Variational approximation method for the long-range force transmission in biopolymer gels

TL;DR

This paper applies variational methods to model long-range force transmission in nonlinear elastic biopolymer gels, explaining experimental observations of cell-induced displacements.

Contribution

It introduces a variational approximation approach to analyze force transmission in biopolymer gels, linking theoretical models with experimental data.

Findings

Variational methods accurately predict slow decay of displacements.

The three-chain model effectively explains experimental force transmission.

The approach bridges theory and experimental observations in biopolymer mechanics.

Abstract

The variational principle of minimum free energy (MFEVP) has been widely used in the study of soft matter statics. MFEVP can be used not only to derive equilibrium equations (including both bulk equations and boundary conditions), but also to develop direct variational methods (such as Ritz method) to find approximate solutions to these equilibrium equations. In this work, we applied these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels. We showed that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in three-dimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels.