The Dynamics of Dorsal Actin Waves

The recent years have shown that waves of actin polyermization are central to the morphodynamics of cells. This thesis is dedicated to deciphering of the propagation mechanism underlying actin waves known as Circular Dorsal Ruffles (CDRs). While these ring-shaped undulations on the dorsal cell side have been known to the biological community for several decades the mechanism underlying their formation and propagation has remained a puzzle. It is the hypothesis of this work that CDRs can be described as waves that form and propagate in an active medium that is constituted by the actin machinery of the cell. The identification of the corresponding functional elements is the aim of this work. For this, the structure, morphology and dynamics of CDRs are investigated in detail and with a view that is guided by the typical structure of models of active media. Throughout the whole thesis, the FitzHugh-Nagumo system serves as a prototype model for the explanation of the mechanisms underlying the phenomena observed for CDRs on an abstract level. Novel results are presented regarding the identification of the processes of actin dynamics within CDRs and their compartmentalization. The systematic analysis of the dynamics of CDR wavefronts reveals that they exhibit a number of previously unknown phenomena, among them breathing modes, spiral waves, and collision annihilation. All these features are well founded in the framework of active media. Since the dynamics of CDRs strongly depends on the cellular morphology, a novel method for their investigation is developed in which cells are forced into disc-shapes via microcontact printing for a quantitative analysis of data of identically shaped cells. This framework allows for direct comparability to numerical studies, which reveals that stochastic elements in protein dynamics are key for the understanding of CDRs

Die Dynamik Dorsaler Aktinwellen

The recent years have shown that waves of actin polyermization are central to the morphodynamics of cells. This thesis is dedicated to deciphering of the propagation mechanism underlying actin waves known as Circular Dorsal Ruffles (CDRs). While these ring-shaped undulations on the dorsal cell side have been known to the biological community for several decades the mechanism underlying their formation and propagation has remained a puzzle. It is the hypothesis of this work that CDRs can be described as waves that form and propagate in an active medium that is constituted by the actin machinery of the cell. The identification of the corresponding functional elements is the aim of this work. For this, the structure, morphology and dynamics of CDRs are investigated in detail and with a view that is guided by the typical structure of models of active media. Throughout the whole thesis, the FitzHugh-Nagumo system serves as a prototype model for the explanation of the mechanisms underlying the phenomena observed for CDRs on an abstract level. Novel results are presented regarding the identification of the processes of actin dynamics within CDRs and their compartmentalization. The systematic analysis of the dynamics of CDR wavefronts reveals that they exhibit a number of previously unknown phenomena, among them breathing modes, spiral waves, and collision annihilation. All these features are well founded in the framework of active media. Since the dynamics of CDRs strongly depends on the cellular morphology, a novel method for their investigation is developed in which cells are forced into disc-shapes via microcontact printing for a quantitative analysis of data of identically shaped cells. This framework allows for direct comparability to numerical studies, which reveals that stochastic elements in protein dynamics are key for the understanding of CDRs

Dynamics of actin waves on patterned substrates : a quantitative analysis of circular dorsal ruffles

Circular Dorsal Ruffles (CDRs) have been known for decades, but the mechanism that organizes these actin waves remains unclear. In this article we systematically analyze the dynamics of CDRs on fibroblasts with respect to characteristics of current models of actin waves. We studied CDRs on heterogeneously shaped cells and on cells that we forced into disk-like morphology. We show that CDRs exhibit phenomena such as periodic cycles of formation, spiral patterns, and mutual wave annihilations that are in accord with an active medium description of CDRs. On cells of controlled morphologies, CDRs exhibit extremely regular patterns of repeated wave formation and propagation, whereas on random-shaped cells the dynamics seem to be dominated by the limited availability of a reactive species. We show that theoretical models of reaction-diffusion type incorporating conserved species capture partially the behavior we observe in our data.Published versio

Correlation and Comparison of Cortical and Hippocampal Neural Progenitor Morphology and Differentiation through the Use of Micro- and Nano-Topographies

Neuronal morphology and differentiation have been extensively studied on topography. The differentiation potential of neural progenitors has been shown to be influenced by brain region, developmental stage, and time in culture. However, the neurogenecity and morphology of different neural progenitors in response to topography have not been quantitatively compared. In this study, the correlation between the morphology and differentiation of hippocampal and cortical neural progenitor cells was explored. The morphology of differentiated neural progenitors was quantified on an array of topographies. In spite of topographical contact guidance, cell morphology was observed to be under the influence of regional priming, even after differentiation. This influence of regional priming was further reflected in the correlations between the morphological properties and the differentiation efficiency of the cells. For example, neuronal differentiation efficiency of cortical neural progenitors showed a negative correlation with the number of neurites per neuron, but hippocampal neural progenitors showed a positive correlation. Correlations of morphological parameters and differentiation were further enhanced on gratings, which are known to promote neuronal differentiation. Thus, the neurogenecity and morphology of neural progenitors is highly responsive to certain topographies and is committed early on in development

Effects of cell size and morphology on CDR morphology and dynamics.

