TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

Mechanical fatigue testing in silico: Dynamic evolution of material properties of nanoscale biological particles

Biological particles have evolved to possess mechanical characteristics necessary to carry out their functions. We developed a computational approach to "fatigue testing in silico", in which constant-amplitude cyclic loading is applied to a particle to explore its mechanobiology. We used this approach to describe dynamic evolution of nanomaterial properties and low-cycle fatigue in the thin spherical encapsulin shell, thick spherical Cowpea Chlorotic Mottle Virus (CCMV) capsid, and thick cylindrical microtubule (MT) fragment over 20 cycles of deformation. Changing structures and force-deformation curves enabled us to describe their damage-dependent biomechanics (strength, deformability, stiffness), thermodynamics (released and dissipated energies, enthalpy, and entropy) and material properties (toughness). Thick CCMV and MT particles experience material fatigue due to slow recovery and damage accumulation over 3-5 loading cycles; thin encapsulin shells show little fatigue due to rapid remodeling and limited damage. The results obtained challenge the existing paradigm: damage in biological particles is partially reversible owing to particle's partial recovery; fatigue crack may or may not grow with each loading cycle and may heal; and particles adapt to deformation amplitude and frequency to minimize the energy dissipated. Using crack size to quantitate damage is problematic as several cracks might form simultaneously in a particle. Dynamic evolution of strength, deformability, and stiffness, can be predicted by analyzing the cycle number (N) dependent damage, [Formula: see text] , where α is a power law and Nf is fatigue life. Fatigue testing in silico can now be used to explore damage-induced changes in the material properties of other biological particles. STATEMENT OF SIGNIFICANCE: Biological particles possess mechanical characteristics necessary to perform their functions. We developed "fatigue testing in silico" approach, which employes Langevin Dynamics simulations of constant-amplitude cyclic loading of nanoscale biological particles, to explore dynamic evolution of the mechanical, energetic, and material properties of the thin and thick spherical particles of encapsulin and Cowpea Chlorotic Mottle Virus, and the microtubule filament fragment. Our study of damage growth and fatigue development challenge the existing paradigm. Damage in biological particles is partially reversible as fatigue crack might heal with each loading cycle. Particles adapt to deformation amplitude and frequency to minimize energy dissipation. The evolution of strength, deformability, and stiffness, can be accurately predicted by analyzing the damage growth in particle structure.

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.

Membrane-containing virus particles exhibit the mechanics of a composite material for genome protection

The protection of the viral genome during extracellular transport is an absolute requirement for virus survival and replication. In addition to the almost universal proteinaceous capsids, certain viruses add a membrane layer that encloses their double-stranded (ds) DNA genome within the protein shell. Using the membrane-containing enterobacterial virus PRD1 as a prototype, and a combination of nanoindentation assays by atomic force microscopy and finite element modelling, we show that PRD1 provides a greater stability against mechanical stress than that achieved by the majority of dsDNA icosahedral viruses that lack a membrane. We propose that the combination of a stiff and brittle proteinaceous shell coupled with a soft and compliant membrane vesicle yields a tough composite nanomaterial well-suited to protect the viral DNA during extracellular transport.