Supplementary Figure 1. Stability constants of metal monohydroxides. The log K values are summarized according to the atomic number of each element

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Supplementary Figure 1. Stability constants of metal monohydroxides. The log K values are summarized according to the atomic number of each element as determined in a previous study 1. The log K value is the logarithm of the equilibrium constant for the following reaction (M indicates a metal): M n+ + OH - M(OH) n-1+ (K = [M(OH) n-1+ ]/[M n+ ][OH - ]). The atomic number of listed elements increases left to right.

Absorbance Absorbance Absorbance Absorbance a.12.8 OH b.2.16.12 OH.4.8.4 c 6 1,1 1,6 2,1 2,6 3,1 3,6 6 1,1 1,6 2,1 2,6 3,1 3,6.12 Wavenumber (cm -1 ) Wavenumber (cm -1 ) d.2.8 OH.16.12 OH.4.8.4 6 1,1 1,6 2,1 2,6 3,1 3,6 6 1,1 1,6 2,1 2,6 3,1 Wavenumber (cm -1 ) Wavenumber (cm -1 ) 3,6 Supplementary Figure 2. FT-IR spectra of hydroxylated Ln 2 O 3 nanoparticles. FT-IR spectra of (a) hydro-dy 2 O 3 and (c) hydro-nd 2 O 3 nanoparticles, which are used as the screening targets for biopanning in Supplementary Figure 3, and (b) Dy(OH) 3 and (d) Nd(OH) 3, which are used for the control measurements. The peaks observed at 2,8 3,6 cm -1 (bracket) indicate that hydroxyl groups are present on the particle surface. 2

Phage titer (pfu ml -1 ) Phage titer (pfu ml -1 ) Phage titer (pfu ml -1 ) Phage titer (pfu ml -1 ) a 1.E+9 b 1.E+9 1.E+8 1.E+8 1.E+7 1.E+7 1.E+6 1.E+6 1.E+5 Wild 1st 2nd 3rd 4th 5th Rounds of biopanning 1.E+5 Wild NC1 Lamp-1 Lamp-2 Phage clone c 4.E+7 d 5.E+7 3.E+7 4.E+7 2.E+7 1.E+7 3.E+7 2.E+7 1.E+7 1.E+5 Wild 1st 2nd 3rd 4th 5th Rounds of biopanning 1.E+5 Wild Lamp-3 Phage clone Supplementary Figure 3. Screening of hydro-ln 2 O 3 binding peptides from peptide libraries. The enrichment of (a) hydro-dy 2 O 3 and (c) hydro-nd 2 O 3 nanoparticle binding phages by five rounds of biopanning analysed by a titering assay. The binding ability of isolated single phages (NC1, Lamp-1, -2, and -3) with (b) hydro-dy 2 O 3 or (d) hydro-nd 2 O 3. The wild type phage was used as a control for all experiments. NC1 phage was isolated by screening against Dy 2 O 3 and has little consensus with the Lamp sequence. Error bars represent the standard deviation of two experiments. The amino acid sequences of the selected clones are summarized in Supplementary Table 1. 3

Absorbance at 6 nm a.3.25.2.15.1 Dy 3+ conc. mm.25 mm.5 mm 1 mm 2.5 mm b V : A(6 nm) S -1.14.12.1.8.6 R 2 =.994 V max =.18 ±.1 S -1 k = 2.62 mm n = 1.5 5 1 Time (s) 5 mm.4.2 1 2 3 4 5 Dy 3+ conc. (mm) Supplementary Figure 4. Turbidity changes of the mineralization media. (a) The optical density of the mineralization media at 6 nm was recorded using a spectrophotometer. The Lamp-1 concentration was 1 µm in all experiments. Each curve represents the cumulative curve of three experiments. (b) The increasing speed of turbidity (V) at early stage (between 3 and 4 s after the measurement in (a)) is plotted as a function of Dy 3+ concentration. The red line indicates the fitting curve analysed by the Hill equation: V = V max x/(k + x), where V max is the maximum speed of increasing turbidity, and the k is half of the concentration at which the reaction speed reached V max, and n is the stoichiometry (fixed to 1). 4

