Values of , and obtained from our model that yield the best agreement with the experimental results of Ref. [18], analyzed with a quadratic fit (see Eq. 18 and Fig. 7).

<p>Results are presented for the fixed-slope boundary condition (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e898" target="_blank">Eqs. 61</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e899" target="_blank">62</a>), with slopes and , and for the free-slope boundary condition (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e930" target="_blank">Eqs. 67</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e931" target="_blank">68</a>).</p

Renormalized spontaneous curvature

<p><b>as a function of the hydrophobic mismatch </b><b>.</b> Data from Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-West1" target="_blank">[16]</a>, which presents fits of simulation results for inclusions with three different hydrophobic thicknesses. Line: linear fit, with slope . Note that our corresponds to twice that in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone-0048306-t002" target="_blank">Table 2</a> of Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-West1" target="_blank">[16]</a>, as we work with total curvatures instead of average curvatures. The error bars on are those listed in that table, and corresponds to in that table.</p

Thickness gradient.

<p>Cut of a bilayer membrane with a symmetric thickness gradient. The dashed blue lines correspond to the hydrocarbon-water interfaces.</p

Values of and obtained from the model of Ref. [22] and from our model with .

<p>The results are presented both for the fixed-slope boundary condition (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e898" target="_blank">Eqs. 61</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e899" target="_blank">62</a>), with slopes and , and for the free-slope boundary condition (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e930" target="_blank">Eqs. 67</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e931" target="_blank">68</a>). The corresponding values of are also given. Recall that the best quadratic fit to the data of Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Goulian1" target="_blank">[18]</a> yields and (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone-0048306-g007" target="_blank">Fig. 7</a>).</p

Thickness deformation due to a mismatched inclusion.

<p>Membrane thickness profile from Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-West1" target="_blank">[16]</a> in the vicinity of a mismatched inclusion with hydrophobic thickness and radius , with center in , as a function of the radial coordinate . The equilibrium membrane hydrophobic thickness is . The unit of length on the graph is 6 Å, as in Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-West1" target="_blank">[16]</a>. Dots: numerical data (the error bars on the data, not reproduced here, are about 1 Å wide <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-West1" target="_blank">[16]</a>). Line: best fit. Exactly as in the original reference, the numerical data is fitted to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e811" target="_blank">Eqs. 46</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e848" target="_blank">53</a> with , taking and the (renormalized) spontaneous curvature as fitting parameters, the other constants being known from the fluctuation spectra.</p

Formation rate

<p><b>of gramicidin channels versus the applied tension </b><b>, analyzed with a quadratic model.</b> Diamonds: experimental data retrieved from Fig. 6b of Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Goulian1" target="_blank">[18]</a>, after subtraction of the baselines . Dotted black line: best quadratic fit, with and ; . Dashed green line: results obtained from the elastic model of Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Nielsen1" target="_blank">[22]</a>, with the constants given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Goulian1" target="_blank">[18]</a>; . Dashed-dotted blue line: <i>idem</i> with more recent values of the constants; . Solid red line: results obtained by taking and the recent values of the constants in the model of Refs. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Huang1" target="_blank">[7]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Nielsen1" target="_blank">[22]</a>; . The values of and corresponding to the curves on this graph are listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone-0048306-t002" target="_blank">Table 2</a>.</p

Renormalized spontaneous curvature

<p><b>as a function of the inclusion radius. </b><b>and the hydrophobic mismatch. </b><b>. </b><b>A</b>) versus . The values of were obtained by fitting each thickness deformation profile of Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Brannigan2" target="_blank">[15]</a>. Circles (blue): positive mismatch, . Squares (red): negative mismatch, . Solid lines: average values; dotted lines: standard deviation over the seven data points (corresponding to the different ), for each value of . <b>B</b>) Average value of (see A) as a function of the hydrophobic mismatch . The equation of the line joining the two data points has a slope .</p

Formation rate

<p><b>of gramicidin channels as a function of the applied tension </b><b>, analyzed with a linear model, for </b><b>.</b> Diamonds: experimental data retrieved from Fig. 6b of Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Goulian1" target="_blank">[18]</a>, after subtraction of the baselines (which are different from those of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone-0048306-g007" target="_blank">Fig. 7</a> since the fitting model is here linear instead of quadratic). Line: best linear fit, yielding ; correlation coefficient: .</p

Renormalized spontaneous curvature

<p><b>versus the relative volume variation </b><b>on the inclusion edge.</b> The values of are extracted from fitting the data of Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Brannigan2" target="_blank">[15]</a>, and the values of are directly taken from Ref. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306-Brannigan2" target="_blank">[15]</a>.</p

Values of and obtained from our model that yield the best agreement with the experimental results of Ref. [18] analyzed with the low-tension linear fit.

<p>More precisely, these values of and are associated with . Results are presented for the fixed-slope boundary condition (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e898" target="_blank">Eqs. 61</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e899" target="_blank">62</a>), with slopes 0, , , and for the free-slope boundary condition (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e930" target="_blank">Eqs. 67</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048306#pone.0048306.e931" target="_blank">68</a>).</p