Cell fusion through slime mould network dynamics

Abstract

Physarum polycephalum is a unicellular slime mould that has been intensely studied owing to its ability to solve mazes, find shortest paths, generate Steiner trees, share knowledge and remember past events and the implied applications to unconventional computing. The CELL model is a cellular automaton introduced in Gunji et al. (Gunji et al. 2008 J. Theor. Biol.253, 659-667 (doi:10.1016/j.jtbi.2008.04.017)) that models Physarum's amoeboid motion, tentacle formation, maze solving and network creation. In the present paper, we extend the CELL model by spawning multiple CELLs, allowing us to understand the interactions between multiple cells and, in particular, their mobility, merge speed and cytoplasm mixing. We conclude the paper with some notes about applications of our work to modelling the rise of present-day civilization from the early nomadic humans and the spread of trends and information around the world. Our study of the interactions of this unicellular organism should further the understanding of how P. polycephalum communicates and shares information.

Keywords: cell fusion; network dynamics; slime mould.

Figure 1.

Node 1 is the source node and node 6 is the sink node. The number on each edge represents the length of that edge.

Figure 2.

The first two steps in a CELL model on a 5 × 5 grid.

Figure 3.

The last two steps in a CELL model on a 5 × 5 grid.

Figure 4.

An example image from the implementation of the described CELL algorithm.

Figure 5.

An example image from the implementation of the CELL algorithm with active zones for tree formation.

Figure 6.

The first two steps in a multi-agent model on a 6 × 6 chemoattractant map. The agent at the grey box in (a) moves forwards and deposits 5 on the chemoattractant map.

Figure 7.

The chemoattractant map after a 3 × 3 mean filter with a dampening factor is applied to the map shown in figure 6b.

Figure 8.

Images from a multi-agent model implementation.

Figure 9.

Graph as in figure 1 but without the edge between nodes 3 and 4. The numbers on each edge represent the length of that edge.

Figure 10.

The spawn of two CELLs at (15, 20) and (35, 20), with parameters: size = 15, s = 3, n = 1000.

Figure 11.

In this image, the two cells have just contacted for the first time.

Figure 12.

Graph of the 1025 trials of each distance: the distance between the centre of the spawn points is on the x-axis, and the number of iterations until they merge is on the y-axis.

Figure 13.

The 1025 trials of each distance: the distance between the centre of the spawn points is on the x-axis and the number of iterations until they merge is on the y-axis.

Figure 14.

To deal with the heavily skewed data as evidenced by the scatter and box plots, we trim 10% from both the upper and lower ends of the data. We then compute the trimmed mean. We use the scipy.optimize.curve_fit function to fit these data to a linear function (equation (3.1)) with the values m = 21 892.74674907 and b = −354 967.6942326. This gives an r²-value of 0.970675949.

Figure 15.

Three cells of size 15, labelled from left to right as 1, 2 and 3. The distance between cells 1 and 2 (distance 1) is 27 and between cells 2 and 3 (distance 2) is 23.

Figure 16.

Using the Python package matplotlib, we create a three-dimensional scatterplot. On the xy plane are the distances between the three cells and on the z-axis is the number of iterations it takes for two cells to combine.

Figure 17.

Using the Python package matplotlib, we compute the mean of each set of distances. For each distance, we have three bars: one for each of the possible two CELLs combining.

Figure 18.

Using the Python package matplotlib, we compute the probability that, for a given set of distances between CELLs, each combination of two cells (1 2, 1 3, 2 3) will be the ones that combine first.

Figure 19.

Using the Python package matplotlib, we create a contour plot. On the xy plane are the distances between the three cells; the colour gradient represents the number of iterations it takes for two cells to combine.

Figure 20.

We compute the 10% trimmed mean of each cell size. We then fit an exponential curve to the data.

Figure 21.

We compute the 10% trimmed mean of each cell size. We then fit an exponential curve to the data.

Figure 22.

We compute the 10% trimmed mean of the 1000 trials. We then attempt to fit the data to the exponential curve (equation (3.2)) with values a = 0.10144046, b = 0.9192343 and c = 0.0046737.

Figure 23.

Two cells of size 15 and 20, respectively. After 5000 iterations, the mixing index is 0.726373742358510.

Figure 24.

Here, we have two CELLs of size 15 (a) and 23 (b). The CELLs have just been spawned so that they are barely touching each other at the centre of the image.

Figure 25.

We compute the 10% trimmed mean of the mean mixing index. We fit these data to an exponential function (equation (3.2)) pictured in blue with values a = 0.67188919, b = 0.99891735 and c = 0.21859742.

Figure 26.

We graph the data from our 1000 trials of each size ranging from 15 to 49 (odd only) using a scatterplot and boxplot.

Figure 27.

We compute the 10% trimmed mean of the mean mixing index. We fit these data to a logistical function (equation (3.3)) pictured in blue. The parameters are L = −0.52639764, k = 0.52639764, x₀ = 34.83393314 and b = 0.96196691.