Statistical mechanics of an elastically pinned membrane: Static profile and correlations
arXiv:1806.05109 · doi:10.1016/j.bpj.2018.12.003
Abstract
The relation between thermal fluctuations and the mechanical response of a free membrane has been explored in great detail, both theoretically and experimentally. However, understanding this relationship for membranes, locally pinned by proteins, is significantly more challenging. Given that the coupling of the membrane to the cell cytoskeleton, the extracellular matrix and to other internal structures is crucial for the regulation of a number of cellular processes, understanding the role of the pinning is of great interest. In this manuscript we consider a single protein (elastic spring of a finite rest length) pinning a membrane modelled in the Monge gauge. First, we determine the Greens function for the system and complement this approach by the calculation of the mode coupling coefficients for the plane wave expansion, and the orthonormal fluctuation modes, in turn building a set of tools for numerical and analytic studies of a pinned membrane. Furthermore, we explore static correlations of the free and the pinned membrane, as well as the membrane shape, showing that all three are mutually interdependent and have an identical long-range behaviour characterised by the correlation length. Interestingly, the latter displays a non-monotonic behaviour as a function of membrane tension. Importantly, exploiting these relations allows for the experimental determination of the elastic parameters of the pinning. Last but not least, we calculate the interaction potential between two pinning sites and show that, even in the absence of the membrane deformation, the pinnings will be subject to an attractive force due to changes in membrane fluctuations.
arXiv commentThis is the version accepted for publishing in the Biophysical Journal. The published version can be found on https://doi.org/10.1016/j.bpj.2018.12.003
References in corpus (21)
- Physics of adherent cells
- Rupture of multiple parallel molecular bonds under dynamic loading
- Interaction of Conical Membrane Inclusions: Effect of Lateral Tension
- N-body Study of Anisotropic Membrane Inclusions: Membrane Mediated Interactions and Ordered Aggregation
- How cells tiptoe on adhesive surfaces before sticking
- Interface mediated interactions between particles -- a geometrical approach
- Interactions between proteins bound to biomembranes
- Bistability of cell-matrix adhesions resulting from non-linear receptor-ligand dynamics
- Interactions between Membrane Inclusions on Fluctuating Membranes
- Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size
- Effective adhesion strength of specifically bound vesicles
- Model for probing membrane-cortex adhesion by micropipette aspiration and fluctuation spectroscopy
- Fluctuation-induced forces between inclusions in a fluid membrane under tension
- Specific Adhesion of Membranes: Mapping to an Effective Bond Lattice Gas
- Fluctuations of the Casimir-like force between two membrane inclusions
- Multiscale approaches to protein-mediated interactions between membranes - Relating microscopic and macroscopic dynamics in radially growing adhesions
- Membrane fluctuations near a plane rigid surface
- Fluctuation induced attraction between adhesion sites of supported membranes
- Coexistence of dilute and densely packed domains of ligand-receptor bonds in membrane adhesion
- Non-monotonic fluctuation spectra of membranes pinned or tethered discretely to a substrate
- Boundary knot method for Laplace and biharmonic problems