Earth’s climate has cooled over the past 50 Myr, including a dramatic shift from greenhouse to icehouse conditions at ~34 Ma1,2. However, as is evident from a decline in the oxygen isotope record (δ18O), this general cooling trend was interrupted by a prolonged period of global warming that peaked during the middle Miocene (~17–15 Ma), the so-called Miocene Climatic Optimum (MCO) (Fig. 1a)1,2. The MCO coincided with a long-lasting positive carbon isotope (δ13C) excursion of ~1‰ between ~17 Ma and ~13 Ma (Fig. 1b)1,2,3,4,5,6,7. Superimposed on this excursion are eccentricity-paced 405 kyr δ13C cycles represented as nine δ13C maxima (CM events)3,6. This climatic change and fluctuations in the global carbon cycle likely caused the retreat of the Antarctic ice sheet8,9 and reshaped terrestrial ecosystems at least on local and regional scales10,11. The MCO was followed by one of the most intense cooling events in the Cenozoic at ~14 Ma, the middle Miocene Climatic Transition (MMCT), and reestablishment of the Antarctic ice sheet (Fig. 1a)1,2,4,12.

Fig. 1: Geochemical records between 10 and 20 Ma.
figure 1

a Deep-sea δ18O4,5,6,7,38,42,43, (b) deep-sea δ13C4,5,6,7,38,42,43, (c) pCO214,15,16,17,18,19,20, (d) global crustal production rate26, (e) 187Os/188Os (errors are 2 SD), and (f) map showing locations of studied sites (IODP Sites U1336, 1337, 1338, and 1438, and ODP Site 1148) and previous studied sites (DSDP Sites 31937, 52138, 59637, 59736,38, and 59836,38). Atmospheric pCO2 was estimated based on the density of stomata in fossil leaves15, δ11B of planktonic foraminifer16,17,19, δ13C of alkenones14,20, and δ13C of paleosols18. The 187Os/188Os of ODP Site 1148 and DSDP Sites 597 and 598 are from both the present and previous studies36,38,39. The previous 187Os/188Os data are shown in pale colors. The hatched area in (a)‒(e) shows the period of δ13C decline marking the onset of the MCO5. The grey area in (a)‒(e) shows the duration of the main eruptive phase of CRB volcanism (15.9–16.7 Ma)27,28.

Until recently, there was limited evidence that the MCO was accompanied by variations in pCO2. An early reconstruction of pCO2 using the δ13C of alkenone indicated that pCO2 was similar to that of preindustrial levels (i.e., 200–300 ppmv) throughout the Miocene13. However, that record may have been biased by algal carbon concentration14. Recent δ13C data of alkenones and other independent CO2 proxies (i.e., stomatal frequency of fossil leaves, δ11B of foraminifera, and δ13C of paleosols) generally agree that pCO2 increased to >400–600 ppmv at ~19–15 Ma and then declined to a lower level (pCO2 = ~300 ppmv) by ~14–13 Ma (Fig. 1c)14,15,16,17,18,19,20. Evidence for high CO2 conditions during the middle Miocene may also be supported by the diversification of browsing ungulates in North America10. Hence, the MCO seems to be tied to the greenhouse effect of elevated atmospheric CO2.

Some studies further suggested that the high-CO2 conditions were caused by enhanced magmatism during this period5,21,22,23,24. Seafloor magnetic records indicate high crustal production rates between 19 and 14 Ma25,26 (Fig. 1d). Substantial amounts of CO2 could accumulate in the atmosphere due to this volcanism, although the reconstructed crustal production rates do not show an increasing trend associated with the MCO22,25,26. Alternatively, the high-CO2 conditions may reflect the emplacement of the Columbia River Basalt (CRB)5,23,24. Biogeochemical modeling shows that CRB volcanism could explain the magnitude of variations in pCO2 and δ13C if a considerable amount of CO2 (i.e., ~6 times that of extrusive magmatism) was emitted through intrusive volcanic activity and metamorphism of carbon-rich country rocks (cryptic degassing) at this time23. However, that model and the U–Pb and 40Ar/39Ar ages of the CRB (16.7–15.9 Ma) also indicate that the primary eruptive phase of CRB volcanism was not long enough to explain the prolonged warming event and positive δ13C excursion of the entire MCO23,27,28. Thus, the reasons for the long-term rise and fall of pCO2 and δ13C remain unresolved.

