advances.sciencemag.org/cgi/content/full/3/5/e1601684/DC1

Supplementary Materials for

Directional mechanical stability of Bacteriophage ϕ29 motor’s

3WJ-pRNA: Extraordinary robustness along portal axis

Zhonghe Xu, Yang Sun, Jeffrey K. Weber, Yi Cao, Wei Wang, Daniel Jasinski, Peixuan Guo,

Ruhong Zhou, Jingyuan Li

Published 26 May 2017, Sci. Adv. 3, e1601684 (2017)

DOI: 10.1126/sciadv.1601684

This PDF file includes:

discussion S1. Divalent ion models studied in this work and the corresponding

results.

discussion S2. Extrapolation of lifetime of folded state to the loaded force of 20

pN from SMD simulations and AFM experiments

table S1. The dimension of simulation systems.

table S2. The parameters of divalent ions.

fig. S1. Force profiles during the unfolding along H1-H3 (16 trajectories).

fig. S2. Structural analysis of 3WJ-pRNA during the unfolding along H1-H3.

fig. S3. Force profiles of 3WJ-pRNA during the unfolding along H1-H3 (eight

trajectories).

fig. S4. Force profiles during the unfolding along H1-H3 (pulling rate is 1 nm/ns).

fig. S5. Cooperativity of two Mg clamps during mechanical unfolding.

fig. S6. Force profiles during the unfolding along H1-H3 using the Merz model of

Mg2+ ions.

fig. S7. Relaxation and mechanical unfolding of 3WJ-pRNA using the Aqvist

model of Ca2+ ions.

fig. S8. Relaxation and mechanical unfolding of 3WJ-pRNA using the Merz

model of Ca2+ ions.

fig. S9. Mechanical unfolding of 3WJ-pRNA under transverse (H1-H2) pulling.

fig. S10. Mechanical unfolding of 3WJ-pRNA under transverse (H2-H3) pulling.

fig. S11. Force profiles of 3WJ-pRNA with force applied to the termini of H1 at a

pulling rate of 0.1 nm/ns.

fig S12. Representative length-time traces of 3WJ-pRNA when constant force is

loaded onto the terminus of H1.

fig S13. Distribution of unfolding times for the pRNA-3WJ under the loading

forces of 1600 and 2000 pN.

fig. S14. Dependence of the rupture force on the loading rate.

fig. S15. Schematic of 3WJ-pRNA in the crystal structure (4KZ2), where three

base pairs (bold) are attached to the terminus of H3.

References (54–56)

discussion S1. Divalent ion models studied in this work and the

corresponding results.

In this work, we employed two recently developed Mg2+ ions models to evaluate the

stabilizing role of Mg2+ ions on the 3WJ-pRNA under investigation. One model was

parameterized, by Villa et al., to reproduce experimental kinetic features of Mg2+ in

aqueous solution, such as the ion-water exchange rate and association properties with

nucleic acid phosphate groups (45). These features of Mg2+ are quite distinct from those

of other divalent cations, making them crucial for modeling the stabilizing effects of

Mg2+ on RNA. Accordingly the model of Villa was applied in our simulations unless

specifically stated otherwise. The alternative set of Mg2+ parameters tested here,

developed by Merz et al, was designed to specifically reproduce experimental

thermodynamic values like the ion-oxygen distance and ion hydration free energy (47).

Another divalent ion, Ca2+, was employed as a control to validate the specific effect of

Mg2+ on RNA stability. Two Ca2+ ion models were applied in our computations: those

of Aqvist and Merz (46, 47). The parameters of all divalent ion models used our

simulations are listed in table S2.

For each of these four systems, 10000 step energy minimization and 5 ns NPT

equilibration runs were conducted with harmonic restraints on RNA heavy atoms and

divalent ions. Subsequently, the divalent ions bound to RNA were further relaxed in 5

ns NPT simulations with the RNA restrained. Finally, the systems were equilibrated for

50 ns (Mg2+ ion) or 100 ns (Ca2+ ion) within the NPT ensemble without any restraints.

These equilibrated RNA configurations were then used as starting structures for steered

molecular dynamic (SMD) simulations.

In addition to using Villa’s Mg2+ model, we also conducted SMD simulations of the

3WJ-pRNA with the Merz model. The unfolding process, in that case, is similar to that

seen with the Villa model, exhibiting an average rupture force of 1918±143 pN (fig. S6).

The potential for the binding of Ca2+ ions to the 3WJ-pRNA was also investigated. In

all instances, Ca2+ ions were initiated in the Mg2+ binding sites. For the Aqvist model,

both Ca2+ ions dissociated from their original binding sites within 20 ns of simulation

time; this 3WJ-pRNA could not resist the force applied in the early stages of pulling

(fig. S7). In the case of the Merz model, the calcium ions do stay in their original

binding sites, but cannot simultaneously interact with the phosphates of both H1 and

H3 to form a “Ca-clamp”. Thus, this Ca-bound 3WJ-pRNA also does not exhibit

resistance to stretching (fig. S8). In short, current divalent ion force fields seem to

effectively discriminate between the binding behaviors of Mg2+ and Ca2+ ions, and

describe the specific effects of Mg2+ ions well.

discussion S2. Extrapolation of lifetime of folded state to the loaded

force of 20 pN from SMD simulations and AFM experiments.

The mechanical unfolding of the 3WJ-pRNA was studied using SMD simulations with

coaxial pulling rates ranging from 0.01 to 1 nm/ns (figs. S1 to S3). The dependence of

the rupture force on the loading rate is summarized in fig. S14, wherein the loading rate,

r, is described by r=ksv (ks and v are the spring constant and pulling rate, respectively).

The relationship between the rupture force, F, and unfolding rate, k0, can be described

by the Bell-Evans formula: F(r)=(kBT/Δx)ln[rΔx/(k0kBT)], where k0 is unfolding rate at

zero force, kB is Boltzmann constant, T is the temperature, and Δx is the distance to the

transition state. For our constant velocity SMD data, we estimated k0 = 0.0121 s-1 and

Δx = 0.53 Å. Both values are close to those derived from constant force simulations: k0

= 0.0078 s-1 and Δx = 0.56 Å. Applying the Bell model k(F)=k0exp(FΔx/kBT) to the

fitting parameters (k0 and Δx), the unfolding rates at operational load (20 pN, the force

exerted by the 29 ATPase) k(20) are estimated to be 0.0156 and 0.0103 s-1 in each

respective dataset.

We also studied average rupture forces as a function of the loading rate on the basis of

AFM experiment results (Fig. 5E). The rupture force increases logarithmically with the

loading rate, r, a relationship that can also be described by Bell-Evans formulas. The

unfolding rate at zero force, k0, and the distance to the transition state, Δx, are extracted

from slope and intercept of plot: k0 = 0.015 s-1 and Δx = 2 Ǻ (Fig. 5E). Applying the Bell

model to the fitting parameters (k0 and Δx), we estimate an unfolding rate at operational

load, k(20), of 0.039 s-1. This value agrees reasonably well with simulation results. The

value of τ20, the lifetime of the folded state, can be obtained simply by taking the

reciprocal of this unfolding rate.

One should note that the assumption of the Bell model (that the distance to the

transition state, Δx, is independent of the applied force) cannot hold true for all forces;

As the force increases, the transition state could move closer to the native state, as

dicatated by the “Hammond effect”(54–56). This effect may account for the shorter Δx

derived from SMD simulations than estimated from AFM experiments.

table S1. The dimension of simulation systems.

Pulling direction X (nm) Y (nm) Z (nm)

H1-H2 7.5 7.5 25

H2-H3 7.5 7.5 25

H1-H3 7.8 7.8 21

H1 7.8 7.8 15

table S2. The parameters of divalent ions.

