A New Approach to Estimating Speed of Microorganisms Uniform Movement 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 correctly estimate the traveled path and true speed of movement, and to perform a correct comparison of the speeds of different microorganisms.