ArticleActa biomaterialia2021
Fluctuating nonlinear spring theory: Strength, deformability, and toughness of biological nanoparticles from theoretical reconstruction of force-deformation spectra.
Article in Acta biomaterialia, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Physical Virology with Atomic Force and Fluorescence Microscopies: Seeing and Touching Viruses and Protein Cages.Methods in molecular biology (Clifton, N.J.) · 2027Article
- Nanomechanical characterization of soft nanomaterial using atomic force microscopy.Materials today. Bio · 2025Review
- Mechanical fatigue testing in silico: Dynamic evolution of material properties of nanoscale biological particles.Acta biomaterialia · 2023Article
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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.
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