Unifying autocatalytic and zeroth order branching models for growing actin networks

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament number. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate, above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, this allows cells to grow stable actin networks over a large range of different conditions.Comment: revtex, 5 pages, 4 figure

Modeling and quantitative analysis of actin cytoskeleton networks

In eukaryotischen Zellen bildet das Strukturprotein Aktin Polymernetzwerke aus, die sehr dynamisch und für viele zelluläre Prozesse lebenswichtig sind. In dieser Arbeit werden theoretische Konzepte vorgestellt, um die Eigenschaften komplexer Aktin-Netzwerkstrukturen zu verstehen und mit Messungen mittels Fluoreszenz- und Elektronenmikroskopie zu vergleichen. Ein Großteil der Arbeit behandelt dabei flache vernetzte Aktinstrukturen, die durch gerichtete Polymerisation gegen eine äußere Kraft anwachsen. Dieser Netzwerktyp ist ein wichtiger Bestandteil von sich bewegenden Zellen, wird aber auch von intrazellulären Pathogenen zur Fortbewegung missbraucht. Eine zentrale, experimentell messbare Eigenschaft solcher Netzwerke ist ihre Kraft-Geschwindigkeits-Relation. Verschiedene aktuelle Messungen ergaben hierfür widersprüchlich erscheinende Ergebnisse. In einem relativ einfachen physikalischen Modell wird gezeigt, dass in wachsenden Aktin-Netzwerken zwei stationäre Filament-Orientierungsverteilungen miteinander konkurrieren. Strukturelle Übergänge zwischen den beiden Architekturen werden durch Änderung der Wachstumsgeschwindigkeit des Netzwerks initiiert. Mit zusätzlichen Annahmen zur mechanischen Stabilität einzelner Filamente werden die experimentell gefundenen Eigenarten der Kraft-Geschwindigkeits-Relation (eine Abfolge von konvexen und konkaven Verläufen sowie Hysterese) theoretisch begründet. Das Modell wird zusätzlich auf Aktinwachstum gegen gekrümmte Hindernisse wie intrazelluläre Pathogene erweitert. Um in der Zukunft spezifische Vorhersagen des Modells experimentell zu überprüfen, wurde eine Methode zur automatischen Analyse von Elektronenmikroskopiebildern von Aktin-Netzwerken entwickelt. Erste Ergebnisse lassen eine gute Übereinstimmung erwarten. Des Weiteren wurde eine Methode entwickelt, um Änderungen in der Aktin-Struktur von adhärenten Zellen in einem Hochdurchsatzverfahren mit Fluoreszenzmikroskopie zu bewerten

The More the Tubular: Dynamic Bundling of Actin Filaments for Membrane Tube Formation

The necessary biophysical conditions for the formation of tubular membrane protrusions by polymerizing actin filament bundles have not yet been fully understood. For this reason we introduce a novel grand canonical simulation model that describes stochastic polymerization of filaments against a fluctuating fluid membrane, while only considering a minimum set of biological proteins. Although still relatively simple and highly tractable, our model explicitly accounts for thermal fluctuations of membrane and filaments, stochastic and quantized polymerization dynamics at the filament tip, cooperativity of multiple filaments, and steric interactions between all model constituents in a physically realistic way. This approach enables us to go well beyond previous static zero-temperature theoretical considerations to filament bundling and explore the physical origins of membrane tube formation dynamics on length and time scales that are currently inaccessible to both experiments and atomistically detailed simulations. Our results suggest a membrane mediated dynamical transition from single filaments to cooperatively growing bundles as an important dynamical bottleneck to tubular protrusion

The More the Tubular: Dynamic Bundling of Actin Filaments for Membrane Tube Formation

The necessary biophysical conditions for the formation of tubular membrane protrusions by polymerizing actin filament bundles have not yet been fully understood. For this reason we introduce a novel grand canonical simulation model that describes stochastic polymerization of filaments against a fluctuating fluid membrane, while only considering a minimum set of biological proteins. Although still relatively simple and highly tractable, our model explicitly accounts for thermal fluctuations of membrane and filaments, stochastic and quantized polymerization dynamics at the filament tip, cooperativity of multiple filaments, and steric interactions between all model constituents in a physically realistic way. This approach enables us to go well beyond previous static zero-temperature theoretical considerations to filament bundling and explore the physical origins of membrane tube formation dynamics on length and time scales that are currently inaccessible to both experiments and atomistically detailed simulations. Our results suggest a membrane mediated dynamical transition from single filaments to cooperatively growing bundles as an important dynamical bottleneck to tubular protrusion

Immobile membrane nodes screen membrane mediated attractions between filaments.

