Mechanics of Biopolymer Networks with Inclusions

• Applicant: Professor Abhinav Sharma, Ph.D.
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Biophysics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 525864799

Biological materials exhibit remarkably unusual mechanical behavior. Their elastic response is highly nonlinear, exhibiting a strong increase in stiffness with strain. Such nonlinear mechanics are manifest at the intracellular level of the cytoskeletal filaments, such as actin, as well as at the larger extracellular level of fibrin clots and even whole tissues (mesentery) and organs (blood-vessels, skin). It is the unusual mechanical response of these systems which sets them apart from most synthetic systems. The mechanical response of biomaterials is governed by the elastic properties of the underlying biopolymer networks. Spatially disordered, fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. Whereas a lot of progress has been made in understanding the nonlinear mechanics at the cytoskeletal level inside a cell, there was no generally accepted model for collagen networks and tissues. Only recently, the applicant has proposed a new framework grounded in the theory of critical phenomena which describes the nonlinear mechanics of collagen networks. Sub-isostatic networks, i.e., under constrained networks, which are ubiquitous in Biology, become rigid when subjected to sufficiently large deformations. We recently showed that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. We demonstrated the critical behaviour specifically in the scaling properties of the mechanics, as well as finite-size effects that reflect the diverging correlation length. We also showed that the nonlinear mechanics of collagen type I networks, which are crucial for the integrity of biological tissues, can be quantitatively captured by the predictions of scaling theory for the strain-controlled critical behaviour over a wide range of network concentrations and strains up to failure of the material. A natural next step is to model tissues by including cells in the extracellular matrix and studying its nonlinear mechanics. The goal of this proposal is to extend the framework to tissues by including cells in the biopolymer networks. Cells could be regarded as extra internal constraints. How will they affect the non-affine displacements? Cells are not passive elements; their traction affects the local stiffness. Could one treat the cell-generated stresses as an auxiliary field? Furthermore, cells adjust their shape and traction forces in response to the local stresses due to the extracellular matrix. This feedback between shape and stresses will again affect the local stiffness. How would this reflect on the macroscopic mechanics of the matrix? The proposed research aims to address these questions by extending our recently proposed framework to model tissue systems.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Dr. Fred MacKintosh