Mg-Villa Mg-Merz Ca-Aqvist Ca-Merz

(kJ/mol) 0.012343 0.042687 1.92376 0.443205

(Å) 2.770 2.423 3.052 2.938

fig. S1. Force profiles during the unfolding along H1-H3 (16 trajectories). The rupture forces

are 2143, 1809, 1917, 1900, 1885, 1719, 2093, 2109, 1923, 1983, 2151, 2176, 2006, 1943, 2083 and

1935 pN; the average rupture force is 1990±126 pN.

fig. S2. Structural analysis of 3WJ-pRNA during the unfolding along H1-H3. (A) The number

of interbase hydrogen bonds within the 3WJ-pRNA as a function of time, as pulling proceeds. (B)

Representative snapshots of the 3WJ-pRNA at t = 80 and 86 ns, i.e. before and after the relative

reconfiguration of strand C with respect to strands A and B.

fig. S3. Force profiles of 3WJ-pRNA during the unfolding along H1-H3 (eight trajectories).

pulling rate is 0.01nm/ns. The rupture forces are 1795, 1865, 1893, 1746, 1974, 1910,1856 and 1778

pN; the average rupture force is 1854±72 pN.

fig. S4. Force profiles during the unfolding along H1-H3 (pulling rate is 1 nm/ns). The rupture

forces are 2185, 2275, 2331, 2181, 2183, 2187, 2257, 2348, 2137, 2110, 2180, 2387, 2204 2210,

2144 and 2165 pN; the average rupture force is 2217±77 pN.

fig. S5. Cooperativity of two Mg clamps during mechanical unfolding. Mechanical unfolding

along the coaxial direction with 0.01 nm/ns (A), 0.1 nm/ns (B), and 1 nm/ns (C) pulling rates and

under biomimetic conditions (D). The force curve (black) is shown along with the interphosphate

distances: G23-A90 (red), C24-A89 (blue).

fig. S6. Force profiles during the unfolding along H1-H3 using the Merz model of Mg2+ ions.

The pulling rate was set to 0.1 nm/ns. The rupture forces are 2119, 1755, 1920 and 1865 pN, and the

average rupture force was 1918±143 pN.

fig. S7. Relaxation and mechanical unfolding of 3WJ-pRNA using the Aqvist model of Ca2+

ions. (A) Representative snapshots of 3WJ-pRNA with Ca2+ bound during relaxation. (B)

Mechanical unfolding of 3WJ-pRNA with Ca2+ ions under coaxial pulling at a rate of 0.1nm/ns. Left:

force profile; Right: The root mean square deviation (RMSD) of 3WJ-pRNA atomic positions

during mechanical unfolding.

fig. S8. Relaxation and mechanical unfolding of 3WJ-pRNA using the Merz model of Ca2+

ions. (A) Coordination interactions of Ca2+ ions during relaxation. (B) Mechanical unfolding of the

3WJ-pRNA with Ca2+ ions under coaxial pulling at a rate of 0.1nm/ns. Left: force profile; Right: the

root mean square deviation (RMSD) of 3WJ-pRNA atomic positions during mechanical unfolding.

fig. S9. Mechanical unfolding of 3WJ-pRNA under transverse (H1-H2) pulling. (A and B)

Representative snapshots of 3WJ-pRNA at t = 0 and 40 ns. (C) The force profile of the

3WJ-pRNA. (D) The root mean square deviation (RMSD) of 3WJ-pRNA atomic positions.

fig. S10. Mechanical unfolding of 3WJ-pRNA under transverse (H2-H3) pulling. (A and B)

Representative snapshots of the 3WJ-pRNA at t = 0 and 60 ns. (C) The force profile of the

3WJ-pRNA. (D) The root mean square deviation (RMSD) of 3WJ-pRNA atomic positions.

fig. S11. Force profiles of 3WJ-pRNA with force applied to the termini of H1 at a pulling rate

of 0.1 nm/ns. The rupture forces are 2148, 1942, 1810, 2227, 1977, 1791, 2226, 1962, 1927, 2156,

2093, 2156, 1827, 2176, 1945 and 1962 pN; the average rupture force is 2020±144 pN.

fig S12. Representative length-time traces of 3WJ-pRNA when constant force is loaded onto

the terminus of H1. (A and B) Distance between termini of H1 and H3 with the loading force of

2000 and 1600 pN, respectively. Both traces show typical two-state unfolding processes.

fig S13. Distribution of unfolding times for the pRNA-3WJ under the loading forces of 1600

and 2000 pN.

fig. S14. Dependence of the rupture force on the loading rate.

fig. S15. Schematic of 3WJ-pRNA in the crystal structure (4KZ2), where three base pairs

(bold) are attached to the terminus of H3.