Figure 1.
A Diagram of Serial Differentiation
The series includes stem cells (stage 0, in white), TACs (in gray), and finally, terminally differentiated cells (stage 3, in black). Stem cells divide asymmetrically with one daughter rejoining the stem cell compartment and one daughter differentiating (black arrows), unless the stem cell population is below homeostatic levels, in which case both daughter cells become stem cells (gray arrow). If there is an overabundance of stem cells, both daughter cells will differentiate (dotted arrow). TACs divide symmetrically so that both daughter cells advance to the next differentiation stage. Thus, every cell division outside the stem cell compartment entails differentiation into the next downstream stage, eventually ending in the terminally differentiated cells, which are purged from the tissue (e.g., sloughing of the outer layer of the skin, or the upper cells of an intestinal crypt into the lumen of the gut).
Figure 2.
Frequency of Fixation (Mutant Reaches >90% of the Cell Population) for Mutations Affecting Cell Division Rate
Frequency of fixation in nondifferentiating populations (filled circles), stem cells (triangles), and TACs (squares) with standard error bars. Because they did not vary, results for all three transient amplifying stages are pooled.
Figure 3.
Frequency of Fixation (Mutant Reaches >90% of Cell Population) for Mutations Affecting Cell Mortality Rate
Frequency of fixation when introduced into nondifferentiating populations (filled circles), stem cells (triangles), and TACs (squares). Bars show standard errors. Because they did not vary, results for all three transient amplifying stages are pooled. Values on horizontal axis show mutant cell's value of d relative to initial value of 0.05. Mutant values of d thus ranged from (0.05 − 100% = 0) to (0.05 + 20% = 0.06).
Figure 4.
Kaplan-Meier Curves for the Probability that a Population of Cells Doubles Its Average Growth Rate as a Function of Time
Each curve is labeled with the number of differentiation stages in the model (1 = self-duplication with no differentiation).
Figure 5.
Kaplan-Meier Curves for the Probability that a Population of Cells Halves Its Average Mortality Rate as a Function of Time
Each curve is labeled with the number of differentiation stages in the model.
Figure 6.
The Probability of Doubling the Population Average Growth Rate as a Function of Time, Asymmetric or Symmetric Differentiation, and Five or Six Differentiation Stages in the Models
Models with asymmetric differentiation evolve more quickly and are therefore more susceptible to pathologies of somatic evolution (RR = 1.56, 95% CI: 1.41–1.73, p < 0.001).
Figure 7.
The Probability That the Average Growth Rate of the Population Doubles as a Function of Time, Number of Differentiation Stages (Six or Seven), and Self-Renewal by TACs Versus Serial Symmetric Differentiation
The tissues with self-renewing TAC stages evolve more quickly than the tissues with strict serial differentiation, where, with the exception of the stem cells, both daughter cells of a mitosis differentiate into the next differentiation stage. TACs, dashed lines; serial symmetric differentiation, solid lines.
Figure 8.
Frequency of Fixation by Mutations Affecting Cell Division in Nondifferentiating Populations, Under Serial Differentiation with Self-Renewal (n = 4 Non-Stem Stages) for Stem Cells, Transient Amplifying Stages Dividing Symmetrically, and Transient Amplifying Stages Dividing Asymmetrically
Each data point represents at least 500 trials with standard error bars. Nondifferentiating populations, filled circles; serial differentiation with self-renewal for stem cells, triangles; transient amplifying stages dividing symmetrically, squares; transient amplifying stages dividing asymmetrically, diamonds.
Figure 9.
Frequency of Fixation by Mutations Affecting Cell Mortality in Nondifferentiating Populations, Under Serial Differentiation with Self-Renewal for Stem Cells, Transient Amplifying Stages Dividing Symmetrically, and Transient Amplifying Stages Dividing Asymmetrically
Each data point represents 500 trials with standard error bars. Cells that cannot apoptose (mortality change = −1.0) may still differentiate into the fully differentiated stage and stop dividing. Nondifferentiating populations, filled circles; serial differentiation with self-renewal for stem cells, triangles; transient amplifying stages dividing symmetrically, squares; transient amplifying stages dividing asymmetrically, diamonds.
Figure 10.
Frequency of Fixation of a Differentiation Knockout Mutant as a Function of Time
The model was run for 500 timesteps to allow the cell populations to equilibrate before a mutant cell that could not differentiate was injected. Those mutant clones that did not go extinct in the next 100 timesteps expanded rapidly. Mutants injected into the stem cell compartment reached fixation more frequently than mutants injected into a TAC compartment. Each data point represents 500 trials with standard error bars.
Figure 11.
Kaplan-Meier Curves for the Time Until Exponential Cell Growth (Cancer) Were Detected Due to a Spontaneous Differentiation Knockout Mutation
The solid line represents 500 trials during which differentiation loss-of-function mutations occurred at a rate of 10−4 per cell division. The dotted line represents the Kaplan-Meier curve for 500 trials in which no differentiation mutations were allowed. A differentiation knockout mutation can cause exponential cell population growth in any nonterminal differentiation stage driven by the feedback loops that normally maintain tissue homeostasis.
Figure 12.
Cell Population Size in Response to Stochastic Occurrence of Differentiation Knockout Mutations
The total population size for more than 400 simulation timesteps is pictured here for ten different runs in different colors. Color-matched arrows indicate when a new differentiation knockout mutation occurred and when the resulting mutant clone went to extinction. Note that the new differentiation knockout mutations (if not lost from the population) develop into cancer with a lag time of between 70 and 150 timesteps. The stochasticity of the process is illustrated in one run (in yellow) that never progressed to cancer even though it acquired and lost several differentiation knockout mutations. In each run, homeostasis of cell numbers can be seen up until the appearance of a differentiation knockout mutation.
Table 1.
Standard Parameter Values