A New Approach to Estimating the Speed of Uniform Movement of Microorganisms along a Helical Trajectory

Analysis of the motion of microscopic organisms is important for understanding their behavior, intrinsic state, and response to external conditions. Many free-swimming microorganisms move in three-dimensional space along a helical trajectory. When a three-dimensional trajectory is analyzed from video frames, it is transformed into a flat curve. This leads to loss of some of the motion data and, in particular, to errors in the estimates of the traveled path and true speed. We propose to estimate the length of a three-dimensional spiral path using the maximum length of the projection of the trajectory segment. The analysis showed that for rectilinear spiral trajectories, along which organisms move uniformly, this method in many cases allows us to estimate correctly the path traveled and the true speed of movement and to make a correct comparison of the speeds of different microorganisms.