Elastic deformation of a fluid membrane upon colloid binding

TL;DR

This paper theoretically investigates how colloidal particles induce elastic deformations in fluid membranes, revealing complex phase transitions and energetic behaviors relevant to biological processes like virus budding.

Contribution

It provides a comprehensive nonlinear analysis of membrane deformation and identifies novel phase transition lines and a triple point in colloid-membrane interactions.

Findings

Identifies continuous and discontinuous binding transition lines.

Derives scaling laws for high tension regimes.

Discusses biological implications for virus budding.

Abstract

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.