Somatic cells protect stem cells from a lethal environment

This model examines the ability of somatic-cell progeny to protect their parent stem cells in an otherwise stochastically lethal environment. From the stem cell's perspective, environmental lethality is an extreme form of environmental unpredictability, i.e. variational free energy. The model thus examines the general hypothesis that somatic cells protect their parent stem cells from the variational free energy of the environment by providing a "safe" predictable environment in which stem cells can maintain homeostasis.

The model depicts an environment (red background) that varies from low potential lethality on the left to high potential lethality on the right. A run begins with stem cells (green) seeded at random locations with an overall density of 5%. The stem cells divide to produce daughter stem cells, or if selected, somatic cells at a resource-dependent rate. If somatic progeny are selected, these are depicted as blue. Both stem and somatic cells can protect their immediate neighbors from environmental lethality, but to different extents. Because they do not divide, the presence of neighboring somatic confers a resource-usage advantage on neighboring stem cells, allowing them to divide faster. Cell division and hence higher resource usage is assumed to increase susceptibility to environmental lethality; therefore somatic cells are more resistant to the environment than stem cells.

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  0%       ←        Lethality       →       100%

Click "Reset" below to generate a new random start state.

Click "Step" to evolve by 1 time step; "Run" runs the model in 0.5 sec time steps; "Stop" stops this process.

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Set reproductive resource availability (1% - 100%).

Set probability (1% - 100%) for somatic-cell progeny.

Set probability (1% - 100%) for somatic-cell neighbor protecting locally against lethality.

Set resource-usage efficiency loss (1% - 100%) from stem-cell neighbor.

Set resource-usage efficiency gain (1% - 100%) from somatic-cell neighbor.

Set somatic-cell lethality resistance (1% -100%).

Stem and somatic cell counts by 10% lethality bin
Stem cells
Somatic cells

Model structure

The 60 X 30 cell grid shown has cylindrical topology: cells along the top and bottom borders are neighbors, but cells on the left and right borders are not. This topology gives cells in the interior of the grid four abutting neighbors, cells on the top and bottom edges three neighbors, and cells on the left and right margins only two neighbors. Note that the word "cell" here is used to indicate a grid cell in the model, not a biological cell. The terms "stem cell" and "somatic cell" are used for biological cells.

Environmental lethality increases from left (dark red background) to right (bright red background) in 60 equal increments. Stem cells respond to environmental lethality by dying before dividing, with the probability of dying determined by the lethality of the four nearest-neighbor grid cells. Somatic cells protect neighboring stem or somatic cells against lethality by an adjustable amount; the default value, 50% corresponds to full protection of two faces of the neirghboring cell, i.e. to a somatic daughter that partially "wraps around" the neighboring cell to shield it from the external environment. Somatic cells also respond to environmental lethality by dying, with a default resistence of 20%.

The grid is initially seeded with stem cells at 5% density. On each time step, both stem and any daughter somatic cells calculate the probability of dying based on the local environmental lethality and the presence of protective neighbors. Surviving stem cells then calculate a resource-dependent probability of dividing. Stem cells compete for reproductive resources; hence neighboring stem cells decrease each other's reproductive rate. Somatic neighbors do not divide and hence free up local reproductive resources; hence somatic neighbors increase the reproductive rate of neighboring stem cells. If somatic progeny are enabled, each stem cell's probability of dividing to produce a somatic-cell daughter is calculated first; if no somatic daughter is produced, the probability of dividing to produce a stem-cell daughter is calculated. Cell division is allowed only if at least one neighboring grid cell is unoccupied; this models the relative rigidity of the somatic body compared to the open environment.

Model behavior

If somatic progeny are not enabled, stem cells only reproduce other stem cells. At default parameter settings, the growing stem cell population stably inhabits only the left, lower-lethality half of the environment; while new stem cells constantly invade the higher-lethality half of the environment, all such cells eventually die. Reducing the resources available for reproduction decreases the density of the stem population; reducing the ability of stem cells to protect each other reduces its range.

When somatic progeny are enabled with default parameter settings, they are produced preferentially. As stem cells are not allowed to replace somatic cells, the population of stem cells in the left, lower-lethality half of the environment is much lower - roughly half in a typical run - than if somatic cells are not enabled. Most stem cells in the right, high-lethality half of the environment die in the first or second generation, but enough survive that stem cells and their protective somatic progeny are able to colonize the higher lethality half of the environment. Increasing the protective power and lethality resistance of somatic cells leads to smaller but more numerous colonies in the high-lethality half of the environment. If an individual somatic cell fully protects its parent, even the highest-lethality part of the environment can be colonized.

Copyright © 2018 Chris Fields
Non-commercial re-use permitted; please cite:
C. Fields and M. Levin
Somatic Multicellularity as a Satisficing Solution to the Prediction-Error Minimization Problem
In review.