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Live imaging-based model selection reveals periodic regulation of the stochastic G1/S phase transition in vertebrate axial development.

Sugiyama M, Saitou T, Kurokawa H, Sakaue-Sawano A, Imamura T, Miyawaki A, Iimura T - PLoS Comput. Biol. (2014)

Bottom Line: 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.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.This approach may have implications for the characterization of the pathophysiological tissue growth mode.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for Cell Function and Dynamics, Advanced Technology Development Group, Brain Science Institute, RIKEN, Wako-city, Saitama, Japan.

ABSTRACT
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.

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KL distance calculations with a probability distribution of the PGC time interval.(A–C) Probability distribution of the time interval for the PGC (posterior-most green cells) in the continuous model (z = 1), periodic model (z = 8) and two-fold periodic model (z = 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 (z = 1), periodic (z = 8), two-fold periodic (z = 16) and three-fold periodic (z = 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 αΔt (αΔt = 0.07, 0.08, 0.09, 0.1, 0.11, 0.12). For each simulation (circle with error bar), the KL distance was calculated repeatedly 300 times, and the mean and standard deviation were determined.
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pcbi-1003957-g006: KL distance calculations with a probability distribution of the PGC time interval.(A–C) Probability distribution of the time interval for the PGC (posterior-most green cells) in the continuous model (z = 1), periodic model (z = 8) and two-fold periodic model (z = 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 (z = 1), periodic (z = 8), two-fold periodic (z = 16) and three-fold periodic (z = 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 αΔt (αΔt = 0.07, 0.08, 0.09, 0.1, 0.11, 0.12). For each simulation (circle with error bar), the KL distance was calculated repeatedly 300 times, and the mean and standard deviation were determined.

Mentions: In order to dissociate the continuous mode from periodic modes regulating the stochastic G1/S transition, we next quantified the positions of the PGC and ARC in these in silico simulations. Consequently, the temporal changes in the position of the PGC under the periodic mode appeared to retain its step-wise progression pattern compared to that observed under the continuous mode (Figure 5D, green lines and Figure S5A and S5B), while the position of the ARC exhibited a largely fluctuating pattern under both of these regulatory waves (Figure 5D, red lines, Figure S5C and S5D). Therefore, we decided to perform a detailed analysis of the progressive mode of the PGC position by measuring the time interval from the appearance time of a PGC to that of the next PGC. An example of the calculation procedure of the time interval of the PGC is illustrated in Figure S6. A set of the interval is first computed from a simulation result, after which the probability distribution is obtained. The probability distribution of three different simulations, the continuous model (z = 1) (Figure 6A), periodic model (z = 8) (Figure 6B) and two-fold periodic model (z = 16) (Figure 6C) are subsequently calculated. In the continuous model, the time interval is concentrated on a smaller range (<20 min), and the frequency decreases as the time interval increases. The probability extends to a larger range around 20–40 minutes in the periodic model and extends further and persists up to 60 minutes in the two-fold periodic model. On the other hand, the same analyses of the ARC exhibited no apparent differences between the distributions obtained from three distinct simulation models (Figure S7). Therefore, these analyses indicated that measuring the time interval of PGC reflects the regulatory mode of the stochastic G1/S transition and that the probability distribution function can be used to provide discrimination information in order to analyze the regulatory mode of stochastic changes.


Live imaging-based model selection reveals periodic regulation of the stochastic G1/S phase transition in vertebrate axial development.

Sugiyama M, Saitou T, Kurokawa H, Sakaue-Sawano A, Imamura T, Miyawaki A, Iimura T - PLoS Comput. Biol. (2014)

KL distance calculations with a probability distribution of the PGC time interval.(A–C) Probability distribution of the time interval for the PGC (posterior-most green cells) in the continuous model (z = 1), periodic model (z = 8) and two-fold periodic model (z = 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 (z = 1), periodic (z = 8), two-fold periodic (z = 16) and three-fold periodic (z = 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 αΔt (αΔt = 0.07, 0.08, 0.09, 0.1, 0.11, 0.12). For each simulation (circle with error bar), the KL distance was calculated repeatedly 300 times, and the mean and standard deviation were determined.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4256085&req=5

pcbi-1003957-g006: KL distance calculations with a probability distribution of the PGC time interval.(A–C) Probability distribution of the time interval for the PGC (posterior-most green cells) in the continuous model (z = 1), periodic model (z = 8) and two-fold periodic model (z = 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 (z = 1), periodic (z = 8), two-fold periodic (z = 16) and three-fold periodic (z = 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 αΔt (αΔt = 0.07, 0.08, 0.09, 0.1, 0.11, 0.12). For each simulation (circle with error bar), the KL distance was calculated repeatedly 300 times, and the mean and standard deviation were determined.
Mentions: In order to dissociate the continuous mode from periodic modes regulating the stochastic G1/S transition, we next quantified the positions of the PGC and ARC in these in silico simulations. Consequently, the temporal changes in the position of the PGC under the periodic mode appeared to retain its step-wise progression pattern compared to that observed under the continuous mode (Figure 5D, green lines and Figure S5A and S5B), while the position of the ARC exhibited a largely fluctuating pattern under both of these regulatory waves (Figure 5D, red lines, Figure S5C and S5D). Therefore, we decided to perform a detailed analysis of the progressive mode of the PGC position by measuring the time interval from the appearance time of a PGC to that of the next PGC. An example of the calculation procedure of the time interval of the PGC is illustrated in Figure S6. A set of the interval is first computed from a simulation result, after which the probability distribution is obtained. The probability distribution of three different simulations, the continuous model (z = 1) (Figure 6A), periodic model (z = 8) (Figure 6B) and two-fold periodic model (z = 16) (Figure 6C) are subsequently calculated. In the continuous model, the time interval is concentrated on a smaller range (<20 min), and the frequency decreases as the time interval increases. The probability extends to a larger range around 20–40 minutes in the periodic model and extends further and persists up to 60 minutes in the two-fold periodic model. On the other hand, the same analyses of the ARC exhibited no apparent differences between the distributions obtained from three distinct simulation models (Figure S7). Therefore, these analyses indicated that measuring the time interval of PGC reflects the regulatory mode of the stochastic G1/S transition and that the probability distribution function can be used to provide discrimination information in order to analyze the regulatory mode of stochastic changes.

Bottom Line: 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.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.This approach may have implications for the characterization of the pathophysiological tissue growth mode.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for Cell Function and Dynamics, Advanced Technology Development Group, Brain Science Institute, RIKEN, Wako-city, Saitama, Japan.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus