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Cell migrations in the cell cultures are found to follow non-Gaussian statistics. We recorded long-term cell migration patterns with more than six hundred cells located in 28 mm2. Our experimental data support the claim that an individual cell migration follows Gaussian statistics. Because the cell culture is inhomogeneous, the statistics of the cell culture exhibit a non-Gaussian distribution. We find that the normalized histogram of the diffusion velocity follows an exponential tail. A simple model is proposed based on the diffusional inhomogeneity to explain the exponential distribution of locomotion activity in this work. Using numerical calculation, we prove that our model is in great agreement with the experimental data.
Bacteria, eukaryotic cells and animals like birds and insects[1–4] are believed to adopt perplexing random walk strategies to explore their environment. Many phenomenological models have been made to classify these random walk strategies by the characteristics of stochastic fluctuation. We notice that these systems have been treated in the same framework of self-propellers[5] with collective motion. The ensembles are always homogenous, if not, they will fall apart in the collective motion. Hence, the ensemble behavior is dependent on the diffusion features of a unit and the interaction relationships between the units.
We address that eukaryotic cell motion may be more complicated than the homogenous collective random motion. As a model system in this field, Dictyostelium discoideum (DD) cell is used in this paper. When individual DD cells are starving, they tend to aggregate to form a multicellular migrating slug.[6] Before the aggregation, cells move randomly to search the space for food in the local environment. Interestingly, many experiments showed that the aggregation is triggered by a specific chemical signal and then the movements of all the cells are synchronized and accelerated.[7] The aggregation process is much like the homogenous collective motion, while before synchronization and acceleration, the assumption of homogeneity may not be suitable for the searching period. In recent research, the inhomogeneity of the diffusion for acetylcholine receptors is reported,[8] suggesting the assumption of homogeneity is not straightforward. Here, we focus on the locomotion activity in the searching period. Anomalous dynamics have been put forward in this region.[9–12] Meanwhile, the search strategy adopted by cells attracted much attention in recent decades.[13–15]
To understand the statistical strategy adapted by DD cells, we analyzed the cell trajectories in the searching process mentioned above. We wonder whether the assumption of homogeneity is still suitable for this system. Our experimental results suggest the cell culture is inhomogeneous. Cells with different diffusion constant exist simultaneously in the cell culture, despite the fact that all cells are divided from the same spore. Starting from the inhomogeneity, we proposed a simple model to describe the searching strategy. In this model, cells have their own diffusion velocity and exhibit different distributions of velocity fluctuations. Meanwhile, the distribution of cell velocities follows an exponential tail. This model gives us a new perspective and method to find the optimal strategy in order to explore the space. Furthermore, we present a straightforward test of our model by numerical calculation.
KAx-3 cells of Dictyostelium Discoideum (DD) were used in our experiments and were obtained by the following procedures, similar to the procedures given in Ref. [16]. Cells were plated on the top of a solid medium with nutrition (20-g agar, 10-g glucose, 10-g trytone, 1-g yeast extract, 1.9-g KH2PO4, 0.78-g K2HPO4
In the experiment, we obtained the DD cell trajectories from consecutive images of the cell culture with spatial resolution of
Figure
Figure
We classified trajectories into five bins with equal width from the slowest velocity to the fastest velocity. Details are in the caption of Fig.
Figure
With the help of empirical equation (
Physically, equation (
Furthermore, to thoroughly understand the significance of the exponential tail of
Finally, one obtains
Equation (
Now we are able to review our understanding of the dynamics of cell motion. Previous studies believed that the cell motion was governed by random motion with an unclear form. We suggest understanding this system in the following steps. First, for an individual cell, the velocity fluctuates around a constant value
To summarize, with the help of a digital camera having spatial resolution of 5138×3456, we analyzed migrating trajectories of cells, and found the exponential tail of the probability distribution function of the cell velocity, which stems from the inhomogeneous weight number of cells for different diffusion motion. We believe this simple model is significant in understanding the random motion of eukaryotic cells, and also in finding the optimal strategy to explore the space.
We thank Prof. Lian-Sheng Hou for the supply of KAx-3 cell samples.
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