pro2797-sup-0001-suppinfo01
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Supplementary Information Population shuffling between ground and high energy excited states T. Michael Sabo,* John O. Trent, and Donghan Lee* Supplementary Information Quantification of population shuffling within the millisecond time-scale for leucine π π· π π· Both βπΏπΏ1 and βπΏπΏ2 can be written in terms of the change in the conditional population of either the trans (Δππ‘ ) or the gauche+ (Δππ ) - gauche effect (ΔπΏπΎ ) using equations 1-7 from the main text as follows : π π· π΄ π΅ βπΏπΏ1 = ππ‘π΄ πΏπ‘ + πππ΄ πΏπ + ππ πΏπ − ππ‘π΅ πΏπ‘ − πππ΅ πΏπ − ππ πΏπ (S1) π π· π΄ π΅ βπΏπΏ2 = ππ‘π΄ πΏπ + πππ΄ πΏπ‘ + ππ πΏπ − ππ‘π΅ πΏπ − πππ΅ πΏπ‘ − ππ πΏπ . (S2) Grouping like terms together yields the following formulations: π π· π΄ π΅ βπΏπΏ1 = (ππ‘π΄ − ππ‘π΅ )πΏπ‘ + (πππ΄ + ππ − πππ΅ − ππ )πΏπ (S3) π π· π΄ π΅ )πΏ βπΏπΏ2 = (πππ΄ − πππ΅ )πΏπ‘ + (ππ‘π΄ + ππ − ππ‘π΅ − ππ π. (S4) Since the conditional populations of the three rotameric states must equal one, π΄ ππ‘π΄ + πππ΄ + ππ =1 (S5) π΅ ππ‘π΅ + πππ΅ + ππ =1 (S6) Δππ‘ and Δππ can be expressed in terms of π‘, π, and π: π΄ π΅ Δππ‘ = ππ‘π΄ − ππ‘π΅ = −(πππ΄ + ππ − πππ΅ − ππ ) (S7) π΄ π΅ ). Δππ = πππ΄ − πππ΅ = −(ππ‘π΄ + ππ − ππ‘π΅ − ππ (S8) π π· π π· From here, βπΏπΏ1 and βπΏπΏ2 are described by the following compact equations: π π· βπΏπΏ1 = Δππ‘ ΔπΏπΎ (S9) π π· βπΏπΏ2 = Δππ ΔπΏπΎ . (S10) Ultimately, by solving equations S5 and S6 using equations S7 and S8 with respect to π΄ ππ , the conditional populations of all three rotameric states in both the major (ground) and the minor (excited) conformational states can be expressed in terms of π΄ measured parameters and one unknown population (ππ ): 1 ππ‘π΄ = 2 − 1 πππ΄ = 2 − π΄ ππ 2 π΄ ππ 2 1 ΔπΏ πΆπ +2 (S11) ΔπΏπΎ 1 ΔπΏ πΆπ −2 (S12) ΔπΏπΎ π΄ π΄ ππ = ππ 1 ππ‘π΅ = 2 − 1 πππ΅ = 2 − (S13) π΄ ππ 2 π΄ ππ 2 1 ΔπΏ πΆπ +2 ΔπΏπΎ 1 ΔπΏ πΆπ −2 ΔπΏπΎ − Δππ‘ (S14) − Δππ (S15) π΅ π΄ ππ = ππ + Δππ‘ + Δππ . (S16) π΄ π΅ Since populations should range between 0 and 1, (0 ≤ ππ‘π΄ , πππ΄ , ππ , ππ‘π΅ , πππ΅ , ππ ≤ 1), π΄ these six constraints for ππ can be applied in order to calculate lower and upper bounds on all six rotameric conditional populations: −1 + −1 − ΔπΏ πΆπ ΔπΏπΎ ΔπΏ πΆπ ΔπΏπΎ π΄ ≤ ππ ≤1+ π΄ ≤ ππ ≤1− ΔπΏ πΆπ (S17) ΔπΏπΎ ΔπΏ πΆπ (S18) ΔπΏπΎ π΄ 0 ≤ ππ ≤1 −1 + −1 − ΔπΏ πΆπ ΔπΏπΎ ΔπΏ πΆπ ΔπΏπΎ (S19) π΄ − 2Δππ‘ ≤ ππ ≤ 1+ π΄ − 2Δππ ≤ ππ ≤1− ΔπΏ πΆπ ΔπΏπΎ ΔπΏ πΆπ ΔπΏπΎ − 2Δππ‘ − 2Δππ π΄ −Δππ‘ − Δππ ≤ ππ ≤ 1 − Δππ‘ − Δππ . (S20) (S21) (S22) Quantification of population shuffling within the millisecond time-scale for valine For valine, chemical shifts for the πΎ1 and πΎ2 methyl groups in [13C,1H]-HSQC spectra originate from the major population state and thus the carbon chemical shifts ο€ο§1 and ο€ο§2 can be described as a population weighted sum of the three rotameric states (Figure S1): π΄ πΏπΎ1 = ππ‘π΄ πΏπ‘ + πππ΄ πΏπ + ππ πΏπ‘ (S23) π΄ πΏπΎ2 = ππ‘π΄ πΏπ‘ + πππ΄ πΏπ‘ + ππ πΏπ , (S24) where πΏπ‘ and πΏπ are the chemical shifts of trans and gauche in terms of the ο§-gauche effect, respectively. πππ΄ is the conditional populations of trans (π‘), gauche+ (π), or gauche- (π) rotameric states in the major population state (π΄). Figure S1: Newman projections of valine rotameric states, where the dihedral angle involving the πΎ1 and πΎ2 methyl groups is either in the trans (π‘), gauche+ (π), or gauche- (π) state. Thus, the difference between chemical shifts of two valine methyl group carbons is given by: π΄ π΄ ΔπΏ πΆπ = πΏπΎ1 − πΏπΎ2 = ππ ΔπΏπΎ − πππ΄ ΔπΏπΎ = (ππ − πππ΄ )ΔπΏπΎ (S25) where ΔπΏπΎ = πΏπ‘ − πΏπ = 5 ppm originates from the ο§-gauche effect.[1] As measured by π π·, the chemical shift difference between the major population state (πΏ π΄ ) and the minor population state (πΏ π΅ ) is Δδπ π· = πΏ π΄ − πΏ π΅ . In the case of valine, the chemical shift difference measured for the πΎ1 and πΎ2 methyl group carbons by π π· is: π π· π΄ π΅ βπΏπΎ1 = πΏπΎ1 − πΏπΎ1 (S26) π π· π΄ π΅ βπΏπΎ2 = πΏπΎ2 − πΏπΎ2 . (S27) π π· π π· Both βπΏπΎ1 and βπΏπΎ2 can be written in terms of the change in the conditional population of either the trans (Δππ‘ ) or the gauche+ (Δππ ) rotameric states and the ο§gauche effect (ΔπΏπΎ ) as follows: π π· π΄ π΅ βπΏπΎ1 = ππ‘π΄ πΏπ‘ + πππ΄ πΏπ + ππ πΏπ‘ − ππ‘π΅ πΏπ‘ − πππ΅ πΏπ − ππ πΏπ‘ (S28) π π· π΄ π΅ βπΏπΎ2 = ππ‘π΄ πΏπ‘ + πππ΄ πΏπ‘ + ππ πΏπ − ππ‘π΅ πΏπ‘ − πππ΅ πΏπ‘ − ππ πΏπ (S29) Grouping like terms together yields the following formulations: π π· π΄ π΅ )πΏ π΄ π΅ βπΏπΎ1 = (ππ‘π΄ + ππ − ππ‘π΅ − ππ π‘ + (ππ − ππ )πΏπ (S30) π π· π΄ π΅ )πΏ βπΏπΎ2 = (ππ‘π΄ + πππ΄ − ππ‘π΅ − πππ΅ )πΏπ‘ + (ππ − ππ π (S31) Since the conditional populations of the three rotameric states must equal one as shown in equations 10 and 11, Δππ and Δππ can be expressed in terms of π‘, π, and π: π΄ π΅) Δππ = −(πππ΄ − πππ΅ ) = (ππ‘π΄ + ππ − ππ‘π΅ − ππ (S32) π΄ π΅) Δππ = −(ππ − ππ = (ππ‘π΄ + πππ΄ − ππ‘π΅ − πππ΅ ). (S33) π π· π π· From here, βπΏπΎ1 and βπΏπΎ2 are described by the following compact equations: π π· βπΏπΎ1 = −Δππ ΔπΏπΎ (S34) π π· βπΏπΎ2 = −Δππ ΔπΏπΎ . (S35) By swapping the populations from equations S17-S22, these constraints can be applied in order to calculate lower and upper bounds on all six rotameric conditional populations for valine π1 dihedral angles. Molecular Dynamics (MD) Simulation Molecular models of protein structures were obtained from the Protein Data Bank, entries 2L2P[2] (I form) and 2LP5[2] (F form). The NMR structure files contained multiple models, and the first model in the PDB file was selected for AMBER MD simulations.