Bayesian Decision Tree for the Classification of the Mode of Motion in Single-Molecule Trajectories

Membrane proteins move in heterogeneous environments with spatially (sometimes temporally) varying friction and with biochemical interactions with various partners. It is important to reliably distinguish different modes of motion to improve our knowledge of the membrane architecture and to understand the nature of interactions between membrane proteins and their environments. Here, we present an analysis technique for single molecule tracking (SMT) trajectories that can determine the preferred model of motion that best matches observed trajectories. The method is based on Bayesian inference to calculate the posteriori probability of an observed trajectory according to a certain model. Information theory criteria, such as the Bayesian information criterion (BIC), the Akaike information criterion (AIC), and modified AIC (AICc), are used to select the preferred model. The considered group of models includes free Brownian motion, and confined motion in 2nd or 4th order potentials. We determine the best information criteria for classifying trajectories. We tested its limits through simulations matching large sets of experimental conditions and we built a decision tree. This decision tree first uses the BIC to distinguish between free Brownian motion and confined motion. In a second step, it classifies the confining potential further using the AIC. We apply the method to experimental Clostridium Perfingens -toxin (CPT) receptor trajectories to show that these receptors are confined by a spring-like potential. An adaptation of this technique was applied on a sliding window in the temporal dimension along the trajectory. We applied this adaptation to experimental CPT trajectories that lose confinement due to disaggregation of confining domains. This new technique adds another dimension to the discussion of SMT data. The mode of motion of a receptor might hold more biologically relevant information than the diffusion coefficient or domain size and may be a better tool to classify and compare different SMT experiments.

膜蛋白在具有空间（有时为时间）变化摩擦且与多种结合伴侣存在生化相互作用的异质性环境中运动。可靠区分不同运动模式，对于深化我们对膜结构的认知、阐明膜蛋白与其所处环境间相互作用的本质均具有重要意义。本文提出一种面向单分子追踪（single molecule tracking, SMT）轨迹的分析技术，可筛选出与观测轨迹匹配度最高的最优运动模型。该方法基于贝叶斯推断（Bayesian inference），可依据预设模型计算观测轨迹的后验概率。研究采用贝叶斯信息准则（Bayesian information criterion, BIC）、赤池信息准则（Akaike information criterion, AIC）及修正赤池信息准则（modified AIC, AICc）等信息论准则完成最优模型筛选。本次考量的模型集合涵盖自由布朗运动（free Brownian motion），以及二阶或四阶势场中的受限运动（confined motion）。本研究确定了适用于轨迹分类的最优信息准则。通过匹配海量实验条件的模拟实验，我们验证了该方法的性能边界，并构建了分类决策树。该决策树首先通过BIC区分自由布朗运动与受限运动；第二步则借助AIC进一步对受限势场类型进行分类。我们将该方法应用于实验测得的产气荚膜梭菌毒素（Clostridium Perfingens -toxin, CPT）受体轨迹，证实此类受体受类弹簧势场约束。我们将该技术的适配版本应用于沿轨迹时间维度的滑动窗口分析，并将此适配版本用于分析因约束结构解聚而丧失约束特性的实验CPT轨迹。这项新技术为单分子追踪数据的分析拓展了全新维度。相较于扩散系数或结构域尺寸，受体的运动模式或许蕴含更多具有生物学意义的相关信息，或可成为分类与对比不同单分子追踪实验的更优工具。