Limits...
Nanomechanics of multiple units in the erythrocyte membrane skeletal network.

de Oliveira M, Vera C, Valdez P, Sharma Y, Skelton R, Sung LA - Ann Biomed Eng (2010)

Bottom Line: While actin protofilaments remain tangent to the network, their yaw (Phi) angles change drastically with addition of neighboring units or an Sp unfolding.It is anticipated that during deformation, transmembrane complexes associated with the network move laterally through the lipid bilayer and increase the diffusion of molecules across the membrane.When protofilament/Sp sweeps under the lipid bilayer, they mix up the submembrane concentration gradient.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, 92093, USA.

ABSTRACT
Erythrocytes undergo deformations when they transport O(2) and CO(2) across the membrane, yet the 3D nanomechanics of the skeletal network remains poorly understood. Expanding from our previous single isolated unit, we now simulate networks consisting of 1-10 concentric rings of repeating units in equibiaxial deformation. The networks are organized with (1) a 3D model for a single unit, (2) a wrap-around mode between Sp and actin protofilament in the intra-unit interaction, and (3) a random inter-unit connectivity. These assumptions permit efficient five-degrees-of-freedom (5DOF) simulations when up to 30 pN of radial forces are applied to the boundary spectrin (Sp) and the center and other units are analyzed. As 6 Sp balance their tensions, hexagonal units become irregular. While actin protofilaments remain tangent to the network, their yaw (Phi) angles change drastically with addition of neighboring units or an Sp unfolding. It is anticipated that during deformation, transmembrane complexes associated with the network move laterally through the lipid bilayer and increase the diffusion of molecules across the membrane. When protofilament/Sp sweeps under the lipid bilayer, they mix up the submembrane concentration gradient. Thus, the nanomechanics of actin protofilaments and Sp may enhance the transport of molecules during erythrocyte deformation.

Show MeSH

Related in: MedlinePlus

A 5DOF multiunit model of the erythrocyte membrane skeleton. (a) A 5-ring network of the erythrocyte membrane skeleton. Actin protofilaments are represented as green cylinders; Pointed-end with a sphere; Sp-t a black string connecting protofilaments. The cartoon represented the steady state reached after a radial force of 2.5 pN applied at every free Sp on all PU. (b) Motion of the protofilament in 5DOF model. It is allowed to freely translate in the x, y, and z directions with two rotations: pitch angle (θ) out of the plane of the membrane and yaw angle (Φ) in the plane of the membrane, producing a 5 DOF model. (c) Modular elongation behavior of Sp modeled by the WLC paradigm according to AFM.26 (d) How a pair of Sp may wrap around the actin protofilament.36Block: G actin; Circle: Sp; Arrow: orientation of α or β Sp; (e) How Sp domains may wrap around the actin filament40
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2914261&req=5

Fig3: A 5DOF multiunit model of the erythrocyte membrane skeleton. (a) A 5-ring network of the erythrocyte membrane skeleton. Actin protofilaments are represented as green cylinders; Pointed-end with a sphere; Sp-t a black string connecting protofilaments. The cartoon represented the steady state reached after a radial force of 2.5 pN applied at every free Sp on all PU. (b) Motion of the protofilament in 5DOF model. It is allowed to freely translate in the x, y, and z directions with two rotations: pitch angle (θ) out of the plane of the membrane and yaw angle (Φ) in the plane of the membrane, producing a 5 DOF model. (c) Modular elongation behavior of Sp modeled by the WLC paradigm according to AFM.26 (d) How a pair of Sp may wrap around the actin protofilament.36Block: G actin; Circle: Sp; Arrow: orientation of α or β Sp; (e) How Sp domains may wrap around the actin filament40

Mentions: The calculations of the network nanomechanics depend on several assumptions chosen as close as possible to the physiological conditions, similar to those in Vera et al.38 In order to simulate large networks in reasonable computational time several simplifications were made (Fig. 3a). These include assuming a rigid body model with 5DOF for the protofilament, which preserves its three translational and two rotational motions (pitch and yaw) in 3D space (Fig. 3b). The protofilament mass and damping coefficients were selected to minimize the time in which the network reached equilibrium (by dynamic relaxation). Here Sp-t was modeled as a nonlinear massless elastic string with a force–extension curve based on the worn-like-chain (WLC) model of Rief et al.28 (Fig. 3c). The WLC model allows Sp to unfold. Sp-t is modeled as two Sp in series (we do not simulate the separation of Sp-t to two Sp) and the contour length for each Sp used is 163.4 nm.28 We also used 30 pN as the maximal tension for any Sp before unfolding, and every time it unfolds the length increases by 31.7 nm. A major difference is that previously, when a single unit was modeled,38 the coordinates of 6 SC were fixed corresponding to specific stretch ratios. Here we allowed them to move in response to the peripheral force applied.FIGURE 3


