心血管疾病是全球造成死亡的首要原因。由動脈粥狀硬化所引起的心臟病和中風為心血管疾病中常見的兩種病徵，而動脈粥狀硬化的形成則與血管內皮細胞的功能失調有關。血管內皮細胞對於維持身體體內的生理平衡具有重要性及多功能性。過去所發展出的內皮細胞數學模型在描述細胞膜電生理和鈣離子的訊息傳遞路徑上已經有顯著的貢獻。但是其在開發細胞模型上所運用到的電流刺激方法和電位箝制技術，是不足以用來研究非電刺激型的細胞如血管內皮細胞之特性。因此，需要一個更全面的檢測技術來進一步分析研究內皮細胞中的訊息傳遞路徑及生化代謝途徑。
本研究採用一個全新的分析方法“濃度箝制技術”來測試內皮細胞模型，所建構的血管內皮細胞模擬模型首先被劃分成三個具有功能性的組件包括細胞膜、細胞質和內質網。接著利用電位箝制和濃度箝制（[Ca2+]i和[IP3]箝制）技術對個別組件進行細部的特性分析。最後，再將各個獨立的組件整合以進行整體細胞的評估及差異分析。透過本研究所建構的內皮細胞模型上進行電化學分析測試，將更能夠釐清細胞膜電生理、細胞內鈣離子訊息傳遞和生化刺激彼此間複雜的關係。
本研究所開發的血管內皮細胞模擬模型除了可以成功地描述細胞膜電生理行為和細胞內鈣離子的訊息傳遞之外，也能正確地模擬出大鼠腸繫膜小動脈內皮細胞中在促效劑誘導下的反應。根據先前學者所提出的內皮細胞模型，本研究在一些數學公式和參數設定上進行修正以達成符合實驗數據的穩定模擬結果。其中，細胞質內鈣離子緩衝的公式經過修改後，可以在維持相同計算精確度之下提升100倍的計算效率。在內皮細胞模型的特性分析測試中，Kir離子通道獨特的電流-電壓關係是造成電位箝制測試中[K+]i不穩定行為以及[Ca2+]i箝制測試中膜電位不穩定行為的主要因素。
本研究建構的特性分析平台能夠使未來在內皮細胞模型中加入新的細胞組件或是加入訊息傳遞路徑上更加容易。此外，此血管內皮細胞模擬模型也可以作為未來研究氧化型陰電性低密度酯蛋白誘導的訊息傳遞路徑及生化代謝途徑之基礎模型。

Cardiovascular diseases (CVDs) are the leading cause of death globally. Heart attacks and strokes, two common features of CVDs resulting from atherosclerosis, are initiated by endothelial dysfunction in vascular endothelial cells. Endothelial cells (ECs) are crucial and multifunctional in the maintenance of normal body hemostasis. Previous EC mathematical models have made substantial progress on describing EC membrane electrophysiology and Ca2+ signaling by applying electrical stimulation and voltage clamp. However, these two methods are insufficient to explore the characteristics of non-electrically excitable cells like ECs. Therefore, a comprehensive examination is needed to further analyze EC signaling transduction pathways and biochemical metabolism.
In the present study, an analytical method named “concentration clamp” is adopted to evaluate the performances of EC models. The proposed EC model updated from a previously developed model is first separated into three functional compartments, plasma membrane, cytosol, and endoplasmic reticulum (ER), for detailed characteristics analysis by voltage clamp and concentration clamp ([Ca2+]i clamp and [IP3] clamp). Finally, the individual compartments are integrated into a complete EC for total assessment and performance comparison. Through the electrochemical performance tests on the proposed EC model, the insights of the complex relationship among membrane electrophysiology, intracellular Ca2+ dynamics, and biochemical stimulation can be gained.
The novel EC model developed in this study can describe the plasma membrane electrophysiology and calcium dynamics successfully as well as replicate agonist-induced EC responses correctly as reported in rat mesenteric artery ECs. A few equations and parameters are adjusted to allow reasonable and stable simulations. In addition, the cytosolic Ca2+ buffering equation is changed to improve computational efficiency by 100 times under the same computational accuracy. For characteristics analysis, the unique current-voltage relationship of Kir channel is identified as the key factor responsible for unstable [K+]i behaviors in voltage clamp and unstable Vm behaviors in [Ca2+]i clamp.
In summary, the established analytical platform makes it possible and easier to implement new cellular compartments or signaling transduction pathways into the present EC model. Furthermore, the present work can form the basis for the development of an EC model that will investigate signaling transduction pathways and metabolism of oxidized electronegative low-density lipoproteins (oxLDLs) on vascular ECs.

