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Rational design and synthesis of postfunctionalizable peptide foldamers as helical templates Takashi Misawa, Yasunari Kanda, and Yosuke Demizu Bioconjugate Chem., Just Accepted Manuscript • DOI: 10.1021/acs.bioconjchem.7b00621 • Publication Date (Web): 14 Nov 2017 Downloaded from http://pubs.acs.org on November 17, 2017

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Bioconjugate Chemistry

Rational design and synthesis of post-functionalizable peptide foldamers as helical templates ,†

Takashi Misawa,* Yasunari Kanda,‡ and Yosuke Demizu*

†

,†

Division of Organic Chemistry, National Institute of Health Sciences, Tokyo 158-8501, Japan

‡

Division of Pharmacology, National Institute of Health Sciences, Tokyo 158-8501, Japan

[email protected], [email protected]

* To whom correspondence should be addressed. Tel: + 81-3-3700-1141. Fax: + 81-3-3707-6950.

†

‡

Division of Organic Chemistry, National Institute of Health Sciences

Division of Pharmacology, National Institute of Health Sciences

ACS Paragon Plus Environment

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Graphical Abstract

Abstract

In this study, we herein developed post-functionalizable helical peptides composed of Leu, Aib, and Azl residues. We show that the synthesized peptides 1 and 2 form helical structures, and may be modified using specific side chain or several functional groups by the click reaction without influencing their secondary structures.

Introduction

Helical peptides are major secondary structures in proteins that regulate human biological functions by interacting with other proteins or DNA/RNA.

1-2

Thus, helical structures in proteins and synthetic

bioactive peptides play pivotal roles in biochemistry and chemistry. Methods that regulate the helical structures of peptides are required in order to develop well-defined functional peptides. Helix-stabilized peptides, also called foldamers3-5, may be applied as cell-penetrating peptides (CPP), protein-protein ACS Paragon Plus Environment

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interaction inhibitors6-8, and organocatalysts9-12. Several methods that regulate peptide secondary structures have been developed to date. 13-21 The introduction of unnatural amino acids, such as cyclized β-amino acids14-19 or α,α-disubstituted amino acid (dAAs) 20, and the stapling of a side chain21-22 into a peptide sequence have been shown to stabilize helical structures and enhance the resistance to digestive enzymes.23-25 Furthermore, the stabilization of helical structures enhances their biological functions and cell membrane permeability.8 We previously developed several functional helical peptides by introducing α-aminoisobutyric acid (Aib), which is a representative dAA residue, into the peptide sequences.26-29 We revealed that the helical structures of peptides may be controlled by the combination of the natural amino acids, leucine (Leu) and Aib residues. We reported that homochiral L-peptides [Boc-(L-Leu-L-Leu-Aib)3-OMe] (A) formed helical structures in solution and in the crystalline state. On the other hand, Tanaka et al. reported that the substitution of Aib residues for the cyclic dAA residue Ac5cOM also stabilized the helical structures, and the resulting peptides were capable of catalyzing the highly enantioselective epoxidation of α,β-unsaturated ketones.30 In case of amphipathic oligopeptides containing a combination of a cationic arginine (Arg) and achiral Aib residues, the peptide FAM-(LArg-L-Arg-Aib)3-NH2 (B; FAM; 5(6)-carboxyfluorescein) formed a stable helix and exhibited cellpenetrating abilities.29 Furthermore, we recently designed and synthesized a novel CPP containing a cyclic dΑΑ bearing side chain guanidino groups (ApiC2Gu), and demonstrated that the peptide containing ApiC2Gu also formed a stable helical structure and showed greater cell membrane permeability than that containing the Aib residues.31 These findings suggest that a helical structure is favorable for the


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development of peptide-based drugs. On the other hand, the appropriate choice of amino acid residues and positioning of side chains are necessary for the exertion of biological activities. Therefore, the regulation of secondary structures and appropriate choice of amino acids need to be mutually compatible for the development of peptide-based drugs, which is difficult to achieve, time-consuming, and effort-intensive. In order to overcome this issue, we speculated that a method that introduces several side chains or functional groups into a helical template peptide may be useful in fields such as peptidebased medicinal chemistry. Zimmerman et al. recently reported a peptide-based helical polymer bearing azido groups on its side chains and performed post-modifications on the polymer in order to randomly introduce guanidino groups and bioactive ligands via copper(Ⅰ)-catalyzed alkyne-azide cycloaddition (CuAAC), resulting in the effective internalization of the bioactive ligands and the exertion of biological activity.32 Their findings demonstrated that post-modification to the helical template is a promising method for the development of functional peptides. However, their helical scaffolds used more than 50 residues of natural amino acids to form a helical structure. Therefore, post-modifications at each azido group with a guanidino group or ligands randomly occurred and the resulting peptides were obtained as mixtures containing different ratios of guanidino groups to ligands.