Variations in seawater 187Os/188Os have been used to assess changes in the intensity of magmatism29,30,31. Osmium in seawater is mainly supplied from the continental crust and the mantle (or young oceanic crust) via fluid-rock interactions32,33. Dissolution of extraterrestrial particles, except during a large impact event34,35, is a minor source of seawater Os32. Among the Os isotopes, 187Os is produced by radioactive β-decay of 187Re with a half-life of 41.6 Gyr33. As Re is relatively incompatible during mantle melting compared to Os, the continental crust possesses higher Re/Os than the mantle32,33. This difference in Re/Os ratios results in a large contrast in 187Os/188Os between the continental crust (currently, 187Os/188Os = ~1.4–1.6) and the mantle (187Os/188Os = 0.12–0.13)32,33. Hence, large-scale extrusive eruptions of mantle-derived materials provide non-radiogenic Os to the oceans and can shift marine 187Os/188Os toward less radiogenic values, although processes that take place beneath the crust (e.g., magma intrusions and associated cryptic degassing) would have little impact on seawater 187Os/188Os. Negative anomalies in seawater 187Os/188Os revealed by studies of marine sedimentary rocks are commonly associated with large-scale eruptions of intraoceanic basalts29,30,31.

Miocene seawater 187Os/188Os records derived from contemporaneous pelagic sediments have been previously reported36,37,38,39 (Fig. 1e, f). Some of them exhibit low 187Os/188Os values of ~0.72 during the middle Miocene (e.g., data from Deep Sea Drilling Project (DSDP) Sites 31937 and 52138; Fig. 1e). However, most records were acquired at a low temporal resolution, except for those reported from carbonate sediments at DSDP Sites 521, 597, and 59836,38. These sites are in open marine conditions: i.e., DSDP Site 521 is at the Mid-Atlantic Ridge, and DSDP Sites 597 and 598 are at the East Pacific Rise (Fig. 1f; Supplementary Notes). Hence, their 187Os/188Os records can be used as baseline data during the Miocene. However, the depositional ages of these cores are not well constrained. Furthermore, these cores do not cover the entire period of the MCO. To better constrain Miocene seawater 187Os/188Os records, we obtained Os isotope records across the MCO from leachable fractions in marine sediments drilled at International Ocean Discovery Program (IODP) Sites U1336, 1337, 1338, and 1438 and Ocean Drilling Program (ODP) Site 1148 (Fig. 1e, f; Supplementary Tables S15; Supplementary Notes). For comparison, we also collected additional data from previously studied DSDP Sites 597 and 598 (Fig. 1d, e; Supplementary Tables S6, S7).

IODP Sites U1336, 1337, and 1338 in the eastern equatorial Pacific Ocean were drilled to collect Neogene sediments40. Continuous carbonate-rich successions were recovered from these sites. IODP Site U1438 is in the Amami Sankaku Basin in the Philippine Sea. The sediments from this site are dominated by carbonate-poor reddish–brownish mud composed of terrigenous, biogenic, and volcaniclastic materials interspersed with discrete ash layers41. ODP Site 1148 is located on the lower continental slope of the northern South China Sea. Hemipelagic sediments at this site are composed primarily of greyish-green and reddish-brown clayey nannofossil ooze42,43,44. Except for IODP Site U1337, the studied cores have well-resolved magnetostratigraphy40,41,44 (Supplementary Tables S8, Fig. S1). In addition, astronomically tuned δ13C and δ18O records are reported for IODP Sites U1336, 1337, and 1338, and ODP Site 1148, although short periods (<104 yr) of dissolution events were recognized from ODP Site 1148 at ~16–15 and ~13–11 Ma4,5,6,7,42,43 (Fig. 1a, b). To compare the 187Os/188Os data and the δ13C and δ18O records, astronomically derived ages are used to plot the 187Os/188Os data from IODP Sites U1336, 1337, and 1338, and ODP Site 1148 in Fig. 1e. For the carbonate-poor samples from IODP Site U1438, the depositional ages are determined by magnetostratigraphy41 assuming linear sedimentation rates between magnetic anomalies.

