the script solves the systems of differential equations numerically using SciPy's odeint function, optimizing the fit by least squares. Because the concentrations ...
Dissipative Assembly of Aqueous Carboxylic Acid Anhydrides Fueled by Carbodiimides Supporting Information Lasith S. Kariyawasam and C. Scott Hartley* Department of Chemistry & Biochemistry, Miami University, Oxford, OH 45056, USA Table of Contents Experimental . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . Starting materials . . . . . . . . . . . . . . . . . . Independent synthesis of MEA-An . . . . . . . . Independent synthesis of TEG-Cy . . . . . . . . TEG-Cy alone . . . . . . . . . . . . . . . . . Mixture of TEG-Cy and linear anhydrides
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S3 S3 S3 S5 S7 S7 S8
Monitoring of assembly by IR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S9 KSB-An IR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S9 MEA-An IR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S9 Monitoring of pH changes during assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S10 KSB-Ac pH changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S10 MEA-Ac pH changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S11 DFT chemical shift predictions for cyclic anhydrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S11 Reaction monitoring by 1H NMR spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S12 TEG-Cy and PEG-Cy without added salts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S13 Multiple injections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S13 DFT geometry predictions of the K+ complexes of 18-crown-6 and TEG-Cy . . . . . . . . . . . . . . . . . . S15 Kinetic models . . . . . . . . . . . . Monoacid systems . . . . . . . . . Diacid systems . . . . . . . . . . . Data analysis in Python . . . . . .
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S15 S15 S16 S17
Kinetic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S18 Fit parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S18 Python script for kinetic fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S19 Raw kinetic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S27 Calculated geometries . . . . . . . . . . . . TEG-Cy (B3LYP/6-31G(d)) . . . . . . . . S2 (B3LYP/6-31G(d)) . . . . . . . . . . . . K+ ⊂ 18-Crown-6 (B3LYP/6-31+G(d,p)) K+ ⊂ TEG-Cy (B3LYP/6-31+G(d,p)) . . .
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S34 S34 S35 S37 S38
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S39
List of Figures S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S32 S33 S34 S35 S36 S37 S38 S39
1H
NMR spectrum (500 MHz, CDCl3 ) of TEG-Ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . . NMR spectrum (126 MHz, CDCl3 ) of TEG-Ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1H NMR spectrum (500 MHz, CDCl ) of PEG-Ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 13C NMR spectrum (126 MHz, CDCl ) of PEG-Ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1H NMR spectrum (500 MHz, CDCl ) of MEA-Ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 13C NMR spectrum (126 MHz, CDCl ) of MEA-Ac. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1H NMR spectrum (500 MHz, CDCl ) of MEA-An. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 13C NMR spectrum (126 MHz, CDCl ) of MEA-An. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1H NMR spectrum (500 MHz, CDCl ) of TEG-Cy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 13C NMR (126 MHz, CDCl ) spectrum of TEG-Cy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1H NMR spectrum (500 MHz, CDCl ) of a mixture of TEG-Cy and linear anhydrides. . . . . . . 3 IR spectroscopy monitoring of KSB-An (0.5 eq EDC). . . . . . . . . . . . . . . . . . . . . . . . . . IR spectroscopy monitoring of MEA-An (4 eq EDC). . . . . . . . . . . . . . . . . . . . . . . . . . . IR spectroscopy monitoring of MEA-An (2 eq EDC). . . . . . . . . . . . . . . . . . . . . . . . . . . pH vs time for KSB-An system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pH vs time for MEA-An system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculated energies and relative chemical shifts for model compound S1. . . . . . . . . . . . . . Optimized geometries of TEG-Cy and S2, with calculated isotropic shieldings PCM indicated. Monitoring of assembly of TEG-Cy and PEG-Cy without added salts. . . . . . . . . . . . . . . . 1H NMR monitoring of the MEA-An system with multiple injections. . . . . . . . . . . . . . . . 1H NMR monitoring of the TEG-Cy system with multiple injections. . . . . . . . . . . . . . . . . Optimized geometries of the potassium ion complexes of 18-crown-6 and TEG-Cy. . . . . . . . Kinetic parameters for the MEA-An system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinetic parameters for the TEG-Cy system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinetic parameters for the PEG-Cy system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of KSB-An. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of MEA-An, without added salt. . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of MEA-An, with 1 M LiCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of MEA-An, with 1 M NaCl. . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of MEA-An, with 1 M KCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of MEA-An, with 1 M CsCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of TEG-Cy, with 1 M LiCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of TEG-Cy, with 1 M NaCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of TEG-Cy, with 1 M KCl. . . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of TEG-Cy, with 1 M CsCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of PEG-Cy, with 1 M LiCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of PEG-Cy, with 1 M NaCl. . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of PEG-Cy, with 1 M KCl. . . . . . . . . . . . . . . . . . . . . . . . . . . . Monitoring of assembly of PEG-Cy, with 1 M CsCl. . . . . . . . . . . . . . . . . . . . . . . . . . . 13C
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S3 S4 S4 S5 S5 S6 S6 S7 S8 S8 S9 S9 S10 S10 S11 S11 S12 S12 S13 S14 S14 S15 S18 S19 S19 S28 S28 S29 S29 S30 S30 S31 S31 S32 S32 S33 S33 S34 S34
List of Schemes S1
General structure of linear anhydride diacids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S16
List of Tables S1 S2 S3
Computational data for TEG-Cy and linear dimer S2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . S12 Computational data for potassium ion complexes of TEG-Cy and 18-crown-6. . . . . . . . . . . . . . S15 Fit parameters for the KSB-An system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S18 S2
Experimental General Unless otherwise noted, all starting materials, reagents, and solvents were purchased from commercial sources and used without further purification. NMR spectra were measured for CDCl3 or D2 O solutions using a Bruker Avance 500 MHz NMR spectrometer. DFT calculations were performed using Gaussian 09, rev. B.01.1 All energy minima were verified to have 0 imaginary frequencies by vibrational frequency analysis.
4.5
ppm
3.75 3.74 3.74 3.74 3.69 3.68 3.68 3.67 3.66 3.66 3.65 3.65 3.64
4.16
Starting materials The monoacids KSB-Ac and MEA-Ac are commercially available and were used without further purification. The diacids TEG-Ac and PEG-Ac are known compounds synthesized according to literature procedures.2 NMR spectra of as-synthesized TEG-Ac and PEG-Ac are shown in Figures S1–S4. They were also characterized by highresolution mass spectrometry, giving m/z = 311.13346 for TEG-Ac (calcd 311.13421 for [TEG-Ac+H+ ]) and m/z = 355.15981 (calcd 355.15987 for [PEG-Ac+H+ ]).
4.0
3.5
10
5
Figure S1. 1H NMR spectrum (500 MHz, CDCl3 ) of TEG-Ac.
S3
0
68.15
70.24 70.17 70.09
70.75
70.75 70.24 70.17 70.09 68.15
173.72
70
ppm
200
68
150
100
50
0
3.58 3.57 3.52 3.50
4.01
Figure S2. 13C NMR spectrum (126 MHz, CDCl3 ) of TEG-Ac.
4.0
ppm
3.5
10
5
Figure S3. 1H NMR spectrum (500 MHz, CDCl3 ) of PEG-Ac.
S4
0
ppm
200
70.72 70.24 70.21 70.13 68.11
68.11
70.24 70.21 70.13
70.72
173.72
70
68
150
100
50
0
Figure S4. 13C NMR spectrum (126 MHz, CDCl3 ) of PEG-Ac.
