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首页> 外文期刊>Applied Mathematical Modelling >Three-dimensional simulation of biological ion channels under mechanical, thermal and fluid forces
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Three-dimensional simulation of biological ion channels under mechanical, thermal and fluid forces

机译：机械，热和流体力作用下生物离子通道的三维模拟

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In this article we address the three-dimensional modeling and simulation of biological ion channels using a continuum-based approach. Our multi-physics formulation self-consistently combines, to the best of our knowledge for the first time, ion electrodiffusion, channel fluid motion, thermal self-heating and mechanical deformation. The resulting system of nonlinearly coupled partial differential equations in conservation form is discretized using the Galerkin Finite Element Method. The validation of the proposed computational model is carried out with the simulation of two ion nanochannels. The first is a voltage operated channel with K~+ and Na~+ ions, and the second is the sodium-potassium pump in which also chlorine (Cl~−) and bicarbonate (HCO_3 ~−) ions are considered. In the first case study, we investigate the coupling between electrochemical and fluid-dynamical effects. Then, we enrich the modeling picture by investigating the influence of a thermal gradient. Finally, we add a mechanical stress responsible for channel deformation and investigate its effect on the functional response of the channel. Results show that fluid and thermal fields have no influence in absence of mechanical deformation whereas ion distributions and channel functional response are significantly modified if mechanical stress is included in the model. These predictions agree with biophysical conjectures on the importance of protein conformation in the modulation of channel electrochemical properties. In the second case study, we exploit our multiphysical mathematical formulation to investigate the effect of permanent surface charge on the function of the sodium-potassium pump. In particular, we consider the biophysical application in which the pump actively participates to the process of aqueous humor production across the transepithelial membrane in the ciliary body of the eye. In this study we are motivated by the fact that several data are available to verify the accuracy of model predictions and that the role of surface charge has not yet been mathematically analyzed in the specific context at hand. Results show that the model is able to predict in a very accurate manner the correct aqueous humor flow direction, the magnitude of aqueous velocity and the experimentally measured transepithelial membrane potential only if the (negative) surface permanent charge is larger than a limiting value, whereas if the charge is below this value, fluid inversion occurs.
机译：在本文中，我们使用基于连续体的方法解决生物离子通道的三维建模和仿真问题。据我们所知，我们的多物理场公式自洽地结合了离子电扩散，通道流体运动，热自热和机械变形。使用Galerkin有限元方法离散化了非线性守恒形式的偏微分方程组的结果。所提出的计算模型的验证是通过模拟两个离子纳米通道进行的。第一个是带有K〜+和Na〜+离子的电压通道，第二个是钠钾泵，其中还考虑了氯（Cl〜-）和碳酸氢根（HCO_3〜-）离子。在第一个案例研究中，我们研究了电化学效应与流体动力学效应之间的耦合。然后，我们通过研究热梯度的影响来丰富建模图。最后，我们添加了导致通道变形的机械应力，并研究了其对通道功能响应的影响。结果表明，在没有机械变形的情况下，流体和热场没有影响，而如果在模型中包含机械应力，则离子分布和通道功能响应会发生显着变化。这些预测与生物物理推测一致，即蛋白质构象在调节通道电化学性质中的重要性。在第二个案例研究中，我们利用我们的多物理数学公式来研究永久性表面电荷对钠钾泵功能的影响。尤其是，我们考虑了生物物理应用，其中泵主动参与了眼睫状体中跨上皮膜的房水生成过程。在这项研究中，我们受到以下事实的鼓舞：有数个数据可用于验证模型预测的准确性，并且尚未在手边的特定情况下对表面电荷的作用进行数学分析。结果表明，仅当（负）表面永久电荷大于极限值时，该模型才能以非常准确的方式预测正确的房水流动方向，房水速度的大小和实验测量的跨上皮膜电位，而如果电荷低于此值，则会发生流体倒转。

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