Supplementary Figure 5. Optical images of Dy 3+ mineralization with Lamp-1 in various conditions. The Lamp-1 concentration was 1 µm in all experiments, and 5 mm of (a) MES or (b) HEPES buffer was used as the solvent. Dy(NO 3 ) 3, Dy(CH 3 COO) 3, and DyCl 3 (3 mm) were used as the source of Dy 3+. (c and d) Optical images of Dy 3+ mineralization at different reaction times. Lamp-1 (1 µm) with Dy(NO 3 ) 3 (3 mm) was incubated for 25 h in (c) MES (5 mm, ph 6.1) or (d) HEPES buffer (5 mm, ph 6.8). 5

a b 15 nm c Dy 3+ Dy 3+ Dy 3+ Dy 3+ Nd 3+ Nd 3+ Lamp-2 LBT3 R E-1 No peptide Lamp-3 No peptide C O S Dy N Dy Dy Si Dy Dy d 1 2 3 4 5 6 7 8 9 1 ev C O S N Nd Nd Nd 1 2 3 4 5 6 7 8 ev Supplementary Figure 6. Mineralization ability of Lamp-2 and Lamp-3. (a) Dy 3+ or (b) Nd 3+ was mixed with synthetic peptides in weak acidic buffer conditions (5 mm MES, ph 6.1). SEM (left) and EDX (right) images of the generated precipitate for (c) Lamp-2 and (d) Lamp-3. The red squares indicate the region for EDX analysis. Scale bars: 3 µm. 6

Absorbance at 215 nm Absorbance at 215 nm a b Lamp-1 Lamp-2 precipitate precipitate 1 2 3 4 5 1 2 3 4 5 Time (min) Time (min) Supplementary Figure 7. The precipitates containing Lamp. The precipitated particles generated by the reaction between Dy 3+ and (a) Lamp-1 or (b) Lamp-2 were dissolved in acidic solution (~ph 1.) and analysed by RP-HPLC. The upper panels show the peptide only and the lower panels the dissolved precipitate. 7

Reacted Ln ion conc. (µm) Reacted Lamp-3 conc. (µm) Reacted Ln ion conc. (µm) Reacted Lamp-2 conc. (µm) Reacted Lamp-1 conc. (µm) a 3 25 2 15 1 5 b 2 La Ce Nd Sm Eu Gd Tb Dy Ho Yb Lu c 3 15 25 2 1 15 5 1 5 d 2 La Dy Lu e 3 La Dy Lu 15 25 2 1 15 5 1 5 La Dy Lu Supplementary Figure 8. Mineralization selectivity of Lamp for Ln 3+. After mixing 3 µm of (a) Lamp-1, (b, c) Lamp-2, and (d, e) Lamp-3 with Ln 3+ (3 mm) at room temperature for 2 h, the generated particles were separated by centrifugation. The precipitated (a, c, e) peptides and (b, d) Ln 3+ were determined by using a spectrophotometer and ICP-OES, respectively. All error bars represent the standard deviation of three experiments. La Dy Lu 8

Supplementary Figure 9. XAFS measurements of generated precipitates. (a) Normalized Dy L 3 -edge XANES spectra of the precipitate generated with Lamp-2 (yellow). The insert shows expanded spectra of the region in the red square. Dy(OH) 3 and Dy 2 O 3 particles were used as a control (blue and black). (b) Fourier transform of the Dy L 3 -edge EXAFS spectra of the precipitates with Lamp-1 (red) and Lamp-2 (yellow). The radial distance is not corrected for phase shifts. (c) Normalized Nd L 3 -edge XANES spectra of the precipitate generated with Lamp- 3 (blue). The insert shows the expanded spectra of the region in the red square. Nd(OH) 3 and Nd 2 O 3 particles were used as a control (red and black). (d) Fourier transform of the Nd L 3 -edge EXAFS spectra of the precipitates with Lamp-3. 9