3.267
3.485 3.480 3.476 3.473 3.467
3.615 3.609 3.606 3.602 3.597
4.039
Independent synthesis of MEA-An MEA-Ac (115 µL, 1.0 mmol), N,N′-dicyclohexylcarbodiimide (DCC) (106 mg, 0.5 mmol, 0.5 eq) and CCl4 (5 mL) were added to a scintillation vial and stirred at r.t. for 1 h. The mixture was then filtered through a cotton plug and the filtrate cooled at −4 ℃ in the freezer. The mixture was then filtered again through a cotton plug and concentrated, giving a mixture of MEA-An and MEA-Ac (2.8:1). NMR spectroscopy (see below) supports the assignments made for the kinetic runs in D2 O (i.e., that the key anhydride methylene signal is deshielded by 0.2–0.3 ppm relative to the acid).
3 2 2 ppm3.2
4.2-15.011
4.04.2
2.02 2.02 3.84.0
Figure S5. 1H NMR spectrum (500 MHz, CDCl3 ) of MEA-Ac.
S5
3.63.8
2.03 2.03
3 3.43.6
3.23.4
150
58.564
71.422 70.426 67.958
173.661 ppm
100
50
ppm
0.704 4.2
3.351
*
*
2
3.389
3.576 3.567 3.562 3.558 3.555 3.549
3.728 3.723 3.719 3.716 3.710 3.707
4.133
4.275
Figure S6. 13C NMR spectrum (126 MHz, CDCl3 ) of MEA-Ac.
2.73 4.0
3.8
2.78 3.6
0.98 3.1 3.4
3.2
Figure S7. 1H NMR spectrum (500 MHz, CDCl3 ) of MEA-An, obtained as a mixture with MEA-Ac (signals labeled *).
S6
59.049
71.979 71.660 71.101 68.938 68.642
166.241
172.880
*
ppm
150
100
50
Figure S8. 13C NMR spectrum (126 MHz, CDCl3 ) of MEA-An, obtained as a mixture with MEA-Ac (signal labeled *).
Independent synthesis of TEG-Cy When anhydride formation is carried out with DCC in CCl4 , we obtain the cyclic anhydride TEG-Cy as the major product (as determined by NMR spectroscopy and mass spectrometry), whereas in CH2 Cl2 we obtain a mixture of cyclic and linear anhydrides.
TEG-Cy alone TEG-Ac (0.3408 g, 1.098 mmol), DCC (0.2290 g, 1.110 mmol, 1.011 equiv) and CCl4 (4 mL) were added into a vial and the reaction mixture was stirred at r.t. for 1 h. It was then filtered through cotton, and the colorless filtrate was let stand in the freezer. No additional precipitate was observed. The solution was concentrated to a yellowish liquid containing a small amount of white solid. It was resuspended in CCl4 , filtered through a cotton plug, and concentrated again to give a mixture of predominantly TEG-Cy: 1H NMR (500 MHz, CDCl3 ) δ 4.41 (s, 4H), 3.74 (m, 4H), 3.67 (m, 4H), 3.65–3.60 (m, 8H); 13C NMR (126 MHz, CDCl3 ) δ 166.7, 71.6, 71.0, 70.72, 70.69, 69.3; MS (ESI) calcd for C12 H21 O8 (M+H+ ) 293.12, found 293.24.
S7
3.75 3.75 3.74 3.74 3.68 3.67 3.66 3.62
4.41 ppm1
4-15.01
34
23
12
72
ppm
150
69.27
71.03 70.72 70.69
71.57
71.57 71.03 70.72 70.69 69.27
166.72
Figure S9. 1H NMR spectrum (500 MHz, CDCl3 ) of TEG-Cy. The impurities correspond to linear anhydrides/acids and DCC/urea.
70
100
50
Figure S10. 13C NMR (126 MHz, CDCl3 ) spectrum of TEG-Cy. Note that there are no signals corresponding to the carboxylic acid functional group, and that the number of signals (6) is consistent with the symmetry of TEG-Cy.
Mixture of TEG-Cy and linear anhydrides TEG-Ac (0.3464 g, 1.11 mmol) and DCC (0.2360 mg, 1.11 mmol, 1.0 eq) were added to a vial, followed by CH2 Cl2 (4 mL). The reaction mixture was stirred overnight at rt, then filtered through cotton and concentrated to give a mixture of TEG-Cy and linear anhydrides and acids.
S8
4.39 4.27 4.27 4.26 4.12 4.11 3.71 3.70 3.70 3.69 3.66 3.65 3.65 3.64 3.64 3.62 3.61 3.60 CH2CO2H –CH2CO2CO– TEG-Cy
ppm
4
3
2
1
Figure S11. 1H NMR spectrum (500 MHz, CDCl3 ) of a mixture of TEG-Cy and linear anhydrides.
Monitoring of assembly by IR spectroscopy
Transmission
KSB-An IR spectroscopy KSB-Ac (24 mg, 0.10 mmol, 1.0 eq) was dissolved in distilled water (0.5 mL). EDC (10 mg, 0.05 mmol, 0.5 eq) was dissolved separately in distilled water (0.5 mL). The two solutions were mixed (time = 0), and immediately monitored as a droplet on the surface of the ATR cell of an IR spectrometer. The background spectrum of distilled water was subtracted from each spectrum. The peak at ~1800 cm−1 is assigned to the symmetric stretch of the anhydride (the asymmetric stretch is typically weaker and should overlap with the carboxylic acid carbonyl stretching mode). The peak(s) at ~1700 cm−1 correspond(s) to both the acid and the EDC; after an initial decrease, this peak grows back in. The peaks at ~1570 and ~1630 cm−1 correspond to the urea.
0.78 3.73 6.77 9.20 11.58 13.95
↑ ↑↓ ↓ ↓
1900
1800
1700 −1 ν (cm )
1600
1500
Figure S12. IR spectroscopy monitoring of KSB-An (0.5 eq EDC). Times are in minutes.
MEA-An IR spectroscopy MEAA (46 µL, 0.40 mmol, 1.0 eq) was initially dissolved in 1.00 mL of distilled water. EDC (155 mg, 2.0 eq; or 310 mg, 4.0 equiv) was also dissolved in 1.00 mL of distilled water in a separate vial. Both the vials were cooled in salt-ice baths. The reactants were mixed (time = 0) and immediately monitored as a droplet on the surface of the ATR cell of an IR spectrometer. The background spectrum of distilled water was subtracted from each spectrum. The assignments parallel those for KSB-An, but note that the relative concentration of anhydride/acid is much lower.
S9
1805
1865
Transmission 1900
0.27 0.55 0.83 1.12 1.38 1.67
1800
1700 −1 ν (cm )
1600
1500
Transmission
Figure S13. IR spectroscopy monitoring of MEA-An (4 eq EDC). The inset shows the evolution of the peak corresponding to the anhydride. Times are in minutes.
0.33 0.68 0.97 1.23 1.52
1800
1805
1865
1900
1700 −1 ν (cm )
1600
1500
Figure S14. IR spectroscopy monitoring of MEA-An (2 eq EDC). The inset shows the evolution of the peak corresponding to the anhydride. Times are in minutes.
Monitoring of pH changes during assembly KSB-Ac pH changes KSB-Ac (362 mg, 101 mM) and pyridine (2.4 µL, 2.0 mM) were added to a volumetric flask and diluted to 10.00 mL with distilled water to prepare a stock solution. A solution of EDC in water (4.0 mL, 0.3 eq) was added to the stock solution (8.0 mL). The pH of the reaction mixture was monitored over time at room temperature using a standard pH meter. The EDC solution (4 mL) was added two more times into the reaction mixture. For the control experiment, pyridine (2.4 µL, 2.0 mM) was diluted to 10.00 mL with distilled water in a volumetric flask to prepare a stock solution. A solution of EDC in water (4.0 mL, same as in KSB-Ac experiment) was added to the stock solution (8.0 mL). The pH of the reaction mixture was monitored over time at room temperature using a standard pH meter.
