Multistability and predominant hybrid phenotypes in a four node mutually repressive network of Th1/Th2/Th17/Treg differentiation

Abstract

Elucidating the emergent dynamics of cellular differentiation networks is crucial to understanding cell-fate decisions. Toggle switch - a network of mutually repressive lineage-specific transcription factors A and B - enables two phenotypes from a common progenitor: (high A, low B) and (low A, high B). However, the dynamics of networks enabling differentiation of more than two phenotypes from a progenitor cell has not been well-studied. Here, we investigate the dynamics of a four-node network A, B, C, and D inhibiting each other, forming a toggle tetrahedron. Our simulations show that this network is multistable and predominantly allows for the co-existence of six hybrid phenotypes where two of the nodes are expressed relatively high as compared to the remaining two, for instance (high A, high B, low C, low D). Finally, we apply our results to understand naïve CD4⁺ T cell differentiation into Th1, Th2, Th17 and Treg subsets, suggesting Th1/Th2/Th17/Treg decision-making to be a two-step process.

Fig. 1. Transcriptomic analysis showing enrichment of Th1, Th2, Th17 and Treg signatures corresponding to specific cell type.

A Schematic showing the regulatory network among the regulators of Th1 (T-bet), Th2 (GATA3), Th17 (RORγt), and Treg (Foxp3), forming a toggle tetrahedron. B Quantification of difference in levels of i) Th1, ii) Th2, iii) Th17 and iv) Treg gene signature enrichment scores across Th1, Th2, Th17, Treg and hybrid Th1/17 cells (GSE135390). C i) Scatterplot showing different cell types on the Th-Treg gene signature enrichment score plane. ii-iv) Same as i) but for Th1-Treg plane, Th2-Treg place and Th17-Treg plane (GSE135390). Pearson’s correlation coefficient values are shown. *: p value < 0.05, **: p value < 0.01; ***: p value < 0.001 for Student's two-tailed t-test.

Fig. 2. Characterization of phenotypes enabled by a toggle tetrahedron.

A Frequency of monostable, bistable, tristable, tetrastable, pentastable solutions, and more than 5 co-existing states in the toggle tetrahedron, shown as a pie chart. B Heatmap showing the solutions obtained via RACIPE and nomenclature shows nodes with high (low) expression levels in an uppercase (lowercase) fashion. C Frequency distribution of states (all solutions taken together) with the most frequent ones highlighted being – {aBcD}, {abCD}, {AbcD}, {aBCd}, {ABcd} and {AbCd}. D Frequency distribution of 15 possible bistable combinations. For the panels C & D, RACIPE data was collected from three independent runs. * shows p < 0.05 for Student's two-tailed t-test.

Fig. 3. State-space analysis of toggle tetrahedron using DSGRN.

A Frequency of all states (i, top) and frequency of bistable states (ii, bottom) for the DSGRN randomly sampled parameters (blue) and all 6561 strict monotone Boolean parameters (orange). Note that four sets of 10,000 parameters were sampled, the black line on the blue bars indicate the standard deviation in frequency between these sets. B Simple linear regression was used to show the relationship between RACIPE and sampled DSGRN frequencies (black dots) for all states (i, top) and bistability (ii, bottom). The line of best fit is indicated by the blue line, while the black line represents the line y = x. C Same as (B) for RACIPE and strict Boolean frequencies. D Same as (B) with strict Boolean and sampled DSGRN frequencies. Notice that when the blue line slope and intercept are close to the black line, as we see in C, indicates that the frequencies between the pairs are very similar.

Fig. 4. Bifurcation analysis of representative parameter sets corresponding to the non-mirror bistable states.

A Bifurcation diagrams of four representative cases (each column denotes a different parameter set – P1-P4) with each row showing the expression levels of the four nodes A–D. Dotted vertical line in each case marks the RACIPE parameter value of the corresponding bifurcation parameter. B Stochastic simulations showing switching between the bistable states (only the two nodes switching between ‘high’ and ‘low’ are shown, the nodes always expressed ‘high’ or always ‘low’ are not shown). Parameter sets P1, P2, P3 and P4 are provided in Supplementary Data 2.

Fig. 5. Link Strength Analysis of monostable and bistable states for toggle tetrahedron.

A i) Schematic showing the links that are expected to be stronger than their counterparts for the state {abcD} ii) Frequency of dominance of all six pairs of mutually inhibitory links between any two nodes in a toggle tetrahedron, for all parameter sets corresponding to the case of monostable {abcD}. B Same as A) but for the monostable state – {abCD}. C Same as A) but for the non-mirror bistable state combination – {AbcD, aBcD}. D Same as A) but for the mirror bistable state combination – {ABcd, abCD}. In C and D panels, the nodes that switch between the two states are written as X(Y), where X and Y can switch.

Fig. 6. Features unique to the toggle tetrahedron topology.

A Frequency of monostable, bistable, tristable and other multistable states for TTr, TTr + SI and TTr + SA. B Scatterplot showing the JSD value between the frequency distribution graphs of the reference network (TTr) and the network specified by the number of inhibiting edges swapped (on x-axis) when all steady states are taken together. C i) Schematic representing how a TTr network is embedded in a larger random network. ii) Sum of the frequencies of all the six ‘double-positive’ states for Boolean simulations of networks of varying sizes and densities. iii) Fraction of sum of frequencies of all the four ‘single-positive’ states (4 SP) over the sum of frequencies of all the six ‘double-positive’ states (6 DP) for Boolean simulations of networks of varying sizes and densities. Inset shows a zoomed in version with the y-axis range – (0,3).

Fig. 7. Schematic representing the two-step differentiation enabled by the toggle tetrahedron.

(left) CD4 + T-cells can acquire hybrid or ‘double-positive’ states and differentiate into a single-positive state, as enabled by dynamics of toggle tetrahedron among T-bet, GATA3, RORγt, and Foxp3 (right).