Live Imaging-Based Model Selection Reveals Periodic Regulation of the Stochastic G1/S Phase Transition in Vertebrate Axial Development

<div><p>In multicellular organism development, a stochastic cellular response is observed, even when a population of cells is exposed to the same environmental conditions. Retrieving the spatiotemporal regulatory mode hidden in the heterogeneous cellular behavior is a challenging task. The G1/S transition observed in cell cycle progression is a highly stochastic process. By taking advantage of a fluorescence cell cycle indicator, Fucci technology, we aimed to unveil a hidden regulatory mode of cell cycle progression in developing zebrafish. Fluorescence live imaging of Cecyil, a zebrafish line genetically expressing Fucci, demonstrated that newly formed notochordal cells from the posterior tip of the embryonic mesoderm exhibited the red (G1) fluorescence signal in the developing notochord. Prior to their initial vacuolation, these cells showed a fluorescence color switch from red to green, indicating G1/S transitions. This G1/S transition did not occur in a synchronous manner, but rather exhibited a stochastic process, since a mixed population of red and green cells was always inserted between newly formed red (G1) notochordal cells and vacuolating green cells. We termed this mixed population of notochordal cells, the G1/S transition window. We first performed quantitative analyses of live imaging data and a numerical estimation of the probability of the G1/S transition, which demonstrated the existence of a posteriorly traveling regulatory wave of the G1/S transition window. To obtain a better understanding of this regulatory mode, we constructed a mathematical model and performed a model selection by comparing the results obtained from the models with those from the experimental data. Our analyses demonstrated that the stochastic G1/S transition window in the notochord travels posteriorly in a periodic fashion, with doubled the periodicity of the neighboring paraxial mesoderm segmentation. This approach may have implications for the characterization of the pathophysiological tissue growth mode.</p></div

One-Pot Preparation of (NH)-Phenanthridinones and Amide-Functionalized [7]Helicene-like Molecules from Biaryl Dicar-boxylic Acids

A one-pot transformation of biaryl dicarboxylic acids to (NH)-phenanthridinone derivatives based on a Curtius rearrangement and subsequent basic hydrolysis was developed. This method is also applicable for the preparation of optically active amide-functionalized [7]helicene-like molecules. Furthermore, aza[5]helicene derivatives with a phosphate moiety were isolated as a product of the Curtius rearrangement step in the case of substrates that bear chalcogen atoms. The stereostructures of these products, revealed by X-ray diffraction analysis, suggested that chalcogen-bonding and pnictogen-bonding interactions might contribute to their stabilization. The configurational stability of the helicene-like molecules and their chiroptical properties were further investigated

Stochastic modeling of the G1/S transition.

<p>(A) Illustration of the stochastic process describing the G1/S transition of a single cell. If the signal comes at time <i>t</i>, the cell undergoes its G1/S transition with the probability <i>αΔt</i>. Schematically shown is a case in which a given cell does not change its G1 phase at (<i>t+1</i>), but rather later, and exhibits its transition to the S phase at (<i>t+2</i>) due to the stochastic response of the G1/S transition. (B) Illustration of the stochastic process of cells arrayed along the one-dimensional axis. The signal transmitting function <i>f(i,t)</i> was introduced in this case to describe time- and space-dependent cell cycle progression (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#s4" target="_blank">Methods</a>). (C) Two dimensional map of <i>f(i,t)</i> on the plane of time and space (anterior-posterior axis). The areas satisfying <i>f(i,t)≤0</i> and <i>f(i,t)>0</i> are filled with black and white, respectively. The continuous and periodic models are defined by setting <i>z</i> = 1 and <i>z</i> = 8, respectively (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#s4" target="_blank">Methods</a>). (D) Searching for the range of the parameter, probability <i>αΔt</i>. The probability distribution of the time difference (<i>Td</i>) of the G1/S transition between pairs of upper and lower cells was calculated from the experimental data. The red line is a curve fitted according to the least squares method.</p

Summary of methodology and findings.

<p>(A) Schematic summary of our methodology. Our methodological approach consisted of three successive processes: 1) live imaging and image processing, 2) model establishment and 3) model selection. Each process was further divided into sub-processes, as noted in each box. (B) Schematic illustration of the regulatory mode of the G1/S transition in the developing notochord. (B-i, B-ii) Once the G1/S transition window was established between populations of anterior green (S) and posterior (G1) red cells, the G1 cells in the window stochastically transitioned into the S phase (B-i), after which the window was finally filled with green (S) cells (B-ii). (B-iii, B-iv) The next transition window was established posteriorly adjacent to the previous window. As observed in the previous cycle, an increasing number of green (S) cells filled the window as time progressed (B-iii), until the window was finally filled with green cells (B-iv).</p

KL distance calculations with a probability distribution of the PGC time interval.

