Quantifying cell fate decisions for differentiation and reprogramming of a human stem cell network: landscape and biological paths

Abstract

Cellular reprogramming has been recently intensively studied experimentally. We developed a global potential landscape and kinetic path framework to explore a human stem cell developmental network composed of 52 genes. We uncovered the underlying landscape for the stem cell network with two basins of attractions representing stem and differentiated cell states, quantified and exhibited the high dimensional biological paths for the differentiation and reprogramming process, connecting the stem cell state and differentiated cell state. Both the landscape and non-equilibrium curl flux determine the dynamics of cell differentiation jointly. Flux leads the kinetic paths to be deviated from the steepest descent gradient path, and the corresponding differentiation and reprogramming paths are irreversible. Quantification of paths allows us to find out how the differentiation and reprogramming occur and which important states they go through. We show the developmental process proceeds as moving from the stem cell basin of attraction to the differentiation basin of attraction. The landscape topography characterized by the barrier heights and transition rates quantitatively determine the global stability and kinetic speed of cell fate decision process for development. Through the global sensitivity analysis, we provided some specific predictions for the effects of key genes and regulation connections on the cellular differentiation or reprogramming process. Key links from sensitivity analysis and biological paths can be used to guide the differentiation designs or reprogramming tactics.

Figure 1. The diagram for the stem cell developmental network including 52 gene nodes and their interactions (arrows represent activation and perpendicular bars represent repression).

The magenta node represent 11 marker genes for the pluripotent stem cell state, cyan nodes represent 11 marker genes for the differentiation state, and the yellow nodes represent genes activated by the stem cell marker genes. The solid black links represent the key links found by the global sensitivity analysis, and the octagon shape nodes represent key stem cell and differentiation markers found by global sensitivity analysis.

Figure 2. A bistable landscape picture for the stem cell network.

Parameters are specified as: (degradation), (repression), (activation), and diffusion coefficient . (A) Three dimensional landscape and dominant kinetic paths. The yellow line represents developmental path, and the magenta line represents reprogramming path. (B) Two dimensional dominant kinetic path and flux on the landscape. The white arrows represent the direction of flux, and the red arrow represent the direction of the negative gradient of potential energy.

Figure 3. Differentiation and reprogramming process represented by 313 nodes (every node denotes a cell state, characterized by expression patterns of the 22 marker genes) and 329 edges (paths).

The sizes of nodes and edges are proportional to the occurrence probability of the corresponding states and paths, respectively. Red nodes represent states which are closer to stem cell states in terms of gene expression pattern, and blue nodes represent states which are closer to differentiation states. The green and magenta paths denote dominant kinetic paths from path integral separately for differentiation and reprogramming. Here, we set a probability cutoff to decrease the number of states and paths, i.e. we only demonstrate the states and paths with higher probability. The largest red node (high NANOG/low GATA6/low CDX2) represents most major ES state (stem cell state), and the largest blue node (low NANOG/high GATA6/high CDX2) represents most major differentiation state. IM1 represents a intermediate state (low NANOG/low GATA6/low CDX2), and IM2 represents another intermediate state (high NANOG/high GATA6/high CDX2).

Figure 4. The barrier height and MFPT (mean first passage time) results when the activation strength , the repression strength as well as the noise level changes (Langevin dynamics).

(A)(B) show that when increases, stem cell state becomes more stable, the barrier for stem cell state (or the barrier for differentiation process ) increases, and the MFPT for differentiation process from stem cell state to differentiation state () increases. By contrast, When increases, differentiation state becomes less stable, the barrier for differentiation state (or the barrier for reprogramming process ) decreases, and the MFPT for reprogramming process from differentiation state to stem cell state () declines. (C)(D) show that when increases, the barrier for stem cell state (), the barrier for differentiation state (), the MFPT for differentiation process (), and the MFPT for reprogramming process () all increase. (E)(F) show that when noise level increases, the barrier for stem cell state (), the barrier for differentiation state (), the MFPT for differentiation process (), and the MFPT for reprogramming process () all decrease.

Figure 5. The differentiation and reprogramming trajectories on the landscape background.

axis represents activation strength . Three 2-dimensional landscape from up to down separately correspond to , and . Green color represents differentiation trajectory (from stem cell state to differentiation state), and magenta color represents reprogramming trajectory (from differentiation state to stem cell state).

Figure 6. Results of the global sensitivity analysis in terms of barrier height and MFPT (mean first passage time) when parameters are changed.

The results in (A) are for 6 repression links (named respectively as R1,R2,…,R6, see Table S2) based on the change of barrier heights (). The results in (B) are for 14 activation links (named respectively as A1,A2,…,R14, see Table S3) based on barrier heights. Blue bars represent the change of (barrier for differentiation process), red color represent the change of (barrier for reprogramming process). (C) and (D) separately show the corresponding results in terms of the change of MFPT (). Blue bars represent the MFPT change for differentiation process, and red bars represent the MFPT change for reprogramming process. (E) shows the corresponding global sensitivity for the knockdown of individual genes.

Figure 7. Global sensitivity for kinetic paths.

The developmental and reprogramming paths comparisons before and after mutations are shown separately for mutation 1 (increase link R1, i.e. the repression of CDX2 to OCT4)(A), mutation 2(increase link R2, i.e. the repression of OCT4 to GATA6)(B), mutation 3 (increase link R3, i.e. the repression of NANOG to GATA6)(C), and mutation 4 (increase link R4, i.e. the repression of GATA4 to GATA6)(D). The blue paths represent kinetic paths before mutations, and the magenta paths represent the kinetic paths after mutations. The blue arrows represent differentiation direction (from left stem cell attractor to the right differentiation attractor), and the magenta arrows represent reprogramming direction (from right attractor to left attractor). The diffusion coefficient .