Modeling geometrical trajectories of actin-based motility

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姓名

温福來(Fu-Lai Wen) 查詢紙本館藏

畢業系所

物理學系

論文名稱

(Modeling geometrical trajectories of actin-based motility)

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摘要(中)

本篇論文探討在實驗中觀察到李斯特菌(Listeria monocytogenes)的幾何形狀運動軌跡。李斯特菌利用其表面特殊蛋白質活化寄主細胞內的肌動蛋白(Actin)進行聚合作用。
這些正在進行聚合作用的肌動蛋白推動著李斯特菌前進，並在其後方留下類似彗星尾巴的肌動蛋白網路(Actin network)。實驗中觀察到李斯特菌的運動軌跡類似幾何圖形，例如：直線、圓形、S形與8字形等。基於實驗觀察結果，我們建立一個以現象學為基礎的模型去探討利用與李斯特菌相同運動方式的圓盤(在二維空間)與圓球(在三維空間)其運動情形。在我們的模型中，分布在圓盤表面上的肌動蛋白密度與每一根肌動蛋白纖維所施的力都受圓盤的移動與轉動所影響，而圓盤的轉動來自於圓盤表面上肌動蛋白密度與每一根肌動蛋白纖維所施的力的不對稱分布。我們的研究顯示，這種回饋機制可以使一個直線運動軌跡變得不穩定，然後透過在圓盤表面上的肌動蛋白密度與每一根肌動蛋白纖維所施的力的分布分歧(bifurcation)，產生許多實驗上所觀察到的幾何形狀運動軌跡。
當直線軌跡因為叉式分歧(pitchfork bifurcation)變得不穩定時，最終的運動軌跡為圓形。另一方面，直線軌跡也可以因為霍普夫分歧(Hopf bifurcation)變得不穩定，而最終的軌跡為S形。為了模擬在李斯特菌表面上特殊蛋白質的不對稱分布，我們也研究只有半個表面可以進行肌動蛋白聚合作用的圓盤其運動情形。研究顯示當這個圓盤的直線運動軌跡變得不穩定時，也經歷類似的對稱性破缺分歧(symmetry-breaking bifurcation)。
然而，比較全部表面可以進行聚合作用的圓盤與只有半個表面可以進行聚合作用的圓盤的運動情形，當這兩個圓盤的軌跡皆為S形時，圓盤的轉動角頻率不同於運動軌跡改變的角頻率。另一方面，當軌跡為圓形時，全部表面可以進行聚合作用的圓盤其轉動角頻率不同於運動軌跡改變的角頻率，但對於只有半個表面可以進行聚合作用的圓盤而言，這兩個角頻率則是相同的。此外，我們也發現在三維空間中運動的圓球，其軌跡由直線到彎曲的轉變機制，與在二維空間中運動的圓盤是一樣的。儘管如此，因為圓球轉動與其表面肌動蛋白密度與每一根肌動蛋白纖維所施的力之間的耦合，使得圓球具有比較豐富的動力學行為。例如，不同於圓盤被侷限在一個平面上運動；一個圓球在三維空間中可以沿著三維軌跡(例如：螺線形軌跡)運動。

摘要(英)

This thesis reports theoretical studies on the experimentally observed geometrical trajectories of Listeria monocytogenes.
The intracellular bacterium Listeria monocytogenes utilizes its specific surface protein to activate actin polymerization inside the host cell.
The polymerizing actin network pushes Listeria forward, and leaves a cometlike actin tail behind the bacterium.
Experiments of Listeria-type actin-based motility have observed fascinating geometrical trajectories such as straight lines, circles, S-shaped curves, and translating figure eights.
Based on the experimental observations, we constructed a phenomenological model for Listeria-type motion of a disk (in two dimensions) and a bead (in three dimensions).
In our model, the actin density and force per filament on the disk surface
are influenced by the translation and self-rotation of the disk,
which in turn is induced by the asymmetric distributions of those densities.
We show that this feedback can destabilize a straight trajectory,
leading to the geometrical trajectories observed in experiments
through bifurcations in the distributions of actin density and force per filament.
When the instability is due to a pitchfork bifurcation, the resulting trajectory is a circle; a straight trajectory can also lose stability through a Hopf bifurcation,
and the resulting trajectory is an S-shaped curve.
To mimic the nonuniform distribution of functionalized protein on Listeria surface,
we have also studied the motion of a disk whose surface is half coated and half clean. We show that a half-coated disk also undergoes similar symmetry-breaking bifurcations when the straight trajectory loses its stability.
For both a fully coated disk and a half-coated disk,
when the trajectory is an S-shaped curve,
the angular frequency of the disk self-rotation is different from that of the disk trajectory. However, for circular trajectories, these angular frequencies are different for a fully coated disk but the same for a half-coated disk.
In addition, for a bead moving in a three-dimensional environment,
we find that the instability mechanism for the transition from a straight trajectory to a curved trajectory is the same as that for a disk in a two-dimensional environment. Despite this similarity, the couplings between bead self-rotation and the evolution of actin density and force per filament are found to give the bead more rich dynamics.
For example, different from the disk motion confined to a plane,
a bead in three dimensions is able to move along trajectories with nonzero torsion such as helical trajectories.

關鍵字(中)

★ 李斯特菌
★ 肌動蛋白
★ 軌跡
★ 對稱性破缺
★ 分歧

關鍵字(英)

★ Listeria monocytogenes
★ Actin
★ trajectories
★ symmetry breaking
★ bifurcation

論文目次

1 Introduction 1
1.1 Actin-based motility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Geometrical trajectories of Listeria-type motion . . . . . . . . . . . . . 12
1.3 Overview of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Model 21
2.1 Force and torque balance . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Evolution equations for actin density and force per filament . . . . . . 25
3 Breaking the rotational symmetry 29
3.1 Rest-to-moving transition . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Generating geometrical trajectories 36
4.1 Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Symmetry-breaking bifurcation analysis . . . . . . . . . . . . . . . . . . 54
4.3 A half-coated disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5 Conclusions and future work 69
5.1 What has been accomplished . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Connection between our model and experiments . . . . . . . . . . . . . 70
5.3 Discussion and future works . . . . . . . . . . . . . . . . . . . . . . . . 72
A Scaling laws of the Fourier modes of n and f 76
B Stability analysis of the straight trajectory 78
C Actin-based motility in three dimensions 82
C.1 Rest-to-moving transition . . . . . . . . . . . . . . . . . . . . . . . . . 83
C.2 From straight to curved trajectories . . . . . . . . . . . . . . . . . . . . 87
C.3 A chiral bead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
C.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
C.5 Calculation Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
C.5.1 Scaling laws of the harmonics of n and f . . . . . . . . . . . . . 102
C.5.2 Stability analysis of the straight trajectory . . . . . . . . . . . . 103
Bibliography 111

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指導教授

陳宣毅(Hsuan-Yi Chen)

審核日期

2013-7-8

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