Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum

Janeš, Josip A.; Schmidt, Daniel; Blackwell, Robert; Seifert, Udo; Smith, Ana-Sunčana (2019) Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum. Biophysical Journal, 117 (3). pp. 542-552. ISSN 0006-3495

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Abstract

In biological settings, membranes typically interact locally with other membranes: the extracellular matrix in the exterior or internal cellular structures such as the cytoskeleton, locally pinning the membrane. Characterizing the dynamical properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modeling pinned membranes has been impeded by the complexity of governing equations. Here, we circumvent these difficulties by calculating analytically the time-dependent Green’s function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, in which the elasticity of the membrane’s attachment to the cytoskeleton could be measured.

Item Type:

Article

Additional Information:

A.-S.S., D.S., and and J.A.J. received funding from the European Research Council Starting Grant MembranesAct 337283. J.A.J. and A.-S.S. were in part supported by the Croatian Science Foundation through the project CompSoLS-MolFlex. R.B. received a fellowship from the Alexander von Humboldt Fundation. D.S. was a member of the Research Training Group 1962 at the Friedrich Alexander Universitat Erlangen-Nurnberg, supported by the German Science Foundation.

Uncontrolled Keywords:

membranes ; power spectrum ; statistical mechanics

Subjects:

NATURAL SCIENCES > Mathematics

Divisions:

Division of Physical Chemistry

Projects: