高分子溶液中紅血球空乏與靜電作用的定量分析

Quantitative Analysis of Depletion and Electrostatic Interactions of Red Blood Cells in Polymer Solutions

范曉義(Shiao-Yi Fan)

指導教授 ： 陳義裕

共同指導教授 ： 陳彥龍(Yeng-Long Chen)

國立臺灣大學/理學院/物理學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201600995

摘要

人體血液中的紅血球具有聚集性，藉由血球扁平狀部位的吸引，紅血球會聚集排列形成一串一串的結構(rouleau)，而紅血球聚集結構的形成乃是基於吸引力與排斥力的平衡。從過去一系列的實驗結果我們了解到，紅血球間的吸引力源自於溶液中巨分子(血漿蛋白或是其他高分子)的存在，而排斥力則來自於紅血球表面糖萼(glycocalyx)所帶有的負電荷。然而時至今日，由巨分子所導致的血球聚集現象，其機制尚有爭論，其中一種說法是，此吸引力就是伴隨因系統亂度改變而產生的熵力，或者稱作空乏力(depletion force)。在本篇文章中，我們重新檢視了由高分子所產生的紅血球間空乏力的大小，和由紅血球表面糖萼負電荷所產生的靜電排斥力大小，並與實驗結果作比較。
紅血球間的空乏能量可以簡單地被兩個物理量來決定：溶液中高分子的滲透壓以及高分子的空乏厚度(depletion layer thickness)，前者為空乏力的大小，後者則為空乏力的作用距離，與高分子的迴轉半徑有關。理論上在良好溶劑的排斥體積極限(excluded volume limit)下，高分子的滲透壓與空乏厚度均滿足各別的標度行為(scaling behavior)，因此我們可以預測在不同高分子濃度下空乏力的大小。另一方面，紅血球間的靜電排斥力則在固定的表面電荷密度以及溶液離子濃度下，藉著給定的糖萼電荷分布，先由線性化的蒲松-波茲曼方程式計算出表面電位，再由蒲松方程式得到兩表面間電偶層的靜電壓力。空乏力與靜電力均為兩表面間距離的函數，二者的和即為兩血球表面間的作用力。結果顯示，藉由控制高分子的迴轉半徑和表面層電荷的分布厚度，此模型能有效地描述紅血球間的交互作用能量。然而在不同大小的高分子中，預測的表面層厚度並不相同，由於此時兩血球間的平衡位置不同，因此暗示著兩個具有靜電交互作用的表面層會在不同的距離下彼此壓縮改變原本的分布。

關鍵字

紅血球聚集 ； 高分子 ； 空乏力 ； 糖萼 ； 蒲松方程式

並列摘要

The normal human RBC usually form aggregates with linear face-to-face structures, which resemble a stack of coins called rouleau. This rouleau formation is determined by the balance between the forces promoting aggregation and those forces opposing aggregation. From the previous significant research effort, macromolecules in solutions, including plasma proteins or other polymers, have been recognized as the main contribution to the aggregating forces; besides, electrostatic repulsion induced by glycocalyx, which is a negatively charged grafting polymer layer on RBC surface, is responsible for the disaggregating forces. Although the disaggregating force have been well recognized, the mechanism for aggregating forces is still in dispute. One possible model proposes that this aggregating force is just a pure entropic force, or the so-called depletion force. In this article, we reexamine this polymer induced depletion force and the electrostatic repulsion, comparing them to the experimental results.
The depletion potential between RBC can be simply characterized by two physical quantities: the osmotic pressure and the depletion layer thickness of bulk polymers. The former is the power of forces, and the latter is just the range of such interactions. In the excluded volume limit, both quantities theoretically satisfy individual scaling behaviors, and therefore we are able to describe them at different polymer concentration. The electrostatic interaction is calculated under widely used surface charge density and ion concentration; in additional, given a constant surface charge distribution, the electrostatic pressure is derived from the Poisson equation with the electric potential calculated by the linearized Poisson-Boltzmann equation. Both depletion and electrostatic forces are functions of surfaces distance, and the summation of them is just the total interaction between RBC surfaces. The results show that by controlling the radius of gyration and the surface charge layer thickness, the interaction potential can be well described. However, the calculation shows different layer thickness for different polymer size. Since the equilibrium distances between surfaces are not equal, this discrepancy probably indicate that two electrostatic interacting layers may compress and deform each other.

並列關鍵字

RBC aggregation ； polymer ； depletion force ； glycocalyx ； Poisson equation

參考文獻

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