Calculation of torsional entropy

YK Young Hun Kim GL Geoffray Leriche KD Karthik Diraviyam TK Takaoki Koyanagi KG Kaifu Gao DO David Onofrei JP Joseph Patterson AG Anirvan Guha NG Nathan Gianneschi GH Gregory P. Holland MG Michael K. Gilson MM Michael Mayer DS David Sept JY Jerry Yang

This protocol is extracted from research article:

Entropic effects enable life at extreme temperatures

**
Sci Adv**,
May 1, 2019;
DOI:
10.1126/sciadv.aaw4783

Entropic effects enable life at extreme temperatures

Procedure

The entropy *S*_{i} associated with torsion angle ϕ_{i} is given by$${\mathit{S}}_{\mathit{i}}=-\mathit{R}{\displaystyle \int}\mathrm{\rho}({\mathrm{\varphi}}_{\mathit{i}})\text{ln}\mathrm{\rho}({\mathrm{\varphi}}_{\mathit{i}})\mathit{d}{\mathrm{\varphi}}_{\mathit{i}}$$(6)where *R* is the gas constant and ρ(ϕ_{i}) is the probability density over ϕ_{i} from an MD simulation—essentially, a normalized histogram of the torsion. The total first-order entropy (*20*) of one lipid molecule is computed as$${\mathrm{S}}^{\mathrm{1}}={\displaystyle \sum _{\mathit{i}=\mathrm{1}}^{{\mathit{N}}_{\text{tors}}}}{\mathit{S}}_{\mathit{i}}$$(7)where *N*_{tors} is the number of torsions considered. Additional MD simulations (Fig. 4) were carried out to compute these quantities in the presence and absence of CF tethered partway through one leaflet (top or upper) of membranes made of tethered and untethered lipids. Simulations were run for T32 and U16 membrane systems, for 400 ns at a temperature of 300 K with and without CF (−2 charge state). For the simulations with CF, the molecule was constrained to remain at the plane of the membrane defined by the mean *z* coordinate of carbon C117 in each lipid (as shown in fig. S10), where we considered the membrane to lie in the *xy* plane. We analyzed the 26 torsional angles in the lipid main chains (for the 26 carbon atoms located in the center of the membrane for the unbranched methylene chain and phytanyl chain), 13 torsional angles in the top (where CF is located), and another 13 angles in the bottom. For the monolayer, T32, these are all in one molecule. For the bilayer-forming lipid U16, they are in different molecules. The T32 and U16 membranes were of essentially the same size, comprising 64 T32 molecules or 128 U16 molecules.

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