﻿ 基于信号分子双向输运的运动细胞极性反转模拟
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 力学学报  2015, Vol. 47 Issue (2): 337-345  DOI: 10.6052/0459-1879-14-242 0

### 引用本文 [复制中英文]

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Feng Shiliang, Zhu Weiping. SIMULATION FOR REVERSAL OF CELL POLARITY BASED ON BIDIRECTIONAL TRANSPORT OF SIGNALING MOLECULES[J]. Chinese Journal of Ship Research, 2015, 47(2): 337-345. DOI: 10.6052/0459-1879-14-242.
[复制英文]

### 文章历史

2014-08-18收稿
2014-10-31录用
2014-11-04网络版发表

 图 1 采用盘基网柄菌细胞进行运动细胞极化反转现象[7]. 图中绿色 为细胞伪足,白色箭头标记外信号方向 Fig. 1 Actin relocalization after reversal of signal (derived from Ref.[7]) Green marks the pesudopod of the cell, and the white arrow indicates the direction of external signal }

1 . 材料和方法 1.1 Rac-PIs反馈回路

 图 2 负责细胞极化的Rac-PIs反馈回路 Fig. 2 Rac-PIs feedback loop considered for studying reversal of cell polarity

1.2 数学模型

 $\frac{{\partial {P_3}}}{{\partial t}} = \underbrace {{D_{\rm{m}}}\frac{1}{{r_{\rm{m}}^2}}\frac{{{\partial ^2}}}{{\partial {\varphi ^2}}}{P_3}}_{{\rm{diffusion}}} + {\rm{ }}\underbrace {k_{{\rm{cat}}}^{({\rm{1}})}\frac{{RG_{\rm{m}}^{(1)}{P_2}}}{{K_M^{(1)} + {P_2}{\rm{ }}}} - k_{{\rm{cat}}}^{({\rm{2}})}{\rm{ }}\frac{{G_{\rm{m}}^{(2)}{P_3}}}{{K_M^{(2)} + {P_3}{\rm{ }}}}}_{{\rm{catalytic}}\;{\rm{effect}}},$ (1a)
 $\frac{{\partial {P_2}}}{{\partial t}} = \underbrace {{D_{\rm{m}}}\frac{1}{{r_{\rm{m}}^2}}\frac{{{\partial ^2}}}{{\partial {\varphi ^2}}}{P_2}}_{{\rm{diffusion}}} + \underbrace {k_{{\rm{cat}}}^{(2)}\frac{{RG_{\rm{m}}^{(2)}{P_3}}}{{K_M^{(2)} + {P_3}}} - k_{{\rm{cat}}}^{(1)}\frac{{RG_{\rm{m}}^{(1)}{P_2}}}{{K_M^{(1)} + {P_2}}}}_{{\rm{catalytic}}\;{\rm{effect}}},$ (1b)

 $\frac{{\partial {P_3}}}{{\partial n}} = 0,\quad \frac{{\partial {P_2}}}{{\partial n}} = 0.$ (1c)

 图 3 运动细胞极性反转模型示意图 Fig. 3 Schematic diagram of cell model and stimulus

 $\begin{array}{l} R({r_{\rm{m}}},\varphi ,t)\\ = \left\{ {\begin{array}{*{20}{l}} {{R_{{\rm{mid}}}} + \frac{{R_{\rm{f}}^{(1)} - R_{\rm{b}}^{(1)}}}{2}\cos \varphi \qquad (t \le {t_1})}\\ {{R_{{\rm{mid}}}} + \left[{\frac{{R_{\rm{f}}^{(1)} - R_{\rm{b}}^{(1)}}}{2} + (R_{\rm{f}}^{(2)} - R_{\rm{f}}^{(1)})\left( {\frac{{t - {t_1}}}{{{t_2} - {t_1}}}} \right)} \right]\cos \varphi \qquad ({t_1} < t \le {t_2})}\\ {{R_{{\rm{mid}}}} + \frac{{R_{\rm{f}}^{(2)} - R_{\rm{b}}^{(2)}}}{2}\cos \varphi \qquad (t > {t_2})} \end{array}} \right. \end{array}$ (2)
2 . 数值算法

