⁻ (146 µmol/L) and sulfide (197.72 µmol/L) concentrations like EP1 though it is cooler (69.3°C) and has distinct values of DIC (60.25 µg C/mL), SO₄²⁻ (6.633 mM), δ¹⁸O_VSMOW (3.85‰), and D/H_VSMOW (−8.68‰) (Table 1). These data indicate that while both pools have a similar input of RLPD (i.e., similar chloride concentrations), EP2 is more strongly impacted by VPD, as highlighted by the order of magnitude higher sulfate and lower DIC concentrations.

4.1.2. Physical surface mixing

The fluids of springs EP1 and EP2 physically mix in the outflow channel that drains into Hot Sulfur Lake (Fig. 1B), producing intermediate values of DOC, δ¹³C, δ¹⁸O, and D/H at the mixing zone compared with the values in each pool (sample TICK-C-MX in Table 1). This sample has very low sulfide concentration and low temperature, resulting in low ionic conductivity, despite high concentrations of other elements (i.e., Ca, Al, Cr, Mn, Fe).

4.1.3. Evaporation and cooling

Changes to fluid composition in the outflow channel are also controlled by additional surface processes, such as evaporation, cooling, and mineral precipitation that arise from low flow rates spread out over relatively large surface areas (e.g., Reed and Palandri, 2006). These processes cause fluid temperature to drop, a loss in DIC (via dissolution and loss to the atmosphere as CO_2(g)) and DOC (taken up into biomass or metabolized into CO_2(g) via microbial activity), and precipitation of various minerals and elements, resulting in decreased conductivity in the fluids (Table 1; Nordstrom et al., 2009; Reed and Palandri, 2006; Havig et al., 2021). These changes are evidenced by comparing the DIC concentration and δ¹³C value for EP1 (177.19 μg C/mL, −6.47‰) and EP2 (60.25 μg C/mL, −5.91 ‰), with the dramatically decreased DIC concentration (10.08 μg C/mL) and enriched δ¹³C value (+4.18‰) in the mixing zone arising from the preferential loss of ¹²CO_2(g) to the atmosphere (Table 1). The loss of DIC down the mixed outflow channel is reflected in the increase in pH of the fluids to 6.51.

Evaporation accompanied by cooling is demonstrated by the fact that elements dissolved within each of the pool fluids increase in concentration down the outflow channel compared with either of pools EP1 and EP2 (including higher concentrations of Cl⁻, SO₄²⁻, Al, P, Ca, V, Cr, Mn, Co, Cu, Zn, As, Rb, Sr, Mo, and Sb; Table 1).

4.1.4. Mineral precipitation

Another critical process in changing the composition of outflow fluids at Tikitere is mineral precipitation. Precipitation of silica in the outflow channel is reflected not only by the observed precipitation of digitate nodules of silica sinter (Fig. 2; Sriaporn et al., 2020), but also in the dissolved silica concentration, which is lower in the outflow channel (7.44 mmol/L) than in the source pools (EP1 = 8.95 mmol/L, EP2 = 10.19 mmol/L). This is despite the evidence for evaporative concentration of other elements in the water discussed above. The amount of Sb dissolved in fluid is controlled by dissolved sulfide concentration, pH, and temperature (Wilson et al., 2012): at increased sulfide concentrations and lower pH, the concentration of Sb decreases due to the precipitation of Sb-sulfides. Indeed, Sb concentration is highest in fluids from the mixing zone, where the concentration of dissolved sulfide (24.32 μmol/L) is the lowest, and the pH (6.51) is the highest (Table 1).

A sediment sample in the mixing zone channel (TIK-C-MX-S2 from point X in Fig. 1B) has Be, Na, and Ca at values somewhat intermediate between the two source pool sediment samples, derived from mixing between the two pool fluids as noted above, though values of Al, Mg, Fe, Cr, Co, Ni, Cu, and Zn are all at significantly lower concentrations than in either source pool, which suggests precipitation/sequestration of elements upstream at the initial mixing point between EP1 and EP2 fluids (Table 2). The concentration of S in the mixing zone sediment, however, is dramatically higher (297,614 μg/g) relative to either of the source pool samples (4967 μg/g at EP1 and 24,226 μg/g at EP2). Elemental sulfur, which can be precipitated as original sulfide, is oxidized by O₂ from the atmosphere or through sulfide-oxidizing bacteria, both processes taking place with increasing evaporation, cooling, and exposure to the atmosphere (e.g., Pokrovski et al., 2008).