ph 6.5 6.2 Lamp-2 Lamp-3 5.9 5.6 5.3 5, Dy 3+ (mm) 3 3 3 3 Peptide (µm) - 1 2 3 Supplementary Figure 1. Changes in the ph of the mineralization media containing Dy 3+ at different peptide concentrations. Lamp and Dy(NO 3 ) 3 were each dissolved in.1 mm MES buffer and the ph was adjusted to 6. 6.3. The ph value (vertical axis) was measured after mixing these two solutions. All error bars represent the standard deviation of two experiments. 1

Dy 3+ conc. (µm ) C5 S11 G1 E12 C17 L6 G2,3 S4 D9 G8 D14 V1 L16 L13 S18 W7 F15.5 D9 1. 2. C5 S11 E12 C17 L6 G2,3 G1 S4 G8 D14 V1 L16 L13 S18 W7 F15 8.4 8.3 8.2 8.1 8. 7.9 7.8 Chemical Shift (ppm) Supplementary Figure 11. NH chemical shift broadening of Lamp-1 with increasing amounts of Dy 3+. The assignments in black represent the residues that can be clearly recognized as a peak. The assignments in red show peaks largely broadened by the paramagnetic effect of Dy 3+. 11

1H Chemical Shift (ppm) 1H Chemical Shift (ppm) a 3.9 S11H-HB3 S11H-HB2 S4H-HB G8H-HA3 G8H-HA2 S18H-HB 4.1 G2H-HA G1H-HA G3H-HA V1H-HA L6H-HA L13H-HA 4.3 S11H-HA E12H-HA S4H-HA L16H-HA S18H-HA 4.5 C5H-HA D9H-HA D14H-HA F15H-HA b 2. 2.5 3. D9H-HB3 D9H-HB2 4.7 E12H-HB3 E12H-HB2 V1H-HB E12H-HG D14H-HB3 D14H-HB2 C17H-HB3 C17H-HB2 3.3 8.3 8.2 8.1 8. 1H Chemical Shift (ppm) C17H-HA W7H-HA 8.4 8.2 8. 7.8 1H Chemical Shift (ppm) 4. c 3.8 3.6 3.4 3.2 3. 4.2 S18HB3-HA Biotin Biotin d S11HB3-HA 4.4 F15HA-HB3 S4HB3-HA F15HA-HB2 S4HB2-HA Biotin Biotin S11HB2-HA 4.6 W7HA-HB3 W7HA-HB2 C5HA-HB3 C5HA-HB2 4.8 C17HB2-HA C17HB3-HA 4.2 4.4 4.6 Biotin Biotin D14HA-HB3 D14HA-HB2 D9HA-HB2 D9HA-HB3 E12HA-HG V1HA-HB E12HA-HB2 E12HA-HB3 2.8 2.6 2.4 2.2 2. 1.8 1H Chemical Shift (ppm) Supplementary Figure 12. Overlaid TOCSY spectra of Lamp-1 free (red) and bound to.5 µm Dy 3+ (blue). Apparent spectral perturbations are observed in the (a) NH-Hα and (b d) Hαside chain regions. The cross peaks for the side chain of Asp9, Asp14, and Glu12 are severely affected, indicating that these residues contact Dy 3+ first. 12

