A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

SIMPLE SUMMARY: Mechanical properties of biological tissues are increasingly recognized as important in biology. Atomic force microscopy (AFM) is one of the main tools used to assess elastic properties of various types of biological samples. It has been noted that elasticity values frequently follow a log-normal distribution. We propose in this communication a physical model explaining this fact, and we propose that distribution-type analysis could increase the information obtained from AFM studies on biological tissues. ABSTRACT: The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.