27. Polyméres et fibrilles

On Stretching, Bending, Shearing, and Twisting of Actin Filaments I: Variational Models

“…Thin rods (or filaments) are characterized by large aspect ratios, allowing for an effectively one-dimensional continuum mechanical description where position in the rod is specified with a single variable. , Several nonlinear theories of thin rod mechanics have been developed which differ from each other in the allowed types of deformations. The Cosserat theory , generalizes the Kirchoff theory , by allowing for transverse shearing and axial extension deformations. Here we build on the Cosserat theory, which has recently been used to develop mathematical models of thin rod dynamics that capture a wide range of observed nonlinear filament behaviors. ,, We next give a brief account of aspects of the Cosserat theory relevant to our model, after which we describe our new variational treatment.…”

“…In the Cosserat theory, a filament is mathematically described by a directed curve. , This consists of backbone curve , where ŝ ∈ [0, L̂ ] is the reference arc-length coordinate, and an orthonormal triad of directors D ( ŝ ) = ( d 1 ( ŝ ), d 2 ( ŝ ), d 3 ( ŝ )). In our notation the caret hat symbol denotes a variable of the reference configuration.…”

“…Here, we introduce a set of options for efficiently modeling a semiflexible filament having a small but finite width. The physical background used in these models is the Cosserat theory of elastic rods, which allows for six degrees of freedom at every point on the filament’s backbone. , A key feature of these modeling approaches is that they use only a small, discrete set of model parameters yet describe a smooth filament shape having all allowable degrees of freedom in the Cosserat theory. We present two main approaches: one in which polynomial spline functions are used to describe the positional and orientational degrees of freedom, and one in which we use the geodesic curve in the space of the orientational degrees of freedom.…”