Some elements dissolved in the pool fluids are incorporated into minerals, such as amorphous silica, pyrite, sulfur, and alunite, as measured in the outflow channel of EP2 (samples TIK-C-EP2 and TIK-C-MX-S3; Table 2). For example, metal and nonmetal elements are at higher concentrations in the sediments close to the source pool and lower concentrations within the sediments of the outflow channel margin (i.e., the unmixed part), as their distribution is controlled by the pH, temperature, and redox state of the fluid.

Microbial cells, biofilms, and exopolymeric substances (EPS), the latter secreted by microorganisms for their survival (e.g., for nutrient and enzyme facilitation, toxin exclusion, and substrate attachment; Briggs, 2003; Hall-Stoodley et al., 2004), may become incorporated into hot spring minerals and mineraloids (e.g., Weed, 1889; Westall et al., 2000; Handley and Campbell, 2011 and references therein). These microbial features have been reported to influence the morphological development of siliceous sinter deposits, for example, as shown in field growth experiments by Handley et al. (2005, 2008), where filamentous microbial colony clusters became coated with amorphous silica around the rim of Champagne Pool. Repeated surface colonization, followed by silicification of biofilms and EPS, produces sinter laminations that accrete as spicular sinter microstromatolites. Silicification of biofilms appears to be passively induced (Urrutia and Beveridge, 1993; Westall et al., 1995), although experimental studies of cyanobacteria undergoing silicification revealed a physiological response to mineral encrustation (i.e., thickening of the polysaccharide sheath; Benning et al., 2004a, 2004b). Furthermore, the active or passive sequestration of metals by microbes and precipitation of silica and iron minerals in association with microorganisms have been reported in several studies (e.g., Cady and Farmer, 1996; Konhauser and Ferris, 1996; Phoenix et al., 2000, 2005; Phoenix and Konhauser, 2008; Churchill et al., 2021; Gangidine et al., 2020, 2021; Murphy et al., 2021; Nersesova et al., 2024).

When considered collectively, these results demonstrate that changes in the geochemical environment down the outflow channel drive changes in mineral precipitation that could potentially lead to variations in mineral/mineraloid/element encrustation and/or templating on microbial colonies and biofilms growing on benthic and marginal hot spring outflow channel surfaces. These changes would then also be subject to shifting discharge volumes and/or subsurface geochemical inputs, as well as variations in precipitation input across seasons, illustrating the potential for multiple types of changes that can occur within a single outflow channel over time.

4.1.5. Turbulent mixing

The final method of increasing the physico-chemical complexity of fluids at this locality is evident at the drainage channel south of the pool called “The Big One” (Fig. 1C). Here, the channel is characterized by rapid flow and displays turbulent eddies that mix hot (50–60°C) fluids draining from the center of The Big One with muddier fluids that have cooled along the pool margins (20–30°C). This mixing results in a fluid with intermediate temperature (41.3°C) that cools further downstream and fills a cool (30–40°C), yet still acidic (pH = 3), unnamed pool to the south (blue-filled pool in main panel of Fig. 1).

4.2.1. Physical surface mixing

Fluids from Champagne Pool overspill in three directions. To the northeast, Champagne Pool fluids mix across a broad sinter terrace with those of a small, light green spring that is hot (c. 90°C), low pH, and S-rich (Fig. 3A).

4.2.2. Evaporation and cooling

To the north-northwest, fluids from Champagne Pool overspill, flow downhill through rotten ground (Fig. 3C), and undergo strong evaporation, finally collecting in Roto Kārikitea, a neon green colored, S-rich pool with a strong acidity (pH = 2) and remarkably cool temperature (14°C) (Fig. 3D).