ΔNH Shift (ppm) Δshift (ppm) a.25.2 Hα NH.15.1.5 - - - G1 G2 G3 S4 C5 L6 W7 G8 D9 V1 S11 E12 L13 D14 F15 L16 C17 S18 Amino acid residues b.1.8.6.4.2 R 2 =.95 Shift max =.11 ±.8 KD = 58.6E-6 ± 14.5.E-6 n = 1. 5 1 15 2 25 3 35 La 3+ conc. (µm) Supplementary Figure 13. The Lamp-1 peak shifts induced by La 3+ titration. (a) The bars represent the absolute peak shift change ( Δshift ) calculated by subtracting the chemical shifts without La 3+ from those following titration with 3 µm of La 3+. - represents residues that could not be assigned after titration with 3 µm of La 3+. (b) Calculation of the binding affinity (K D ) of Lamp-1 with La 3+. The NH shift of Val1 versus La 3+ concentration was plotted and the curve was fitted to a one-site binding model: ΔNH shift = NH shift max x/(k D + x). 13

ph ph a Dy 3+ A.a. 6.4 6.2 6 5.8 5.6 5.4 5.2 5. (mm) (µm) - 3 3 3 3 3 6 1,2 Al a Ser Val Leu Met Phe Trp Glu Asp b Nd 3+ A.a. 6.4 6.2 6. 5.8 5.6 5.4 5.2 5. (mm) (µm) - 3 3 3 3 3 6 1,2 Al a Ser Val Leu Met Phe Trp Glu Asp Supplementary Figure 14. Changes in the ph of the media containing Ln 3+ at different amino acid concentrations. Each amino acid and Ln(NO 3 ) 3 were dissolved in.1 mm MES buffer and the ph was adjusted to 6. 6.2. The ph value (vertical axis) was measured after mixing the amino acid solutions with (a) Dy 3+ and (b) Nd 3+. All error bars represent the standard deviation (n = 4). 14

kcal mol -1 of injectant kcal mol -1 of injectant a µcal s -1.4.2.1. b µcal s -1.4.3.2 -.1.1 -.2..2 2..15 1.5.1 1..5.5 c kcal mol -1 of injectant µcal s -1. 2. 1.5 1..5..8.6.4.2. 5 1 15 2 25 Molar Ratio -2 2 4 6 8 1 12 14 16 Molar Ratio d µcal s -1..5 1. 1.5 2. 2.5 Molar Ratio.4.3.2.1 -.1 2 4 6 8 1 12 Time (minute) Supplementary Figure 15. Thermodynamic analysis of the mineralization reaction. ITC experiments for the reaction of Dy 3+ with (a) Lamp-2 and (b) LBT3, and (c) Nd 3+ with Lamp-3 in MES buffer. The upper panels show the calorimetric titration profile. The lower panels show a least squares fit of the data to the heat absorbed/mol of titrant versus the ratio of the total Dy 3+ or Nd 3+ concentration to the total peptide concentration. The solid line is the best fit of the data to a single binding site model using a non-linear least squares fit. The thermodynamic parameters are summarized in Supplementary Table 4. (d) Typical calorimetric titration profile of Dy 3+ (5 mm) with MES buffer. 15

Supplementary Figure 16. Analysis of the protonation enthalpy for the reaction of Dy 3+ with Lamp-1. (a) ITC experiments for the reaction of Dy 3+ with Lamp-1 in Bis-Tris buffer. The upper panel shows the calorimetric titration profile. The lower panel shows a least squares fit of the data to the heat absorbed/mol of titrant versus the ratio of the total Dy 3+ concentration to the total peptide concentration. The solid line is the best fit of the data to a single binding site model using a non-linear least squares fit. The thermodynamic parameters are summarized in Supplementary Table 4. (b) Plot of ΔH obs (observed enthalpy change) versus ΔH i (ionization enthalpy change) for the interaction of Dy 3+ with Lamp-1 in MES or Bis-Tris buffer. 16

Precipitated Dy 3+ (nmol) 1,4 1,2 1, Dy/Lamp-1 = 1.62 8 6 Dy/Lamp-1 = 1.87 4 2 1 2 3 4 5 6 Precipitated Lamp-1 (nmol) Supplementary Figure 17. Reaction stoichiometry of Dy 3+ and Lamp-1 in synthetic seawater conditions. The amount of precipitated Dy 3+ was plotted as a function of the amount of precipitated Lamp-1. The value displayed under each point indicates the reaction stoichiometry calculated using the following equation: precipitated Dy 3+ /precipitated Lamp-1. 17