TABLE OF CONTENTS

論文審定書 i
摘要 ii
ABSTRACT iv
TABLE OF CONTENTS vi
LIST OF FIGURES xiii
LIST OF TABLES xvii
INTRODUCTION
Vascular Endothelial Cells 1
Endothelial Dysfunction 2
Mathematical Modeling of Biological Systems 3
The Hodgkin-Huxley Model 5
The Luo-Rudy Model 8
A Mathematical Model of the Vascular Endothelial Cell 11
METHODS
The construction of an EC model 16
Plasma Membrane Compartment 20
General Approach 20
Characteristics of the Transmembrane Ionic Currents 21
IKir : Inward Rectifier Potassium Channel Current 21
ISKCa and IIKCa : Calcium-Activated Potassium Channel Currents 23
ICaCl : Calcium-Activated Chloride Channel Current 25
IVRA : Volume-Regulated Anion Channel Current 28
ISOC : Store-Operated Cation Channel Current 29
INSC : Nonselective Cation Channel Current 32
INaCa : Sodium-Calcium (Na+/Ca2+) Exchanger Current 35
I INaK : Sodium-Potassium (Na+/K+) ATPase Current 36
INaKCl : Sodium-Potassium-Chloride (Na+/K+/2Cl-) Cotransport Flux 37
ICap : Plasma Membrane Calcium ATPase Current 39
Cytosolic and Endoplasmic Reticulum Compartments 40
Geometrical Considerations 40
Characteristics of the Cytosolic and ER Compartments 40
ER Ca2+ store 40
IP3 dynamics and IP3R current 41
SERCA and ER leak currents 44
Ca2+ buffering process 46
Experimental Protocols 48
Voltage Clamp Protocols 49
Concentration Clamp Protocols 50
[Ca2+]i Clamp Protocols 50
[IP3] Clamp Protocols 51
Numerical Methods 53
RESULTS
Model Modification 54
Model Verification 55
Plasma Membrane/Cytosolic Compartment Analysis 56
Voltage Clamp Analysis 57
Inward Rectifier Potassium Channel Current (IKir) 57
Calcium-Activated Potassium Channel Currents (ISKCa and IIKCa) 58
Calcium-Activated Chloride Channel Current (ICaCl) 59
Volume-Regulated Anion Channel Current (IVRA) 61
Store-Operated Cation Channel Current (ISOC) 62
Nonselective Cation Channel Current (INSC) 62
Sodium-Calcium (Na+/Ca2+) Exchanger Current (INaCa) 63
Sodium-Potassium (Na+/K+) ATPase Current (INaK) 64
Plasma Membrane Calcium ATPase Current (ICap) 66
Intracellular Ionic Concentration ([Na+]i, [K+]i, [Cl-]i, and [Ca2+]i) 66
Sodium-Potassium-Chloride (Na+/K+/2Cl-) Cotransport Flux (INaKCl) 68
[Ca2+]i Clamp Analysis 70
Membrane Potential (Vm) 71
Intracellular Ionic Concentration ([Na+]i, [K+]i, and [Cl-]i) 73
Sodium-Potassium-Chloride (Na+/K+/2Cl-) Cotransport Flux (INaKCl) 75
Inward Rectifier Potassium Channel Current (IKir) 77
Calcium-Activated Potassium Channel Currents (ISKCa and IIKCa) 79
Calcium-Activated Chloride Channel Current (ICaCl) 80
Volume-Regulated Anion Channel Current (IVRA) 81
Store-Operated Cation Channel Current (ISOC) 81
Nonselective Cation Channel Current (INSC) 82
Sodium-Calcium (Na+/Ca2+) Exchanger Current (INaCa) 82
Sodium-Potassium (Na+/K+) ATPase Current (INaK) 83
Plasma Membrane Calcium ATPase Current (ICap) 85
Endoplasmic Reticulum Compartment Analysis 85
[IP3] Clamp Analysis 86
IP3 dynamics 86
Intracellular and ER stored Ca2+ concentration ([Ca2+]i and [Ca2+]ER) 87
IP3 Receptor Current (IIP3R) 90
SERCA and ER leak currents (ISERCA and Ileak) 91
EC Model Analysis 92
Voltage Clamp Analysis 92
Intracellular and ER stored Ca2+ concentration ([Ca2+]i and [Ca2+]ER) 93
[Ca2+]i-associated transmembrane ionic currents 94
[Ca2+]i Clamp Analysis 95
ER stored Ca2+ concentration, SERCA and ER leak currents
([Ca2+]ER, ISERCA and Ileak) 95
[IP3] Clamp Analysis 97
Intracellular and ER stored Ca2+ concentration ([Ca2+]i and [Ca2+]ER) 97
Membrane Potential (Vm) 98
DISCUSSION AND CONCLUSIONS
Voltage Clamp Analysis 100
[Ca2+]i Clamp Analysis 102
Model Future Applications 105
Conclusions 110
APPENDIX 1: Formulation of the Model 112
APPENDIX 2: Definition of Symbols 117
REFERENCES 121