4.2.3. Mineral precipitation

The overspilled fluids of Champagne Pool have precipitated a broad sinter terrace that fills a valley (Fig. 3E) that extends for ∼300 m south, downslope to the Alum Cliffs study area (Fig. 3F; see Section 4.3). Silica precipitation, input from small acidic springs and seeps, evaporation, and cooling across the terrace lead to a dramatic change in the fluid that flows out the bottom end, which is strongly acidic (pH = 2.51) and significantly cooler (32.4°C) than Champagne Pool itself.

4.3.1. Geochemical variability from subsurface processes

The hot spring pools sampled at Alum Cliffs (WT-A-3, −6, −8, −10, and −13 on Fig. 4) have relatively elevated Cl⁻ (18.6–23.3 mmol/L) and SO₄²⁻ concentrations (10.7–15.4 mmol/L) that are higher than the predicted pre-near-surface-boiling source fluid (Cl⁻ ≈ 10 mmol/L, SO₄²⁻ ≈ 1 mmol/L, Supplementary Fig. S1; Havig et al., 2021) but consistent with mixed residual liquid phase and vapor phase source inputs. The bright yellow arsenic-precipitating acidic pool WT-B-13 is unique relative to the other fluids analyzed here in having high dissolved SiO₂ (523 mg/L), DOC (3.5 ppm), and As, P, Ca, and Zn, but low Al (56.7 mmol/L) (Table 1).

The acidic stream that flows into the Alum Cliffs Lake is fed by discharge from Champagne Pool, from adjacent springs to the north, as well as from the acidic Lake Whangioterangi (Echo Lake) to the east (pH = 2.4, Cl⁻ = 6.80 mmol/L, SO₄²⁻ = 3.96 mmol/L: Timperley and Vigor‐Brown, 1986). This stream (samples WT-A-1 and -2) has a Cl⁻ concentration of 8.56 mmol/L and a high concentration of SO₄²⁻ (10.26 mmol/L), which suggests that the primary source of Champagne Pool, adjacent springs, and Lake Whangioterangi derives from a high SO₄²⁻ concentration vapor phase.

4.3.2. Physical surface mixing

At the Alum Cliffs site, the fluid composition of two hot, clear, and slightly elevated source pools (WT-A-8 and -10, both at ∼90°C) was analyzed and compared with the composition of two warm, turbid, and somewhat lower elevation pools (WT-A-6 and -3, at ∼72°C and 53°C, respectively). The hot pools were found to have higher total dissolved ionic concentrations and DIC than the warm pools; total SO4²⁻, Cl⁻, Al; and the values of many of the other elements analyzed were all at higher or variable concentration levels in the warm pools relative to the hot pools (Table 1). These findings indicate that temperature variations between the connected pools do not simply reflect dilution by cool surface waters, but that there are variable fluid components and variable degrees of mixing between all of the different pools in this area. Temperature plays a clear role in the level of ionic concentration across all of the fluids in this area, with pH having a lesser role (Fig. 5).

These hot springs have Li, B, Na, K, Ca, As, S²⁻, and DIC concentrations that are higher than in the inflowing acidic stream, whereas Mg, Fe, Co, and Ni concentrations are lower than in the stream, and Al, Ti, Mn, Cu, Zn, Mo, Sb, and W, as well as NH₄(T) and Fe²⁺ concentrations, overlap with the stream values (Table 1). These data illustrate how input from the Alum Cliffs hot to warm springs and pools, and from the springs that bubble up into Alum Cliffs Lake itself, has changed the composition of fluids of the inflowing acidic creek, as also reflected by the composition of the outflow creek fluids (sample WT-C-14) that show increases in Li, B, Na, Al, K, Ca, Fe, Cu, Zn, As, and W, as well as S²⁻, Fe²⁺, and DIC concentrations, and decreases in the concentrations of Mg, Mo, Sb, as well as NH₄(T) and NO₃⁻ (Table 1). The impact of this mixing is also reflected by the increased concentration of Cl⁻ (11.63 mmol/L) and SO₄²⁻ (11.74 mmol/L) in the outflow stream that—uniquely in this area—hosts a thriving sulfur-based microbial community (Fig. 6), reflective of the high S contents (e.g., Sriaporn et al., 2023).