S10
Injection 1
Injection 2
Injection 3
pH
pH
Control
8.0
3.5
3.0
7.5
7.0 2.5 0
5
10
0
5 10 Time (min)
0
5
10
0
2
4
6 8 Time (min)
10
12
Figure S15. pH vs time for KSB-An system. The control experiment is identical but with no KSB-Ac.
MEA-Ac pH changes MEA-Ac (170 µL, 100 mM) and pyridine (2.4 µL, 2.0 mM) were added to a volumetric flask and diluted to 10.00 mL with distilled water to prepare a stock solution. An ice-cold solution of EDC in water (4 mL, 4 eq) was added to the ice-cold stock solution (8 mL). The pH of the reaction mixture was monitored over time with the reaction mixture kept in an ice-salt bath. For the control experiment, pyridine (2.4 µL, 2.0 mM) was diluted to 10.00 mL with distilled water in a volumetric flask to prepare a stock solution. An ice-cold solution of EDC in water (4 mL, same as in MEA-Ac experiment) was added to the ice-cold stock solution (8 mL). The pH of the reaction mixture was monitored over time with the reaction mixture kept in an ice-salt bath. 9.0
Control
3.5
pH
pH
8.5 3.0
8.0 2.5 7.5 0
1
2
3 4 Time (min)
5
6
7
0
1
2
3 4 Time (min)
5
6
7
Figure S16. pH vs time for MEA-An system. The control experiment is identical but with no MEA-Ac.
DFT chemical shift predictions for cyclic anhydrides The general effect of conformation on chemical shifts in the MEA-An, TEG-Cy, and PEG-Cy systems was first probed using model compound S1. A conformational energy surface for rotation about the O1 –C2 –C3 –O4 bond was generated at the PCM(water)/B3LYP/6-31G(d) level. Two conformers, one with O1 and O4 syn-periplanar (φ ≈ 0◦ ) and one with them anti-periplanar (φ ≈ 180◦ ) were identified. The anti-periplanar conformer is predicted to be roughly 1.3 kcal/mol more stable at this level of theory, and thus presumably favored in the acyclic anhydrides (whereas the cyclic anhydrides would be forced into the syn-periplanar conformation). NMR isotropic shieldings were calculated for each geometry at the PCM(water)/WP04/6-31G(d) level.3,4 The chemical shifts for the methylene protons α to the carbonyl group (on C2 ) were found to be deshielded by 0.07 ppm in the (less favorable) synperiplanar conformer.
S11
H
0
2
0.05
(ppm)
3 O O 2 4 1 O O S1
0.05
0.07 ppm
Rel.
H
Rel. E (kcal/mol)
3
0.10
1
0.15 0
180
120 60 0 60 120 Dihedral O1–C2–C3–O4 (°)
Figure S17. Calculated energies (PCM(water)/B3LYP/6-31G(d)) (PCM(water)/WP04/6-31G(d)) for model compound S1.
and
180
relative
chemical
shifts
These results were then extended to explicit models of TEG-Cy and linear dimer S2. Their geometries were optimized at the B3LYP/6-31G(d) level with NMR isotropic shieldings calculated at the PCM(water)/WP04/6-31G(d) level. The results are in line with those for S1: a chemical shift difference of 0.10 ppm, with the cyclic anhydride predicted to be deshielded relative to the (all anti) linear anhydride. This is consistent with the assignments made in the experimental spectra. Cartesian coordinates for the optimized geometries are provided below (pp S34, S35). IS = 28.26 ppm
IS = 28.36 ppm TEG-Cy
S2
Figure S18. Optimized geometries of TEG-Cy and S2 (B3LYP/6-31G(d)), with calculated isotropic shieldings (IS) (PCM(water)/WP04/6-31G(d)) indicated.
Structure TEG-Cy (C 2 ) S2
Energy (Eh ) −1071.029995 −2218.551138
ZPC (Eh ) 0.331503 0.688198
Total Energy (Eh ) −1070.698492 −2217.862940
IF 0 0
Table S1. Computational data (B3LYP/6-31G(d)) for TEG-Cy and linear dimer S2. ZPC = zero-point correction, IF = number of imaginary frequencies.
Reaction monitoring by 1H NMR spectroscopy The reactions were monitored by 1H NMR spectroscopy (500 MHz). All concentrations were referenced to the methyl peak of the acetyl group of N,N -dimethylacetamide (DMA), included as an internal standard (this peak was also used to calibrate the chemical shift scale). Stock solutions (10.00 mL) were prepared of the appropriate carboxylic acid (150 mM for monoacids, 75 mM for diacids), DMA (100 mM), and pyridine-d 5 (3.0 mM). The appropriate salts (LiCl, NaCl, KCl, or CsCl) were added to portions of this stock solution depending on the specific experiment being run (such that the final concentration of salt would be 1.0 M). A separate solution of EDC in D2 O was also prepared at such a concentration that 200 μL would deliver the target stoichiometry. For the lowtemperature experiments at 276 K (MEA-An, TEG-Cy, PEG-Cy), all of the solutions were cooled in an ice bath until immediately before beginning a run. The NMR spectrometer was locked and shimmed on a 600 μL aliquot of the stock solution (after being equilibrated at the appropriate temperature). For each run, a standard NMR tube was charged with 400 μL of the acid-containing S12
solution, then treated with 200 μL of the EDC solution. The reaction mixture was quickly mixed, inserted into the spectrometer, and acquisition started. The time of first mixing was taken as t = 0. Each time point constitutes a single scan, with the time taken as the midpoint of acquisition. All experiments were done in triplicate. The raw data is given in Figures S27–S39. TEG-Cy and PEG-Cy without added salts As mentioned in the text, assembly of TEG-Cy and PEG-Cy was also attempted in the absence of added salts. As shown in Figure S19, the reaction works as expected, but is inconveniently faster than in the presence of any of the salts. TEG-Cy
PEG-Cy
Figure S19. Monitoring of assembly of TEG-Cy (left) and PEG-Cy (right) without added salts (276 K). 2 eq of EDC (per acid group) were used (to achieve roughly 50% conversion).
Multiple injections The response to multiple injections was tested for the MEA-An and TEG-Cy systems (with 1 M KCl). Briefly, initial experiments were carried out as for the single-injection runs. The samples were then removed from the spectrometer, treated with another dose of the EDC, and then monitored again (hence the dilution with each injection). Three total injections were attempted in both cases; however, for the MEA-An system, the buildup of byproducts gave complex behavior after the third injection that could not be satisfactorily analyzed.
S13
800
Conc (mM)
600
400
200
0
Conc (mM)
80 60 40 20 0
0
5 10 Time (min) (1st inj.)
0
5 10 Time (min) (2nd inj.)
Figure S20. 1H NMR monitoring of the MEA-An system with multiple injections (276 K, D2 O, 2 mM pyridine-d 5 ).
Conc (mM)
800 600 400 200 0 50
Conc (mM)
40 30 20 10 0
0
5 10 0 5 10 Time (min) (1st inj.) Time (min) (2nd inj.)
0
5 10 Time (min) (3rd inj.)
Figure S21. 1H NMR monitoring of the TEG-Cy system with multiple injections (276 K, D2 O, 2 mM pyridine-d 5 , 1 M KCl).
S14
DFT geometry predictions of the K+ complexes of 18-crown-6 and TEG-Cy To compare the (possible) binding of K+ by TEG-Cy to that of 18-crown-6, the (gas phase) geometries of the complexes were optimized at the B3LYP/6-31+G(d,p) level, which has been previously used to study (hydrated) 18-crown-6 complexes.5 The results show that while the anhydride oxygen atom in TEG-Cy is more weakly coordinated than the others, its bond length to K is predicted to be actually very similar to those in 18-crown-6.
