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Thermodynamic free energy methods to investigate shape transitions in bilayer membranes

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Abstract

The conformational free energy landscape of a system is a fundamental thermodynamic quantity of importance particularly in the study of soft matter and biological systems, in which the entropic contributions play a dominant role. While computational methods to delineate the free energy landscape are routinely used to analyze the relative stability of conformational states, to determine phase boundaries, and to compute ligand-receptor binding energies its use in problems involving the cell membrane is limited. Here, we present an overview of four different free energy methods to study morphological transitions in bilayer membranes, induced either by the action of curvature remodeling proteins or due to the application of external forces. Using a triangulated surface as a model for the cell membrane and using the framework of dynamical triangulation Monte Carlo, we have focused on the methods of Widom insertion, thermodynamic integration, Bennett acceptance scheme, and umbrella sampling and weighted histogram analysis. We have demonstrated how these methods can be employed in a variety of problems involving the cell membrane. Specifically, we have shown that the chemical potential, computed using Widom insertion, and the relative free energies, computed using thermodynamic integration and Bennett acceptance method, are excellent measures to study the transition from curvature sensing to curvature inducing behavior of membrane associated proteins. The umbrella sampling and WHAM analysis has been used to study the thermodynamics of tether formation in cell membranes and the quantitative predictions of the computational model are in excellent agreement with experimental measurements. Furthermore, we also present a method based on WHAM and thermodynamic integration to handle problems related to end-point-catastrophe that are common in most free energy methods.

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Notes

  1. Calculated as (nanocarrier radius + length of the antibody + length of the receptor + \(d_{0}\)).

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Acknowledgments

This work was supported in part by the US National Science Foundation Grants DMR-1120901, and CBET-1244507. The research leading to these results has received funding from the European Commission Grant FP7-ICT-2011-9-600841, US NIH U01-EB016027, and NIH 1U54CA193417. Computational resources were provided in part by the National Partnership for Advanced Computational Infrastructure under Grant No. MCB060006 from XSEDE.

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Authors and Affiliations

  1. Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, 19104, USA

    N. Ramakrishnan & Ravi Radhakrishnan

  2. Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Richard W. Tourdot & Ravi Radhakrishnan

  3. Department of Biochemistry Biophysics, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Ravi Radhakrishnan

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  1. N. Ramakrishnan
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Correspondence to Ravi Radhakrishnan.

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Ramakrishnan, N., Tourdot, R.W. & Radhakrishnan, R. Thermodynamic free energy methods to investigate shape transitions in bilayer membranes. Int J Adv Eng Sci Appl Math 8, 88–100 (2016). https://doi.org/10.1007/s12572-015-0159-5

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