doi:10.1016/j.biosystems.2007.02.006
Copyright © 2007 Elsevier Ireland Ltd All rights reserved.
Early onset of regionalization in EMS lineage of C. elegans embryo: A quantitative study
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Ali Tiraihia and Taki Tiraihib, 
, 
,
aDepartment of Computer Engineering, College of Electrical and Computer Engineering, Shaheed Beheshti University, Tehran, Iran
bDepartment of Anatomical Sciences, School of Medical Sciences, Tarbiat Modares University, P.O. Box 14155-4838, Tehran, Iran
Received 19 March 2006;
revised 18 February 2007;
accepted 19 February 2007.
Available online 3 March 2007.
Abstract
Early localization of C. elegans founder cell descendents in certain regions of embryo has been documented. The purpose of this investigation is to evaluate the onset of ABp and EMS descendent cell regionalization in the embryo using the random motility coefficient as a quantitative parameter. The forward migration index (FMI) was also calculated in order to evaluate the chemotatic biases of ABp-dc and EMS-dc during regionalization.
The results showed that the random motility coefficient declined as the cells tended to regionalize. The mean squared displacement (MSD) versus time plot showed a non-linear model which indicated non-random cell movement. FMI showed progressive increase as the cells tended to regionalized, and it was significantly higher in EMS-dc than ABp-dc, moreover the chemotatic biases were higher in EMS-dc than ABp-dc.
The circular plots showed that the statistical differences between the two lineages were significant, while ABp-dc showed significant differences in xy, xz and yz planes; EMS derived cells showed no significant differences except in yz planes. The conclusion of this study is that the onset of early regionalization occurs in EMS-dc sooner than in ABp-dc.
Keywords: Kinetics; C. elegans; Embryogenesis; Random motility coefficient; Development
Fig. 1. A non-linear curve fitting of the square of the mean accumulated displacement of the cells (SMAD) (μ2) vs. time (t) (minute) in ABp derived cells with a logarithmic model (SMAD = −49.8 + 23.9 ln(t), or y(t) = −49.8 + 23.9 ln(t); standard error = 1.05, correlation coefficient = 0.998) (upper panel), a third degree polynomial model in EMS derived cells (SMAD = −23.7 + 0.5t + 0.0015t2 − 0.000016t3, or y(t) = −23.7 + 0.5t + 0.0015t2 + 0.000016t3; standard error = 0.18, correlation coefficient = 0.9999838) (lower panel).
Fig. 2. The three-dimensional reconstruction of the spaces occupied by AB-dc or EMS-dc at the last time interval (140 min time interval) forming the final shape of the space occupied by Abp-dc (left) or EMS-dc (right), each space was divided into several pyramids represented by different color. The volume of each pyramid was calculated, and then the volumes of pyramids in each space (ABp or EMS) were summed in order to estimate the final volume.
Fig. 3. A non-linear curve fitting of the mean squared displacement (MSD) (μ2) vs. time (minute) in ABp derived cells with a quadratic model in ABp-dc (MSD = −668.23 + 59.7t − 0.16t2, or y(t) = −668.23 + 59.7t − 0.16t2; standard error = 97.5, correlation coefficient = 0.998889) (upper panel), while that of EMS-dc shows a third degree non-linear model (MSD = 808.3 + 5.1t + 0.76t2 + 0.004t3, or y(t) = 808.3 + 5.1t + 0.76t2 + 0.004t3; standard error = 14.9, correlation coefficient = 0.9999921) (lower panel).
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Fig. 4. The regression line of the initial phases of FMI (IPFMI: m) (abscissa) plotted against the subsequent phases of FMI (SFMI) (ordinate) in set B (upper panel): (SFMI = 0.34 + 2.86 IPFMI, or y(m) = 0.34 + 2.68m; standard error = 0.6498382, correlation coefficient = 0; SFMI = 1.54 + 1.33 IPFMI, or y(m) = 1.54 + 1.33m; standard error = 0.3343313 and correlation coefficient = 0, for both Abp-dc and EMS-dc, respectively), the insets show the linear regression of the same data in Abp-dc and EMS-dc but on a different graph scale for x- and y-axes, the graph shows that the cells are not separated into several clusters, as graphically can be seen in sets C and D. The linear regression in set C (middle panel) of the initial phases of FMI (IPFMI: m) (abscissa) are plotted against the subsequent phases of FMI (SFMI) (ordinate) (SFMI = −1.41 + 6.18 IPFMI, or y(m) = −1.41 + 6.18m; standard error = 0.5358830, correlation coefficient = 0.7931062; SFMI = 0.85 + 1.84 IPFMI, or y(m) = 0.22 + 3.98m; standard error = 0.3933540, correlation coefficient = 0.2514220, for both Abp-dc and EMS-dc, respectively), the insets show the linear regression of the same data in ABp-dc and EMS-dc but on a different graph scale for x- and y-axes. The graph shows that the cells in ABp-dc are graphically separated into four clusters, while in EMS-dc are graphically separated into two clusters. The linear regression in set D (lower panel) of the initial phases of FMI (IPFMI: m) (abscissa) are plotted against the subsequent phases of FMI (SFMI) (ordinate) SFMI = 0.22 + 3.98 IPFMI, or y(m) = 0.22 + 3.98m; standard error = 1.1519832, correlation coefficient = 0.5437420; SFMI = 3.4 + 0.52 IPFMI, or y(m) = 3.4 + 0.52m; standard error = 0.9209539, correlation coefficient = 0.0622637, for both Abp-dc and EMS-dc, respectively), the insets show the linear regression of the same data in ABp-dc and EMS-dc but on a different graph scale for x- and y-axes, the graph shows that the cells in ABp-dc are graphically separated into eight clusters, while in EMS-dc they are graphically separated into five clusters.
