Nanomechanical properties of MscL α helices: A steered molecular dynamics study

Abstract

Gating of mechanosensitive (MS) channels is driven by a hierarchical cascade of movements and deformations of transmembrane helices in response to bilayer tension. Determining the intrinsic mechanical properties of the individual transmembrane helices is therefore central to understanding the intricacies of the gating mechanism of MS channels. We used a constant-force steered molecular dynamics (SMD) approach to perform unidirectional pulling tests on all the helices of MscL in M. tuberculosis and E. coli homologs. Using this method, we could overcome the issues encountered with the commonly used constant-velocity SMD simulations, such as low mechanical stability of the helix during stretching and high dependency of the elastic properties on the pulling rate. We estimated Young's moduli of the α-helices of MscL to vary between 0.2 and 12.5 GPa with TM2 helix being the stiffest. We also studied the effect of water on the properties of the pore-lining TM1 helix. In the absence of water, this helix exhibited a much stiffer response. By monitoring the number of hydrogen bonds, it appears that water acts like a 'lubricant' (softener) during TM1 helix elongation. These data shed light on another physical aspect underlying hydrophobic gating of MS channels, in particular MscL.

Keywords: Escherichia coli; Young's modulus; all-atom simulation; constant velocity; mechanosensitive channel; mycobacterium tuberculosis; nanovalve.

Figure 1.

Three dimensional structures of the closed (resting) state of (A) MtMscL (PDB code: 2OAR) on the left and a homology model of EcMscL obtained based on 2OAR and 4LKU on the right side. (B) A subunit of EcMscL has been shown after equilibrated in POPE lipid bilayer. The residues that anchor the protein to the membrane (F7, F10) have been highlighted. (C) TM1 helix becomes aligned with the N-terminus in the open state.

Figure 2.

Steered molecular dynamics (SMD) simulation using constant-velocity (CV) method. In this method, the α carbons of the first 2 residues (ILE14 and VAL15) in TM1 helix of MtMscL have been fixed on the left hand side. Helical properties such as helix initial length, L₀, pulling rate, v, time t, vector position of the helix end, ${\displaystyle \overrightarrow{r}}$, and the assigned spring constant of the dummy atom, ${\displaystyle k_{dummy}}$, have been indicated. (A) A schematic unidirectional pulling test on the TM1 helix of MtMscL solvated in water. (B) The force versus elongation (ΔL) curve during constant-velocity simulations. The typical spring constant here is 3 kcal/mol/Ų (i.e. ∼210 pN/Å). Four different constant velocities have been assigned to the α carbon of the dummy atom, from 0.1 Å/ps, to 5 Å/ps. The helix elongation trend can be divided into 2 main quasi-linear regions. As shown in the inset multiple regions can be observed in the first regions which are indicative of sequential rupture of the hydrogen bonds (i.e., breakage of the hydrogen bonds during the pulling test). The length of TM1 increases up to a maximum length (>100 % of elongation), when the helix becomes almost unfolded due to the applied stretch. Before this point, helix response is rate dependent, i.e. the higher the pulling rate, the stiffer is the helix response. After this point the helix behavior becomes much stiffer and not rate dependent. It should be noted that the rationale for testing the helix behavior upon application of such high forces and large elongations was to find the reason for the rate dependency observed in the CV simulations. (C) A typical helical behavior under low forces. The spring constant here was 0.6 kcal/mol/Ų (i.e., ∼42 pN/Å) and the pulling rate was 0.1 Å/ps. Similar to previous studies, the slope of the best linear fit to the initial part of the diagram (dashed red line) indicates the elasticity modulus, which is ∼0.7 kcal/mol/Ų (i.e., ∼45 pN/Å).

Figure 3.

Mechanical behavior of the TM1 helix of MtMscL using constant-force (CF) method (A) A schematic unidirectional pulling of the TM1 helix of MtMscL solvated in water. (B) TM1 helix elongates over time as a result of constant pulling force applied on its end. The TM1 length increases to maximum length of ∼52 Å then fluctuates around this value. (C) Stress-strain curve of the unidirectional traction applied to the TM1 helix in water. The range of axial force applied in these simulations ranges from 0.1 to 1.5 kcal/mol/Å (i.e., from ∼7 to 70 pN). The Young's modulus of the TM1 helix can be calculated from the slope of this curve, which in this case is ∼3.2 ± 0.9 GPa (Mean ± SEM). To obtain each point on the stress-strain curve, 3 simulations were performed. The strain at each force has been averaged over 3 simulations. The Young's modulus has been estimated based on 95 % confidence of both stress and strain axis.