2.82
2.83
2.74
2.79
2.67
Figure S22. Optimized geometries (B3LYP/6-31+G(d,p)) of the potassium ion complexes of 18-crown-6 (left) and TEG-Cy (right). Predicted O−K bond lengths are given in Å.
Structure 18-Crown-6–K+ (Ci ) TEG-Cy–K+ (C 1 )
Energy (Eh ) −1522.883502 −1670.916013
ZPC (Eh ) 0.370689 0.331585
Total Energy (Eh ) −1522.512813 −1670.584428
IF 0 0
Table S2. Computational data for potassium ion complexes of TEG-Cy and 18-crown-6 (B3LYP/631+G(d,p)). ZPC = zero-point correction, IF = number of imaginary frequencies.
Kinetic models Monoacid systems The monoacid systems were analyzed using the following model: k
1 → I Ac + E −
kAn
i I + Ac −− → An + U
kAc
i I −−→ Ac + U
k
2 An − → 2Ac
where Ac is the monoacid, E is the EDC, I is an activated carboxylic acid intermediate (e.g., O-acylurea, acyl pyridinium ion, or equivalent), An is the anhydride, and U is the urea. This system yields the following system of differential equations: d[Ac] dt d[An] dt d[I] dt d[E] dt d[U] dt
Ac = −k1 [Ac][E] − kAn i [I][Ac] + ki [I] + 2k2 [An]
(1)
= +kAn i [I][Ac] − k2 [An]
(2)
Ac = +k1 [Ac][E] − kAn i [I][Ac] − ki [I]
(3)
= −k1 [Ac][E]
(4)
An = +kAc i [I] + ki [I][Ac]
(5)
S15
If we assume a steady-state in [I], we obtain instead: d[Ac] dt d[An] dt d[E] dt d[U] dt
= −k1 [E][Ac] + 2k2 [An] + =+
k1 K[Ac][E] k1 [E][Ac]2 − K + [Ac] K + [Ac]
k1 [E][Ac]2 − k2 [An] K + [Ac]
(6) (7)
= −k1 [E][Ac]
(8)
= +k1 [E][Ac]
(9)
An where K = kAc i /ki (i.e., direct hydrolysis of the intermediate vs anhydride formation). As discussed in the text, a steady-state was assumed for the MEA-An assembly. However, for the KSB-An system, a species believed to be an intermediate was detected at short reaction times, so [I] was explicitly included in the analysis. The k’s and K are explicitly fit as parameters, as are the initial concentrations of EDC ([E]0 ) and acid ([Ac]0 ). The other starting concentrations ([An]0 , [I]0 , [U]0 ) are assumed to be 0. Anhydride “yields” can be calculated from fits of these models. Equation (7) can be dived into two terms: anhydride formation and anhydride destruction (an identical argument can be made for equation (2)). Under the conditions of the experiments, we begin and end with no anhydride; that is, the total amount formed is the amount hydrolyzed:
∫
∞
0
∫ d[An] = +k1
0
∞
[E][Ac]2 dt − k2 K + [Ac]
∫
∞
[An]dt = 0
(10)
0
The total amount of anhydride formed can be determined from either term but, in practice, it is more straightforward to do it from the destruction term. Thus, the yield is given by:
Yield =
k2
∫∞
[An]dt [E]0
0
(11)
where the initial concentration of EDC ([E]0 ) is obtained from the kinetic fits. Diacid systems The principal challenge in the diacid systems is that we can determine the total concentrations of linear anhydride and diacid functionality by NMR, but not the concentrations of specific species. We need to be able to establish the concentration of the starting diacids at any given moment since (to a first approximation) only they can cyclize to the macrocycles. We define a general diacid structure in the system as DAn (Scheme S1). That is, the starting materials TEG-Ac or PEG-Ac would be DA0 (x = 4 or 5, respectively), and linear anhydride oligomers would be all DAn with n > 0. O HO
O O x
O
O O
O O
O x
OH
n
DAn
Scheme S1. General structure of linear anhydride diacids.
By analogy with the monoacid system, we describe the diacid systems as follows:
S16
k
1 DAn + E − → In
kAc
i In −−→ DAn + U
kL
i DAn+m + U In + DAm −→
kC
i I0 −→ Cy + U
kL
2 DAn>0 −→ DAn + DAm
kC
2 Cy −→ DA0
where E and U are defined as above, DAn represents the total diacid species (Scheme S1), In represents all possible intermediate species (with n defined as for DAn ), and Cy is the cyclic anhydride. L L To analyze this system we assume that the rate constants k1 , kAc i , ki , and k2 are independent of n, and that the concentration of the starting diacids DA0 can be estimated from the total diacid concentration using a conversion factor ρ. We define ρ by analogy with a simple condensation polymerization: [DA0 ] = ρ[DAn ]
(12)
[Ac]0 = [Ac] + [L] + [Cy] [Ac] [Ac] ρ= = [Ac]0 − [Cy] [Ac] + [L]
(13) (14)
where [Ac] is the measured diacid concentration, [Ac]0 is the initial (total) diacid concentration, and [L] is the measured linear anhydride concentration. This estimate of ρ is clearly an approximation, but it behaves correctly at the limits of high/low conversion and should suffice given the other approximations inherent to this model. Framing this in terms of the measurable concentrations [Ac] (diacid), [L] (linear anhydride), [Cy], [E], and [U], and assuming a steady state in the intermediate, gives the following system of differential equations: d[Ac] dt d[L] dt d[Cy] dt d[E] dt d[U] dt
1 1 k1 K[Ac][E] 1 k1 [E][Ac]2 1 k1 ρKEM [Ac][E] = − k1 [Ac][E] + kL2 [L] + kC2 [C] + − − 2 2 K + [Ac] + ρKEM 2 K + [Ac] + ρKEM 2 K + [Ac] + ρKEM 2 k1 [E][Ac] =+ − kL2 [L] K + [Ac] + ρKEM k1 ρKEM [Ac][E] =+ − kC2 [Cy] K + [Ac] + ρKEM
(15) (16) (17)
= −k1 [Ac][E]
(18)
= +k1 [Ac][E]
(19)
L C L where K = kAc i /ki (as for the monoacid) and KEM = ki /ki (i.e., the effective molarity). As before, we fit the k’s, K’s, [Ac]0 , and [E]0 as parameters, and set the other starting concentrations to 0 ([L]0 , [Cy]0 , [U]0 ).
Data analysis in Python The models described above (equations (1)–(5), (6)–(9), and (15)–(19)) were fit to the experimental data using a script written in Python 3.5.2 with NumPy 1.12.0 and SciPy 0.18.1. The full script is given below on p S19. Briefly, the script solves the systems of differential equations numerically using SciPy’s odeint function, optimizing the fit by least squares. Because the concentrations are derived from NMR integration (which is expected to yield relative errors of roughly 10%), the errors for the minimization were weighted by a factor 1/(0.1 × conc), subject to a
S17
maximum to avoid overemphasizing low concentrations (≤5 mM). The script reads csv files with columns listing concentrations in the following order: time, anhydrides (linear then cyclic for diacids), acid, EDC, and urea. The script takes two arguments. The first specifies the model to use: 1 for monoacid, 1SS for monoacid with steady-state approximation, 2SS for diacid with steady-state approximation. The second is the filename of the csv file. The script automatically outputs the parameters, the best-fit curves from the kinetic model, and the plots of the data (shown in Figures S27–S39).
Kinetic data Fit parameters Parameters extracted from the fits to the kinetic models are summarized in Table S3 and Figures S23–S25. The plots themselves, including the raw parameters for each run, are given in Figures S27–S39.
k1 kAn i kAc i k2
0.034 ± 0.002 mM−1 min−1 0.0205 ± 0.0006 mM−1 min−1 0.286 ± 0.005 min−1 0.0494 ± 0.0005 min−1
Table S3. Fit parameters for the KSB-An system. The parameters are the means of three replicates, with error bars corresponding to the standard errors.