Nanomechanics of multiple units in the erythrocyte membrane skeletal network.

de Oliveira M, Vera C, Valdez P, Sharma Y, Skelton R, Sung LA - Ann Biomed Eng (2010)

A 5DOF multiunit model of the erythrocyte membrane skeleton. (a) A 5-ring network of the erythrocyte membrane skeleton. Actin protofilaments are represented as green cylinders; Pointed-end with a sphere; Sp-t a black string connecting protofilaments. The cartoon represented the steady state reached after a radial force of 2.5 pN applied at every free Sp on all PU. (b) Motion of the protofilament in 5DOF model. It is allowed to freely translate in the x, y, and z directions with two rotations: pitch angle (θ) out of the plane of the membrane and yaw angle (Φ) in the plane of the membrane, producing a 5 DOF model. (c) Modular elongation behavior of Sp modeled by the WLC paradigm according to AFM.26 (d) How a pair of Sp may wrap around the actin protofilament.36Block: G actin; Circle: Sp; Arrow: orientation of α or β Sp; (e) How Sp domains may wrap around the actin filament40
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2914261&req=5

Fig3: A 5DOF multiunit model of the erythrocyte membrane skeleton. (a) A 5-ring network of the erythrocyte membrane skeleton. Actin protofilaments are represented as green cylinders; Pointed-end with a sphere; Sp-t a black string connecting protofilaments. The cartoon represented the steady state reached after a radial force of 2.5 pN applied at every free Sp on all PU. (b) Motion of the protofilament in 5DOF model. It is allowed to freely translate in the x, y, and z directions with two rotations: pitch angle (θ) out of the plane of the membrane and yaw angle (Φ) in the plane of the membrane, producing a 5 DOF model. (c) Modular elongation behavior of Sp modeled by the WLC paradigm according to AFM.26 (d) How a pair of Sp may wrap around the actin protofilament.36Block: G actin; Circle: Sp; Arrow: orientation of α or β Sp; (e) How Sp domains may wrap around the actin filament40
Mentions: The calculations of the network nanomechanics depend on several assumptions chosen as close as possible to the physiological conditions, similar to those in Vera et al.38 In order to simulate large networks in reasonable computational time several simplifications were made (Fig. 3a). These include assuming a rigid body model with 5DOF for the protofilament, which preserves its three translational and two rotational motions (pitch and yaw) in 3D space (Fig. 3b). The protofilament mass and damping coefficients were selected to minimize the time in which the network reached equilibrium (by dynamic relaxation). Here Sp-t was modeled as a nonlinear massless elastic string with a force–extension curve based on the worn-like-chain (WLC) model of Rief et al.28 (Fig. 3c). The WLC model allows Sp to unfold. Sp-t is modeled as two Sp in series (we do not simulate the separation of Sp-t to two Sp) and the contour length for each Sp used is 163.4 nm.28 We also used 30 pN as the maximal tension for any Sp before unfolding, and every time it unfolds the length increases by 31.7 nm. A major difference is that previously, when a single unit was modeled,38 the coordinates of 6 SC were fixed corresponding to specific stretch ratios. Here we allowed them to move in response to the peripheral force applied.FIGURE 3

Bottom Line: While actin protofilaments remain tangent to the network, their yaw (Phi) angles change drastically with addition of neighboring units or an Sp unfolding.It is anticipated that during deformation, transmembrane complexes associated with the network move laterally through the lipid bilayer and increase the diffusion of molecules across the membrane.When protofilament/Sp sweeps under the lipid bilayer, they mix up the submembrane concentration gradient.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, 92093, USA.

ABSTRACT
Erythrocytes undergo deformations when they transport O(2) and CO(2) across the membrane, yet the 3D nanomechanics of the skeletal network remains poorly understood. Expanding from our previous single isolated unit, we now simulate networks consisting of 1-10 concentric rings of repeating units in equibiaxial deformation. The networks are organized with (1) a 3D model for a single unit, (2) a wrap-around mode between Sp and actin protofilament in the intra-unit interaction, and (3) a random inter-unit connectivity. These assumptions permit efficient five-degrees-of-freedom (5DOF) simulations when up to 30 pN of radial forces are applied to the boundary spectrin (Sp) and the center and other units are analyzed. As 6 Sp balance their tensions, hexagonal units become irregular. While actin protofilaments remain tangent to the network, their yaw (Phi) angles change drastically with addition of neighboring units or an Sp unfolding. It is anticipated that during deformation, transmembrane complexes associated with the network move laterally through the lipid bilayer and increase the diffusion of molecules across the membrane. When protofilament/Sp sweeps under the lipid bilayer, they mix up the submembrane concentration gradient. Thus, the nanomechanics of actin protofilaments and Sp may enhance the transport of molecules during erythrocyte deformation.

Show MeSH
Related in: MedlinePlus