Figure 4. Template model reproduces experimentally observed phenotypes.

(A) Effective spring constants in our model represent coarse-grained PG network. Here the angle between neighboring stem peptides that belong to a single glycan is assumed to be 90°. Therefore, every other stem peptide is in plane with glycan sheet (Nguyen et al., 2015, Huang et al., 2008). The role of effective glycan persistence length on engulfment is negligible (see Figure 4—figure supplement 3). (B) Simulations for different values of effective peptide $k_{\mathrm{pep}}$ and glycan $k_{\mathrm{gly}}$ spring constants are compared with experimentally measured forespore surface area, volume and engulfment using mutual ${\chi }^2$ statistics (Equation 2). Arrows point to effective literature $k_{\mathrm{pep}}$ and $k_{\mathrm{gly}}$ (Nguyen et al., 2015). Dark blue region corresponds to simulation parameters that best fit experimental data (Figure 4—figure supplement 4, Video 3). For large enough $k_{\mathrm{gly}}$ $>$ 200 pN/nm mutual ${\chi }^2$ is almost independent of $k_{\mathrm{gly}}$. (C) Snapshots of WT simulations for parameters ($k_{\mathrm{gly}}$ = 200 pN/nm, $k_{\mathrm{pep}}$ = 25 pN/nm, $N_{\mathrm{IDC}}$ = 5) marked with ’$\times$’ in panel (B) (Video 2). The thick septum is treated as outer cell wall, and is assumed degraded once IDCs move along. (D–E) Time traces of experimentally measured engulfment, forespore surface area and forespore volume (green) in comparison with results from a single simulation (orange). Parameters used in simulation are marked with ’$\times$’ in panel (B). For all other parameters see Appendix 2, Appendix-table 1. (F) Snapshots of fully engulfed forespores for various peptidoglycan elastic constants. (G) For various values of independent parameters $p_{\mathrm{rep}}$ and $p_{\mathrm{pro}}$ roughness of the LE is calculated at the end of stochastic simulations (see Figure 4—figure supplement 1, and Video 4). Here 0 roughness correspond to perfectly symmetric LE; for high enough $p_{\mathrm{rep}}=p_{\mathrm{pro}}$ $>$ 0.8 LE forms symmetric profiles. (H) Simulation for asymmetric engulfment is obtained for same parameter as WT except $p_{\mathrm{rep}}=p_{\mathrm{pro}}$ = 0.7 (marked with ’$\times$’ in panel (G)). Average ± SD. Scale bars 1 μm.

DOI: http://dx.doi.org/10.7554/eLife.18657.015

Figure 4—figure supplement 1. Simulation of the stochastic model of insertion at the leading edge (LE).

(A–D) Stochastic insertion at the LE of discretized cell circumference with 1570 segments. The details are explained in the Materials and Methodes SI section (2.1). Simulations are run until the LE reaches 500 glycans in height. For obtained LE profiles roughness and their widths are calculated. For each set of independent parameters $p_{\mathrm{rep}}$, $p_{\mathrm{pro}}$ and $N_{\mathrm{IDC}}$ we run 100 simulations and plot the average roughness and width. Parameters $p_{\mathrm{rep}}$ and $p_{\mathrm{pro}}$ are varied in steps of 0.1. (A,C) For $N_{\mathrm{IDC}}$ = 10 smooth LEs are obtained for $p_{\mathrm{rep}}$ and $p_{\mathrm{pro}}\mathrm{>}$ 0.80. For such parameters changing $N_{\mathrm{IDC}}$ by an order of magnitude marginally affects LE width while keeping LE roughness within 10%.

DOI: http://dx.doi.org/10.7554/eLife.18657.016

Figure 4—figure supplement 2. In simulations majority of peptide extensions are in the linear elastic regime.

(A) Histogram of all peptide link lengths during one engulfment ($k_{\mathrm{pep}}$ = 25 pN/nm,$k_{\mathrm{gly}}$ = 200 pN/nm,$\mathrm{\Delta }\mathrm{}p$ = 86.31 kPa). Black arrow points to the linear extension regime (i.e. where each peptide is extended <1 nm or <50% of its equilibrium length of 2 nm) (Nguyen et al., 2015). (B) Percentage of peptide links in simulations that are extended in linear regime as a function of time during the process of engulfment. Dashed vertical line is same as in Figure 4D,E.