−1
k2 (min )
0.8 0.6 0.4 0.2 0
K (mM)
200
100
0.010
−1
−1
k1 (mM min )
0
0.005
0
No Salt
LiCl
NaCl
KCl
CsCl
Figure S23. Kinetic parameters for the MEA-An system. The parameters are the means of three replicates, with error bars corresponding to the standard errors.
S18
K (mM)
300 200 100 0 1.5
10
1
20
1.0
C
k2 (min )
EM (mM)
30
0.5 0 1.0
1
k2 (min )
1
0.010 0.005 0
0.5
L
k1 (mM min )
0.015
1
0
LiCl
NaCl
KCl
0
CsCl
LiCl
NaCl
KCl
CsCl
Figure S24. Kinetic parameters for the TEG-Cy system. The parameters are the means of three replicates, with error bars corresponding to the standard errors.
K (mM)
200 150 100 50
1.5
20
1
10
1.0
C
k2 (min )
EM (mM)
0
0.5 0 0.8
L
1
k2 (min )
1
0.010
k1 (mM min )
0.015
1
0
0.005 0
LiCl
NaCl
KCl
0.6 0.4 0.2 0
CsCl
LiCl
NaCl
KCl
CsCl
Figure S25. Kinetic parameters for the PEG-Cy system. The parameters are the means of three replicates, with error bars corresponding to the standard errors.
Python script for kinetic fits Note: This script is also provided as a .py (ASCII) file to facilitate use/adaptation. import numpy, scipy, sys, itertools, platform
S19
from matplotlib import pyplot as plt, rcParams from scipy.optimize import least_squares # Set name of data file as second argument. raw_data_file = sys.argv[2] # First argument specifies kinetic model. if sys.argv[1] == ”1SS”: def solved_kin_sys(starting_concs, ks, times): ”””Defines the kinetic model for the monoacid: (1) Ac + E -> I (k1) (2) I + Ac -> An + U (kiAn) (3) I -> Ac + U (kiAc) (4) An -> 2Ac (k2) where Ac is the acid, E is the EDCI, U is the urea, and An is the anhydride. I is the activated intermediate (e.g., O-acylisourea or acyl pyridinium). Applying a steady-state approximation in I: K = kiAc/kiAn ””” def kin_sys(concs, t, *ks): Ac, E, U, An = concs k1, K, k2 = ks # Return equations of Ac’, E’, U’, An’ return [ - k1*E*Ac + 2*k2*An + (k1*K*Ac*E)/(K+Ac) - (k1*E*Ac**2)/(K+Ac), - k1*E*Ac, + k1*E*Ac, + (k1*E*Ac**2)/(K+Ac) - k2*An ] return scipy.integrate.odeint(kin_sys, starting_concs, times, args=tuple(ks), mxstep=10000) # Initial guesses for parameters INIT_ks = [0.02, 200, 0.5]
# k1, K, k2
INIT_STARTING_CONCS = [100, 400] # Ac, E optimized BOUNDS = (0, numpy.inf)
# All must be >0
CONST_STARTING_CONCS = [0, 0]
# U, An unoptimized
# Input order and processing order not necessarily the same, as in # script_col[n] = csv_col[SORT_ORDER[n]] SORT_ORDER = [1, 2, 3, 0] # Simulated data to integrate: INTEGRATE = [3] # Labels for the parameters.
S20
PARAMS = [”k1”, ”K”, ”k2”, ”Acid0”, ”EDCI0”] # Labels for the concentrations. LEGEND = [”Acid”, ”EDCI”, ”Urea”, ”Anhydride”] # Lists of list indices for top/bottom plots. TOP_PLOT = [1, 2] BOTTOM_PLOT = [0, 3] elif sys.argv[1] == ”1”: def solved_kin_sys(starting_concs, ks, times): ”””Defines the kinetic model for the monoacid. Follows the 1SS model, but without a steady-state approximation. ””” def kin_sys(concs, t, *ks): Ac, E, U, An, I = concs k1, kiAc, kiAn, k2 = ks # Return the equations for Ac’, E’, U’, An’, I’ return [ - k1*Ac*E - kiAn*I*Ac + kiAc*I + 2*k2*An, - k1*E*Ac, + kiAc*I + kiAn*I*Ac, + kiAn*I*Ac - k2*An, + k1*Ac*E - kiAn*I*Ac - kiAc*I ] return scipy.integrate.odeint(kin_sys, starting_concs, times, args=tuple(ks), mxstep=10000) INIT_ks = [0.02, 0.5, 0.03, 0.05] INIT_STARTING_CONCS = [100, 30] BOUNDS = (0, numpy.inf) CONST_STARTING_CONCS = [0, 0, 0] SORT_ORDER = [1, 4, 3, 0, 2] INTEGRATE = [3] PARAMS = [”k1”, ”kiAc”, ”kiAn”, ”k2”, ”Acid0”, ”EDCI0”] LEGEND = [”Acid”, ”EDCI”, ”Urea”, ”Anhydride”, ”Intermediate”] TOP_PLOT = [1, 2] BOTTOM_PLOT = [0, 3, 4] elif sys.argv[1] == ”2SS”: def solved_kin_sys(starting_concs, ks, times): ”””Defines the kinetic model for the diacid. (1) DAn + E -> In (k1) (2) In -> DAn + U (kiAc) (3) In + DAn -> DAn+m + U (kiL) (4) I0 -> C + U (kiC) (5) DAn+m -> DAn + DAm (k2L) (6) C -> DA0 (k2C)
S21
System above must be translated to the experimentally observed concentrations: Ac (total diacic), L (total linear anhydride), C (total cyclic anhydride), E (EDCI), and U (urea). Applying a steady-state approximation in I. K = kiAc/kiL EM - kiC/kiL ””” def kin_sys(concs, t, *ks): Ac, E, U, L, C = concs k1, K, EM, k2L, k2C = ks p = Ac/(Ac+L) # Approx fraction of diacid that is monomer. # Return the equations for Ac’, E’, U’, L’, C’ return [ - k1*Ac*E/2 + k2L*L + k2C*C + k1*K*Ac*E/(K+Ac+p*EM)/2 - k1*Ac**2*E/(K+Ac+p*EM)/2 - k1*p*EM*Ac*E/(K+Ac+p*EM)/2, - k1*Ac*E, + k1*Ac*E, + k1*Ac**2*E/(K+Ac+p*EM) - k2L*L, + k1*p*EM*Ac*E/(K+Ac+p*EM) - k2C*C ] return scipy.integrate.odeint(kin_sys, starting_concs, times, args=tuple(ks), mxstep=10000) INIT_ks = [0.02, 100, 10, 0.5, 1] INIT_STARTING_CONCS = [50, 400] BOUNDS = (0, numpy.inf) CONST_STARTING_CONCS = [0, 0, 0] SORT_ORDER = [2, 3, 4, 0, 1] INTEGRATE = [3,4] PARAMS = [”k1”, ”K”, ”EM”, ”k2L”, ”k2C”, ”Acid0”, ”EDCI0”] LEGEND = [”Acid”, ”EDCI”, ”Urea”, ”Linear”, ”Cyclic”] TOP_PLOT = [1, 2] BOTTOM_PLOT = [0, 3, 4] # Constants used elsewhere in script NUM_concs = len(SORT_ORDER)
# Number of experimentally observed concs
NUM_ks = len(INIT_ks)
# Number of rate constants
NUM_params = NUM_ks + len(INIT_STARTING_CONCS) # Total number of parameters # Parameters and settings for plots. SMOOTH_POINTS_PLOT = 1000
# Number of points in simulated plots
SMOOTH_EXTENSION_PLOT = 1.1 # Expansion factor for time axis COLORS = [’b’,’g’,’r’,’c’,’m’,’y’,’k’]
S22
MARKER_SIZE = 6 rcParams[’font.size’] = 6 rcParams[’font.family’] = ’sans-serif’ rcParams[’font.sans-serif’] = [’Arial’] rcParams[’lines.linewidth’] = 0.5 rcParams[’axes.linewidth’] = 0.5 rcParams[’legend.frameon’] = False rcParams[’legend.fontsize’] = 6 plt.figure(figsize=(2.2,3.5)) # Settings for output file SMOOTH_POINTS_OUT = 3000
# Number of points in output curves
SMOOTH_EXTENSION_OUT = 3
# Expansion factor for time axis
# Prevent line breaking and format numbers in correlation matrix numpy.set_printoptions(linewidth=numpy.nan) numpy.set_printoptions(precision=2,suppress=True) # Longest parameter label LEN_params = max([len(n) for n in PARAMS])
def residual(pars, consts, times, exp_concs): ”””Calculates the residuals (as a numpy array) at a given time for a given set of parameters, passed as a list. The list of parameters (pars) begins with the rate constants and ends with the starting concentrations. The list of constants (consts) represents initial concentrations that will not be optimized. Residuals are weighted as 1/(0.1*exp_val) (i.e., according to expected error on NMR measurement). Maximum weighting factor is 2, equivalent to 1/(0.1*5) (i.e., 5 mM signal). ””” ks = pars[:NUM_ks] start_concs = numpy.append(pars[NUM_ks:], consts) calcd_concs = solved_kin_sys(start_concs, ks, times) residuals = [] # List of residuals. for n,r in itertools.product(range(len(times)), range(NUM_concs)): # Ignores values for which there is no experimental data point. if not numpy.isnan(exp_concs[n][r]): residuals.append(((float(exp_concs[n][r]) calcd_concs[n][r]))*min(numpy.divide(1,0.1*float(exp_concs[n][r])), 2)) # Print the sum of squares of the residuals to STDOUT, for the # purpose of monitoring progress.