We herein designed two types of helical template peptides [Boc-(L-Azl-L-Azl-Aib)3-OMe] (1) and [Boc(L-Leu-L-Azl-Aib)3-OMe] (2) (Azl: azidolysine, has an azido group at the ε position of lysine) for functionalization by post-modifications using CuAAC (Figure 1). We expected these peptides to be uniformly modified andform stable helical structures.


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Figure. 1 Chemical structures of helical functional peptides A and B containing dAA residues, and the post-functionalizable peptides designed in this study.

Results and discussion

Peptides [Boc-(L-Azl-L-Azl-Aib)3-OMe (1)] and [Boc-(L-Leu-L-Azl-Aib)3-OMe (2)] were synthesized by conventional solution-phase methods using 1-Ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) and 1-Hydroxybenzotriazole (HOBt) as the coupling reagent as shown in Scheme 1. Alkaline hydrolysis of tripeptide 5 afforded 6, whereas acidic deprotection of the Boc group in tripeptide 5 furnished 7. Tripeptide 6 was coupled with tripeptide 7 to give hexapeptide 8. After acidic deprotection of Boc in 8, coupling with 6 was performed to obtain the target nonapeptide 1. Hexapeptide 12 and nonapeptide 2 were prepared in a similar manner from tripeptide 9. ACS Paragon Plus Environment

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Scheme 1. Synthesis of [Boc-(L-Azl-L-Azl-Aib)3-OMe] (1) and [Boc-(L-Leu-L-Azl-Aib)3-OMe] (2).

We initially investigated the preferred secondary structure of the synthesized peptides using CD spectral analysis, which was carried out for a peptide concentration of 50 µM in 2,2,2-trifluoroethanol (TFE) (Figure 2). The CD spectra of the synthesized peptides 1 and 2 exhibited negative maxima at approximately 208 nm and 222 nm, and the ellipticity ratio of R ([θ]222/[θ]208) was 0.47. These results indicated that peptides 1 and 2 formed right-handed 310-helical structures33, whereas the shortened peptides 5, 8, 9, and 12 had random structures (Figure 2). Furthermore, there were no significant differences between the CD specta of peptides 1 and 2.


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Figure 2. CD spectra of peptides (a) Boc-(L-Azl-L-Azl-Aib)n-OMe (5: n = 1, 8: n = 2, 1: n = 3) and (b) Boc-(L-Leu-L-Azl-Aib)n-OMe (9: n = 1, 12: n = 2, 2: n = 3) in 2,2,2-trifluoroethanol (TFE). Peptide concentration: 50 µM.

We then investigated whether specific side chains or functional groups could be introduced into the synthesized peptides using CuAAC. In order to prove our hypothesis, we focused on CPPs, which generally contain cationic Arg residues. Cell-penetrating abilities are dependent on the interactions between the guanidino groups of the Arg residues and the acidic groups existing in the cell membranes. Therefore, we previously developed the helical CPP FAM-βAla-(L-Arg-L-Arg-Aib)3-NH2 (FAM-13) and ACS Paragon Plus Environment

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demonstrated that its helical structure is capable of enhancing cell membrane permeability. We then designed FAM-βAla-(L-Azl-L-Azl-Aib)3-NH2 (FAM-1), inserted βAla as a spacer following FAM-1, and synthesized FAM-1 using a general Fmoc-based solid-phase peptide synthesis. We also designed peptide FAM-14 [Sequence: FAM-βAla-(L-Azlx-L-Azlx-Aib)3-NH2], which is modified with propargyl guanidine using CuAAC, as a mimetic of FAM-13. Post-modifications to the synthesized peptides were performed using 4 equivalent CuAAC per azido of propargyl guanidine, 20 equivalent of CuSO4, and ascorbic acid to obtain FAM-14 (Scheme 2). On the other hand, it is well known that the PEG moiety enhances the retention and permeability in cancer tissues (ERP effects), and the reaction of the maleimide moiety with thiol groups is broadly utilized for bioconjugation and labeling of biomolecules including proteins and peptides. Therefore, we also demonstrated the introduction of functional groups into FAM-1 by CuAAC using the PEG (FAM-15) and maleimide (FAM-16) moiety. The modified peptide was characterized by HPLC and LC-MS analyses.


