Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

TL;DR

This paper introduces a nonlinear spring model that captures the complex mechanical deformation behavior of biological particles under force, explaining spectral features and collapse phenomena through combined Hertzian and bending deformations.

Contribution

The novel theory integrates nonlinear Hertzian contact and bending deformations to interpret force-deformation spectra of biological particles, including collapse transitions.

Findings

Successfully characterizes spectral features of virus particles

Identifies mechanical parameters like Young's moduli and failure probabilities

Explains force drops during particle collapse

Abstract

We present a new theory for modeling forced indentation spectral lineshapes of biological particles, which considers non-linear Hertzian deformation due to an indenter-particle physical contact and bending deformations of curved beams modeling the particle structure. The bending of beams beyond the critical point triggers the particle dynamic transition to the collapsed state, an extreme event leading to the catastrophic force drop as observed in the force (F)-deformation (X) spectra. The theory interprets fine features of the spectra: the slope of the FX curves and the position of force-peak signal, in terms of mechanical characteristics --- the Young's moduli for Hertzian and bending deformations E_H and E_b, and the probability distribution of the maximum strength with the strength of the strongest beam F_b^* and the beams' failure rate m. The theory is applied to successfully characterize the $FX$ curves for spherical virus particles --- CCMV, TrV, and AdV.