The study of moving particles (e.g. molecules, virus, vesicles, organelles, or whole cells) is crucial to decipher a plethora of cellular mechanisms within physiological and pathological conditions. Powerful live-imaging approaches enable life scientists to capture particle movements at different scale from cells to single molecules, that are collected in a series of frames. However, although these events can be captured, an accurate quantitative analysis of live-imaging experiments still remains a challenge. Two main approaches are currently used to study particle kinematics: kymographs, which are graphical representation of spatial motion over time, and single particle tracking (SPT) followed by linear linking. Both kymograph and SPT apply a space-time approximation in quantifying particle kinematics, considering the velocity constant either over several frames or between consecutive frames, respectively. Thus, both approaches intrinsically limit the analysis of complex motions with rapid changes in velocity. Therefore, we design, implement and validate a novel reconstruction algorithm aiming at supporting tracking particle trafficking analysis with mathematical foundations. Our method is based on polynomial reconstruction of 4D (3D+time) particle trajectories, enabling to assess particle instantaneous velocity and acceleration, at any time, over the entire trajectory. Here, the new algorithm is compared to state-of-the-art SPT followed by linear linking, demonstrating an increased accuracy in quantifying particle kinematics. Our approach is directly derived from the governing equations of motion, thus it arises from physical principles and, as such, it is a versatile and reliable numerical method for accurate particle kinematics analysis which can be applied to any live-imaging experiment where the space-time coordinates can be retrieved.

翻译：移动粒子（例如分子、病毒、囊泡、细胞器或整个细胞）的研究对于解析生理和病理条件下的多种细胞机制至关重要。强大的活体成像方法使生命科学家能够捕获从单细胞到单分子等不同尺度上的粒子运动，这些运动被收集在一系列图像帧中。然而，尽管这些事件可以被捕获，对活体成像实验进行精确的定量分析仍然是一个挑战。目前，研究粒子运动学主要采用两种方法：时间序列图（kymographs），即空间运动随时间变化的图形表示；以及单粒子跟踪（SPT）结合线性连接。时间序列图和SPT在量化粒子运动学中都采用时空近似，前者认为速度在若干帧内恒定，后者则认为速度在连续帧之间恒定。因此，这两种方法本质上都限制了分析速度快速变化的复杂运动。为此，我们设计、实现并验证了一种基于数学基础支持粒子运输轨迹分析的新型重构算法。我们的方法基于4D（3D+时间）粒子轨迹的多项式重构，能够在整个轨迹上的任意时刻评估粒子的瞬时速度和加速度。本文将新算法与最先进的SPT结合线性连接方法进行对比，证明其在量化粒子运动学方面具有更高的精度。我们的方法直接源于运动控制方程，因而基于物理原理，是一种通用且可靠的精确粒子运动学分析数值方法，可应用于任何能够获取时空坐标的活体成像实验。