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Scheme 2. Functionalization of helical template peptide FAM-1 to FAM-14 (X = Gu), FAM-15 (X = PEG) and FAM-16 (X = mal) using CuAAC.

We subsequently evaluated the effects of post-modifications to the peptides on their secondary structures using CD spectral analysis and evaluated cell membrane permeability using flow cytometry analysis. The CD spectral analysis was performed in a 1:1 solution of 20 mM phosphate buffer and methanol, and the results showed that the synthesized peptide FAM-14, FAM-15, and FAM-16 also formed an α-helical structure similar to FAM-13 and FAM-1 (Figure 3; the ellipticity ratio of R ([θ]222/[θ]208) is 0.75). These results demonstrated that the helical template peptide (FAM-1) formed a helical structure via the effects of Aib residues, and that post-modifications did not affect its secondary structure. The CD spectra in Figures 2 and 3 showed the difference in the secondary structure between peptide 1 (310-helix) and FAM-1 (α-helix), although they have a similar sequence. We speculated that the differences of their structures are due to both solvent effects and the difference in their terminal protecting groups.

We also assessed the cell membrane permeability of the synthesized peptides against HeLa cells. Figure 4 shows the intracellular uptake of peptides FAM-13 and FAM-14; the intracellular uptake of the modified peptide FAM-14 was similar to that of FAM-13. A comparison of the cell permeabilities of FAM-13 and FAM-14 revealed that the modified guanidine group of FAM-14 functions in the same


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manner as the natural Arg residue. These results suggest that FAM-1 functions as a novel helical scaffold and may be functionalized by post-modifications.

Figure 3. CD spectra of synthesized peptides (a) FAM-1, FAM-13, and FAM-14, (b) FAM-1, FAM-15 and FAM-16 in a 1:1 solution of 20 mM phosphate buffer and methanol. Peptide concentration; 50 µM.


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250

Mean Fluorescence Intensity

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200

150

100

50

0

1

FAM-13

2

FAM-14

Figure 4. Intracellular uptake of FAM-13 and FAM-14 (1 µM) into HeLa cells, as determined using flow cytometry. Data are expressed as means of ±S.E. of three independent experiments.

Conclusion

In conclusion, we herein designed and synthesized novel helical template peptides 1 and 2 composed of Leu, Aib, and Azl residues. We also demonstrated that 1 formed a helical structure be modified by CuAAC, resulting in the peptide exerting its cell membrane permeability without any effects on the helical structure. We also performed post-modification to [FAM-βAla-(L-Leu-L-Azl-Aib)3-NH2] (FAM-2) and confirmed that the resulting peptide [FAM-βAla-(L-Leu-L-Azlx-Aib)3-NH2] (FAM-17: X = Gu) retained its helical structure (Figure S1). We previously developed CPPs31, organocatalysts30 (as shown in Figure 1), and microbial peptides34 consisting of Lys and Aib residues. These functionalized ACS Paragon Plus Environment

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peptides are based on the same sequence H-(X-X-Aib)3-NH2, (X: Arg, Leu, Lys); therefore, our simple helical template peptide may be widely functionalized for applications in organocatalysis and tuning microbial activity.

Experimental Procedure General information Chemicals were purchased from Sigma-Aldrich Co. LLC, Kanto Chemicals Co. Inc., Tokyo Chemical Industry Co. Ltd., Wako Pure Chemical Industries Ltd., Watanabe Chemical Industries, Ltd., and used without further purification. Reactions were monitored by thin-layer chromatography (TLC, Merck silica gel 60F254) plate. Bands were visualized using UV light or appropriate reagents followed by heating. Column chromatography was performed with silica gel (spherical, neutral) purchased from Kanto Chemical. The microwave reactions were carried out using Biotage Initiator.

1

H and 13C NMR

spectra were obtained on a Varian AS 400 Mercury spectrometer (400 MHz for 1H and 100 MHz for 13

C). FT-IR spectra were recorded on a JASCO FT/IR-4100 spectrometer at 1 cm—1 resolution, with an

average of 128 scans used for the solution (CDCl3) method and a 0.1 mm path length for NaCl cells. Chemical shifts are expressed as ppm downfield from a solvent residual peak or internal standard tetramethylsilane (TMS). Mass spectra were obtained on a Shimadzu IT-TOF MS equipped with an electrospray ionization source.


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Synthesis of the peptides. The peptide synthesis was carried out according to a stepwise method, in which EDC and HOBt were used as coupling reagents. All compounds were purified by column chromatography on silica gel.

Boc-(L-Azl-L-Azl-Aib)-OMe (5): White solid; [α]24D = -2.429 (c 0.5, CDCl3); IR (CDCl3, cm-1): 3455, 3487, 3310, 2935, 2100, 1665, 1529; 1H NMR (400MHz, CDCl3): δ 6.67 (s, 1H), 6.64 (d, J = 8.0 Hz, 1H), 5.00 (d, J = 8.0 Hz, 1H), 4.39-4.34 (m, 1H), 4.07-4.05 (m, 1H), 3.73 (s, 3H), 3.29-3.25 (m, 4H), 1.91-1.80 (m, 3H), 1.69-1.37 (m, 24H) ;

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C NMR (100MHz, CDCl3): δ 174.6, 171.9, 170.1, 155.8,

80.5, 77.3, 77.2, 77.0, 76.7, 56.5, 54.7, 52.8, 52.6, 51.1, 31.7, 31.4, 28.7, 28.3, 24.7, 22.8, 22.4; [HRESI(+)] m/z calcd for C22H39N9O6Na [M+Na]+ 548.2916; found 548.2899.

Boc-(L-Azl-L-Azl-Aib)2-OMe (8): White foam; [α]24D = -0.980 (c 0.5, CDCl3); IR (CDCl3, cm-1): 3464, 3401, 2940, 2100, 1703, 1500; 1H NMR (400MHz, CDCl3): δ 7.60 (s, 1H), 7.50 (d, J = 8.0 Hz, 1H), 7.26 (m, 1H), 7.12 (s, 1H), 6.71 (s, 1H), 5.17 (s, 1H), 4.34-4.30 (m, 1H), 4.15-4.12 (m, 1H), 4.02-3.98 (m, 1H), 3.92-3.89 (m, 1H), 3.68 (s, 3H), 3.38-3.21 (m, 8H), 2.05-1.99 (m, 2H), 1.91-1.24 (m, 33H); 13C NMR (100MHz, CDCl3): δ 175.9, 175.1, 173.6, 172.2, 171.9, 171.5, 156.8, 82.0, 77.3, 77.2, 77.0, 76.7, 57.2, 56.9, 55.8, 55.7, 55.5, 53.3, 52.2, 51.4, 51.3, 51.0, 30.8, 30.3, 30.2, 30.1, 28.5, 28.4, 28.2, 27.3,


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25.3, 24.8, 23.6, 23.5, 23.3, 23.0, 22.6; [HR-ESI(+)] m/z calcd for C38H66N18O9Na [M+Na]+ 941.5152; found 941.5110.

Boc-(L-Azl-L-Azl-Aib)3-OMe (1): White foam; [α]24D = -0.241 (c 0.5, CDCl3); IR (CDCl3, cm-1): 3312, 2939, 2100, 1653, 1533; 1H NMR (400MHz, CDCl3): δ 7.76 (d, J = 5.2 Hz, 1H), 7.70 (s, 1H), 7.59 (d, J = 8.0 Hz,1H), 7.47 (s, 1H), 7.42 (d, J = 4.8 Hz, 1H), 7.28 (s, 1H), 7.23 (s, 1H), 6.98-6.97 (brs, 1H), 5.55 (s, 1H), 4.29-4.26 (m, 1H), 4.10-4.08 (m, 1H), 4.01-3.95 (m, 1H), 3.91-3.86 (m, 4H), 3.68 (s, 3H), 3.373.23 (m, 12H), 2.02-1.80 (m, 14H), 1.75-1.50 (m, 48H);

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C NMR (100MHz, CDCl3): δ 176.4, 176.3,