Results and discussion

187Os/188Os as a proxy of enhanced magmatism

The isotopic compositions of Os leached from IODP Sites U1336, 1337, 1338, and 1438 and ODP Site 1148 sediments range between 0.66 and 0.90 (Fig. 1e; Supplementary Tables S17). The most prominent feature of the data is an excursion in the 187Os/188Os values at all sites between ~20 Ma and ~13 Ma: i.e., the 187Os/188Os values decrease from ~0.80 to 0.72 for samples aged 20–17 Ma, remain at low values (~0.72) for samples aged ~17–15.8 Ma with a spike to a lower value (~0.66) at samples aged 16.7 Ma, and then gradually increase to ~0.80 for samples aged ~15–13 Ma. The 187Os/188Os values at ODP Site 1148 recover to the pre-excursion value earlier than other sites. Because ODP Site 1148 is located at a marginal sea, the quick recovery may reflect the influence of local riverine input, such as Xijiang and Hong He rivers, possessing radiogenic values32. Alternatively, it may be partly caused by the short period of dissolution events42. Nevertheless, on the basis of magnetostratigraphy40,41,44, the timing of low 187Os/188Os intervals (~0.72) in the studied sites can be constrained within the magnetochrons C5Cr (17.235–16.721 Ma) to C5Br (15.974–15.16 Ma), although the top of the magnetochron C5Br is not well resolved at IODP Site U1438B and ODP Site 1148 (Supplementary Fig. S1; Table S8). In addition, if we closely compare the 187Os/188Os records to the δ13C records at IODP Sites U1336, 1337, and 1338 and ODP Site 1148, the low 187Os/188Os values at these sites start slightly before the same δ13C minimum at 16.9–16.7 Ma which has been recently interpreted to mark the onset of the MCO5 (Supplementary Fig. S2). It is also likely that the low 187Os/188Os values at these sites end at the same δ13C maximum at ~15.8 Ma frequently called CM3b3,6 (Supplementary Fig. S2). Considering that we used an acidic peroxide leaching technique to preferentially derive hydrogenous Os (Supplementary Table S9) and found a similar excursion from multiple sites, the low 187Os/188Os signals represent a global shift to a low seawater 187Os/188Os (~0.72) between ~17.0 Ma and ~15.8 Ma.

Our interpretation is basically consistent with previously published Miocene 187Os/188Os records36,37,38 showing high 187Os/188Os values (~0.80) for samples aged ~20–18 Ma at DSDP Site 597, and an increasing trend for samples aged ~15–13 Ma at DSDP Sites 521 and 598 (Fig. 1e). Negative 187Os/188Os excursions reported from ferromanganese crusts may also support our interpretation, although the ages of those anomalies remain poorly constrained45,46. An exception is the trend observed in the older part (>15.1 Ma) of DSDP Site 598 which does not show the low 187Os/188Os value (~0.72) found in other sites (Fig. 1e). At DSDP Site 598, a depositional age as old as 16.4 Ma (N8/N7 zone) was reported based on the first occurrence of Globigerinoides sicanus38. However, this fossil was found from the basal part of the studied section and may not represent the first appearance datum (FAD). Large deviations in the benthic δ13C record of DSDP Site 598 from those of other sites may be also caused by this age uncertainty (Fig. 1b)38. Stronger age controls are required to fully understand the 187Os/188Os trend in the older part of DSDP Site 598 core.

Overall, the existing Os isotope records of Miocene sediments suggest an increase in non-radiogenic Os in global seawater at ~17.0–15.8 Ma (Fig. 1e). Non-radiogenic Os can be effectively supplied from extraterrestrial and/or mantle-derived materials. There was a meteorite impact event that formed the Nördlinger Ries crater during the middle Miocene47. However, 40Ar/39Ar ages of tektites (14.8 Ma) from the crater are younger than the observed 187Os/188Os anomaly. In addition, a typical time scale for 187Os/188Os anomalies induced by an impact event is less than 0.5 Myr34. Instead, the observed excursion can be directly interpreted as evidence of enhanced magmatism. This interpretation is supported by a small decrease in the δ7Li found in marine sediments, suggesting excess input of isotopically light Li from mantle-derived materials to seawater during the middle Miocene48.

Two large-scale volcanic events have been documented for the middle Miocene: i.e., enhanced ocean-ridge magmatism25,26 and CRB eruption27,28. Both of them are potential sources of non-radiogenic Os to the oceans49,50,51. The magnetic anomalies recorded on the seafloor suggest that the global oceanic crustal production rate was high between ~19–15 Ma25,26 (Fig. 1d). The opening of the East Asia marginal basins (e.g., the South China Sea and the Sea of Japan) also occurred between the late Oligocene to middle Miocene52,53,54 which is not included in the global production rate. The global oceanic crustal production rate decreased by ~20% since 15 Ma and reached a steady state at ~11 Ma (Fig. 1d). The waning stage of the ridge-magmatism roughly coincides with the increase in the 187Os/188Os between ~16 and 11 Ma. In contrast, the reconstructed crustal production rate does not necessarily support the decline of the 187Os/188Os between ~20 and ~17 Ma. This discrepancy may reflect the limited temporal resolution of the magnetic polarity reversals used to reconstruct the crustal production rate25,26. Alternatively, the low 187Os/188Os interval (~17.0–15.8 Ma) may reflect the main period of CRB eruption (16.7 and 15.9 Ma)27,28 because there is broad agreement in their ages, although our samples lack radiometric ages. The negative 187Os/188Os spike to 0.67 at ~16.7 Ma may mark a pulse during the main eruptive phase. However, the main phase of CRB eruption is not long enough to explain the entire 187Os/188Os excursion (Fig. 1e)27,28. Hence, the 187Os/188Os excursion most likely reflects the combined influence of enhanced ocean ridge magmatism and CRB eruption.

It is also possible that the ocean-ridge magmatism and CRB eruption were associated with subduction-related volcanism, although there could be a time lag between these events. In general, plate motions are driven primarily by the downward motion of subducting slabs55. Subduction of the Pacific Plate and/or rupture and sinking of the Izanagi Plate slab played a role in the opening of the East Asia marginal basins between the late Oligocene to middle Miocene52,54. Rapid subduction of the Philippine Sea plate, due to the rotation of the SW Japan arc sliver, could have caused forearc volcanism in southwestern Japan between 17 and 12 Ma56. In addition, recent studies suggest that CRB eruption was triggered by thermochemical erosion of the Farallon/Juan de Fuca slab57,58. This change in the tectonic configuration may have renewed the subduction beneath the North American Plate and allowed the rejuvenation of arc volcanism in the eastern Pacific region58,59. The subduction-related arc/oceanic volcanism could have been an additional source of Os with low isotopic compositions60,61, although their eruption volume has yet to be constrained.

To estimate the amount of mantle-derived Os (Fman) required to reproduce a decline in 187Os/188Os from 0.80 to 0.72, we employed simple mass balance calculations. Although crustal contamination is documented during the late stage of CRB eruption62, the Os isotopic compositions of the early-erupted CRB are low (187Os/188Os < 0.13)50,51. Because both ocean-ridge magmatism and CRB eruption are potential sources of non-radiogenic Os, a chondritic value (187Os/188Os = 0.126) was assumed for the isotopic composition of mantle derived Os32. In contrast, we used a wide range of values for the parameters related to the continental Os input (Supplementary Fig. S3). Although we varied the continental Os flux (Fcon) from 150 to 600 kg yr−1, the calculated Fman do not change considerably (<7%). The Fman is more sensitive to the isotopic composition of the continental Os (Rcon) than Fcon. To cause a drop in seawater 187Os/188Os from 0.80 to 0.72, Fman has to increase 38–45% for Rcon = 1.2, 26–29% for Rcon = 1.54, and 22–23% for Rcon = 1.9 from the pre-perturbation condition (i.e., seawater 187Os/188Os = 0.80; Supplementary Fig. S3). Because this calculation is relatively insensitive to Fcon, we did not consider changes in Fcon associated with global warming during the MCO. Based on these calculations, we infer a 22–45% increase of mantle-derived Os between 17.0 and 15.8 Ma.