[3] The force fields used were ff14SB, ff12SB, ff99SB-ildn, and ff99SB, and the system was solvated in a rectilinear box of TIP3P water molecules with 15 Å buffers and neutralizing Na+ ions were added to the protein using standard Leap rules. The system was heated and equilibrated using the following protocol: (i) minimize water and ions holding the protein fixed (50 kcal/mol/Å), (ii) 25 ps MD (heating to 100 K) holding the protein fixed, (iii) repeat step (i), (iv) minimize all atoms, (v) 25 ps MD (heating to 300 K) holding the protein fixed (ii), (vi) 10 ns MD (T = 300 K) equilibration holding the protein fixed (10 kcal/mol/Å) to finish the equilibrium. Production runs of 500 ns after the final equilibration step were carried out to obtain snapshots at 20 ps interval for a total of 25,000 snapshots. Simulations were performed in the isothermal isobaric ensemble (P = 1 atm, T = 300 K) using sander and the GPU version of pmemd. Periodic boundary conditions and Particle-MeshEwald algorithms were used. A 2.0 fs time step was used with bonds involving hydrogen atoms frozen using SHAKE. Analysis of the trajectory was performed using the cpptraj module of the AmberTools 15 Package.[3] Leucine ο£2 dihedral angles were binned as gauche+ (0°-120°), trans (121°-240°), and gauche- (241°-360°) rotamers (Figures S2, S3, S4, and S5). L3 1500 L29 2000 1500 1000 1000 500 500 0 0 50 100 150 200 250 300 Counts 1000 350 L7 50 100 150 200 250 300 350 L42 1200 1000 800 800 600 600 400 400 200 200 0 0 50 100 150 200 250 1400 300 350 L18 1200 50 100 150 200 250 300 L55 1500 1000 1000 800 600 500 400 200 0 0 50 100 150 200 250 300 50 100 150 200 250 300 350 Leucine c2 dihedral angle Figure S2: Histogram representation of the leucine π2 dihedral angle determined from 500 nanosecond molecular dynamics simulations with the ff14SB force field of 2LP5 for the F form (blue) and 2L2P for the I form (orange). For L55 centered at 100° is a significant population of a gauche 100 rotamaric state, which has been observed for the π2 dihedral angle in isoleucine.[4,5] 2000 L3 L29 1000 1500 800 600 1000 400 500 200 0 50 100 150 200 250 300 1400 350 L7 0 50 100 150 200 250 300 L42 800 Counts 1200 1000 600 800 400 600 400 200 200 0 50 100 150 200 250 300 350 L18 0 50 100 150 200 250 300 350 L55 1500 1500 1000 1000 500 500 0 0 50 100 150 200 250 300 50 100 150 200 250 300 350 Leucine c2 dihedral angle Figure S3: Histogram representation of the leucine π2 dihedral angle determined from 500 nanosecond molecular dynamics simulations with the ff12SB force field of 2LP5 for the F form (blue) and 2L2P for the I form (orange). For L55 centered at 100° is a significant population of a gauche 100 rotamaric state, which has been observed for the π2 dihedral angle in isoleucine.[4,5] L3 1400 L29 2000 1200 1500 1000 800 1000 600 400 500 200 0 50 100 150 200 250 300 1200 350 L7 50 100 150 200 250 300 350 L42 1500 1000 Counts 0 800 1000 600 400 500 200 0 0 50 100 150 200 250 300 350 L18 1200 50 100 150 200 250 300 2000 350 L55 1000 1500 800 1000 600 400 500 200 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Leucine c2 dihedral angle Figure S4: Histogram representation of the leucine π2 dihedral angle determined from 500 nanosecond molecular dynamics simulations with the ff99SB-ildn force field of 2LP5 for the F form (blue) and 2L2P for the I form (orange). For L55 centered at 100° is a significant population of a gauche 100 rotamaric state, which has been observed for the π2 dihedral angle in isoleucine.[4,5] L3 1400 L29 1500 1200 1000 1000 800 600 500 400 200 0 0 50 100 150 200 250 L7 2000 Counts 300 50 100 150 200 250 300 350 L42 1500 1500 1000 1000 500 500 0 0 50 100 150 200 250 2000 300 L18 50 100 150 200 250 300 1400 L55 1200 1500 1000 800 1000 600 400 500 200 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Leucine c2 dihedral angle Figure S5: Histogram representation of the leucine π2 dihedral angle determined from 500 nanosecond molecular dynamics simulations with the ff99SB force field of 2LP5 for the F form (blue) and 2L2P for the I form (orange). For L55 centered at 100° is a significant population of a gauche 100 rotamaric state, which has been observed for the π2 dihedral angle in isoleucine.[4,5] Table S1: Conditional π2 rotamer populations for leucine methyl groups from the major (folded) and minor (unfolded) states of the G48M Fyn SH3 domain. Major (Folded) state Minor (Unfolded) state π΄ π΄ πΆπ π΅ π΅ π΅ ππ ππ ππ ππ‘ ππ‘π΄ ππ‘ ππ Residue Boundsa 0.60 0.40 0 0.51 0.27 0.22 L3 0.6 0.47 ± 0.13 0.27 ± 0.13 0.27 ± 0.27 0.38 ± 0.13 0.13 ± 0.13 0.49 ± 0.27 Medianb Bounds 0.73 0.07 0.21 0.63 0.37 0 L7 0.83 0.69 ± 0.03 0.03 ± 0.03 0.27 ± 0.07 0.60 ± 0.03 0.34 ± 0.03 0.07 ± 0.07 Median Bounds 0.56 0.44 0 0.48 0.11 0.41 L18 0.56 0.51 ± 0.05 0.39 ± 0.05 0.11 ± 0.11 0.43 ± 0.05 0.05 ± 0.05 0.52 ± 0.11 Median Bounds 0.81 0.13 0.06 0.65 0.36 0 L29 0.84 0.74 ± 0.07 0.07 ± 0.07 0.19 ± 0.13 0.58 ± 0.07 0.29 ± 0.07 0.13 ± 0.13 Median Bounds 0.66 0.34 0 0.61 0.25 0.14 L42 0.66 0.53 ± 0.13 0.21 ± 0.13 0.25 ± 0.25 0.48 ± 0.13 0.13 ± 0.13 0.39 ± 0.25 Median aBounds refer to the upper bounds for π and π and the lower bound for π . π‘ π π bMedian refers to the spread of potential populations between the upper and lower bounds for each rotameric state. ππ‘πΆπ is calculated according to reference [6] and presented in reference [7]. Table S2: Conditional π2 rotamer populations for leucine methyl groups from the major (folded) and minor (folding intermediate) states of the A39V/N53P/V55L Fyn SH3 domain. Major (Folded) state Minor (Folding Intermediate) state π΄ πΆπ π΄ π΄ π΅ π΅ πππ΅ π ππ‘ ππ ππ‘ ππ‘ ππ Residue π Bounds 0.63 0.29 0.08 0.63 0.37 0 L3 0.67 0.48 ± 0.14 0.23 ± 0.14 0.29 ± 0.29 Median 0.47 ± 0.14 0.14 ± 0.14 0.37 ± 0.29 Bounds 0.76 0.09 0.15 0.78 0.22 0 L7 0.83 0.73 ± 0.05 0.18 ± 0.05 0.09 ± 0.09 Median 0.71 ± 0.05 0.05 ± 0.05 0.24 ± 0.09 0.61 0.40 0 0.61 0.27 0.13 Bounds L18 0.61 0.47 ± 0.13 0.26 ± 0.13 0.27 ± 0.27 0.47 ± 0.13 0.13 ± 0.13 0.39 ± 0.27 Median Bounds 0.84 0.16 0 0.84 0.16 0 L29 0.84 0.76 ± 0.08 0.08 ± 0.08 0.16 ± 0.16 Median 0.76 ± 0.08 0.08 ± 0.08 0.16 ± 0.16 Bounds 0.70 0.30 0 0.70 0.23 0.07 L42 0.70 0.59 ± 0.11 0.11 ± 0.11 0.30 ± 0.23 Median 0.59 ± 0.11 0.19 ± 0.11 0.23 ± 0.23 Bounds 0.68 0.15 0.17 0.64 0.36 0 L55 0.77 0.56 ± 0.07 0.29 ± 0.07 0.15 ± 0.15 Median 0.60 ± 0.07 0.07 ± 0.07 0.32 ± 0.15 aBounds