Stability of Localized Wave Fronts in Bistable Systems

Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation, and spatially inhomogeneous activating agents. We determine the conditions under which wave-front localization is possible and analyze the stability thereof with respect to extrinsic perturbations and internal noise. It is found that stability is enhanced upon regulating a positional signal and, surprisingly, also for a low degree of binding cooperativity. We further show a contrasting impact of self-activation to the stability of these two sources of destabilization. DOI: 10.1103/PhysRevLett.110.03810

GDI-Mediated Cell Polarization in Yeast Provides Precise Spatial and Temporal Control of Cdc42 Signaling

<div><p>Cell polarization is a prerequisite for essential processes such as cell migration, proliferation or differentiation. The yeast <i>Saccharomyces cerevisiae</i> under control of the GTPase Cdc42 is able to polarize without the help of cytoskeletal structures and spatial cues through a pathway depending on its guanine nucleotide dissociation inhibitor (GDI) Rdi1. To develop a fundamental understanding of yeast polarization we establish a detailed mechanistic model of GDI-mediated polarization. We show that GDI-mediated polarization provides precise spatial and temporal control of Cdc42 signaling and give experimental evidence for our findings. Cell cycle induced changes of Cdc42 regulation enhance positive feedback loops of active Cdc42 production, and thereby allow simultaneous switch-like regulation of focused polarity and Cdc42 activation. This regulation drives the direct formation of a unique polarity cluster with characteristic narrowing dynamics, as opposed to the previously proposed competition between transient clusters. As the key components of the studied system are conserved among eukaryotes, we expect our findings also to apply to cell polarization in other organisms.</p></div

Cluster widths for changing parameters and experimental verification.

<p><b>A–D</b> Full width at half maximum of Cdc42 density as obtained in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi-1003396-g002" target="_blank">Figure 2</a> for different Cdc24 (A) and Bem1 (B) concentrations, as well as for different Cdc42 extraction (C) and hydrolysis (D) rates. Arrows indicate the corresponding control cell values. <b>E</b> Examples of Cdc42 cluster density calculated for different hydrolysis rates. <b>F, G</b> Images and quantification of GFP-Cdc42 cap widths in control and Δ<i>bem2</i> cells in the presence (F, unpaired t-test with Welch correction, p<0.001) or absence (G, unpaired t-test with Welch correction, p = 0.01) of latrunculin B. Broad caps are also seen in cells expressing a slowly hydrolyzing GFP-Cdc42^G60A mutant. Images and cap widths were acquired 30–50 min after release from G1 arrest. Bar graphs correspond to mean ± SEM. Scale bars: 4 µm.</p

Predicted dynamics of GDI-mediated polarization.

<p><b>A</b> Cdc42 density on the plasma membrane for different points in time as obtained from numerical simulations (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi.1003396.s002" target="_blank">Movie S1</a>) starting from the unpolarized homogenous solution disturbed by a small random perturbation using control cell parameters. <b>B</b> Development of simulated Cdc42 cluster height (maximum density over background) over time starting with a random initial perturbation (green curve) or using a broad cap as initial perturbation (blue curve). The black lines correspond to a growth rate of the corresponding cluster of 0.00417 s⁻¹ as predicted from the linear stability analysis. <b>C</b> Full width at half maximum (FWHM) of simulated Cdc42 cluster height measured along a great circle through the cap center over circumference 2πR (blue) and simulated Cdc42 cluster height (green) with a broad faint cap as initial perturbation for different points in time.</p

Details of the mechanistic model for GDI-mediated cell polarization in yeast.

<p><b>A</b> Schematic representation of model reactions. A list of all model reactions is given in the <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#s4" target="_blank">Materials and Methods</a> section. <b>B</b> Numerically obtained polarized Cdc42 distribution on the membrane for control conditions. <b>C</b> Corresponding cytosolic distribution of Cdc42 in the x-z plane. Arrows indicate protein flux.</p

Experimental characterization of GDI-mediated polarization.

<p><b>A,B</b> Representative images and cap intensity profiles of latrunculin B-treated control cells expressing GFP-Cdc42 at an early (20–30 min after release, A) and late (30–50 min after release, B) time point during polarization. <b>C</b> Comparison of full width at half maximum (FWHM) of GFP-Cdc42 + latrunculin B caps at early (N = 13, SEM = 0.15; 20–30 min after release) and late time points (N = 28, SEM = 0.10; 30–50 min after release), unpaired t-test with Welch correction, p<0.001. <b>D</b> Time series showing GFP-Cdc42 cap establishment in a control cell treated with latrunculin B (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi.1003396.s003" target="_blank">Movie S2</a>, every second frame starting from frame 12, 30 s time steps between frames). <b>E</b> Time evolution of full width at half maximum of GFP-Cdc42 cap shown in (D) and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi.1003396.s003" target="_blank">Movie S2</a> (first width corresponds to frame 10 of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi.1003396.s003" target="_blank">Movie S2</a>). <b>F</b> Time series showing Bem1-GFP cap establishment in a control cell treated with latrunculin B (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi.1003396.s004" target="_blank">Movie S3</a>, every frame starting from frame 8, 60 s time steps between frames). <b>G</b> Time evolution of full width at half maximum of Bem1-GFP cap shown in (F) and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi.1003396.s004" target="_blank">Movie S3</a> (first width corresponds to frame 8 of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003396#pcbi.1003396.s004" target="_blank">Movie S3</a>). Scale bars: 4 µm.</p

Attosecond pulse characterization

In this work we propose a novel procedure for the characterization of attosecond pulses. The method relies on the conversion of the attosecond pulse into electron wave-packets through photoionization of atoms in the presence of a weak IR field. It allows for the unique determination of the spectral phase making up the pulses by accurately taking into account the atomic physics of the photoionization process. The phases are evaluated by optimizing the fit of a perturbation theory calculation to the experimental result. The method has been called iPROOF (improved Phase Retrieval by Omega Oscillation Filtering) as it bears a similarity to the PROOF technique [Chini et al. Opt. Express 18, 13006 (2010)]. The procedure has been demonstrated for the characterization of an attosecond pulse train composed of odd and even harmonics. We observe a large phase shift between consecutive odd and even harmonics. The resulting attosecond pulse train has a complex structure not resembling a single attosecond pulse once per IR period, which is the case for zero phase. Finally, the retrieval procedure can be applied to the characterization of single attosecond pulses as well