Links between enhanced magmatism and the MCO

To evaluate the influence of Miocene magmatism on the global climate system and carbon cycle, we used a box modeling approach and imposed a 22–45% increase in magmatic activity (i.e., CO2 degassing) as inferred from the obtained 187Os/188Os data (Fig. 2a; Supplementary Methods). The carbon cycle model adopted here is similar to that used by a previous study63. That model includes carbon mass and isotopic fluxes from the continental crust to the atmosphere-ocean system through weathering and volcanism, and subsequent removal fluxes from atmosphere-ocean system into marine sediments. The previous model63 also incorporates the sensitivity of photosynthetic isotope effect (PIE) to changes in pCO2. To understand the Miocene carbon cycle, the following four points are modified. First, we tune our model to a condition like the present-day (Supplementary Table S10)64. This is because the previous model63 is designed to understand carbon cycles of a Phanerozoic average condition with a high pCO2 condition (pCO2 = 560 ppmv). Such a high pCO2 condition is inconsistent with Miocene background pCO2 values of ~200–500 ppmv (Fig. 1c). Second, CO2 degassing rate (Fdg) is separated into mantle degassing (Fvc; initial value of 2.5 × 1012 mol yr−1) and metamorphism (Fmc; initial value of 3.5 × 1012 mol yr−1). Fmc is a CO2 flux due to metamorphism of carbonate and organic carbon at subduction zones. Because Miocene volcanism considered here could be associated with changes in subduction processes, both Fvc and Fmc are increased at 17.0–15.8 Ma. Third, our model includes the greenhouse effect of atmospheric CO2 and temperature dependence of silicate weathering rates64. The climate sensitivity of our model is ~3 K per doubling of pCO2, which is consistent with that of IPCC 6th Assessment report65. Fourth, changes in oceanic phosphorus inventory (Mp) are calculated in the model because phosphorus exerts primary control on marine primary productivity on geological timescales66. Using this model, we investigate changes in pCO2, seawater δ13C, mean surface temperature (Ts), continental weathering rates (Fws), phosphorus inventory, and burial rates of organic carbon (Fbo) in response to Miocene magmatism (Fig. 2b–g). Because of the lack of a sharp δ13C drop associated with the MCO1,2,3,4,5,6,7 (Fig. 1b), we do not consider the greenhouse effect of CH4 released through gas hydrate dissolution. The influence of excess input of volcanic aerosols is also not considered in the model, although volcanic aerosols could affect the planetary albedo and surface temperature. This climatic forcing may only cause a short cooling event (<~102 yr) and would be overtaken by the greenhouse effect of CO2 in longer time scales67. In the following discussion, we focus on a model scenario that includes the phosphorous cycle, CO2 dependence of PIE, and Fmc variations. Sensitivity analyses excluding these processes are also conducted (Supplementary Figs. S4S6). We also test calculations using different burial rates of inorganic (Fbc) and organic carbon to examine the effects of using different initial conditions (Supplementary Fig. S7).

Fig. 2: The results of carbon cycle modeling.
figure 2

a Changes in CO2 degassing rate (Fdg = Fvc + Fmc), (b) atmospheric pCO2, (c) seawater δ13C, (d) mean surface temperature (Ts), (e) carbon flux via continental weathering (Fws), (f) seawater phosphate inventory (Mp), and (g) burial rates of organic carbon (Fbo). The shaded area shows the interval of enhanced magmatism. pCO2 and δ13C from Fig. 1 are also plotted in (b) and (c). Fluxes shown in (a), (e), (f), and (g) are normalized to pre-perturbation values (i.e., Fdg*, Fws*, Mp*, and Fbo*, respectively).

The model demonstrates that 22–45% increase in magmatic activity inferred from the Os isotope records can elevate pCO2 by ~65–140 ppmv from the initial value of 320 ppmv and raise Ts by ~0.8–1.6 K (Fig. 2b, d). As the magmatism wanes, pCO2 and temperature decrease to the pre-perturbation levels. Our model also shows a prolonged seawater δ13C excursion of ~0.4–0.7‰ during the interval of increased magmatism inferred from the Os isotope record (Fig. 2c). These trends are generally consistent with those derived from Miocene sediments, although the magnitude of the calculated variations is relatively small. Our sensitivity analyses reveal that an initial condition with a high Fbc/Fbo ratio (or low Fbo) can dampen the excursion (Supplementary Fig. S7). The absence of pCO2 dependence of PIE and Fmc variations also reduces the amplitude of δ13C excursion (Supplementary Figs. S5, S6). However, the presence of these processes is not the primary cause of the δ13C excursion in the model. On the contrary, the absence of the phosphorus cycle would not cause a clear positive δ13C excursion (Supplementary Fig. S4). Hence, the calculated δ13C positive excursion can be explained by an excess accumulation of organic carbon with low isotopic compositions due to an increase in the oceanic phosphorous inventory caused by enhanced chemical weathering under warm climatic conditions (Fig. 2d–g).

