A multiscale model of mechanotransduction by the ankyrin chains of the NOMPC channel

Abstract

Our senses of touch and hearing are dependent on the conversion of external mechanical forces into electrical impulses by the opening of mechanosensitive channels in sensory cells. This remarkable feat involves the conversion of a macroscopic mechanical displacement into a subnanoscopic conformational change within the ion channel. The mechanosensitive channel NOMPC, responsible for hearing and touch in flies, is a homotetramer composed of four pore-forming transmembrane domains and four helical chains of 29 ankyrin repeats that extend 150 Å into the cytoplasm. Previous work has shown that the ankyrin chains behave as biological springs under extension and that tethering them to microtubules could be involved in the transmission of external forces to the NOMPC gate. Here we combine normal mode analysis (NMA), full-atom molecular dynamics simulations, and continuum mechanics to characterize the material properties of the chains under extreme compression and extension. NMA reveals that the lowest-frequency modes of motion correspond to fourfold symmetric compression/extension along the channel, and the lowest-frequency symmetric mode for the isolated channel domain involves rotations of the TRP domain, a putative gating element. Finite element modeling reveals that the ankyrin chains behave as a soft spring with a linear, effective spring constantof 22 pN/nm for deflections ≤15 Å. Force-balance analysis shows that the entire channel undergoes rigid body rotation during compression, and more importantly, each chain exerts a positive twisting moment on its respective linker helices and TRP domain. This torque is a model-independent consequence of the bundle geometry and would cause a clockwise rotation of the TRP domain when viewed from the cytoplasm. Force transmission to the channel for compressions >15 Å depends on the nature of helix-helix contact. Our work reveals that compression of the ankyrin chains imparts a rotational torque on the TRP domain, which potentially results in channel opening.

Figure 1.

Structural features and mechanical abstraction of the NOMPC ion channel. (A) The NOMPC structure (Jin et al., 2017). The channel is a homotetramer with the N-terminal domain starting at AR 1 in contact with an MT (blue and gray blocks). The four-helix bundle extending up from the MT is 29 ARs long terminating in the linker helices (violet) before moving into the preS1 elbow and first TM helix S1 of the membrane spanning region. Like K_V and Na_V voltage-gated ion channels, the TM domain is composed of six TM segments labeled S1–S6 with the S4–S5 linker (orange) connecting S1–S4 to the pore domain (S5–S6). The S6 inner pore helix, which occludes the pore domain in this closed structure, is connected to the TRP domain (dark blue), a long helix that runs parallel to the membrane on the cytoplasmic side and makes contact with the linker helices and the S4–S5 linker. Adjacent helical chains come into close contact at two points along the length of the helical bundle (#1 and #2). The three consecutive sets of six AR repeats used in our molecular simulations are colored blue (ANK1), red (ANK2), and green (ANK3), and the inset shows a zoomed-in representation of ANK1. The approximate position of the membrane is indicated with black lines. (B) A finite element model of NOMPC. The four chains of the bundle were modeled as cylindrical rods with radius r = 1.0 nm and a shape matching the NOMPC structure in panel A (effective helical radius R = 3.43 nm used for analytic calculations). The C-terminal AR 29 terminates into the TRP region, a rigid plate representing the linker helices and TRP domain. The contact points from panel A are indicated in the model.

Figure 2.

Normal modes of the NOMPC channel. (A) Side view of the lowest-order NMA performed on the entire NOMPC channel. The starting structure is represented as a white tube, and the cyan and black tube representations of a single AR chain depict the maximum displacement of the chains along mode 1. The trajectory is superposed on the TM domain. The inset shows the cytoplasmic view of the channel highlighting the extreme displacements of the TRP domain (cyan and black) for this mode. As can be seen, the TRP domain moves as a rigid body. The TM domain is at the top, and the MT binding domain is at the bottom. (B) Side view of the lowest-order NMA performed on the entire NOMPC channel with the N-terminal residues clamped. This mode mimics NOMPC binding to an MT. The lowest-order mode still shows the largest deflections along the z axis, but the amplitude is suppressed compared with A. The color scheme is as in A.

