Electrostatic Interactions of Bodies Bearing Thin Double-Layers III. Dissimilar Double-Layers

Cell shape recognition by colloidal cell imprints: energy of the cell-imprint interaction

The results presented in this study are aimed at the theoretical estimate of the interactions between a spherical microbial cell and the colloidal cell imprints in terms of the Derjaguin, Landau, Vervey, and Overbeek (DLVO) surface forces. We adapted the Derjaguin approximation to take into account the geometry factor in the colloidal interaction between a spherical target particle and a hemispherical shell at two different orientations with respect to each other. We took into account only classical DLVO surface forces, i.e., the van der Waals and the electric double layer forces, in the interaction of a spherical target cell and a hemispherical shell as a function of their size ratio, mutual orientation, distance between their surfaces, their respective surface potentials, and the ionic strength of the aqueous solution. We found that the calculated interaction energies are several orders higher when match and recognition between the target cell and the target cell imprint is achieved. Our analysis revealed that the recognition effect of the hemispherical shell towards the target microsphere comes from the greatly increased surface contact area when a full match of their size and shape is produced. When the interaction between the surfaces of the hemishell and the target cell is attractive, the recognition greatly amplifies the attraction and this increases the likelihood of them to bind strongly. However, if the surface interaction between the cell and the imprint is repulsive, the shape and size match makes this interaction even more repulsive and thus decreases the likelihood of binding. These results show that the surface chemistry of the target cells and their colloidal imprints is very important in controlling the outcome of the interaction, while the shape recognition only amplifies the interaction. In the case of nonmonotonous surface-to-surface interaction we discovered some interesting interplay between the effects of shape match and surface chemistry which is discussed in the paper. The results from this study establish the theoretical basis of cell shape recognition by colloidal cell imprints which, combined with cell killing strategies, could lead to an alternative class of cell shape selective antimicrobials, antiviral, and potentially anticancer therapies.

Calculations of Double-Layer Electrostatic Interactions for the Sphere/Plane Geometry

A numerical scheme for solving the nonlinear Poisson-Boltzmann equation for the sphere/sphere and plane/sphere geometries has been developed. The method is based on an alternating direction overrelaxation procedure using the Newton-Raphson iteration to solve the nonlinear equation stemming from finite-difference discretization. The novelty of the algorithm consists in using the grid transforming functions that allow a more uniform distribution of mesh points in the vicinity of the particle. The method was used to perform extensive calculations for opposite surface potentials of the interface and the particle immersed in a symmetric electrolyte solution. The electric potential distribution (within and outside the sphere) was calculated, as well as the force and energy of interaction (from the integral of the force over separation distance), for the constant potential, the constant charge, and the mixed cases. The energy profiles calculated for various kappaa were compared with the analytical approximations derived using the Hogg-Healy-Fuerstenau method and the linear superposition approach (LSA). These calculations enabled us to conclude that the LSA can be used as a good estimate of interaction energy for a broad range of kappaa values at distances greater than kappa-1, i.e., for problems pertinent to colloid particle adsorption.