175.2, 174.7, 174.3, 173.7, 172.7, 172.5,171.9, 157.0, 81.8, 77.3, 77.2, 77.0, 76.7, 57.0, 56.9, 56.7, 56.6, 56.2, 55.8, 55.7, 53.7, 52.2, 51.3, 51.2, 51.0, 50.9, 30.7, 30.4, 30.3, 30.2, 30.0, 28.6, 28.4, 28.3, 28.2, 27.3, 25.2, 24.8, 23.8, 23.3, 23.2, 23.1, 22.9, 22.7; [HR-ESI(+)] m/z calcd for C54H93N27O12Na [M+Na]+ 1334.7389; found 1334.7399.

Boc-(L-Leu-L-Azl-Aib)-OMe (9): White solid; [α]24D = -3.878 (c 0.5, CDCl3); IR (CDCl3, cm-1): 3458, 3412, 2956, 2100, 1738, 1500; 1H NMR (400MHz, CDCl3): δ 6.80 (s, 1H), 6.64 (d, J = 8.0 Hz, 1H), 4.88 (d, J = 7.6 Hz, 1H), 4.39-4.34 (m, 1H), 4.06 (s, 1H), 3.71 (s, 3H), 3.27 (t, J = 7.2 Hz, 2H), 1.911.73 (m, 3H), 1.71-1.54 (m, 5H), 1.52-1.45 (m, 6H), 1.44-1.38 (m, 12H), 0.94 (t, J = 7.0 Hz, 6H); 13C NMR (100MHz, CDCl3): δ 174.6, 172.7, 170.2, 155.8, 80.5, 77.3, 77.2, 77.0, 76.7, 56.4, 53.5, 52.8,


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52.6, 51.1, 40.9, 31.3, 28.5, 28.3, 24.8, 24.7, 22.9, 22.4, 21.8; [HR-ESI(+)] m/z calcd for C22H40N12O9Na [M+Na]+ 507.2902; found 507.2869.

Boc-(L-Leu-L-Azl-Aib)2-OMe (12): White foam; [α]24D = -0.867 (c 0.5, CDCl3); IR (CDCl3, cm-1): 3466, 3431, 2960, 2100, 1665, 1528; 1H NMR (400MHz, CDCl3): δ 7.58 (s, 1H), 7.50 (d, J = 8.0 Hz, 1H), 7.32 (d, J = 6.0 Hz , 1H), 7.16 (s, 1H), 6.86 (s, 1H), 5.38 (s, 1H), 4.33-4.29 (m, 1H), 4.18-4.15 (m, 1H), 3.96-3.91 (m, 2H), 3.67 (s, 3H), 3.36-3.18 (m, 4H), 2.04-1.69 (m, 10H), 1.64-1.31 (m, 28H), 0.990.89 (m, 12H);

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C NMR (100MHz, CDCl3): δ 176.0, 175.1, 174.5, 173.2, 172.2, 171.8, 156.8, 81.7,

77.3, 77.2, 77.0, 76.7, 57.2, 55.9, 55.8, 55.3, 54.0, 53.4, 52.2, 51.3, 50.9, 40.2, 39.4, 30.2, 28.5, 28.3, 28.2, 27.4, 25.3, 25.2, 24.9, 24.8, 23.4, 23.3, 22.9, 22.6, 21.5, 20.7; [HR-ESI(+)] m/z calcd for C38H68N12O9Na [M+Na]+ 859.5124; found 859.5148.

Boc-(L-Leu-L-Azl-Aib)3-OMe (2): White foam; [α]24D = -0.651 (c 0.5, CDCl3); IR (CDCl3, cm-1): 3315, 2960, 2100, 1652, 1533; 1H NMR (400MHz, CDCl3): δ 7.82 (d, 1H), 7.67 (s, 1H), 7.59 (d, J = 8.0 Hz, 1H), 7.47 (d, J = 5.2 Hz, 1H), 7.43 (s, 1H), 7.32 (d, J = 7.0 Hz , 1H), 7.25 (s, 1H), 6.99 (s, 1H), 5.52 (s, 1H), 4.30-4.26 (m, 1H), 4.17-4.13 (m, 1H), 4.01-3.83 (m, 4H), 3.68 (s, 3H), 3.36-3.22 (m, 6H), 1.991.70 (m, 14H), 1.64-1.42 (m, 40H), 1.01-0.90 (m, 18H);

