Fluctuating nonlinear spring theory: Strength, deformability, and toughness of biological nanoparticles from theoretical reconstruction of force-deformation spectra. (1st March 2021)

• Record Type: Journal Article
• Authors: Maksudov, Farkhad; Kononova, Olga; Llauró, Aida; Ortega-Esteban, Alvaro; Douglas, Trevor; Condezo, Gabriela N.; Martín, Carmen San; Marx, Kenneth A.; Wuite, Gijs J.L.; Roos, Wouter H.; de Pablo, Pedro J.; Barsegov, Valeri
• Is Part Of: Acta biomaterialia. Volume 122(2021)
• Page Start: 263
• Page End: 277
• Publication Date: 2021-03-01
• Subjects: Fluctuating nonlinear spring (FNS) model -- Force-deformation spectra -- Probability distribution of critical forces -- Probability distribution of critical deformations -- Fracture toughness; xH (Hertzian) deformation of protein layer under the indenter -- xb bending deformation of side portion (beams) -- xb* maximum deformation of side portion before beams start to fail -- XH* maximum value of total deformation X in Regime I of Hertzian indentation -- Xb* maximum value of total deformation X in Regime II of beam bending -- Fb* maximum value of total force F in Regime II of beam bending -- xH˜(X) (Hertzian) deformation of protein layer as a function of total deformation X in Regime III -- xb(X)˜ bending deformation of side portion as a function of total deformation X in Regime III -- Kb elastic constant of the side portion of particle (curved beams) -- kH Hertzian spring constant of protein layer -- Fb˜ strength scale in Weibull distribution -- Xcr average critical (maximum) total deformation of the particle at fracture -- Fcr average critical (maximum) deformation force of the particle at fracture -- m shape parameter (mechanical cooperativity among the beams); Biomedical materials -- Periodicals; 610.28
• DOI: 10.1016/j.actbio.2020.12.043
• Languages: English
• ISSNs: 1742-7061

Abstract

Abstract: 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. Graphical abstract: Image, graphical abstract