Determination of Condensate Material Properties from Droplet Deformation

Abstract

I derive theoretical results that relate the effective spring constant, χ, of protein droplets to their material properties. χ, defined as the ratio between a uniaxial applied force and the extent of the corresponding deformation, can be measured by optical tweezers. When the deformation is static, where the applied force is balanced by the interfacial tension of the droplet, the spring constant allows for the determination of the surface tension (γ). When a sinusoidal force is applied (at frequency ω), the dynamic spring constant χ(ω) is related to both γ and the complex shear modulus, G(ω) of the droplet. The results derived here enable accurate extraction of γ and G(ω) from χ(ω) data.

Viscoelasticity of biomolecular condensates conforms to the Jeffreys model

“…13 The corrected analysis of those data has been published. 14 Here I show that the Jeffreys model of linear viscoelasticity can be used to fit the data of PGL-3 and other biomolecular droplets. This finding makes it possible to not only resolve practical problems in the extraction of viscoelastic properties from experimental data but also gain deeper physical understanding of biomolecular condensates.…”

“…The expression contains an infinite sum, which Jawerth et al truncated at the 5th term because their expressions for the terms grow rapidly in complexity. I have obtained a compact expression for χ ( ω ) that allows for the summation to be evaluated to any order: 14 where θ 0 = a / R and is small, at 0.1 or less, and P l ( x ) are Legendre polynomials. 15 This summation turns out to converge very slowly, requiring l up to 40,000 to 100,000.…”

Shape Recovery of Deformed Biomolecular Droplets: Dependence on Condensate Viscoelasticity

“…This solution easily lends itself to generalization from viscous fluids to viscoelastic fluids. The derivation here for droplets largely follows the solution of a related fluid-dynamics problem [20]. We assume that the shape deformation is axisymmetric ( Fig.…”

“…In all the studies so far on the dynamics of such shape changes, biomolecular condensates have been modeled as purely viscous, reporting viscosities that are orders of magnitude higher than that of water [1,8,[14][15][16][17][18]. However, recent work has shown that condensates are viscoelastic [12,[19][20][21]. In viscoelastic fluids, shear relaxation is not instantaneous [21] and its effects, when coupled with viscocapillary effects, can lead to unexpected observations.…”

“…These authors suggested that the disparity in timescales between the two kinds of shape dynamics indicated viscoelasticity. While theoretical results of viscous fluids have been used for qualitative as well as quantitative analysis of droplet fusion dynamics [1,[14][15][16][17][18]26] and a theoretical model of viscoelastic fluids has been introduced to treat deformation of droplets under external force [19,20], up to now no theory has been presented for shape recovery of biomolecular droplets.…”