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C NMR (100MHz, CDCl3): δ 176.5, 175.5,

175.3, 175.0, 173.8, 173.5, 172.6, 172.0, 156.9, 81.6, 77.3, 77.2, 77.0, 76.7, 57.0, 56.9, 56.8, 56.2, 55.8,


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55.4, 54.8, 54.0, 53.7, 52.2, 51.3, 51.0, 40.2, 39.4, 30.4, 30.2, 30.0, 28.7, 28.6, 28.3, 28.2, 27.3, 25.2, 25.1, 24.9, 24.8, 23.8, 23.4, 23.3, 23.2, 23.1, 22.9, 22.6, 21.5, 20.8, 20.7; [HR-ESI(+)] m/z calcd for C54H96N18O12Na [M+Na]+ 1211.7347; found 1211.7369.

Synthesis and purification of peptides; Peptide FAM-1, 2, 14 and 15 were synthesized using Fmocbased solid-phase methods. A representative coupling and deprotection cycle is described as follows. NovaPEG Rink amide resin was soaked for 30 min in CH2Cl2. After the resin had been washed with DMF, Fmoc-amino acid (4 equiv.), and HBTU (4 equiv.) dissolved in N-methyl-2-pyrrolidone (NMP) were added to the resin. DIPEA (4 equiv.) and 0.1 M HOBt in NMP were added for the coupling reaction. Fmoc protective groups were deprotected using 20% piperidine in DMF. The resin was suspended in cleavage cocktail (95% TFA, water 2.5%, 2.5% triisopropylsilane) at room temperature for 3 h. TFA was evaporated to a small volume under a stream of N2 and dripped into cold ether to precipitate the peptide. The peptides were dissolved in DMSO, purified using reverse-phase high performance liquid chromatography, and characterized using liquid chromatography-mass spectrometry.

Peptide purity was assessed using analytical HPLC with a Discovery® Bio Wide Pore C18 column (25 cm x 4.6 mm; solvent A: 0.1% TFA/water, solvent B: 0.1% TFA/MeCN, flow rate 1.0 mL/min, gradient: 10-90% (FAM-1 and FAM-2) and 10-60% (FAM-14, FAM-15, FAM-16 and FAM-17) gradient of solvent B over 30 min).


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Click reaction of peptide FAM-1. A mixture of peptide FAM-1, alkyne (4.0 Eq/Azido group), CuSO4 (20 Eq), and sodium ascorbate (20 Eq) in DMF/H2O (2.0 mL/1.0 mL) was stirred for 72 hr at room temperature. The mixture was purified in accordance with the abovementioned method.

Cellular uptake of peptides.

HeLa cells were seeded in 6-well dishes at a density of 2.0 x 105 cells/well and cultured in DMEM for 24 hr. The cells were treated with each peptide (peptide concentration; 1 µM) and incubated for each time 2 hr. Then, the cells were washed three times with phosphate buffer (PBS) supplemented with heparin (20 units/mL) and detached by treatment of trypsin-EDTA. The collected cells were pelleted by centrifugation at 3000 rpm for 5 min and the supernatant was removed. The cells were washed twice with PBS buffer. Then, the collected cells were suspended in 500 µL of PBS buffer and mean fluorescence intensity in cells was measured by flow cytometer. The results are presented as the mean and standard deviation obtained from 3 samples.


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Supporting Information Available: Information about the synthetic scheme and copies of the 1H NMR and

13

C NMR spectra of compounds 1, 2, 5, 8, 9, and 12, and HPLC data of peptides FAM-1,

FAM-2, FAM-14, FAM-15, FAM-16 and FAM-17 are available free of charge at http://pubs.acs.org.

Abbreviation.

Ac5c, 1-aminocyclopentane-1-carboxylic acid; Boc, tert-butoxycarbonyl group; CD, circular dichroism; βAla, β-alanine; DMEM, Dulbecco’s modified eagle medium; Gu, guanidine group; PEG, polyethylene group; Mal, maleimide; Fmoc, 9-fluorenylmethylcarbonyl group; TFA, trifluoroacetic acid;

Acknowledgments. This work was supported in part by a Grant-in-Aid for Scientific Research (KAKENHI, No. 15K18905 to T.M).

References and Notes

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