Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon

© 2018 American Physical Society. Molecular dynamics (MD) simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistencies between them have been occasionally reported in the literature. Here we give an in-depth comparison of them in terms of heat transport in three allotropes of Si: three-dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire. By multiplying the correlation time in the Green-Kubo formula with an appropriate effective group velocity, we can express the running thermal conductivity in the EMD method as a function of an effective length and directly compare it to the length-dependent thermal conductivity in the NEMD method. We find that the two methods quantitatively agree with each other for all the systems studied, firmly establishing their equivalence in computing thermal conductivity

Binding kinetics and affinities for interaction of Mtb deacylated substrates with LprG and LprG-V91W.

<p>Values were calculated using BIAevaluation 3.1 software. Data shown are representative of at least three independent experiments.</p><p>Binding kinetics and affinities for interaction of Mtb deacylated substrates with LprG and LprG-V91W.</p

SPR analysis of substrate binding to LprG.

<p>(<b>A</b>) Schematic representation of mycobacterial glycolipids and lipoglycans used in this study. (<b>B–F</b>) Substrate binding to LprG was assessed by SPR. LprG was immobilized on a CM5 sensor chip. Sensograms were obtained by injecting increasing concentrations of (<b>B</b>) PIM₂ (<b>C</b>) PIM₆ (<b>D</b>) LM (<b>E</b>) ManLAM and (<b>F</b>) PI-LAM. Binding was measured as response units (RU). Binding curves were calculated with BIA evaluation 3.1 software with subtraction of non-specific binding of the substrates to the sensor chip control cells without immobilized LprG. Results are representative of three independent experiments.</p

Deacylated ManLAM and LM retain binding to LprG at reduced levels.

<p>Binding to LprG was assessed as in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1004471#ppat-1004471-g002" target="_blank">Fig. 2</a> for (<b>A</b>) deacylated LM and (<b>B</b>) deacylated ManLAM. Results are from one experiment and representative of at least three independent experiments.</p

Binding kinetics and affinities for interaction of Mtb substrates with LprG and LprG-V91W.

<p>Binding kinetics and affinities for interaction of Mtb substrates with LprG and LprG-V91W.</p

Mannan competition with Mtb lipoglycans for binding to LprG implicates a role for polysaccharide components of lipoglycans in LprG binding.

<p>(<b>A</b>) Binding of Mannan to LprG was assessed as in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1004471#ppat-1004471-g002" target="_blank">Fig. 2</a> at the indicated concentrations of mannan. (<b>B</b>) The ability of LM to compete with mannan for binding to LprG was assessed by SPR with sequential injection of LM (“1^st injection”) for 3 min followed by buffer for ∼10 min as the instrument prepared for injection of mannan (“2^nd injection”). This injection order was chosen due to the fast dissociation rate for mannan. The dissociation rate for LM (shown here) is slower than for LAM, but experiments with LAM provided qualitatively similar results. Results for mannan binding in panels A and B are directly comparable except for the absence (panel A) or presence (panel B) of prior LM injection. Results for panels A and B are representative of two independent experiments. (<b>C</b>) Mannan inhibited LAM binding to LprG in a solid phase competitive binding assay. LprG was incubated with mannan at the indicated concentrations for 30 min and added to wells of plates coated with ManLAM. After incubation and washing, the plates were incubated with anti-LprG antibody followed by an HRP-linked secondary antibody to detect LprG binding to ManLAM (see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1004471#s4" target="_blank">Materials and Methods</a>). Data are expressed as the means from three independent experiments.</p

Binding kinetics and affinity for interaction of <i>Saccharomyces cerevisiae</i> mannan with LprG.

<p>Binding kinetics and affinity for interaction of <i>Saccharomyces cerevisiae</i> mannan with LprG.</p

Deletion of <i>lprG</i> reduces LAM expression on the Mtb cell surface.

<p>Cultures of H37Rv, H37Rv Δ<i>lprG</i> and H37Rv Δ<i>lprG</i>::<i>lprG-Rv1410c</i> were seeded at a starting density of 0.05 OD₆₀₀ and harvested after 1 week. Bacteria were stained with rabbit anti-ManLAM antiserum or control normal rabbit serum and analyzed by flow cytometry. (<b>A, B</b>) Histograms showing LAM surface staining of H37Rv, H37Rv Δ<i>lprG</i> and H37Rv Δ<i>lprG</i>::<i>lprG-Rv1410c</i>. (<b>C</b>) Median fluorescence values (MFVs) from panel A. **P<0.001. Specific MFV was defined as MFV with anti-LAM minus MFV with control serum. Specific MFVs were 900 for H37Rv, 360 for H37Rv Δ<i>lprG</i> and 870 for H37Rv Δ<i>lprG</i>::<i>lprG-Rv1410c</i>. Results are representative of two independent experiments.</p

Acylated LprG binds lipoglycans in Mtb.

<p>SDS-PAGE analysis of proteins and co-purifying molecules isolated from Mtb H37Ra, <i>M. smegmatis</i> or <i>E. coli</i>. (<b>A</b>) Western blot with monoclonal anti-hexahistidine (anti-His₆) to detect LprG or LprA. Mycobacterial components associated with lipoproteins were detected using (<b>B</b>) monoclonal anti-LAM antibody CS-35 or (<b>C and D</b>) rabbit polyclonal anti-Mtb antibody that detects both LAM and LM. Blots are representative of at least three independent experiments.</p

LprG V91W hydrophobic pocket mutation reduces binding of Mtb glycolipids and lipoglycans.

<p>LprG-V91W was immobilized on a CM5 sensor chip, and sensograms were obtained as in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1004471#ppat-1004471-g002" target="_blank">Fig. 2</a> for (<b>A</b>) PIM₂ (<b>B</b>) PIM₆ (<b>C</b>) LM and (<b>D</b>) ManLAM. Results are from one experiment and representative of three independent experiments.</p