Journal of Chemical Theory and Computation Article Figure 5. Left panel: free energy profiles calculated for coumarin with PRODRG (red dotted curve), Mulliken (blue dashed curve), and RESP charges (black curve) by constraint simulation (CF) with initial structures obtained by free simulation using 10 ns windows. Coumarin with PRODRG partial charges is shifted to the outer part of the lipid bilayer. The bilayer center penetration barriers grow and the water/ lipids barriers decrease with increasing dipole moment. The right panel shows that the partial charges (mapped on the vdW surface) calculated by RESP (upper part) and Mulliken population analysis (middle) are spread along the whole molecule, while partial charges assigned by PRODRG (lower part) are localized close to coumarin oxygens. dipole moment, and reversely the energy barrier between lipid bilayer and water decreases with the growing dipole moment. Comparison with Experimental Data. To our knowl- edge, the precise positioning of bare coumarin in a DOPC bilayer has not yet been studied experimentally; therefore, we compared the results of our theoretical calculations to data obtained in experiments with coumarin derivatives. Depths of several coumarin derivatives in dimyristoylphosphatidylcholine (DMPC) bilayer have been studied in NMR investiga- tions,2,46,47 in which chemical shifts of 13C-labeled derivatives were used to assess the polarity of the surroundings of 13C atoms and hence estimate their depth in the lipid bilayer. Results of the cited experiments indicate that the mean position of 7-acetoxy-4-methylcoumarin is at the border of regions 2 and 3 in DMPC lipid bilayer (0.7 nm from the DMPC choline nitrogens, corresponding to 1.2 nm from the center of the bilayer); 13C-labeled carbons of the derivative (C2 and C4, see Figure 6) appeared to be located 0.72 and 0.70 nm from the choline nitrogens, corresponding to 1.18 and 1.20 nm from the bilayer center, respectively. Another coumarin derivative, 7- acetoxycoumarin, was apparently located closer to the bilayer interface in region 2, with its 13C-labeled (C2 and C4) carbons 0.44 and 0.59 nm from the choline nitrogen, corresponding to 1.46 and 1.31 nm from the bilayer center, respectively. We recalculated the experimental positions (originally expressed as distances from the bilayer surface) as distances from the bilayer center to facilitate direct comparison with results of this study. In this recalculation, the distance between the DMPC bilayer surface and center was set at 1.9 nm: the mean distance between the bilayer center and maximum density of nitrogens (regarded as the membrane surface in the cited NMR experiments) in corresponding MD simulations. Figure 6. Free energy profiles and structures of coumarin derivatives (7-acetoxy-4-methylcoumarin, upper panel (a), and 7-acetoxycoumar- in, lower panel (b)) along a DMPC lipid bilayer normal calculated from constraint simulation with initial structures obtained by free simulation (CF). NMR-observed positions of 13C-labeled carbons (C2 and C4) are displayed as red and green circles, respectively, and the positions of C2 and C4 carbons calculated from simulation are depicted as green and red curves, respectively. The positions of marked carbons of both coumarin derivatives are in good agreement with the positions observed by NMR. For the comparison we employed the most effective simulation protocol of those considered here to calculate the free energy profiles of the coumarin derivatives described above, briefly comprising unbiased simulation followed by constraint simulation with 10 ns simulation bins (see Methods for details). The profile obtained for 7-acetoxy-4-methylcou- marin indicated the free energy minimum position of its COM to be 1.0 nm from the center of the DMPC bilayer (Figure 6), with a thermally accessible region between 0.8 and 1.3 nm. The thermally accessible region estimated from the simulation (0.8−1.3 nm) matched that acquired from NMR experiments, where 7-acetoxy-4-methylcoumarin was located 1.2 ± 0.1 nm from the bilayer center. In addition, the positions of its C2 and C4 carbons calculated from simulations (1.25 and 1.21 nm, respectively) agreed well with those estimated from experi- ments (1.18 and 1.20 nm, respectively), although the C4 carbon seems to flip-flop between two positions in the bilayer (the other at 0.76 nm, with ca. 14% population, see Figure 6 up). The free energy minimum position of the COM of 7- acetoxycoumarin in the simulation was located 1.2 nm from the bilayer center, with a thermally accessible region between 0.75 and 1.35 nm. The simulated distances of the C2 and C4 carbons from the bilayer center at this point (1.34 and 1.19 nm, respectively) again matched those obtained from the NMR data 1207 dx.doi.org/10.1021/ct2009208 | J. Chem. Theory Comput. 2012, 8, 1200−1211