Native state conformation of the I27 domain of titin (PDB ID: 1TIT). There are 8 -strands: A (4–7), A′ (11–15), B (18–25), C (32–36), D (47–52), E (55–61), F(69–75), and G (78–88). (a) PDB structure in cartoon representation. (b) Schematic view of the same structure. Red and black -strands belong to different -sheets. N- and C-terminal residues are marked N and C, respectively.
The f − T phase diagram obtained by the extended histogram method. The results were averaged over 30 trajectories. The vertical dashed line marks K at which most of our calculations have been performed.
Averaged force-extension profiles of the I27 titin domain. The results obtained by Go-model simulations performed at different pulling speeds are shown on the right. The inset shows an enlargement of the starting region. Results have been averaged over 50 trajectories. Values of pulling rates are given in Table I .
Individual force-extension profiles of the I27 titin domain. Four individual trajectories at 2.5 × 104 nm/s obtained by Go-model simulations are presented. There is no second peak in two trajectories.
(a)–(f) End-to-end distance dependence of averaged fractions of native contacts. Native contacts are formed by 8 -strands marked in Fig. 1 at different loading rates. Clearly, the unfolding at high forces starts from the C-terminus detaching G-strand first. In contrast, at low forces the A and A′ strands are unfolded first, but it should be noted that the extension at which complete detachment of the A strand takes place is rather large, 75 Å.
(a)–(f) End-to-end distance dependence of averaged fractions of native contacts. Same as Fig. 5 but for the end-to-end distance up to 15 Å. Within 15 Å the detachment of the A strand out of the protein core is not observed for any speed studied.
Typical unfolding pathway of titin from Go-model simulation. Green and blue squares mark AB and A′G regions, respectively. The N-terminal residue is shown in magenta. (a) NS conformation. (b) Conformation at 4 Å extension, contacts between AG are missing, both A′G and AB remained formed. (c) Conformation at 9 Å extension (after the main peak), contacts between G with A and A′ are broken, those between the A and B strands are preserved. It should be emphasized that 100% trajectories at the beginning of unfolding (within 10 Å) proceed via the same pathway presented here regardless of the applied pulling rate.
Typical unfolding pathways of titin. (a)–(d) High pulling speed and (e)–(h) low pulling speed regions. The N-terminal residue is shown in magenta.
Force dependence on pulling speeds at T = 285 K. Force at a given value of pulling speed is computed as an average of maximum forces over 50 trajectories. Grey boundaries of the polygon illustrate the interval of pulling rates used in the AFM experiment. Black circles correspond to data for F max1. Solid and dashed black curves represent linear and nonlinear fits for F max1. Similarly, red color is used for F max2. Straight lines are fits to the Bell-Evans-Ritchie equation (Eq. (7) ), y = 109.6 + 9.59ln (x) and y = −90.332 + 12.108ln (x) for F max1 and F max2, respectively. Using a linear fit we found x u(N → TS1) = 3.76 Å and x u(IS → DS) = 2.95 Å for F max1 and F max2, respectively. From a nonlinear fit and Eq. (8) , we got x u = 6.68 Å and ΔG ‡ = 32.48k B T for F max1 and x u = 3.88 Å and ΔG ‡ = 9.22k B T for F max2. Extrapolation to the experimental pulling speed, v = 200 nm/s, gives a negative value of F max2 regardless of the fit used. Extrapolated values of F max1 to 200 nm/s are 160 and 152 pN using linear and nonlinear fits, respectively.
List of pulling speeds used in simulations. The upper limit for pulling speed used in the AFM experiment is 104 nm/s (taken from Ref. 28 ).
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