Defining the free-energy landscape of curvature-inducing proteins on membrane bilayers

Richard W. Tourdot, N. Ramakrishnan, and Ravi Radhakrishnan
Phys. Rev. E 90, 022717 – Published 25 August 2014
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Abstract

Curvature-sensing and curvature-remodeling proteins, such as Amphiphysin, Epsin, and Exo70, are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors; they aggregate to membrane regions matching their intrinsic curvature; as well as induce curvature in cell membranes to stabilize emergent high curvature, nonspherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains incomplete. Here, within a continuum framework and using the machinery of Monte Carlo simulations, we introduce and compare three free-energy methods to delineate the free-energy landscape of curvature-inducing proteins on bilayer membranes. We demonstrate the utility of the Widom test particle (or field) insertion methodology in computing the excess chemical potentials associated with curvature-inducing proteins on the membrane—in particular, we use this method to track the onset of morphological transitions in the membrane at elevated protein densities. We validate this approach by comparing the results from the Widom method with those of thermodynamic integration and Bennett acceptance ratio methods. Furthermore, the predictions from the Widom method have been tested against analytical calculations of the excess chemical potential at infinite dilution. Our results are useful in precisely quantifying the free-energy landscape, and also in determining the phase boundaries associated with curvature-induction, curvature-sensing, and morphological transitions. This approach can be extended to studies exploring the role of thermal fluctuations and other external (control) variables, such as membrane excess area, in shaping curvature-mediated interactions on bilayer membranes.

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  • Received 5 February 2014
  • Revised 19 May 2014
  • Corrected 22 April 2016

DOI:https://doi.org/10.1103/PhysRevE.90.022717

©2014 American Physical Society

Corrections

22 April 2016

Erratum

Authors & Affiliations

Richard W. Tourdot*

  • Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

N. Ramakrishnan

  • Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

Ravi Radhakrishnan

  • Department of Chemical and Biomolecular Engineering, Department of Bioengineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

  • *tourdot@seas.upenn.edu
  • ramn@seas.upenn.edu
  • Corresponding author: rradhak@seas.upenn.edu

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Issue

Vol. 90, Iss. 2 — August 2014

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