Dataset Information

Combining laser microsurgery and finite element modeling to assess cell-level epithelial mechanics.

ABSTRACT: Laser microsurgery and finite element modeling are used to determine the cell-level mechanics of the amnioserosa-a morphogenetically crucial epithelium on the dorsal surface of fruit fly embryos (Drosophila melanogaster). In the experiments, a tightly focused laser ablates a subcellular hole (1 microm in diameter) that passes clean through the epithelium. The surrounding cells recoil from the wound site with a large range of initial recoil velocities. These depend on the embryo's developmental stage and the subcellular wound site. The initial recoil (up to 0.1 s) is well reproduced by a base finite element model, which assumes a uniform effective viscosity inside the cells, a constant tension along each cell-cell boundary, and a large, potentially anisotropic, far-field stress--one that far exceeds the stress equivalent of the cell-edge tensions. After 0.1 s, the experimental recoils slow dramatically. This observation can be reproduced by adding viscoelastic rods along cell edges or as a fine prestressed mesh parallel to the apical and basal membranes of the cell. The mesh also reproduces a number of double-wounding experiments in which successive holes are drilled in a single cell.

SUBMITTER: Hutson MS

PROVIDER: S-EPMC2793361 | biostudies-literature | 2009 Dec

REPOSITORIES: biostudies-literature

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Combining laser microsurgery and finite element modeling to assess cell-level epithelial mechanics.

Hutson M Shane MS Veldhuis J J Ma Xiaoyan X Lynch Holley E HE Cranston P Graham PG Brodland G Wayne GW

Biophysical journal 20091201 12

Laser microsurgery and finite element modeling are used to determine the cell-level mechanics of the amnioserosa-a morphogenetically crucial epithelium on the dorsal surface of fruit fly embryos (Drosophila melanogaster). In the experiments, a tightly focused laser ablates a subcellular hole (1 microm in diameter) that passes clean through the epithelium. The surrounding cells recoil from the wound site with a large range of initial recoil velocities. These depend on the embryo's developmental s ...[more]

PMID: 20006944

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Project description:We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L(∞) estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein.

Dataset Information

Combining laser microsurgery and finite element modeling to assess cell-level epithelial mechanics.

Publications

Combining laser microsurgery and finite element modeling to assess cell-level epithelial mechanics.

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