Entropy, Ergodicity, and Stem Cell Multipotency

Populations of mammalian stem cells commonly exhibit considerable cell-cell variability. However, the functional role of this diversity is unclear. Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. We propose an information-theoretic interpretation of these results that views cellular multipotency as an instance of maximum entropy statistical inference.

Figure 1

Model fit to experimental data. Model simulations using the same estimates of $\psi (x)$ and $\sigma$ are shown against the three independent experimental time series; simulations differ only in the experimentally prescribed initial conditions. Data are in dark red and the fitted model is in black. The potential $\psi (x)$ was estimated numerically via Eq. (2) using aggregated data from the final time point.

Figure 2

(Left panel) Convergence to equilibrium with respect to the free energy. Exponential convergence was observed from all three initial conditions for large time, in accordance with Eq. (1). First passage time (FPT) distributions in the Sca1 low (middle panel) and high (right panel) states. The FPT distributions $F_X(x_X,t)$ starting at the local minima of the potential $\psi (x)$ are shown in black; the expected FPT distributions $⟨F_X⟩(t)$ averaging over all of the initial conditions in $X\in \{L,H\}$ are shown in blue.

Figure 3

(Left panel) Entropy of the stationary distribution relative to the maximum entropy distribution over the $\alpha \gamma$ plane. The empirical distribution is marked with a magenta cross, and the maximum entropy distribution ${\rho }_{\infty }^{\max }(x)$ is marked with a green circle. Color shows the percentiles. (Right panel) Minimum MFPT $\tau$ in the vicinity of the maximum entropy distribution (the dashed box in the left panel). The critical lines separating the bistable and monostable regimes are shown in blue. The empirical distribution lies in the small region of the $\alpha \gamma$ plane that is both close to critical and of high entropy. Color shows dimensionless time.