Lateral Diffusion on Tubular Membranes: Quantification of Measurements Bias

Single Particle Tracking (SPT) is a powerful technique for the analysis of the lateral diffusion of the lipid and protein components of biological membranes. In neurons, SPT allows the study of the real-time dynamics of receptors for neurotransmitters that diffuse continuously in and out synapses. In the simplest case where the membrane is flat and is parallel to the focal plane of the microscope the analysis of diffusion from SPT data is relatively straightforward. However, in most biological samples the membranes are curved, which complicates analysis and may lead to erroneous conclusions as for the mode of lateral diffusion. Here we considered the case of lateral diffusion in tubular membranes, such as axons, dendrites or the neck of dendritic spines. Monte Carlo simulations allowed us to evaluate the error in diffusion coefficient (D) calculation if the curvature is not taken into account. The underestimation is determined by the diameter of the tubular surface, the frequency of image acquisition and the degree of mobility itself. We found that projected trajectories give estimates that are 25 to 50% lower than the real D in case of 2D-SPT over the tubular surface. The use of 3D-SPT improved the measurements if the frequency of image acquisition was fast enough in relation to the mobility of the molecules and the diameter of the tube. Nevertheless, the calculation of D from the components of displacements in the axis of the tubular structure gave accurate estimate of D, free of geometrical artefacts. We show the application of this approach to analyze the diffusion of a lipid on model tubular membranes and of a membrane-bound GFP on neurites from cultured rat hippocampal neurons.

单粒子追踪（Single Particle Tracking, SPT）是一种功能强大的技术，可用于分析生物膜脂质与蛋白质组分的侧向扩散特性。在神经元中，SPT能够用于研究持续在突触内外扩散的神经递质受体的实时动态行为。在最简单的场景中，若生物膜平坦且与显微镜焦平面平行，基于SPT数据的扩散分析过程相对直观。然而在绝大多数生物样本中，生物膜往往呈弯曲状态，这会使扩散分析过程变得复杂，甚至可能针对侧向扩散模式得出错误结论。本研究聚焦于管状生物膜内的侧向扩散场景，例如轴突、树突或树突棘颈部的管状结构。我们通过蒙特卡洛模拟（Monte Carlo simulation），评估了未考虑膜曲率时扩散系数（diffusion coefficient, D）计算过程中产生的误差。该低估程度由管状表面的直径、图像采集频率以及分子自身的迁移速率共同决定。我们发现，在管状表面开展二维单粒子追踪（2D-SPT）时，通过投影得到的轨迹所估算得到的扩散系数D，较真实值偏低25%至50%。若图像采集频率相较于分子迁移速率与管道直径足够高，则采用三维单粒子追踪（3D-SPT）可有效提升测量精度。尽管如此，通过管状结构轴向的位移分量计算扩散系数D，仍可得到不受几何伪影干扰的精准估算结果。我们展示了该方法的应用实例：分别用于分析脂质在模型管状生物膜上的扩散行为，以及膜结合绿色荧光蛋白（green fluorescent protein, GFP）在培养大鼠海马神经元神经突上的扩散情况。