Table 1. Force–Distance Regimes Used To Describe AFM Data in Figure 5ba.
regimes | approximate fitting function | parameters | definition | ||
---|---|---|---|---|---|
(I) double layer |
|
λD | Debye screening length (nm) | ||
(II) osmotic brush |
|
δL0 = exp(a1/b1) | the onset of linear compliance, capsule thickness: H ≈ 2δL0 (nm) | ||
(III) Hertzian |
|
E | Young’s modulus (Pa) | ||
(IV) Hookean |
|
kbac | elastic constant of bacteria cells (N/m) |
A0 describes the short-range van der Waals force (negligible when compared with the electrostatic force in this scenario), A1 is the force magnitude for the long-range electrostatic interaction, d is the separation distance, d0 is used to correct the relative separation distance, a1 and b1 are the reduced parameters of the full osmotic brush model for grafted polyelectrolyte brushes29 (where ln(δ0L) = a1/b1), δ is the indented distance after probe contact, c is the correction term of the indented distance from a relative separation distance, R is the effective radius (Rprobe, Rbac/(Rprobe + Rbac)), where Rprobe, Rbac are the radius of the probe and the indented bacteria, respectively, and v is the Poisson ratio of the bacterial cells, e.g., assumed equal to 0.5 as a first approximation for an isotropic elastic solid.60 The main parameters that we investigated were the bacterial capsule thickness, the Debye screening length (λD), the effective Young’s modulus (Eeff), and the elastic constant of the K1 bacterial cells (k).