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Hierarchical multiscale model for biomechanics analysis of microfilament networks
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Image of FIG. 1.
FIG. 1.

The multiscale approach for microfilament networks. (a) Crystallography of Oda 2009 G-actin model, there are two G-actin monomers in an elementary bead. (b) A single F-actin constructed from Oda 2009 G-actin model following the nature from G-actin to F-actin22. (c) Part of an idealized two-dimensional microfilament network in rectangular shape.

Image of FIG. 2.
FIG. 2.

Schematic of the CG serial bead model. Every bead in the lattice has two adjacent beads in longitudinal direction, between which tensile relation is applied. Rotational constraint is defined within three adjacent monomers on the same filament.

Image of FIG. 3.
FIG. 3.

The model box in molecular simulations. Points in cyan are water molecules. The four G-actin monomers, numbered from i to iv in different colors, are divided into two groups (i & ii and iii & iv), which are correspondingly abstracted as two beads in the multiscale bead model.

Image of FIG. 4.
FIG. 4.

The constitutive relation in tensile and compression numerical simulations. In compression region, there is a stiffness transition at 5.512 nm. The balance distance between different beads is 5.529 nm. In tension region, there are two stiffness transitions, respectively, at 5.546 nm and 5.556 nm. Transition points are correspondingly marked as A, B, C, and D.

Image of FIG. 5.
FIG. 5.

Force-deformation relation during simulations of the tension of a 1.1 m single F-actin. (a) Stiffening and softening strains all have dependence on loading strain rate. (b) When loading strain is under the physiological limit (the linear region at the beginning of the tensile tests), the stiffness evaluation agrees with experimental results. The blue area represents the stiffness region of single F-actin (1.1 m) based on experimental results.

Image of FIG. 6.
FIG. 6.

The first order natural frequency of double clamped F-actin from 50 to 300 nm, square dots represent the results from the multiscale method proposed in this paper and circular dots represent the theoretical solution of Euler-Bernoulli beam.

Image of FIG. 7.
FIG. 7.

The tensile performance of a 4.43 m × 9.93 m microfilament networks. (a) Geometry of the networks and the loading illustration; (b) force-deformation relation, which is similar to single F-actin simulation results; (c) the strain stiffening and softening; (d) the stress stiffening and softening.


Generic image for table
Table I.

The stiffness evaluation by experiments and the multiscale model in this paper.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hierarchical multiscale model for biomechanics analysis of microfilament networks