3 . 结 果

3.1 "极性反转''的基本过程和特征

 图 4 细胞前、后活性态Rac分数时程曲线图(高梯度) Fig. 4 Fraction of activated Rac varying with time at the cell front and the back (high gradient)

 图 5 质膜结合态、胞质游离态PI3K/PTEN分子总量时程曲线图 Fig. 5 Total amount of cytosolic and membrane-bound PI3K/PTEN varying with time
 图 6 胞质游离态PTEN分子在t= 300 s时刻空间分布图 Fig. 6 Spatial distribution pattern of cytosolic PTEN t= 300 s

 图 7 细胞反转极化进程中PIP3时空演化图 Fig. 7 Spatial-temporal evolution of PIP3 (upon high gradient reversal signal: Rf(2)=0.12, Rb(2)=0.68)

 图 8 细胞前、后两端PIP3浓度时程曲线图 Fig. 8 Concentration of PIP3 varying with time at the cell front and the back
3.2 反向Rac梯度对极性反转影响

 图 9 中等梯度反转输入信号时程图 Fig. 9 Fraction of activated Rac varying with time at the cell front and the back (middle gradient)

 图 10 中等梯度反转输入信号对应的PIP3时空演化图 Fig. 10 Spatial-temporal evolution of PIP3 (upon medium gradient reversal signal: Rf(2)=0.26, Rb(2)=0.54)

 图 11 低梯度反转输入信号时程图 Fig. 11 Fraction of activated Rac varying with time at the cell front and the back (low gradient)

 图 12 低梯度反转输入信号对应的PIP3时空演化图 Fig. 12 Spatial-temporal evolution of PIP3 (upon low gradient reversal signal:Rf(2)=0.34, Rb(2)=0.46)

(1)反向信号梯度较高,这使得细胞前部伪足快速解离,尾部能在短时期内能够获得游离态激活酶,细胞得以在反方向迅速建立极性;

(2)反向信号梯度适中,细胞前部伪足需要较长时间解离,细胞极性建立较慢;

(3)反向信号梯度较弱,细胞前部长期维持一定量PIP3,细胞后部始终无法获得游离态激活酶,因此无法极性反转.

4 . 讨 论

 图 13 盘尼网柄菌极性反转实验所获得的细胞前后端 F-actin 时程曲线[7] Fig. 13 Concentration of F-actin varying with time at the cell head and the rear (derived from Ref.[7])

5 . 结 论

(1)理论计算得出的极性反转所需时间与实验观测一致,约为100s; 进一步提高反转信号梯度能够加快极性反转进程.

(2)细胞新的伪足延滞生成,这主要是由于细胞前端PIP3积聚对胞质游离态激活酶(例如: PI3K)展开竞争,使得激活因子无法有效到达细胞后部.

(3)反转信号梯度需要超过一定阈值才能引起细胞极性反转否则,细胞仍然维持之前极化方向.

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SIMULATION FOR REVERSAL OF CELL POLARITY BASED ON BIDIRECTIONAL TRANSPORT OF SIGNALING MOLECULES
Feng Shiliang,Zhu Weiping
Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
Fund: The project was supported by the National Natural Science Foundation of China (31370940)..
Abstract: To investigate the mechanisms underlying the reversal of cell polarity, a mathematical model consisting of a pair of reaction-di usion equations was presented and solved numerically with the Lattice—Boltzmann method. It was found that, by applying a reversal gradient of Rac signal in a cell, labels for lamellipod (i.e., PI3K, and PIP3) would disappear from the front of cell, and redistribute to the rear, while labels for tail (i.e., PTEN, PIP2) would act oppositely. The spatiotemporal patterns of lamellipod and tail interconversion derived from our numerical simulation agreed well with that of the experimental observations. Besides, the time delay taking place between actin assembly at the new front and disassembly at the previous front was medicated by the completion of an activator (i.e., PI3K), without the help of a supposed "global inhibitor".
Key words: motile cells    repolarization    cytoskeleton    signaling transduction    mathematical model