Nanorheology of viscoelastic shells: Applications to viral capsids

Abstract

We study the microrheology of nanoparticle shells [Dinsmore et al. Science 298, 1006(2002] and viral capsids [Ivanovska et al. PNAS 101, 7600 (2004)] by computing the mechanical response function and thermal fluctuation spectrum of a viscoelastic spherical shell that is permeable to the surrounding solvent. We determine analytically the damped dynamics of the shear, bend, and compression modes of the shell coupled to the solvent both inside and outside the sphere in the zero Reynolds number limit. We identify fundamental length and time scales in the system, and compute the thermal correlation function of displacements of antipodal points on the sphere and the mechanical response to pinching forces applied at these points. We describe how such a frequency-dependent antipodal correlation and/or response function, which should be measurable in new AFM-based microrheology experiments, can probe the viscoelasticity of these synthetic and biological shells constructed of nanoparticles.

Measurement of red blood cell mechanics during morphological changes

“…The response matrix χ depends on all the elastic constants of the material, the viscosities of the interior and exterior fluids, the radius of curvature, the order ℓ of the spherical harmonic, and the frequency ω. From the eigenvalues of this matrix we derive the decay rates of each normal mode (23). The decay rates are shown and discussed in more detail in SI Text.…”

“…The hydrodynamics can be described by the incompressible Stokes equation (i.e. zero Reynolds number) (18,22,23). We allow for a difference between the interior cytosol viscosity η c and the exterior solvent viscosity η s .…”

Cellular normoxic biophysical markers of hydroxyurea treatment in sickle cell disease

“…3, there is a steady increase in the shear modulus of the cell membrane as the cell density increases, whereas bending modulus remains relatively constant for all density fractions. It has been suggested (32,38) that changes in shear modulus can be attributed to the spectrin network supporting the cell membrane, whereas bending properties are mainly a function of the configuration of phospholipids, fatty acids, and cholesterols in the RBC membrane. These results are consistent with previous reports that the mechanical damage of RBCs is mainly caused by the rearrangement of the membrane scaffold proteins rather than a change in lipid bilayer or integral proteins (41,42).…”

“…2). (32,38). Specifically, this analytical model links membrane fluctuations to four biomechanical properties: in-plane shear modulus (μ), bending stiffness (κ), and area expansion modulus (K A ) of the cell membrane, as well as the viscosity of the cytosol (η).…”

“…It was first shown by Brochard and Lennon (56) that the decay rate of the thermal fluctuations of a flat lipid bilayer can be linked to the mechanical properties of the membrane. Their model was later modified to account for the geometry of the RBCs and contribution of the spectrin network beneath the lipid bilayer, the details of which can be found elsewhere (32,38). In short, in the improved methodology, RBCs are modeled as a composite There is no statistically significant difference between patients with low and high clinically measured HbF levels.…”