S23
print(sum([n**2 for n in residuals])) return numpy.array(residuals)
def get_raw_data(raw_data_file): ”””Load data from file, formated as a csv file. The file is assumed to include a header row, and the order of columns must match that specified by the SORT_ORDER list. Returns the times (numpy array), data (numpy array), and total number of data points (int) ””” with open(raw_data_file) as datafile: next(datafile)
# Skip header
ts = []
# List of experimental times
raw_data = []
# List of lists of experimental concentrations
total_points = 0
# Total number of experimental points
for line in datafile: curline = line.replace(”\n”, ””).split(’,’) ts.append(float(curline[0])) concs = [] for n in range(NUM_concs): if n+1 < len(curline): if curline[n+1] != ’’: total_points += 1 concs.append(float(curline[n+1])) else: concs.append(numpy.nan) else: concs.append(numpy.nan) raw_data.append(concs) unsorted_data = numpy.array(raw_data) sorted_data = numpy.empty_like(unsorted_data) for n in range(NUM_concs): sorted_data[:,n] = unsorted_data[:,SORT_ORDER[n]] return numpy.array(ts), sorted_data, total_points
if __name__ == ’__main__’: # Get data from input file. times, exp_concs, total_points = get_raw_data(raw_data_file)
S24
# Perform the actual optimization by least squares minimization of # the residuals. results = least_squares(residual, INIT_ks + INIT_STARTING_CONCS, bounds=BOUNDS, args=(CONST_STARTING_CONCS, times, exp_concs)) # Predictions of optimized model at each experimental time point. predicted_data = solved_kin_sys(numpy.append(results[’x’][NUM_ks:], CONST_STARTING_CONCS), results[’x’][:NUM_ks], times) # Generate smoothed curves with optimized parameters. # For output txt file: smooth_ts_out, deltaT = numpy.linspace(0, max(times)*SMOOTH_EXTENSION_OUT, SMOOTH_POINTS_OUT, retstep=True) smooth_curves_out = solved_kin_sys(numpy.append(results[’x’][NUM_ks:], CONST_STARTING_CONCS), results[’x’][:NUM_ks], smooth_ts_out) # For plots: smooth_ts_plot = numpy.linspace(0, max(times)*SMOOTH_EXTENSION_PLOT, SMOOTH_POINTS_PLOT) smooth_curves_plot = solved_kin_sys(numpy.append(results[’x’][NUM_ks:], CONST_STARTING_CONCS), results[’x’][:NUM_ks], smooth_ts_plot) # Various fitting data. # Sum squared residuls. sum_squares_errors = sum(results[’fun’]*results[’fun’]) # Degrees of freedom dof = total_points - NUM_params # Integrals integrals = {} for n in INTEGRATE: integrals[n] = sum(smooth_curves_out[:,n]) * deltaT # Write the data to output txt file. with open(”{}_{}.txt”.format(raw_data_file, sys.argv[1]), ’w’) as write_file: print(”**Regression results for file \”{}\”**”.format( raw_data_file), file=write_file) print(file=write_file) print(”Python version: {}”.format(platform.python_version()), file=write_file) print(”Numpy version: {}”.format(numpy.version.version), file=write_file)
S25
print(”Scipy version: {}”.format(scipy.version.version), file=write_file) print(file=write_file) print(”Optimized parameters”, file=write_file) print(”====================”, file=write_file) for n in range(len(results[’x’])): print(”{:>{l}} = {:+5e}”.format( PARAMS[n], results[’x’][n], l=LEN_params), file=write_file) print(file=write_file) print(”Integrals”, file=write_file) print(”=========”, file=write_file) for n in INTEGRATE: print(”{}: {:+5e}”.format(LEGEND[n], integrals[n]), file=write_file) print(file=write_file) print(”Regression info”, file=write_file) print(”===============”, file=write_file) print(”Success: {}”.format(results[’success’]), file=write_file) print(”Msg: {}”.format(results[’message’]), file=write_file) print(”Total points (dof): {} ({})”.format(total_points, dof), file=write_file) print(”Std Deviation of errors: {}”.format( numpy.sqrt(sum_squares_errors/dof)), file=write_file) print(”Sum square errors: {}”.format( sum_squares_errors), file=write_file) print(file=write_file) print(”Results”, file=write_file) print(”=======”, file=write_file) print(”t”, end=” ”, file=write_file) for l in LEGEND: print(l, end=” ”, file=write_file) print(file=write_file) for n in range(len(smooth_ts_out)): print(smooth_ts_out[n], end=” ”, file=write_file) for m in smooth_curves_out[n]: print(m, end=” ”, file=write_file) print(file=write_file) # Plot the data and save as pdf. plt.subplot(211) col = 0 for n in [numpy.array(exp_concs).T[n] for n in TOP_PLOT]: plt.scatter(times, n, c=COLORS[col], s=MARKER_SIZE, linewidths=0) col += 1 col = 0 for n in [smooth_curves_plot.T[n] for n in TOP_PLOT]:
S26
plt.plot(smooth_ts_plot, n, COLORS[col] + ’-’) col += 1 plt.legend([LEGEND[n] for n in TOP_PLOT], loc=4) plt.ylim(ymin=0) plt.xlim(xmin=0, xmax=smooth_ts_plot[-1]) plt.ylabel(”C (mM)”) # Print parameters on plot. pars_to_print = ”” for n in range(len(results[’x’])): pars_to_print += ”{} = {:.2e}\n”.format(PARAMS[n], results[’x’][n]) plt.text(0.5, 0.2, pars_to_print, transform=plt.gca().transAxes, fontsize=6) plt.subplot(212) col = 0 for n in [numpy.array(exp_concs).T[n] for n in BOTTOM_PLOT]: plt.scatter(times, n, c=COLORS[col], s=MARKER_SIZE, linewidths=0, zorder=2) col += 1 col = 0 for n in [smooth_curves_plot.T[n] for n in BOTTOM_PLOT]: plt.plot(smooth_ts_plot, n, COLORS[col] + ’-’, zorder=3) col += 1 plt.legend([LEGEND[n] for n in BOTTOM_PLOT], loc=2) plt.ylim(ymin=0) plt.xlim(xmin=0, xmax=smooth_ts_plot[-1]) plt.xlabel(’t (min)’) plt.ylabel(’C (mM)’) plt.tight_layout() plt.savefig(raw_data_file + ”_{}.pdf”.format(sys.argv[1]))
Raw kinetic data Note: Some of the fits show systematic deviations that likely reflect variations in pH and temperature that are not accounted for in the simplified kinetic models.