Figure 4.

Comparing the constant-velocity (CV) method with the constant-force (CF) method for testing the mechanical behavior of α-helices using TM1 helix of MtMscL in water as an example. (A) The effect of pulling rate and stiffness of spring constant of the dummy atoms using constant-velocity method on the mechanical behavior of the TM1 helix of MtMscL. For higher pulling rates (> 1 Å/ps), there is a considerable fluctuation in the Young's modulus depending on the spring constant assigned to the dummy atoms. This fluctuation becomes larger as the spring constant becomes higher. As the rate of pulling decreases from 5.0 Å/ps to 0.1 Å/ps, the average of E values decreases from 42 to 11 GPa. (B) Change in the number of hydrogen bonds of TM1 α helix of MtMscL during the simulation time. The black trace shows the number of hydrogen bonds in the TM1 helix in the CV method, compared to those when the CF method was used. For this typical CV example, the spring constant is 0.6 kcal/mol/Ų (i.e. ∼42 pN/Å) and the pulling velocity is 0.1 Å/ps. The force used in the CF method was 27 pN. The values of Young's moduli are Mean ± SEM. One-way ANOVA was used for statistical analysis with p-value < 0.05 and it was confirmed in groups with low n number using non-parametric Kruskal-Wallis test.

Figure 5.

Mechanical properties of MtMscL and EcMscL α-helices in the presence of water measured by all-atom steered molecular dynamic (SMD) simulation. We used constant-force (CF) method here to estimate (A) the elasticity constant and (B) the Young's modulus. The elasticity constant is between 1.0 to 72.2 pN/Å (Young's moduli are between 0.2 to 12.5 GPa). Overall, the mechanical properties of MscL α-helices of both species are similar to each other except for their TM2 and C-terminal helices. TM2 helix in MtMscL is almost 4 times stiffer than the TM2 helix of EcMscL. But the C-terminal helix of EcMscL is about 8 times stiffer than the C-terminal helix of MtMscL. The values of Young's moduli are Mean ± SEM for n = 3. Each Young's modulus is obtained from the stress-strain graphs exemplified in Fig. 3. Student's t-test was used for statistical analysis between each α-helix in MtMscL with its corresponding α-helix in EcMscL. The differences were considered significant for *p-value < 0.05.

Figure 6.

Effect of water on mechanical properties of the TM1 helix in MtMscL (A,B) and in EcMscL (C,D) using constant-force SMD simulation. (A) The Young's modulus of TM1 helix in MtMscL is E = 3.2 ± 0.9 GPa when it is solvated in water, and E = 8.8 ± 0.2 GPa in the absence of water (vacuum). Thus, in the absence of water (vacuum), TM1 helix is more than 3 times stiffer in MtMscL. (B) Change in number of the hydrogen bonds of TM1 α helix of MtMscL during 10 ns of SMD simulation. About 41 hydrogen bonds stabilize the secondary structure of TM1 helix in vacuum, while when it is solvated in water, the number of hydrogen bonds becomes significantly reduced to ∼30 bonds. This indicates that water acts as a ‘lubricant’ (softener) during TM1 helix elongation in water. (C) The Young's modulus of the TM1 helix of EcMscL solvated in water is E = 2.6 ± 0.5 GPa whereas it is E = 3.5 ± 0.1 GPa in the absence of water (vacuum). (D) The number of hydrogen bonds does not change considerably when the TM1 helix of EcMscL is solvated in water, thus its elasticity modulus only increases by ∼30 %. For all the hydrogen bond calculations, we used a donor-acceptor distance of 3.5 Å and angle cut-off of 40°. The values presented in (A) and (C) are Mean ± SEM for n = 3. Student's t-test was used for statistical analysis and differences were considered significant for *p-value < 0.05.