refer to the upper bounds for π and π and the lower bound for π . π‘ π π bMedian refers to the spread of potential populations between the upper and lower bounds for each rotameric state. ππ‘πΆπ is calculated according to reference [6] and presented in reference [7]. π π· π π· Table S3: βπΏπΏ1 and βπΏπΏ2 calculated from the NMR data and from the Molecular Dynamics simulations of the major (folded) and minor (folding intermediate) states of the A39V/N53P/V55L Fyn SH3 domain. Residue NMR ff14SB ff12SB ff99SB-ildn ff99SB L3 0.00 1.34 0.54 0.60 0.19 L7 -0.10 -0.18 -0.49 -0.12 -0.51 π π· L18 0.00 -2.19 1.28 -1.17 -0.12 βπΏπΏ1 L29 0.00 -0.05 0.21 0.23 0.72 L42 0.00 -1.09 0.00 -1.23 -0.53 L3 -0.40 -1.32 -0.44 -0.27 -0.08 L7 -0.65 0.28 0.60 0.25 0.55 π π· L18 0.65 2.18 -1.30 1.16 0.09 βπΏπΏ2 L29 0.00 0.06 -0.20 -0.14 -0.68 L42 0.35 0.81 0.01 0.83 0.49 ππ‘πΆπ 0.62 0.63 0.69 0.65 0.68 ππ‘πΆπ 0.63 0.78 0.67 0.84 0.74 0.64 Table S4: Conditional π2 rotamer populations for leucine methyl groups calculated from the Molecular Dynamics simulations of major (folded) and minor (folding intermediate) states of the A39V/N53P/V55L Fyn SH3 domain. ff14SB Major (Folded) state Minor (Folding Intermediate) state π΄ π΅ πππ΅ Residue πππ΄ ππ‘π΄ ππ ππ‘π΅ ππ L3 0.83 0.15 0.02 0.56 0.41 0.02 L7 0.57 0.43 0 0.61 0.37 0.02 L18 0.36 0.64 0 0.80 0.20 0 L29 0.91 0.08 0.01 0.92 0.07 0.01 L42 0.53 0.40 0.07 0.74 0.24 0.01 ff12SB Major (Folded) state Minor (Folding Intermediate) state π΄ π΅ πππ΅ Residue πππ΄ ππ ππ‘π΅ ππ‘π΄ ππ L3 0.60 0.38 0.02 0.49 0.47 0.04 L7 0.36 0.64 0 0.46 0.52 0.02 L18 0.82 0.17 0 0.56 0.43 0 L29 0.92 0.08 0 0.88 0.12 0 L42 0.55 0.44 0.02 0.54 0.43 0.02 ff99SB-ildn Major (Folded) state Minor (Folding Intermediate) state π΄ π΅ πππ΅ Residue πππ΄ ππ ππ‘π΅ ππ ππ‘π΄ L3 0.73 0.25 0.02 0.61 0.31 0.08 L7 0.61 0.39 0.01 0.63 0.33 0.03 L18 0.71 0.28 0 0.95 0.05 0 L29 0.94 0.05 0 0.90 0.08 0.02 L42 0.60 0.30 0.10 0.85 0.13 0.02 ff99SB Major (Folded) state Minor (Folding Intermediate) state π΄ π΄ π΄ π΅ πππ΅ Residue π ππ‘π΅ ππ‘ ππ ππ π L3 0.33 0.66 0.01 0.29 0.68 0.03 L7 0.07 0.93 0 0.18 0.82 0.01 L18 0.10 0.89 0.01 0.13 0.87 0 L29 0.73 0.26 0.02 0.58 0.39 0.03 L42 0.14 0.81 0.05 0.25 0.71 0.04 Supplementary References [1] A. E. Tonelli, F. C. Schilling, Acc. Chem. Res. 1981, 14, 233–238. [2] P. Neudecker, P. Robustelli, A. Cavalli, P. Walsh, P. Lundström, A. ZarrineAfsar, S. Sharpe, M. Vendruscolo, L. E. Kay, Science 2012, 336, 362–366. [3] D. A. Case, V. Babin, J. Berryman, R. M. Betz, Q. Cai, D. S. Cerutti, T. E. Cheatham III, T. A. Darden, R. E. Duke, H. Gohlke, et al., 2015 AMBER 2015, University of California, San Francisco. [4] D. F. Hansen, P. Neudecker, L. E. Kay, J. Am. Chem. Soc. 2010, 132, 7589– 7591. [5] S. C. Lovell, J. M. Word, J. S. Richardson, D. C. Richardson, Proteins 2000, 40, 389–408. [6] F. A. A. Mulder, Chembiochem 2009, 10, 1477–1479. [7] D. F. Hansen, P. Neudecker, P. Vallurupalli, F. A. A. Mulder, L. E. Kay, J. Am. Chem. Soc. 2010, 132, 42–43.