As shown in the sensitivity tests, the model results are sensitive to the initial Fbc/Fbo value and the absence/presence of pCO2 dependency of PIE and Fmc variations (Supplementary Figs. S5S7). A ~600 m shoaling of the carbonate compensation depth between ~18.5 and 16 Ma was described previously68. This shoaling is not consistent with a ~20% increase of Fbc in our model results during the enhanced magmatism. However, the model prediction is consistent with planktic foraminiferal B/Ca records suggesting an elevation of oceanic dissolved inorganic carbon during the MCO24. The variations in the carbonate compensation depth may be caused by sea level changes due to the retreat and expansion of Antarctic ice sheet23,24 rather than a different carbon cycle system. Hence, Miocene baseline carbon fluxes, including Fbc/Fbo, probably did not considerably differ from the present-day values. In addition, given that the δ13C records of the alkenone also suggest pCO2 elevation associated with the MCO14,20, inclusion of the pCO2 dependence of PIE in the model is reasonable. The sensitivity test of our model for Fmc variations suggests that an increase in this parameter is required to match the geochemical records (Supplementary Fig. S5). This is consistent with our inference that the enhanced Miocene magmatism was associated with changes in subduction processes.

Although the directions of pCO2, δ13C, and Ts changes found in our model agree with those derived from Miocene sediments3,4,5,6,7,14,15,16,17,18,19,20,22,69, the amplitude of the calculated changes is relatively small. Ts variations are considerably small if we compare to the estimate of changes in sea surface temperature of mid-latitude based on the alkenone proxy (~5–10 K)22,69. The lack of orbital forcing should be partly responsible for the muted δ13C variations in the model results. However, this process is likely related to the ice sheet expansion and increase in marine productivity that would cause low pCO2 and Ts conditions24. Instead, the mismatches between the model and geochemical data may suggest cryptic degassing associated with CRB eruption played a role in elevating pCO2 and Ts because this process is not reflected in the 187Os/188Os records. In contrast to our interpretation, the previous study assumes high climate sensitivity (~5–8 K per doubling of pCO2) to explain the paleotemperature records22. Although this possibility cannot be ruled out, constraining climate sensitivity is beyond the scope of the present study.

Despite the uncertainties in the estimates for model parameters, our modeling shows that the enhanced Miocene magmatism indicated by the Os isotope records can generally explain the long-term pCO2 and δ13C variations of the geochemical records. Our model predicts that an increase in Fbo (by ~0.4–0.7 × 1012 mol yr−1) due to an elevation of oceanic phosphate is a prerequisite to cause a positive δ13C excursion. Because the rate of phosphorous regeneration from sediments would increase under anoxic conditions70, the inclusion of changes in oceanic redox may magnify the δ13C excursion. Nevertheless, a previous study using a more complicated carbon cycle model also suggests that an increase in Fbo of 1.0 × 1012 mol yr−1 can explain the δ13C excursion during the middle Miocene, although changes in degassing rate are not considered in that study71. Large-scale deposition of organic-rich sediments in the Pacific margin at ~16–14 Ma72,73 also supports the implications made by the present study. Hence, combined with our 187Os/188Os data, our model results support the previous idea that enhanced magmatism was the trigger of the MCO5,21,22,23,24. Since the existing model results could be sensitive to several parameters, further investigations using sophisticated models are preferred to better understand Miocene climate change and its influence on the global and regional ecosystems. Those investigations could be subjected to the same forcing inferred by our 187Os/188Os data.


For Os isotope analysis, we used a H2O2–HNO3 leaching technique to derive only hydrogenous isotopic composition. After leaching, the leachates were combined with 190Os-enriched spike in sealed Carius tube and digested for 12 hr at 80 °C. Osmium was separated from the matrix through solvent extraction and microdistillation. The isotopic composition was measured using a negative thermal ionization mass spectrometry at JAMSTEC. A carbon cycle model used in the present study follows that of Kump and Arthur63, but includes greenhouse effect of atmospheric CO2, temperature dependence of silicate weathering rate, and phosphorous cycle. Full descriptions of the analysis and model, Os isotope data, and additional references are shown in Supplementary Information.