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Computational Studies of Biomembrane Systems: Theoretical Considerations, Simulation Models, and Applications

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From Single Molecules to Nanoscopically Structured Materials

Part of the book series: Advances in Polymer Science ((POLYMER,volume 260))

Abstract

This chapter summarizes several approaches combining theory, simulation, and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane-mediated interactions, attraction between transmembrane proteins, and aggregation in biomembranes leading to large superstructures such as the light-harvesting complex of green plants. After a general overview of theoretical considerations and continuum theory of lipid membranes we introduce different options for simulations of biomembrane systems, addressing questions such as: What can be learned from generic models? When is it expedient to go beyond them? And, what are the merits and challenges for systematic coarse graining and quasi-atomistic coarse-grained models that ensure a certain chemical specificity?

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Notes

  1. 1.

    Observe that 1/K 0 is not the optimal radius R opt of a spherical vesicle. Minimizing the energy per area with respect to K shows that instead this radius is given by \( {R}_{\mathrm{opt}}{K}_0=2+\overline{\kappa}/\kappa \).

  2. 2.

    It is easy to see that \( \delta h\equiv {\left\langle h{\left(\boldsymbol{r}\right)}^2\right\rangle}^{1/2}=L\sqrt{k_{\mathrm{B}}T/16{\uppi}^3\kappa}\approx L/100 \) (assuming κ ≃ 20 k B T), which is a few Ångström for typical simulation sizes.

  3. 3.

    Observe that the part of the membrane above the buckle and the part below the buckle can be connected through the periodic boundary of the simulation box.

  4. 4.

    The requirement that the Hamiltonian (1) is bounded below demands that \( -2\kappa \le \overline{\kappa}\le 0 \).

  5. 5.

    Unfortunately, in the first paper that discusses this force, Goulian et al. [253] claim that the prefactor is 12, a mistake that is not fixed during the prefactor-fixing in [254].

  6. 6.

    They used the same techniques that also led to the exact Eq. (14), only that in the cell model case the sign is evident from the expression.

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Acknowledgements

We would like to thank the many coworkers and colleagues who have contributed to the research reported here, in particular Ira Cooke, Jemal Guven, Vagelis Harmandaris, Gregoria Illya, Martin Müller, Benedict Reynwar, Ira Rothstein, Cem Yolcu, Frank Brown, Olaf Lenz, Sebastian Meinhardt, Peter Nielaba, Beate West, Ananya Debnath, Christoph Globisch, Christoph Junghans, Shahoua Ding, Sabine Wiegand, Sandra Ritz, and Eva Sinner.

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Authors and Affiliations

  1. Department of Physics, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, 15213, USA

    Markus Deserno

  2. Max-Planck-Institute for Polymer Research, Ackermannweg 10, 55128, Mainz, Germany

    Kurt Kremer

  3. Department of Biology, University of Mainz, Johannes-von-Müller-Weg 6, 55128, Mainz, Germany

    Harald Paulsen

  4. Department of Chemisty, University of Konstanz, Universitätsstraße 10, 78457, Constance, Germany

    Christine Peter

  5. Institute of Physics, University of Mainz, Staudingerweg 9, 55128, Mainz, Germany

    Friederike Schmid

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  1. Markus Deserno
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  2. Kurt Kremer
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  3. Harald Paulsen
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  4. Christine Peter
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  5. Friederike Schmid
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Correspondence to Markus Deserno .

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Editors and Affiliations

  1. Johannes Gutenberg University Mainz, Institute of Physical Chemistry, Mainz, Germany

    Thomas Basché

  2. Max Planck Institute for Polymer Research, Mainz, Germany

    Klaus Müllen

  3. Johannes-Gutenberg-University Mainz, Institute of Physical Chemistry, Mainz, Germany

    Manfred Schmidt

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Deserno, M., Kremer, K., Paulsen, H., Peter, C., Schmid, F. (2013). Computational Studies of Biomembrane Systems: Theoretical Considerations, Simulation Models, and Applications. In: Basché, T., Müllen, K., Schmidt, M. (eds) From Single Molecules to Nanoscopically Structured Materials. Advances in Polymer Science, vol 260. Springer, Cham. https://doi.org/10.1007/12_2013_258

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