Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

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

Fluctuating nonlinear spring theory:Strength, deformability, and toughness of biological nanoparticles from theoretical reconstruction of force-deformation spectra

We developed the Fluctuating Nonlinear Spring (FNS) model to describe the dynamics of mechanical deformation of biological particles, such as virus capsids. The theory interprets the force-deformation spectra in terms of the “Hertzian stiffness” (non-linear regime of a particle's small-amplitude deformations), elastic constant (large-amplitude elastic deformations), and force range in which the particle's fracture occurs. The FNS theory enables one to quantify the particles’ elasticity (Young's moduli for Hertzian and bending deformations), and the limits of their strength (critical forces, fracture toughness) and deformability (critical deformations) as well as the probability distributions of these properties, and to calculate the free energy changes for the particle's Hertzian, elastic, and plastic deformations, and eventual fracture. We applied the FNS theory to describe the protein capsids of bacteriophage P22, Human Adenovirus, and Herpes Simplex virus characterized by deformations before fracture that did not exceed 10–19% of their size. These nanoshells are soft (~1–10-GPa elastic modulus), with low ~50–480-kPa toughness – a regime of material behavior that is not well understood, and with the strength increasing while toughness decreases with their size. The particles’ fracture is stochastic, with the average values of critical forces, critical deformations, and fracture toughness comparable with their standard deviations. The FNS theory predicts 0.7-MJ/mol free energy for P22 capsid maturation, and it could be extended to describe uniaxial deformation of cylindrical microtubules and ellipsoidal cellular organelles