DOI: http://dx.doi.org/10.7554/eLife.18657.017

Figure 4—figure supplement 3. Engulfment is unaffected by glycan persistence length.

(A) ${\chi }^{\mathrm{2}}$ (defined in Materials and methods) is used to quantify the impact of effective glycan persistence length ($l_{\mathrm{p}}$) on engulfment dynamics. In weakly crosslinked bundles $l_{\mathrm{p}}\mathrm{=}n\mathrm{}{l}_{\mathrm{p0}}$, where $n$ is the number of glycans in the bundle and $l_{\mathrm{p0}}$ is the persistence length of a single glycan; in strongly cross-linked bundles $l_{\mathrm{p}}\mathrm{=}{n}^{\mathrm{2}}\mathrm{}{l}_{\mathrm{p0}}$ (Claessens et al., 2006; Piechocka et al., 2010). Since our simulated filaments represent bundles of seven glycans (Figure 4B), the effective persistence length can reach ∼2 μm ($l_{\mathrm{p0}}$ = 40 nm). (B–C) Engulfment, forespore surface area and forespore volume are not affected even for high values of effective glycan persistence length ($l_{\mathrm{p}}\mathrm{=}\mathrm{4}\mathrm{}\mu$m).

DOI: http://dx.doi.org/10.7554/eLife.18657.018

Figure 4—figure supplement 4. Simulations with different peptidoglycan (PG) elastic constants.

(A–C) Simulation snapshots for three different sets of PG elastic constants marked with ’$\mathrm{\times }$’ in panel B (A: $k_{\mathrm{pep}}$= $k_{\mathrm{gly}}$ = 50 pN/nm; B: $k_{\mathrm{pep}}$ = 25 pN/nm,$k_{\mathrm{gly}}$ = 200 pN/nm C; $k_{\mathrm{pep}}$ = 25 pN/nm,$k_{\mathrm{gly}}$ = 5 570 pN/nm ). Elastic constants in C are obtained from molecular dynamic simulations (Nguyen et al., 2015). $\mathrm{\Delta }\mathrm{}T$ = 0.28 hr; scale bar 1 μm. (D) Same as Figure 4B, repeated here for clarity. (E) Relative forespore curvature at the end of engulfment where ${\kappa }_{\mathrm{0}}$ is the curvature of spherical cap. At the end of engulfment curvature was experimentally measured with $\sigma \mathrm{}\mathrm{\left(}\kappa \mathrm{\right)}\mathrm{/}\kappa \mathrm{\sim }\mathrm{0.15}$, where $\sigma \mathrm{}\mathrm{\left(}\kappa \mathrm{\right)}$ is the standard deviation (see Figure 1—figure supplement 3A). Therefore, curvatures in , B, and C are within the experimentally measured standard deviation. (F) Snapshots of fully engulfed forespores for various PG elastic constants.

DOI: http://dx.doi.org/10.7554/eLife.18657.019

Figure 4—figure supplement 5. Simulations with decoupled synthesis and degradation.

(A) Simulation snapshots for different values of time delay ${\tau }_{\mathrm{delay}}$. Newly inserted glycans are separated from the old cell wall by cutting connecting peptides with typical ${\tau }_{\mathrm{delay}}$. Double arrow shows distance between synthesis and membrane leading edge. (B) Euclidian distance between insertion and degradation (ID separation) vs time for different values of ${\tau }_{\mathrm{delay}}$. Average over five insertion complexes is plotted vs time. (C) Exploration of delay model when degradation erroneously cuts vertical peptide bonds with probability $p_{\mathrm{pcut}}$. (D) For relatively small $p_{\mathrm{pcut}}\mathrm{=}$ 0.1, an irregular peptidoglycan meshwork is formed. (E–F) Exploration of role of random peptide degradation when synthesis is stopped. (E) Simulation snapshots for various random peptide degradation rates $p_{\mathrm{rpep}}$ = 2.2, 22, and 33 min⁻¹. (F) Forespore volume vs time for different peptide degradation rates after synthesis is stopped. Scale bars 1 μm.

DOI: http://dx.doi.org/10.7554/eLife.18657.020