Fig. 5. The rose plots of ABp derived cells (A–C) and EMS derived cells (D–F) on xy, xz and yz planes, respectively, where the plotted angle of each cell was obtained by transforming the Cartesian coordinates into polar ones.
Fig. 6. The schematic sample of the pyramid (left panel) were used in order to calculate the volume of the space occupied by ABp and EMS lineages, where the spaces occupied by either ABp-dc or EMS-dc were constructed and divided into small pyramids (see Fig. 2) in order to perform the calculation of the volume by either lineages. Right panel: present Cartesian, spherical and polar coordinates.
Table 1.
The means and the standard errors of the mean of the random motility coefficients (RMC) in sets A, B, C and D in ABp derived cells (ABp) and EMS derived cells (EMS)
The 1st time interval begins at cleavage time and ends at the end of 28 min. The 2nd time interval begins at the start of the 29th minute and ends at the end of the 56th minute. The 3rd time interval begins at the start of the 57th minute and ends at the end of the 84th minute. The 4th time interval begins at the start of the 85th minute and ends at the end of the 112th minute. The 5th time interval begins at the start of the 113th minute and ends at the end of the 140th minute.
a μ2 (min
−1).
b P value was significant between ABp and EMS.
Table 2.
The equations of the non-linear and linear regressions of the square of the mean accumulated displacement of the cells (SMAD: dependent variable) against time (t: independent variable) in both ABp and EMS lineages, and the equations of the linear regression of the mean squared displacement (MSD: dependent variable) against the time (t: independent variable) in both ABp and EMS lineages
Finally, the linear regression of the forward migration index (FMI) parameter with initial phase forward migration index used as independent variable and subsequent forward migration index (SFMI) as a dependent variable in B, C and D sets.
a SMAD, MSD, IPMFMI and IPMFMI variables were used in
Fig. 1,
Fig. 3 and
Fig. 4, respectively.
b The independent variable in SMAD and MSD parameters is the time (
t), and these equations are expressed as a function of the independent variable.
c The independent variable in FMI parameter is the initial phase FMI (IPFMI:
m), and these equations are expressed as a function of the independent variable.
Table 3.
The means and the standard errors of the mean of the apparent diffusion coefficient (ADC), the early phase of the apparent diffusion coefficient (ADC-early phase) and the late phase of the apparent diffusion coefficient (ADC-late phase) of ABp derived cell (ABp) and EMS derived cells (EMS)
the early phase includes 1st and 2nd time intervals, and the late phase includes 3rd, and 5th time intervals. The 1st time interval begins at cleavage time and ends at the end of 28 min. The 2nd time interval begins at the start of the 29th minute and ends at the end of the 56th minute. The 3rd time interval begins at the start of the 57th minute and ends at the end of the 84th minute. The 4th time interval begins at the start of the 85th minute and ends at the end of the 112th minute. The 5th time interval begins at the start of the 113th minute and ends at the end of the 140th minute.
a μ2 (min
−1).
b P value was significant between ABp and EMS.
c P value was not significant between ABp and EMS.
Table 4.
The means and the standard errors of the mean of the forward migration index (FMI) in sets A, B, C and D in ABp derived cells (ABp) and EMS derived cells (EMS)
The sets are divided into an initial phase and a subsequent phase. The 1st time interval begins at cleavage time and ends at the end of 28 min. The 2nd time interval begins at the start of the 29th minute and ends at the end of the 56th minute. The 3rd time interval begins at the start of the 57th minute and ends at the end of the 84th minute. The 4th time interval begins at the start of the 85th minute and ends at the end of the 112th minute. The 5th time interval begins at the start of the 113th minute and ends at the end of the 140th minute.
a P value was significant between ABp and EMS in all comparisons.
Corresponding author. Tel.: +98 21 8801 1001; fax: +98 21 8801 6544.
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