<p>CDRs usually avoid the nucleus region (encircled in red). Cell edge and nucleus therefore define a bounded region available for CDR propagation, which limits the maximal size CDRs can attain. In the panels <i>A-D</i> the size of this region is increasing from left to right. The isotropy of CDRs decreases with increasing CDR size, while the tendency to mimic cell morphology increases with CDR size. CDRs in small regions (<i>A</i>) cannot extend much, typically forming oscillatory reappearing objects of high isotropy. All scale bars correspond to 25 µm. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s006" target="_blank">S1</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s009" target="_blank">S4</a> Movies (corresponding to panel <i>A-D</i> respectively) for the respective characteristic dynamics.</p

Space-time correlations of CDRs on circular paths.

<p>(<i>A</i> and <i>B</i>) Using microcontact printing, cells can be patterned into well-defined morphologies. (<i>B</i>) On disk-like cells CDRs propagate in lateral direction between the cell nucleus and the cell edge (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s019" target="_blank">S14 Movie</a>). (<i>C</i>) Circular kymograph sampled at the red circle in (<i>B</i>). Waves propagating in lateral direction show up as dark stripes. “<“-shaped objects correspond to wave initiation (the green arrow highlights one example) and “>“-shaped objects to wave annihilation. The solid red arrow shows an example of mutual annihilation while the hollow red arrow marks an event in which one pulse survives the collision. (<i>D</i>) The apparent high regularity in slopes and frequency of occurrence in <i>C</i> is emphasized in an autocorrelation function <i>c</i>(Δ<i>s</i>, Δ<i>t</i>). In this specific example we find propagation velocities of 0.10 µm/s and a typical period of 6 min between two CDR events at the same position (see the cut <i>c</i>(Δ<i>s</i> = 0, Δ<i>t</i>) and <i>F</i> for the sample average). The cut <i>c</i>(Δ<i>s</i>, Δ<i>t</i> = 0) emphasizes the dominant number of four DCRs at the same time on this cell. (<i>E</i>) A histogram of velocity data obtained from an autocorrelation analysis of 38 cells. The mean velocity is 0.12 (± 0.03) µm/s (± SD). (<i>F</i>) A cut through the average correlation function of the same 38 cells at constant position. The mean period between two CDR events at the same position is approximately 6 min. The scale bars in <i>A</i> and <i>B</i> correspond to 50 µm and 25 µm respectively. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s001" target="_blank">S1 Text</a>, <i>Materials and Methods</i> for details regarding the calculation of autocorrelation functions and derived values form these.</p

Oscillatory reappearing CDRs.

<p>(<i>A</i>) CDRs under spatial confinement exhibit oscillatory patterns of pulsating re-appearance (scale bar: 25 µm, full sequence: <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s010" target="_blank">S5 Movie</a>). (<i>B</i>) Stills from the region of interest highlighted red in the time-lapse sequence <i>A</i> (Δ<i>t</i> = 36 s). (<i>C</i>) A plot of the minimal intensity value of the ROI in <i>A</i> as a function of time shows CDR events as negative peaks and CDR-free periods, corresponding to the recovery time τ, as plateaus of high intensity. The ROI was smoothed with a Gaussian with <i>σ</i> = 2 µm prior to intensity sampling. (<i>D-F</i>) Kymographs of CDRs taken along lines crossing CDR origins (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.g004" target="_blank">Fig. 4<i>A</i></a> for illustration) show both the recovery time τ between successive events and their radial extension <i>R</i>_max (cells not shown). (<i>G</i>) The recovery times increase with CDR size. The data was binned in <i>R</i>_max-direction (box width: 10 µm) and plotted as boxes with whiskers (red lines: median, upper box edge: 75th percentile, lower box edge: 25th percentile). <i>N</i> values denote the number of observations. Note that oscillatory behavior was rare for large CDRs.</p

Wavefront dynamics of opening and closing CDRs.

<p>(<i>A-C</i>) A typical life course of a CDR exhibiting opening and closing (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s016" target="_blank">S11 Movie</a>). The coordinate system in <i>A</i> is the basis for calculation of the kymographs shown in <i>B</i> and <i>C</i>. Together with time-lapse sequence <i>A</i> these kymographs show the dependency of CDR dynamics on cell features. CDR propagation without encounter of obstacles and absence of instability has a parabolic evolution of the CDR radius with time (red dashed line in <i>B</i>: empirical parabola fit). In positive <i>x</i>-direction, however, the wavefront becomes unstable and partially decays, leading to an asymmetric profile in kymograph <i>B</i>. (<i>D</i> and <i>E</i>) Using active contours, the wavefronts of CDRs can be tracked yielding sets of contours for each CDR (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s017" target="_blank">S12 Movie</a>). (<i>F</i>) The contour mean velocity data of 13 CDRs as a function of the normalized area roughly follow one trajectory. Positive velocities correspond to CDR growth and negative velocities to CDR shrinking. Original data points are shown in black, red circles correspond to average velocities calculated using a box median of width 0.05 in normalized area. The red line is an empirical fit function used for extrapolation to a CDR area of zero. See the main text and the <i>SI Methods</i> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0115857#pone.0115857.s001" target="_blank">S1 Text</a> for details. All spatial scale bars correspond to 25 µm.</p