A computational model of stem cells' decision-making mechanism to maintain tissue homeostasis and organization in the presence of stochasticity

Abstract

The maintenance of multi-cellular developed tissue depends on the proper cell production rate to replace the cells destroyed by the programmed process of cell death. The stem cell is the main source of producing cells in a developed normal tissue. It makes the stem cell the lead role in the scene of a fully formed developed tissue to fulfill its proper functionality. By focusing on the impact of stochasticity, here, we propose a computational model to reveal the internal mechanism of a stem cell, which generates the right proportion of different types of specialized cells, distribute them into their right position, and in the presence of intercellular reactions, maintain the organized structure in a homeostatic state. The result demonstrates that the spatial pattern could be harassed by the population geometries. Besides, it clearly shows that our model with progenitor cells able to recover the stem cell presence could retrieve the initial pattern appropriately in the case of injury. One of the fascinating outcomes of this project is demonstrating the contradictory roles of stochasticity. It breaks the proper boundaries of the initial spatial pattern in the population. While, on the flip side of the coin, it is the exact factor that provides the demanded non-genetic diversity in the tissue. The remarkable characteristic of the introduced model as the stem cells' internal mechanism is that it could control the overall behavior of the population without need for any external factors.

Figure 1

The model’s regulatory networks together with their corresponding force-field representations. The nullclines are drawn in red and black (a) A bi-stable regulatory network. (b) The stem cell’s force-field representation. (c) A tristable regulatory network. (d) The progenitor cell’s force-field representation. (e) The signalling molecules’ bi-stable regulatory network. (f) The signalling molecules’ force-field representation. Two critical zones around two attractors in the field are zoomed in in two red frames.

Figure 2

Hypothetical dish as a main scene for our system dynamics, and the filters representation for scoring algorithm. (a) the hypothetical dish is occupied with four types of cells, S (cyan), P (green), A (yellow), and B (red). Yellow, and red triangles represent signalling molecules namely, $S_1$, and $S_2$, produced by cell types A and B, respectively. (b,c) Filters representing template, and penalty matrices corresponding to the perfect borders of the population initial pattern and the valid territory of the entire dish, respectively.

Figure 3

The system behaviour in the absence/presence of inter-cellulat interactions. (a,d) The initial state of the system. (b,e) The final states of the system in the absence/presence of signalling molecules, in row. (c,f) The corresponding score diagrams. (g) The maintenance of fours cell types’ abundance through time.

Figure 4

The system behaviour for different simulations. The first, and second rows represent the initial, an final states of the system, respectively. The corresponding score diagram of five mentioned simulations are shown in the last row. (a) Five different simulations with the dish radius of 50, but different inner disk size, 5, 15, 25, 35, and 45 from left to right. (b) Five different simulations with the dish radius of 50, but different inner disk size, 5, 15, 25, 35, and 45 from left to right.

Figure 5

The system behaviour for rectangle shape, and triangle shape dishes. The length of the middle area is always the half of the dish side length. The first, and second rows represent the initial, an final states of the system, respectively. The corresponding score diagram of five mentioned simulations are shown in the last row. (a) Five different simulations starting with five rectangle shape dishes of side length, 10, 30, 50, 70, and 100 from left to right. (b) Five different simulations starting with five triangle shape dishes of side length, 10, 30, 50, 70, and 100 from left to right.

Figure 6

The system behaviour in the face of more complex initial spatial patterns. (a,d) The initial state of the system. (b,e) The final states of the system. (c,f) The corresponding score diagrams.

Figure 7

The system behaviour in the face of injuries. The first, and second rows represent the initial, an final states of the system, respectively. The corresponding score diagram of five mentioned simulations are shown in the last row. (a) Injuries in different regions in the population. (b) Injuries with different regions size.