<p>(a) & (b) Two simulated tubes at equal height, generated by simulations with the same initial filament conditions and parameters, differing only by the presence in (b) of one additional immobilized membrane node at the center. Bundle formation is delayed and fewer filaments join the bundle in (b) compared to (a) (cf. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s002" target="_blank">S1</a> & <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s003" target="_blank">S2</a> Movies). Insets: Top view of the simulation snapshot indicating immobile nodes (black circles) and initial positions of tube filaments (red crosses) and as yet unbundled filaments (green crosses). (c) Fraction of 50 simulation trajectories with and without the central frozen node that yield a membrane tube before time <i>t</i>, plotted as a function of <i>t</i>. At any given time, fewer of the constrained trajectories (dashed line) formed tubes than in the unconstrained case (solid line).</p

GCMC simulation of a triangulated membrane patch.

<p>(a) Sketch of the simulation setup. The area of a small fluctuating membrane patch is coupled grand canonically to an implicit lipid reservoir at constant surface tension, mimicking the large excess of vesicle area in typical experiments. (b) The control parameter fugacity <i>z</i> can be mapped to surface tension <i>γ</i> in simulation (black crosses) and fitted using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.e002" target="_blank">Eq (2)</a> (red line). Simulation snapshots are shown for fugacities, <i>z</i> = 13 and <i>z</i> = 29. Inset sketch: GCMC node removal and insertion moves. (c) Membrane force-extension curves (black) compared to zero-temperature calculations at <i>κ</i> = 20<i>k</i>_B<i>T</i> and <i>γ</i> = {0.005;0.01;0.02}<i>k</i>_B<i>T</i>nm⁻² (red solid lines from bottom to top, respectively). Asymptotic pulling force, (red dashed lines). Simulation snapshots are shown at tube extensions <i>L</i> around 72nm, 188nm, and 540nm, with <i>γ</i> = 0.01<i>k</i>_B<i>T</i>nm⁻². (d) Effective polymerization rate <i>k</i>_on(<i>n</i>)/<i>k</i>_on,0 (black solid) of a single rigid filament comprising <i>n</i> monomers compared to the expected near-equilibrium behavior (red dashed), for <i>κ</i> = 20<i>k</i>_B<i>T</i> and <i>γ</i> = {0.005;0.01}<i>k</i>_B<i>T</i>nm⁻² (upper and lower curves, respectively). Snapshots are shown for <i>γ</i> = 0.01<i>k</i>_B<i>T</i>nm⁻².</p

Membrane induced dynamic filament bundling.

<p>(a) Contour lengths of growing filaments vs. simulation time. <i>N</i>_fil = 10 semiflexible filaments (<i>L</i>_p = 15<i>μ</i>m) are initialized at random positions 50nm below and perpendicular to the membrane. Initially, a collection of nearby filaments (red) begin to bundle where filament density is high. Remote filaments (colors other than red) then bend and subsequently join the bundle in a cascade of dynamic transitions (black box). Insets: Snapshots at intermediate simulation times (cf. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s004" target="_blank">S3 Movie</a>). (b) Left inset: An individual filament with a fixed base at <i>L</i>₀ = 60nm below the membrane and at relative angle <i>θ</i> = 45° grows against the membrane. Rare polymerization events lead to a bent filament state growing tangentially to the membrane (cf. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.s005" target="_blank">S4 Movie</a>). Main figure: First passage time distribution <i>p</i>(<i>τ</i>_FP) to reach the bent and growing filament state. GCMC simulation results (black bars) are compared to the master equation <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004982#pcbi.1004982.e008" target="_blank">Eq (5)</a> (red solid line). Vertical dashed lines indicate mean first passage times (MFPT). Right inset: Probability <i>P</i>_bend(<i>n</i> → <i>n</i> + 1) that a gap of sufficient size is available to add a monomer to a filament of contour length <i>nδ</i>_fil. (c) Heat map of the MFPT for the filament bending transition vs. the initial angle and distance of the filament relative to the membrane. Color scale is logarithmic, and cooler colors indicate longer waiting times. Top inset: Each individual dynamic filament bending transition I→II can be understood as a single filament interacting with a predeformed membrane.</p