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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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Stochastic modeling of the G1/S transition.(A) Illustration of the stochastic process describing the G1/S transition of a single cell. If the signal comes at time t, the cell undergoes its G1/S transition with the probability αΔt. Schematically shown is a case in which a given cell does not change its G1 phase at (t+1), but rather later, and exhibits its transition to the S phase at (t+2) 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 f(i,t) was introduced in this case to describe time- and space-dependent cell cycle progression (see Methods). (C) Two dimensional map of f(i,t) on the plane of time and space (anterior-posterior axis). The areas satisfying f(i,t)≤0 and f(i,t)>0 are filled with black and white, respectively. The continuous and periodic models are defined by setting z = 1 and z = 8, respectively (see Methods). (D) Searching for the range of the parameter, probability αΔt. The probability distribution of the time difference (Td) 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.
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pcbi-1003957-g004: Stochastic modeling of the G1/S transition.(A) Illustration of the stochastic process describing the G1/S transition of a single cell. If the signal comes at time t, the cell undergoes its G1/S transition with the probability αΔt. Schematically shown is a case in which a given cell does not change its G1 phase at (t+1), but rather later, and exhibits its transition to the S phase at (t+2) 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 f(i,t) was introduced in this case to describe time- and space-dependent cell cycle progression (see Methods). (C) Two dimensional map of f(i,t) on the plane of time and space (anterior-posterior axis). The areas satisfying f(i,t)≤0 and f(i,t)>0 are filled with black and white, respectively. The continuous and periodic models are defined by setting z = 1 and z = 8, respectively (see Methods). (D) Searching for the range of the parameter, probability αΔt. The probability distribution of the time difference (Td) 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.

Mentions: In order to unveil a possible regulatory mode of the G1/S transition in notochordal cells, we employed a mathematical modeling approach. The model was constructed according to a Markov process describing the stochastic transition from the G1 phase to the S phase. At each time step t, a cell undergoes the G1/S transition with a probability αΔt over a short time interval Δt (Figure 4A). The spatial position of the notochordal cells is represented as a one-dimensional lattice in the order of anterior to posterior (left to right, respectively, as shown in Figure 4B). Each cell in the lattice is identified by an index i (i = 1,…,n). Based on our biological observations described in Figure 1, we assumed the presence of a regulatory wave that conveys a signaling cue to promote the G1/S transition in notochordal cells in a stochastic fashion. This signaling cue on a single dimensional axis is controlled by the signal transmitting function f(i,t) of t and i (Figure 4C). By introducing a tuning parameter z in f(i,t), we were able to examine how the probability affects the distinct mode of the regulatory cue (for details, see the Methods section). In other words, z corresponds to the step size, which is defined by the width of a given number cells. For example, in the model of z = 8, the step size is the total width of eight cells. Based on our observations described above, we assumed modes of continuously traveling waves (continuous mode) and periodically traveling waves (periodic modes) with different periodicity.


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)

Stochastic modeling of the G1/S transition.(A) Illustration of the stochastic process describing the G1/S transition of a single cell. If the signal comes at time t, the cell undergoes its G1/S transition with the probability αΔt. Schematically shown is a case in which a given cell does not change its G1 phase at (t+1), but rather later, and exhibits its transition to the S phase at (t+2) 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 f(i,t) was introduced in this case to describe time- and space-dependent cell cycle progression (see Methods). (C) Two dimensional map of f(i,t) on the plane of time and space (anterior-posterior axis). The areas satisfying f(i,t)≤0 and f(i,t)>0 are filled with black and white, respectively. The continuous and periodic models are defined by setting z = 1 and z = 8, respectively (see Methods). (D) Searching for the range of the parameter, probability αΔt. The probability distribution of the time difference (Td) 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.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003957-g004: Stochastic modeling of the G1/S transition.(A) Illustration of the stochastic process describing the G1/S transition of a single cell. If the signal comes at time t, the cell undergoes its G1/S transition with the probability αΔt. Schematically shown is a case in which a given cell does not change its G1 phase at (t+1), but rather later, and exhibits its transition to the S phase at (t+2) 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 f(i,t) was introduced in this case to describe time- and space-dependent cell cycle progression (see Methods). (C) Two dimensional map of f(i,t) on the plane of time and space (anterior-posterior axis). The areas satisfying f(i,t)≤0 and f(i,t)>0 are filled with black and white, respectively. The continuous and periodic models are defined by setting z = 1 and z = 8, respectively (see Methods). (D) Searching for the range of the parameter, probability αΔt. The probability distribution of the time difference (Td) 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.
Mentions: In order to unveil a possible regulatory mode of the G1/S transition in notochordal cells, we employed a mathematical modeling approach. The model was constructed according to a Markov process describing the stochastic transition from the G1 phase to the S phase. At each time step t, a cell undergoes the G1/S transition with a probability αΔt over a short time interval Δt (Figure 4A). The spatial position of the notochordal cells is represented as a one-dimensional lattice in the order of anterior to posterior (left to right, respectively, as shown in Figure 4B). Each cell in the lattice is identified by an index i (i = 1,…,n). Based on our biological observations described in Figure 1, we assumed the presence of a regulatory wave that conveys a signaling cue to promote the G1/S transition in notochordal cells in a stochastic fashion. This signaling cue on a single dimensional axis is controlled by the signal transmitting function f(i,t) of t and i (Figure 4C). By introducing a tuning parameter z in f(i,t), we were able to examine how the probability affects the distinct mode of the regulatory cue (for details, see the Methods section). In other words, z corresponds to the step size, which is defined by the width of a given number cells. For example, in the model of z = 8, the step size is the total width of eight cells. Based on our observations described above, we assumed modes of continuously traveling waves (continuous mode) and periodically traveling waves (periodic modes) with different periodicity.

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