Simple lattice model for biological gels

Details Simple lattice model for biological gels Simple lattice model for biological gels

2011-08-22

arxiv.org/abs/1108.4328v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 5 figures

Scientific paper

We construct a three-dimensional lattice model for biological gels in which straight lines of bonds correspond to filamentous semi-flexible polymers and lattice sites, which are exactly four-fold coordinated, to crosslinks. With only stretching central forces between nearest neighbors, this lattice is sub-isostatic with an extensive number of zero modes; but all of its elastic constants are nonzero, and its elastic response is affine. Removal of bonds with probability $1-p$ leads to a lattice with average coordination number less than four and a distribution of polymer lengths. When bending forces are added, the diluted lattice exhibits a rigidity threshold at $p=p_b<1$ and crossover from bending-dominated nonaffine to stretching-dominated affine response between $p_b$ and $p=1$.

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