S27
Figure S26. Monitoring of assembly of KSB-An. Solid lines are the best fits to the kinetic model.
Figure S27. Monitoring of assembly of MEA-An, without added salt. Solid lines are the best fits to the kinetic model.
S28
Figure S28. Monitoring of assembly of MEA-An, with 1 M LiCl. Solid lines are the best fits to the kinetic model.
Figure S29. Monitoring of assembly of MEA-An, with 1 M NaCl. Solid lines are the best fits to the kinetic model.
S29
Figure S30. Monitoring of assembly of MEA-An, with 1 M KCl. Solid lines are the best fits to the kinetic model.
Figure S31. Monitoring of assembly of MEA-An, with 1 M CsCl. Solid lines are the best fits to the kinetic model.
S30
Figure S32. Monitoring of assembly of TEG-Cy, with 1 M LiCl. Solid lines are the best fits to the kinetic model.
Figure S33. Monitoring of assembly of TEG-Cy, with 1 M NaCl. Solid lines are the best fits to the kinetic model.
S31
Figure S34. Monitoring of assembly of TEG-Cy, with 1 M KCl. Solid lines are the best fits to the kinetic model.
Figure S35. Monitoring of assembly of TEG-Cy, with 1 M CsCl. Solid lines are the best fits to the kinetic model.
S32
Figure S36. Monitoring of assembly of PEG-Cy, with 1 M LiCl. Solid lines are the best fits to the kinetic model.
Figure S37. Monitoring of assembly of PEG-Cy, with 1 M NaCl. Solid lines are the best fits to the kinetic model.
S33
Figure S38. Monitoring of assembly of PEG-Cy, with 1 M KCl. Solid lines are the best fits to the kinetic model.
Figure S39. Monitoring of assembly of PEG-Cy, with 1 M CsCl. Solid lines are the best fits to the kinetic model.
Calculated geometries TEG-Cy (B3LYP/6-31G(d)) --------------------------------------------------------------------Center
Atomic
Atomic
Number
Number
Type
Coordinates (Angstroms) X
Y
Z
S34
--------------------------------------------------------------------1
6
0
-1.042692
-2.165139
-2.043552
2
1
0
-1.082960
-3.011364
-2.747538
3
1
0
-2.056330
-2.051400
-1.619099
4
6
0
-0.286686
-3.526665
-0.280925
5
1
0
-1.326196
-3.586716
0.077628
6
1
0
-0.085717
-4.419278
-0.897289
7
6
0
0.651577
-3.496855
0.910398
8
1
0
1.647524
-3.179005
0.565563
9
1
0
0.748516
-4.512001
1.332960
10
6
0
1.102839
-2.104950
2.773151
11
1
0
1.533122
-2.918033
3.384872
12
1
0
1.926424
-1.621464
2.224334
13
6
0
0.452573
-1.090793
3.694722
14
1
0
1.200555
-0.769225
4.440832
15
1
0
-0.384693
-1.558183
4.240481
16
6
0
-0.452573
1.090793
3.694722
17
1
0
-1.200555
0.769225
4.440832
18
1
0
0.384693
1.558183
4.240481
19
6
0
-1.102839
2.104950
2.773151
20
1
0
-1.533122
2.918033
3.384872
21
1
0
-1.926424
1.621464
2.224334
22
6
0
-0.651577
3.496855
0.910398
23
1
0
-1.647524
3.179005
0.565563
24
1
0
-0.748516
4.512001
1.332960
25
6
0
0.286686
3.526665
-0.280925
26
1
0
1.326196
3.586716
0.077628
27
1
0
0.085717
4.419278
-0.897289
28
6
0
1.042692
2.165139
-2.043552
29
1
0
1.082960
3.011364
-2.747538
30
1
0
2.056330
2.051400
-1.619099
31
8
0
0.000000
0.000000
-2.197203
32
8
0
0.082049
2.345890
-1.040520
33
8
0
-0.135168
2.599369
1.871333
34
8
0
0.000000
0.000000
2.924274
35
8
0
0.135168
-2.599369
1.871333
36
8
0
-0.082049
-2.345890
-1.040520
37
6
0
0.764026
0.925514
-2.878866
38
6
0
-0.764026
-0.925514
-2.878866
39
8
0
1.239755
0.744030
-3.965359
40
8
0
-1.239755
-0.744030
-3.965359
---------------------------------------------------------------------
S2 (B3LYP/6-31G(d)) --------------------------------------------------------------------Center
Atomic
Atomic
Number
Number
Type
Coordinates (Angstroms) X
Y
Z
--------------------------------------------------------------------1
6
0
-18.776651
-1.266893
0.195625
2
1
0
-18.832169
-1.535878
1.262695
S35
3
1
0
-18.730777
-2.211997
-0.369363
4
6
0
-15.339477
-0.053112
-0.100229
5
1
0
-15.392506
0.212737
-1.167424
6
1
0
-15.476423
0.870446
0.483374
7
8
0
-21.123115
-1.322288
0.088513
8
1
0
-21.922297
-0.825143
-0.172299
9
6
0
-20.055508
-0.544358
-0.185059
10
8
0
-20.133968
0.563644
-0.665978
11
6
0
-11.730678
-0.620995
0.282787
12
1
0
-11.689205
-1.549471
-0.307787
13
1
0
-11.751108
-0.901213
1.347514
14
6
0
-8.276647
0.578271
-0.068399
15
1
0
-8.396242
1.498125
0.524807
16
1
0
-8.347436
0.853138
-1.132261
17
6
0
-16.438499
-1.049472
0.239860
18
1
0
-16.394769
-1.309351
1.308492
19
1
0
-16.298780
-1.975219
-0.338858
20
6
0
-12.986578
0.162292
-0.072183
21
1
0
-13.030182
1.090154
0.519100
22
1
0
-12.964033
0.443246
-1.136580
23
6
0
-9.376120
-0.413474
0.284151
24
1
0
-9.253512
-1.334248
-0.307207
25
1
0
-9.308600
-0.686874
1.348727
26
8
0
-17.678807
-0.435763
-0.080600
27
8
0
-14.100870
-0.668222
0.207189
28
8
0
-10.617207
0.208678
-0.000489
29
8
0
-7.033802
-0.044515
0.210121
30
6
0
-5.923191
0.781103
-0.091897
31
1
0
-5.950387
1.710370
0.497973
32
1
0
-5.917383
1.059075
-1.157228
33
6
0
-4.666133
-0.008766
0.242772
34
1
0
-4.662801
-0.280994
1.308814
35
1
0
-4.637405
-0.938253
-0.345251
36
8
0
-3.553556
0.820238
-0.069282
37
6
0
-2.325896
0.195855
0.193139
38
1
0
-2.193158
-0.728866
-0.390817
39
1
0
-2.215971
-0.079831
1.255175
40
8
0
-0.000015
0.481944
-0.000101
41
6
0
-1.206461
1.152350
-0.159900
42
8
0
-1.313730
2.280938
-0.548077
43
6
0