Supplementary Figure 18. Accumulation of Dy on the sepharose resin. SEM (upper panel) and EDX (lower panel) analyses of sepharose resins conjugated with (a, b, e h) Lamp-1 and (c and d) control samples. (e, g, i, and k) Captured Dy was eluted with acetic buffer (5 mm) at ph 4., (f, h, j, and l) and the sepharose resin was recycled. Scale bars: 1 nm. 18

1 45 9 1 atgtcccctatactaggttattggaaaattaagggccttgtgcaacccactcgacttcttttggaatatcttgaagaaaaatatgaagag M S P I L G Y W K I K G L V Q P T R L L L E Y L E E K Y E E 3 91 135 18 31 61 91 121 151 181 catttgtatgagcgcgatgaaggtgataaatggcgaaacaaaaagtttgaattgggtttggagtttcccaatcttccttattatattgat H L Y E R D E G D K W R N K K F E L G L E F P N L P Y Y I D 181 225 27 ggtgatgttaaattaacacagtctatggccatcatacgttatatagctgacaagcacaacatgttgggtggttgtccaaaagagcgtgca G D V K L T Q S M A I I R Y I A D K H N M L G G C P K E R A 271 315 36 gagatttcaatgcttgaaggagcggttttggatattagatacggtgtttcgagaattgcatatagtaaagactttgaaactctcaaagtt E I S M L E G A V L D I R Y G V S R I A Y S K D F E T L K V 361 45 45 gattttcttagcaagctacctgaaatgctgaaaatgttcgaagatcgtttatgtcataaaacatatttaaatggtgatcatgtaacccat D F L S K L P E M L K M F E D R L C H K T Y L N G D H V T H 451 495 54 cctgacttcatgttgtatgacgctcttgatgttgttttatacatggacccaatgtgcctggatgcgttcccaaaattagtttgttttaaa P D F M L Y D A L D V V L Y M D P M C L D A F P K L V C F K 541 585 63 aaacgtattgaagctatcccacaaattgataagtacttgaaatccagcaagtatatagcatggcctttgcagggctggcaagccacgttt K R I E A I P Q I D K Y L K S S K Y I A W P L Q G W Q A T F 6 9 12 15 18 21 631 675 72 211 ggtggtggcgaccatcctccaaaatcggatggttcaactagttcaggtggaggttcgtgtttgtggggtgatgttagtgagctggatttt G G G D H P P K S D G S T S S G G G S C L W G D V S E L D F 24 241 721 732 ctgtgtagctga L C S * 244 Supplementary Figure 19. DNA (upper) and amino acid (lower) sequence of GST-Lamp-1. The underlined amino acid sequences show GST (blue) and Lamp-1 (green). 19

Absorbance at 215 nm a GST GST-Lamp-1 b GST GST-Lamp-1 M 1 2 3 4 M 1 2 3 4 5 k 5 k 37 k 37 k 25 k 2 k 25 k 2 k 15 k 1 k 15 k 1 k c d GST trimer Dimer GST-Lamp-1 MW Marker 67 k 158 k 44 k 17 k 1.35 k 1 2 3 4 5 6 7 8 GST GST-Lamp-1 Supplementary Figure 2. The function of genetically engineered GST-Lamp-1. (a) SDS- PAGE and (b) Western blot analysis of the recombinant proteins before (lanes 1, 3) and after (lanes 2, 4) the purification. (c) The purified proteins were analysed by gel permeation chromatography using a Superdex2 1/3 column (GE Healthcare). (d) Optical image of Dy 3+ mineralization by GST-Lamp-1 just after the reaction at room temperature. Each protein (1 µm) was incubated with Dy(NO 3 ) 3 (1 mm) in HEPES buffer (5 mm, ph 6.8) containing 15 mm NaCl. 2

