A new approach to estimating speed of microorganisms uniform movement along a helical trajectory

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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.

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A. Lyakh

Kovalevskii Institute of Biology of the Southern Seas, Russian Academy of Sciences

编辑信件的主要联系方式.
Email: me@antonlyakh.ru
俄罗斯联邦, Sevastopol, 299011

T. Rauen

Kovalevskii Institute of Biology of the Southern Seas, Russian Academy of Sciences

Email: antonlyakh@gmail.com
俄罗斯联邦, Sevastopol, 299011

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2. Fig. 1. Relative errors between the maximum projection (ςmax) and true length of trajectory segments with different characteristics.

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3. Fig. 2. Relative difference, Δma, between the true velocity of motion, Va, and (a) the maximum projected velocity Vm or (b) the normal projected velocity Vp for trajectories with different characteristics: different turn ratios and different rotation angles. The same color is used to mark Δma calculated for the same turn ratios but different Vc.

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4. Fig. 3. Situations in which one absolute speed of movement corresponds to many projection speeds – normal (a) and maximum (b), equal to other absolute speeds. Each horizontal line shows a fixed value of absolute speed (or the true path traveled by the organism in a second). Each curved line shows the dynamics of change in projection speed (projection path traveled in a second), calculated for trajectories with different characteristics. A horizontal intersection of a line with curved lines indicates a coincidence of speed values that are initially different, i.e., signals an error. For convenience, we have depicted only the case when Vc = 1; for other values of Vc, the graphs are similar.

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