LIST OF FIGURES

Fig. 1. Schematic Diagram of the EC Model 19
Fig. 2. IKir 23
Fig. 3. IKCa 25
Fig. 4. ICaCl 27
Fig. 5. IVRA 29
Fig. 6. ISOC 31
Fig. 7. INSC 34
Fig. 8. INaCa 36
Fig. 9. INaK 37
Fig. 10. INaKCl 38
Fig. 11. ICap 39
Fig. 12. IP3 and IIP3R 43
Fig. 13. ISERCA and Ileak 45
Fig. 14. Voltage clamp protocols 50
Fig. 15. [Ca2+]i clamp protocols 51
Fig. 16. [IP3] clamp protocols 53
Fig. 17. Voltage clamp analysis on KCa channels 59
Fig. 18. Voltage clamp analysis on CaCl channel 60
Fig. 19. Voltage clamp analysis on VRA channel 61
Fig. 20. Voltage clamp analysis on NaCa exchanger 64
Fig. 21. Voltage clamp analysis on NaK pump 65
Fig. 22. Voltage clamp analysis on intracellular Na+, K+, and Cl- concentration 67
Fig. 23. Voltage clamp analysis on intracellular Ca2+ concentration 68
Fig. 24. Voltage clamp analysis on NaKCl cotransporter 70
Fig. 25. [Ca2+]i clamp on membrane potential Vm 72
Fig. 26. [Ca2+]i clamp analysis on membrane potential Vm 73
Fig. 27. [Ca2+]i clamp analysis on intracellular Na+, K+, and Cl- concentration 75
Fig. 28. [Ca2+]i clamp analysis on NaKCl cotransporter 76
Fig. 29. [Ca2+]i clamp analysis on Kir channel 78
Fig. 30. [Ca2+]i clamp analysis on KCa channels 80
Fig. 31. [Ca2+]i clamp analysis on NaCa exchanger83
Fig. 32. [Ca2+]i clamp analysis on NaK pump 84
Fig. 33. Dynamics of [IP3] clamp 87
Fig. 34. [IP3] clamp analysis on intracellular and ER stored Ca2+ concentration 88
Fig. 35. [IP3] clamp analysis on intracellular and ER stored Ca2+ concentration 90
Fig. 36. [IP3] clamp analysis on IP3 receptor current 91
Fig. 37. [IP3] clamp analysis on SERCA and ER leak currents 92
Fig. 38. Voltage clamp analysis on intracellular and ER stored Ca2+ concentration
94
Fig. 39. [Ca2+]i clamp analysis on ER stored Ca2+ concentration, SERCA, and ER
leak currents 96
Fig. 40. [IP3] clamp analysis on intracellular and ER stored Ca2+ concentration
98
Fig. 41. [IP3] clamp analysis on membrane potential 99
Fig. 42. Voltage clamp analysis on K+ Nernst potential 102
Fig. 43. [Ca2+]i clamp analysis on K+ Nernst potential 104
Fig. 44. Schematic diagram of the lectin-like oxidized low-density lipoprotein
(oxLDL) receptor-1 (LOX-1) and platelet-activating factor receptor
(PAF-R) pathways 108
Fig. 45. Curve fitting with the endothelial internalization of oxLDL to HCAECs
109

LIST OF TABLES

Table 1. Model initial conditions 46
Table 2. Model standard parameter values 46
Table 3. The dependent elements of transmembrane ionic currents 57
Table 4. The dependent elements of the ER compartment and IP3 dynamics 85

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