2.325878
0.195519
-0.192666
44
1
0
2.216253
-0.081307
-1.254439
45
1
0
2.192877
-0.728555
0.392248
46
6
0
4.666110
-0.009200
-0.241855
47
1
0
4.662992
-0.282073
-1.307734
48
1
0
4.637191
-0.938329
0.346722
49
6
0
5.923156
0.780782
0.092593
50
1
0
5.917293
1.059175
1.157812
51
1
0
5.950398
1.709816
-0.497644
52
6
0
8.276611
0.577852
0.069416
S36
53
1
0
8.347425
0.852768
1.133264
54
1
0
8.396171
1.497681
-0.523834
55
6
0
9.376089
-0.413886
-0.283140
56
1
0
9.308572
-0.687255
-1.347724
57
1
0
9.253479
-1.334678
0.308191
58
6
0
11.730655
-0.621294
-0.282077
59
1
0
11.751019
-0.901195
-1.346888
60
1
0
11.689256
-1.549946
0.308224
61
6
0
12.986554
0.161936
0.073022
62
1
0
12.964158
0.442465
1.137534
63
1
0
13.029999
1.090036
-0.517898
64
6
0
1.206428
1.152524
0.158952
65
8
0
1.313686
2.281633
0.545615
66
8
0
3.553521
0.820071
0.069441
67
8
0
7.033770
-0.044969
-0.209044
68
8
0
10.617175
0.208258
0.001518
69
8
0
14.100861
-0.668387
-0.206860
70
6
0
15.339472
-0.053298
0.100587
71
1
0
15.392710
0.212034
1.167900
72
1
0
15.476191
0.870560
-0.482594
73
6
0
16.438525
-1.049371
-0.240246
74
1
0
16.394567
-1.308730
-1.308995
75
1
0
16.299052
-1.975417
0.338051
76
6
0
18.776715
-1.266525
-0.196748
77
1
0
18.831952
-1.534970
-1.263968
78
1
0
18.731130
-2.211918
0.367781
79
8
0
17.678842
-0.435678
0.080214
80
8
0
21.123219
-1.321650
-0.090394
81
1
0
21.922411
-0.824524
0.170421
82
6
0
20.055589
-0.544011
0.183919
83
8
0
20.134046
0.563749
0.665394
---------------------------------------------------------------------
K+ ⊂ 18-Crown-6 (B3LYP/6-31+G(d,p)) --------------------------------------------------------------------Center
Atomic
Atomic
Number
Number
Type
Coordinates (Angstroms) X
Y
Z
--------------------------------------------------------------------1
6
0
1.192226
3.452321
0.301637
2
1
0
1.203105
4.509227
-0.002467
3
1
0
1.239942
3.407880
1.399724
4
6
0
-1.192333
3.452407
0.301643
5
1
0
-1.240081
3.407868
1.399725
6
1
0
-1.203127
4.509333
-0.002380
7
6
0
-2.394688
2.759221
-0.302075
8
1
0
-2.333700
2.779541
-1.400206
9
1
0
-3.303745
3.297548
0.003675
10
6
0
-3.587342
0.693769
-0.302372
11
1
0
-4.508040
1.212736
0.002044
12
1
0
-3.573561
0.629654
-1.400434
13
6
0
3.587342
-0.693769
0.302372
S37
14
1
0
3.573561
-0.629654
1.400434
15
1
0
4.508040
-1.212736
-0.002044
16
6
0
2.394688
-2.759221
0.302075
17
1
0
3.303745
-3.297548
-0.003675
18
1
0
2.333700
-2.779541
1.400206
19
6
0
1.192333
-3.452407
-0.301643
20
1
0
1.203127
-4.509333
0.002380
21
1
0
1.240081
-3.407868
-1.399725
22
6
0
-1.192226
-3.452321
-0.301637
23
1
0
-1.239942
-3.407880
-1.399724
24
1
0
-1.203105
-4.509227
0.002467
25
6
0
-2.394572
-2.759071
0.302024
26
1
0
-2.333594
-2.779319
1.400156
27
1
0
-3.303619
-3.297437
-0.003682
28
6
0
-3.587278
-0.693691
0.302341
29
1
0
-4.507983
-1.212715
-0.001935
30
1
0
-3.573355
-0.629543
1.400399
31
8
0
2.442229
1.409461
0.162057
32
8
0
-2.442229
-1.409461
-0.162057
33
8
0
0.000079
-2.818813
0.163433
34
8
0
2.442269
-1.409577
-0.161894
35
8
0
-2.442269
1.409577
0.161894
36
8
0
-0.000079
2.818813
-0.163433
37
6
0
2.394572
2.759071
-0.302024
38
1
0
3.303619
3.297437
0.003682
39
1
0
2.333594
2.779319
-1.400156
40
6
0
3.587278
0.693691
-0.302341
41
1
0
3.573355
0.629543
-1.400399
42
1
0
4.507983
1.212715
0.001935
43
19
0
0.000000
0.000000
0.000000
---------------------------------------------------------------------
K+ ⊂ TEG-Cy (B3LYP/6-31+G(d,p)) --------------------------------------------------------------------Center
Atomic
Atomic
Number
Number
Type
Coordinates (Angstroms) X
Y
Z
--------------------------------------------------------------------1
6
0
-0.392403
2.421046
-2.357928
2
1
0
-1.184436
2.854125
-2.986892
3
1
0
0.431904
3.147291
-2.321148
4
6
0
-1.250419
3.308715
-0.334793
5
1
0
-0.353681
3.906417
-0.121246
6
1
0
-1.940856
3.914010
-0.938159
7
6
0
-1.948515
2.921983
0.952583
8
1
0
-2.837240
2.310377
0.733724
9
1
0
-2.282246
3.840585
1.456636
10
6
0
-1.615018
1.790991
3.031152
11
1
0
-1.972005
2.665693
3.593744
12
1
0
-2.474005
1.127404
2.847546
13
6
0
-0.564811
1.070192
3.856743
14
1
0
-1.042385
0.708921
4.777473
S38
15
1
0
0.251873
1.752483
4.128820
16
6
0
0.596272
-1.059186
3.845068
17
1
0
1.060940
-0.652431
4.752736
18
1
0
-0.151306
-1.807391
4.139669
19
6
0
1.688575
-1.690985
3.000749
20
1
0
2.134253
-2.525613
3.561340
21
1
0
2.479971
-0.954733
2.793119
22
6
0
2.088791
-2.804936
0.928549
23
1
0
2.922693
-2.121323
0.708772
24
1
0
2.498035
-3.695142
1.427930
25
6
0
1.421245
-3.241170
-0.359294
26
1
0
0.578360
-3.914031
-0.149768
27
1
0
2.158787
-3.781325
-0.968542
28
6
0
0.524963
-2.389614
-2.388276
29
1
0
1.367852
-2.734919
-3.006224
30
1
0
-0.234979
-3.183310
-2.394162
31
8
0
0.010695
0.005483
-2.399734
32
8
0
0.950073
-2.085165
-1.071401
33
8
0
1.132621
-2.159728
1.769716
34
8
0
-0.042530
-0.021288
3.094546
35
8
0
-1.043873
2.198157
1.785756
36
8
0
-0.877248
2.124550
-1.059676
37
19
0
-0.127243
-0.060646
0.426776
38
6
0
-0.078244
-1.198918
-3.115018
39
6
0
0.131552
1.207870
-3.108018
40
8
0
0.642321
1.286570
-4.185068
41
8
0
-0.612259
-1.289740
-4.179132
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