Supplementary Table 1. The peptide library and isolated peptide sequences Library Diversity Concentration Peptide Sequence Frequency Type (pfu) (pfu/ml) SCX9CS 3.76E+7 8.11E+11 - - - SCX1CS 6.78E+6 9.56E+11 Lamp-2 SCLYPSWSDYAFCS 3/24 SCX11CS 1.25E+7 5.E+11 Lamp-1 SCLWGDVSELDFLCS 2/24 SCX12CS 1.56E+6 9.E+11 Lamp-3 SCPVWFSDVGDFMVCS 11/88 The T7 phage libraries displaying SCX 9 12 CS random peptides, where X represents the randomized amino acids, were constructed. T7 phage displays an average of 5 15 copies of the peptide on the phage surface. Two Cys residues cause the formation of an intra-disulfide bond. Supplementary Table 2. Characteristics of the synthetic peptides Peptide Sequence Length pi Other Lamp-1 GGGSCLWGDVSELDFLCS 18 aa 3.38 cyclic Lamp-2 GGGSCLYPSWSDYAFCS 17 aa 3.75 cyclic Lamp-3 GGGSCPVWFSDVGDFMVCS 19 aa 3.49 cyclic LBT3 GGGSFIDTNNDGWIEGDELLA 21 aa 3.2 linear RE-1 GGGSACTARSPWICG 15 aa 8.23 cyclic NC1 GGGSCVKGEFFRSISTCS 18 aa 8.23 cyclic NC1: a peptide with little consensus with Lamp. pi: isoelectric point. 21

Supplementary Table 3. Binding strength of synthetic peptides with hydroxylated Ln 2 O 3 Lamp-1 Lamp-2 Lamp-3 LBT3 RE-1 EC 5 (µm) Hydroxylated Dy 2 O 3 Hydroxylated Nd 2 O 3.1 ±. - 1.2 ±.3 - -.6 ±.2 17.5 ± 6.4-24.2 ± 12. 65.5 ± 18.5 N-terminally biotinylated peptides were used for detection. The EC 5 values were obtained from triplicate measurements. Supplementary Table 4. Thermodynamic parameters of the peptide and Ln 3+ reaction Peptide Target H (kcal/mol) -T S (kcal/mol) G (kcal/mol) K (x1 4 M -1 ) N Lamp-1 a Dy 3+ 7.34 ±.5-12.79 ±.6-5.73 ±.1 1.59 ±.4 1 d Lamp-2 a Dy 3+ 1.35 ±.4-5.63 ±.6-4.42 ±.6.17 ±.1 1 d LBT3 a Dy 3+ 1.81 ±.4-1.91 ±.27-9.11 ±.27 477 ± 174 1.8 ±.1 RE-1 a Dy 3+ n.d n.d n.d n.d n.d Lamp-3 a Nd 3+ 2.41 ±.9-7.48 ±.11-5.8 ±.6.52 ±.5 1 d Lamp-1 b Dy 3+.52 ±.8-6.92 ±.36-6.12 ±.58 7.34 ± 2.52 1 d Lamp-1 c Dy 3+ 14.41 2.14-5.73 1.59 1 d ΔG was calculated using the equation ΔG = -RT ln K. -TΔS was calculated using the equation ΔG = ΔH - TΔS. R: gas constant. T: absolute temperature. N: reaction stoichiometry. n.d.: not detected (below the detection limit). a MES buffer was used for ph regulation. b Bis-Tris buffer was used for ph regulation. c In consideration of the protonation enthalpy, the thermodynamic parameters were recalculated based on the data using MES buffer. d N is assumed to be 1. 22

Supplementary References 1. Smith, M.R., Martell, E.A. & Eds. Critical Stability Constants Vol. 4 (Springer US, 1976). 23