4.3.3. Mineral precipitation

The shifts in aqueous geochemistry documented for this site are mirrored by changes in sediment element contents (Table 2). For example, light tan turbid pool WT-A-6 (pH = 3.80, T = 71.7°C) flows into light yellow-green pool WT-A-7 (pH = 2.94, T = 52.9°C). The sediments in the mixing zone between these pools (Wt-A-7S) have higher Al, Na, Mg, and Ca concentrations than sediments from the rim of the source pool (WT-A-6S), suggesting precipitation of aluminosilicate minerals. An increase in relative Fe content and a decrease in total sulfur (likely reflecting a decrease in the amount of elemental sulfur present) from the source pool to the mixing zone suggest pyrite precipitation, although trace element concentrations (e.g., Cr, Mn, Co, Ni, Cu, and Zn) show no change between the two sites.

Discharge from dark brown turbid source pool WT-A-8 (pH = 3.07, T = 86.0°C) flows into a light yellow-green pool (WT-A-9, with pH = 3.09, T = 44.3°C). Sediments in the source pool (WT-A-8s) and in the outflow mixing zone (WT-A-9S) showed no discernible changes in either the concentration of the major elements (Al, Na, Mg, K, Ca) or the trace elements, which is interpreted to reflect the similarity in pH, which minimizes any mineral saturation changes. However, Fe and S concentrations were higher in the mixing zone sediments, which attests to precipitation of pyrite and oxidation of sulfide to elemental sulfur.

The clear and dark brown source pool WT-A-10 (pH 5.50, T = 92.9°C) discharges into an unlabeled yellowish-green pool (pH 3.11, T = 45.8°C), which then flows into another unlabeled light yellowish-green pool (pH ∼ 3, T = 44.0°C) (Fig. 4). Sediments were collected from the source pool rim (WT-A-10S), from the entry point into the first unlabeled pool (WT-A-11S), and at the entry point to the second unlabeled pool (WT-A-12S). Whereas Na and Mg increased in concentration in the sediments from the first pool through to the second mixing zone, K and Ca values decreased at site 11S compared with site 10S but then increased again at site 12S. The trace elements Cr, Ni, Cu, and Zn increased across the three sites, whereas Al decreased across the 10S and 11S transition, suggesting mineral precipitation in the outflow from pool 10 due to the decrease in pH or a shift in porewater element concentration. Across this transition, Fe concentration decreased by half, whereas total sulfur increased, suggesting that there was greater precipitation of Fe as pyrite in the source pool, while more oxidation of sulfide to elemental sulfur occurred in the mixing zones.

Bright yellow, As-rich pool WT-A-13 (pH = 3.10, T = 90.7°C) discharges directly into the Alum Cliffs Lake (pH = 2.50, T = 42.1°C) (Fig. 4). Sediments collected from the rim of the As-rich pool (WT-A-13-1S) were compared with those from the small delta deposit at the mixing zone between the discharge fluid from this spring and the water of Alum Lake (WT-A-13-2S) and ∼30 cm further away from the outflow channel water on the shore of the lake (WT-A-13-3S) (Table 2). Sample 13-2S contained higher concentrations of the major elements (Al, Na, Mg, K, Ca) compared with the source pool sediments (WT-A-13-1S), suggesting precipitation of aluminosilicates. Total Fe also increased in relative concentration across this first transition, whereas total S decreased, suggesting precipitation of Fe as pyrite at both localities, but accompanied by the additional precipitation of S as elemental sulfur at the source pool. The relative concentration of trace elements showed no distinct trend across all three sites, though P increased at all three sites, perhaps reflecting an increase in biological activity away from the hot source pool. The Alum Cliffs lakeshore sediment (13-3S) was lower in major element concentrations and three times higher in total sulfur concentration.

Reflecting the input of the Alum Cliffs hydrothermal area, sediments from the acidic stream flowing out from Alum Cliffs Lake (sample WT-A-14S) show a relative decrease in Al, Na, Mg, Ca, Cr, Mn, Fe, No, Ni, Li, and Zn concentration, but an increase in Cu, Mo, Sn, Sb, Pb, and U compared with sediments from the inflowing acidic stream (samples WT-A-1S and -2S) (Table 2).