Article pubs.acs.org/JPCB
Perfluoroalkane Force Field for Lipid Membrane Environments Guido Falk von Rudorff,† Tobias Watermann,‡ and Daniel Sebastiani*,‡ †
Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany Institute of Chemistry, Martin-Luther-Universität Halle-Wittenberg, von-Danckelmann-Platz 4, 06120 Halle, Germany
‡
S Supporting Information *
ABSTRACT: In this work, we present atomic parameters of perfluoroalkanes for use within the CHARMM force field. Perfluorinated alkanes represent a special class of molecules. On the one hand, they are considerably more hydrophobic than lipids, but on the other hand, they are not lipophilic either. Instead, they represent an independent class of philicity, enabling a whole portfolio of applications within both materials science and biochemistry. We performed a thorough parametrization of all bonded and nonbonded parameters with a particular focus on van der Waals parameters. Here, the general framework of the CHARMM and CGenFF force fields has been followed. The van der Waals parameters have been fitted to experimental densities over a wide range of temperatures and pressures. This newly parametrized class of molecules will open the gate for a variety of simulations of biologically relevant systems within the CHARMM force field. A particular perspective for the present work is the influence of polyphilic transmembrane molecules on membrane properties, aggregation phenomena, and transmembrane channels.
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INTRODUCTION Despite their structural similarity to hydrocarbons, fluorocarbons have highly different properties and applications. They are useful for medical purposes as gas-carrier fluids,1,2 can aid purification or polymerization,1 and have further applications as lubricant.3 Perfluoroalkanes are especially interesting due to their phase separation behavior in hydrocarbon environments.4−7 Together with hydrophilic and hydrophobic segments, fluorocarbons can help building polyphilic molecules. Some of these molecules and their behavior have been investigated by experiment recently8−11 and were found to exhibit a phase ordering pattern similar to liquid crystals.12 Molecules containing (per-)fluorinated alkane chains and conjugated oligomers influence the channel formation when being added to a membrane environment13,14 as well as the overall stability15 and surface properties16 of a lipid membrane. Although synthesis is possible for a whole family of polyphilic compounds containing fluorinated side chains, the aggregation mechanisms are not fully understood on an atomistic scale. On the way to membrane environments, perfluoro-n-alkanes have to be parametrized for lipid bilayer simulations to prepare elucidating the physical processes and mechanisms that are responsible for the macroscopic behavior that has been observed so far. Among the many force fields available, there are some that have been either specialized to treat fluorocarbons1,17,18 and some that include parameters for fluorocarbons among others.19 In the beginning of force field development, unitedatom force fields have been extended more quickly, mainly due to the reduced computational effort necessary to actually perform simulations using these force fields. As hardware became more powerful, a tendency toward all-atom force fields © XXXX American Chemical Society
emerged due to the alleged higher accuracy of all-atom force fields. This reasoning is reflected in the history of force field development for fluorocarbons as well. The earliest force fields were based on a united-atom approach and yielded comparably poorer results.1 We have screened the literature for an all-atom force field for perfluoroalkanes which is adequate for a phospholipid membrane environment. However, no parametrization for perfluorinated chains was found to allow a broad application to biochemical problems, which led us to developing a suitable force field ourselves. To our knowledge, there is no force field which comes with support for both perfluoroalkanes and lipids. Regarding the integration of the new set of parameters for perfluorinated chains, we chose the CHARMM force field package,20,21 which has been extensively benchmarked in literature to a broad range of lipids. An additional plus is the clear parametrization procedure defined for this force field type, which ensures compatibility with the other parameters within the force field. As van der Waals interactions are known to be very prominent in membrane environments, we have put particular emphasis on carefully tuning the Lennard-Jones parameters.
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COMPUTATIONAL METHODS CHARMM Force Field. Model interactions and parameter usage for the total energy function of the CHARMM force field are provided in Figure 1. Received: April 11, 2014 Revised: October 2, 2014
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dx.doi.org/10.1021/jp507464m | J. Phys. Chem. B XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry B
Article
case, the van der Waals interaction is only modeled by the Lennard-Jones potential. Although a repulsive exponential and an attractive r−6 would be more realistic, one typically employs a repulsive r−12 expression for easier computation. Naturally, this model cannot be optimal for all combinations of atoms with their different interactions. It has been shown25,26 that for interactions of atoms of highly different van der Waals radii, the Lorentz−Berthelot combination rules may yield an effective potential energy surface which considerably deviates from the results of molecular beam experiments. While the most prominent van der Waals interaction of perfluoroalkanes with membranes will be the one between fluorine and hydrogen, we stick to the Lorentz−Berthelot definition to allow for seamless integration of the parameters presented in this work into CHARMM-based setups. Optimization Procedure for Bonded Parameters and Charges. Although there is a procedure (see Figure 2) how to
Figure 1. Model interactions and parameter usage for the total energy function of the CHARMM force field (see eq 1).
The total energy function of the CHARMM force field20 and its extensions21 is given as E=
∑
Kb(b − b0)2 +
bonds
+
∑
∑
K θ(θ − θ0)2
angles
Kϕ(1 + cos(nϕ − δ))
dihedrals
+
∑ improper
Kφ(φ − φ0)2 +
∑
K u(u − u0)2
Urey − Bradley
⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij + ∑ 4ε⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ i