Figure 3.

Mechanical properties of the AR chains extracted from equilibrium MD simulations. (A) Structure of ANK1 highlighting the six ARs and the second (cyan) and fifth (red) repeats used to calculate the COM-to-COM distance from AR₂ to AR₅ (d_2,5). (B) The time evolution of the distance d_2,5 from A for ANK1 (blue), ANK2 (red), and ANK3 (green). (C) The stiffness spring constant and 95% CI for k_s for ANK1–ANK3 computed from the data in B using Eq. 2. (D) Structure of ANK1 highlighting the six ARs and the second (cyan) and fifth (red) repeats used to calculate the angular displacement of AR₂ with respect to AR₅ (θ_2,5). The dots represent the COM and C_α atoms used to define AR orientations. (E) The time evolution of the angle θ_2,5 from D for ANK1 (blue), ANK2 (red), and ANK3 (green). (F) The torsional spring constant and 95% CI for k_θ for ANK1–ANK3 computed from the data in E using Eq. 3. Error bars in C and F are the 95% CI obtained using a Monte Carlo bootstrap technique.

Figure 4.

Shape, force, and energy of helical bundle deformation computed from the finite element model. (A–C) Starting (gray) and final representation (dark gray, blue, and red) of NOMPC for the no-contact (A), frictionless (B), and rough contact models (C). (D) The force per chain is represented as a function of the vertical displacement (Δz) for the three different models (black dashed curve, no contact; blue, frictionless contact; and red, rough contact). These force–displacement curves are per-chain values, and the entire force of the bundle is four times the reported value. (E) The energy is represented as a function of the vertical displacement (Δz) for the three different models (black dashed curve, no contact; blue, frictionless contact; and red, rough contact). These energy–displacement curves are for the entire four-helix bundle. The gray region in D and E represents displacements before helix–helix contact.

Figure 5.

Force and twisting moment exerted on the TRP domain. (A) Cytoplasmic view of the channel domain with TRP domain highlighted blue. The radial/parallel direction r_||, angular/tangential direction r_⊥, and direction of positive torque m_z are defined with respect to an isolated TRP domain. (B–D) Radial force (B), tangential force (C), and twisting moment (D) exerted by each chain on the TRP region as a function of vertical displacement (Δz) for the three contact models (black dashed curve, no contact; blue, frictionless contact; and red, rough contact). The gray region in B–D represents displacements before helix–helix contact.

Figure 6.

Model of how ankyrin chain compression influences the mechanics at the NOMPC channel domain. In stage 1 of compression (upper box), before helix–helix contact at 15 Å, the channel mechanics can be decomposed into three motions: (1) compression of the helical bundle along the z axis, (2) rigid body CCW rotation of the entire channel domain in the membrane, and (3) CW torques applied to each linker/TRP domain that would cause the TRP domain to rotate CW opening the pore as suggested for TRPV1 (Cao et al., 2013). In stage 2, once the compression exceeds 15 Å, the mechanics of the channel differ depending on the type of interactions that occur after helix–helix contact. Both models continue to experience a compression of the helical bundle, but in the frictionless contact model, the channel domain switches directions, causing a rigid body rotation in the CW direction and a change in the torque applied to each TRP domain (right lower box). This later torque change would cause the linker helices and TRP domain to move back to its original position, potentially closing the channel. The rough contact model always experiences a CW torque on the linker helices/TRP domain that continues to move it into the putative open configuration, but the channel domain undergoes minor, rigid body rotations back and forth in the membrane, ultimately continuing the CCW rotation experienced early on (left lower box). Another important difference with the rough contact model is that the chains lock up dramatically increasing the stiffness to vertical displacements. In all figures, the initial configurations are gray and/or black, and the final configurations are cyan. The view of the channel domains is from the cytoplasm.