<p>(A–C) Probability distribution of the time interval for the PGC (posterior-most green cells) in the continuous model (<i>z</i> = 1), periodic model (<i>z</i> = 8) and two-fold periodic model (<i>z</i> = 16). (D) The distribution of the experiments was calculated by summing all three datasets for the time-lapse imaging. (E) KL distances for four different types of simulation: continuous (<i>z</i> = 1), periodic (<i>z</i> = 8), two-fold periodic (<i>z</i> = 16) and three-fold periodic (<i>z</i> = 24). For each model, the KL distance was calculated repeatedly 300 times, and the mean and standard deviation were then calculated. A significance test (Kolmogorov-Smirnov test) was applied for each combination of the KL distance datasets. All combinations exhibited statistical significance, with a p-values of <0.001. (F) The KL distance for six different probability values <i>αΔt</i> (<i>αΔt = 0.07</i>, <i>0.08</i>, <i>0.09</i>, <i>0.1</i>, <i>0.11</i>, <i>0.12</i>). For each simulation (circle with error bar), the KL distance was calculated repeatedly 300 times, and the mean and standard deviation were determined.</p

<i>In silico</i> simulation reproduces noisy cell cycle progression.

<p>(A and B) Two-dimensional map of simulated cell cycle progression on the plane of time and space (anterior-posterior axis). Simulations of the continuous model (<i>z = 1</i>) and periodic model (<i>z = 8</i>) were implemented. (C) Total number of cells in the G1 and S phases as a function of time, respectively. The green and red lines, and the dark-green and orange lines denote the simulation results obtained by the continuous model and the periodic model, respectively. (D) Positions of the ARC (red line) and PGC (green line) as a function of time, respectively. The results obtained by the continuous and periodic models were drawn individually.</p

Enumeration of green cells in the G1/S transition window.

<p>Total number of green (S) cells in the stochastic window as a function of time for the continuous (A), periodic (B) and two-fold periodic (C) models. The blue and green lines with ‘+’ markers indicate two independent simulation datasets corresponding to the upper and lower sequence data from the experiment, respectively.</p

Systematic analyses of binarized images of the G1/S transition.

<p>(A) Two quantitative indices, the anterior-most red cell (ARC) and posterior-most green cell (PGC), are introduced as illustrated. (B) The positions of the ARC and PGC as a function of time. The upper and lower sequences of notochordal cells along the anterior-posterior axis are drawn individually. (C) The total number of green (S) cells in the G1/S transition window, defined as seven cells anterior to the PGC, as well as the PGC (total: 8 cells) (also demonstrated in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#pcbi.1003957.s001" target="_blank">Figure S1</a>), as a function of time. The blue and green lines with ‘+’ markers indicate the upper and lower sequence data, respectively. (D) Number of green cell pairs in the G1/S transition window as a function of time. The red ‘+’ markers indicate the data obtained from the experiments. The black and blue lines indicate data obtained using random and biased simulation, respectively (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#s4" target="_blank">Methods</a>).</p

Progressive mode of the stochastic G1/S transition in the notochordal cells during embryonic body elongation.

<p>(A) Fucci (fluorescent ubiquitination-based cell cycle indicator) labels nuclei of G1 phase cells red (orange) and those of cells in the S/G2/M phase green. During the cell cycle of cells expressing Fucci, two chimeric proteins, mKO2-zCdt1 and mAG-zGeminin, reciprocally accumulate in the G1 and S/G2/M phases <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#pcbi.1003957-Sugiyama1" target="_blank">[48]</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#pcbi.1003957-SakaueSawano1" target="_blank">[49]</a> (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#pcbi.1003957-Sugiyama1" target="_blank">[48]</a> for detailed molecular construction). (B) Cecyil (cell cycle illuminated: a zebrafish line producing zFucci) embryos at the 17 somite stage. A Z-stacking lateral view of optical sections. The anterior view is to the left, the posterior is to the right. (C) A mid-sagittal optical section of a fixed Cecyil embryo at 22 hpf counterstained with phalloidin Alexa Fluor 647. (D, E) Mid-sagittal optical section of a fixed Cecyil embryo at 18 hpf. A DIC (differential integrative phase contrast) image (D) and fluorescence image (E) are shown. The posterior-most green cell (PGC) and anterior-most red cell (ARC) in the upper and lower notochordal cells are indicated by green and red arrowheads, respectively. The posterior tip of the precursor pool of the notochord and the last formed somitic border are marked by sky blue and blue arrowheads, respectively. (F–K) Mid-sagittal optical sections of a developing Cecyil embryo. DIC images obtained at three different time points (F–H) and their corresponding fluorescence images are shown (I–K). The colored arrowheads indicate the same structures of cells as shown in D and E. The white arrow indicates a single cell whose cell cycle phase was transitioning from G1 (I) to S (J and K). Embryonic stages are indicated by somite stages (s.s.). (L) The temporal changes in the red and green fluorescence intensity of the cell indicated by the white arrow in G–H are plotted. The time course of the live imaging observations and embryonic stages is indicated in minutes and somite stages (s.s.), respectively. The vertical broken lines indicate the observation times corresponding to the images in g–i. The crossing time point of the red and green lines is indicated by the yellow point (115 min, in 18 somite stages). This time was selected as the time at which the G1/S transition occurred (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003957#s4" target="_blank">Methods</a>). White scale bars: 100 <i>µm</i>. Anterior to the left, posterior to the right. Dorsal to the top, ventral to the bottom. s.s, somite stage.</p