Structure-based model fails to probe mechanical unfolding pathways of titin I27 domain Maksim Kouza∗ Faculty of Chemistry, University of Warsaw, Pasteura 1 02-093 Warsaw, Poland Chin-Kun Hu† Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan Mai Suan Li‡ Institute of Physics, Polish Academy of Science, Al. Lotnikow 32/46 02-668 Warsaw, Poland Andrzej Kolinski§ Faculty of Chemistry, University of Warsaw, Pasteura 1 02-093 Warsaw, Poland and (Dated: August 14, 2013)
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Supplementary Material Existence of two peaks in force-extension profile by all-atom modeling. An interesting question is whether the peak around 8 nm is an artefact of Go-models. To check this, we performed all-atom simulations in explicit solvent. We used the AMBER99SB force field [1] to model I27 (pdb code: 1TIT) which has 89 amino acids, and the TIP3P water model [2] to describe the solvent. The GROMACS version 4.6 [3] has been employed. The protein was placed in a box with the edges of 5.2, 4.8, and 39 nm with 31805 water molecules. Six sodium ions were injected to neutralize the system’s charge. The equations of motion were integrated by using a leap-frog algorithm with a time step of 2 fs. The LINCS [4] was used to constrain bond lengths with a relative geometric tolerance of 10−4 . We used the particle-mesh Ewald method to treat the long-range electrostatic interactions[5]. The nonbonded interaction pair-list were updated every 10 fs, using a cutoff of 1.0 nm. The protein was minimized using the steepest decent method. Subsequently, the system was equilibrated at constant temperature T= 300 K and constant volume. Afterward, the N-terminal was kept fixed and the force was applied to the C-terminal through a virtual cantilever moving at the constant velocity v along the biggest z-axis of simulation box. The spring constant was chosen as k = 1700 pN/nm which is an upper limit for k of a cantilever used in AFM experiments. Movement of the pulled termini causes an extension of the protein and the total force can be measured by F = k(vt − x), where x is the displacement of the pulled atom from its original position. The resulting force is computed for each time step to generate a force extension profile, which has peaks showing the most mechanically stable places in a protein. Overall, the simulation procedure is similar to the experimental one, except that pulling speeds in our simulations are several orders of magnitude higher than those used in experiments. We performed simulations for v = 5 × 108 nm/s, while in the AFM experiments one used v = 102 − 104 nm/s. The resulting force-extension profiles of three trajectories are shown on Fig. S1. The presence of the peak around 8 nm extension is clearly observed in all three trajectories. Therefore, in agreement with the Go-model simulation results the existence of previously undetected additional transition state is predicted using more sophisticated all-atom modeling in explicit solvent. The molecular origin of the hump and the first peak are in full accord with AFM exper2
iments. Fig. S2b shows that at about 7.5˚ A when protein passes the first transition state, all hydrogen bonds between A and B strands are broken while those between A’ and G are preserved. On Fig. S2c it is shown the conformation shortly after the protein passes the second transition state. Strands A’ and G are no longer connected by hydrogen bonds.
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Force (kJ/mol/nm)
700 600 500 400 300 200 100 0
TRAJ1 TRAJ2 TRAJ3
0
2.5
5
7.5
10
12.5
End-To-End Distance (nm)
FIG. 1: Fig. S1. Force-extension profiles of three trajectories for v = 5 × 108 nm/s. The data suggest that the presence of two peaks is not an artefact of Go-modeling
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NS
7.5 A
(a)
(b)
12 A
(c)
FIG. 2: Fig. S2. Typical unfolding pathway of titin from all-atom simulation in explicit solvent. The green and blue squares mark AB and A’G regions, respectively. The N-terminal residue is ˚ extension. A and shown in magenta. (a) Native state conformation. (b) Conformation at 7.5A B strands are separated, HBs between them are broken. At same time strands A’ and G are still ˚ extension (after main peak). HBs between A and B connected by HBs. (c) Conformation at 12A as well as A’ and G are broken.
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Fmax1
Fmax2
TS1
Force
Fhump TS2 TS2
TS1 IS IS
End−To−End Distance
FIG. 3: Fig. S3. Sketch of force-extension profile of titin I27 domain. Black curve represents the data obtained in AFM experiments. Fhump shows approximately the position of the hump, Fmax1 indicates the position of the first (or main) peak. Since IS is populated, the the hump is related to TS1, while the first peak is related to TS2. Red curve represents force-extension profile obtained by Go-model simulation at pulling velocities above v = 104 nm/s. As discussed in text, an experimentally determined IS is not populated in Go-model simulation and hump is not a signature of transition state. Thus, main peak is the TS1, while the second peak, which position is marked by Fmax2 , is TS2.
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[1] W. D. Cornell et al., JACS 117, 5179 (1995). [2] W. L. Jorgenson, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983). [3] B. Hess, C. Kutzner, D. van der Spoel, and E. Lindahl, J. Chem. Theory Comput. 4, 435 (2008). [4] B. Hess, H. Bekker, H. J. C. Berendsen, and J. G. E. M. Fraaije, J. Comp. Chem. 18, 1463 (1997). [5] T. Darden, D. York, and L. Pedersen, J. Chem. Phys. 98, 10089 (1993).
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