Figure 1.
A minimal model of multilineage commitment.
A multipotent progenitor expresses lineage-specific receptors (RA and RB) and inactive transcription factors (ITFA and ITFB) at low levels with the potential to differentiate into lineage A or B. Addition of ligand (LA, LB) leads to complex formation (CA, CB), which activates the corresponding lineage-specific transcription factor. Active TF (ATFA, ATFB) binds to the response elements present upstream of the transcription factor and receptor genes and induces two positive feedback loops (dashed green arrows). To account for cross-antagonism between the lineages, the active transcription factors are modeled to competitively inhibit the activation of the positive feedback loops in the other lineage (dashed red lines). F1A and F2A denote the respective strengths of the transcription factor and receptor feedback loops for lineage A; similarly, F1B and F2B represent the corresponding feedback strengths for lineage B. Inhibitor dissociation constants KIA and KIB denote the inhibitory effect of A on B and B on A, respectively.
Figure 2.
Effect of the positive feedback loops on the on-state ATFA levels.
A. Strengths of the autofeedback loops (F1A and F1B) are varied for both lineages and the steady-state values of ATFA are plotted for the no inhibition condition (KIA = KIB = ∞), keeping the strengths of the receptor feedback (F2) constant. B. Strengths of the receptor feedback loops (F2A and F2B) are varied and the values of ATFA are plotted for the no inhibition condition, keeping the strengths of the autofeedback (F1) constant. C. Same as part A except with moderate inhibition (KIA = KIB = 400 molecules). D. Same as part B except with moderate inhibition. E. Cross-sectional plot from C for various values of F1A. F. Cross-sectional plot from D for various values of F2A. G. Same as part A except with strong inhibition (KIA = KIB = 50 molecules). H. Same as part B except with strong inhibition. No inhibition and strong inhibition give rise to only on or off populations, whereas moderate inhibition can generate a third intermediate population.
Figure 3.
Effect of ligand on the on-state ATF levels.
A. Phase plot showing the steady-state ATFA levels (blue – low, yellow – medium, red – high) when LA and LB values are varied. B. Phase plot showing the steady-state ATFB levels when LA and LB values are varied. Low LA and low LB do not commit the uncommitted cell to either lineage (overlapping blue region in panels A and B). Low LA and high LB values commit the cell to lineage B (blue region in panel A and red region in panel B). High LA and low LB values commit the cell to lineage A (red region in panel A and blue region in panel B). High LA and high LB commit the cell to the bipotent state (overlapping yellow region in panels A and B). Steady-state response plots: C. Increasing LA from 0, with LB constant at 300, abruptly switches the cell from the committed B state to the bipotent state (increase in ATFA to intermediate level) after reaching a threshold concentration (solid red line). After achieving the bipotent state, decreasing LA to sub-threshold values does not immediately switch the cell state, suggesting significant memory in the system (dotted red line). D. Increasing LA from 0, with LB constant at 300, decommits the cell to the bipotent state (decrease in ATFB to intermediate level) after reaching the threshold concentration (solid blue line). After achieving the bipotent state, decreasing LA to sub-threshold values does not immediately switch the cell state, again suggesting significant memory (dotted blue line). E. Increasing LA from 0, with LB constant at 100, abruptly switches the committed B cell to the bipotent state (increase in ATFA to intermediate level) and then again to the committed A state (increase in ATFA to high level) after reaching the corresponding threshold concentrations (solid red line). After achieving the bipotent state or the committed state, decreasing LA to sub-threshold values does not immediately switch the cell response, suggesting significant memory in both states (dotted and dot-dash red line). F. Increasing LA from 0, with LB constant at 100, decommits the cell to the bipotent state (decrease in ATFB to intermediate level) and then again to the committed lineage A state (decrease in ATFB to low level) after reaching the corresponding threshold concentrations (solid blue line). After achieving the bipotent state or the committed lineage A state, decreasing LA to sub-threshold values does not immediately switch the cell response, suggesting significant memory in both states (dotted and dot-dash blue line). Plots C and D show bistable expression of ATFA and ATFB; plots E and F exhibit both bistable and tristable expression of the transcription factors.
Figure 4.
External regulation of stochastic transitions.
Three different LA|LB combinations (0|350, 100|250, and 175|175) were run using the stochastic version of the model with no, moderate, or strong inhibition conditions and the system was allowed to reach steady state. ATFA and ATFB values from 10,000 runs for each condition are plotted here as three-dimensional histograms. With strong inhibition, the system cannot achieve the intermediate, bipotent state that is seen with moderate inhibition. When induced with only one ligand (e.g., 0|350), the initial population, for all inhibition conditions, commits predominantly to the lineage corresponding to that ligand. When the uncommitted state is stimulated with equal values of ligand (175|175), the no inhibition condition primarily results in a state that corresponds to high activation of both transcription factors (unlikely to be a biologically relevant state for cell-commitment decisions); the strong and the moderate inhibition conditions result in significant population of all of the available states except the uncommitted state. When one ligand value is higher (e.g., 100|250), in the presence of inhibition, the majority of the cells committed to the lineage corresponding to the higher ligand concentration. The number next to each individual population denotes the percentage of the total population when treated with the given combination of LA and LB.
Figure 5.
Time trajectories during lineage commitment.
A. Phase plot of total transcription factor (ITF+ATF) for the four steady-state populations (uncommitted, A, B, and bipotent). B. Phase plot of active transcription factor (ATF). C. Time trajectories for ATFA in panel B for the transition from the uncommitted cell to committed A state (blue line) and bipotent state (orange line) and from the bipotent state to committed A state (green line). The error bars represent the standard deviation of the mean. The red line shows the level of ATFB as the bipotent cell transitions to the committed A state. D. Phase plot of total receptor (R+C). E. Phase plot of active complex (C). F. Time trajectories for CA in panel E for the transition from the uncommitted cell to committed A state (blue line) and bipotent state (orange line) and from the bipotent state to committed A state (green line). The error bars represent the standard deviation of the mean. The red line shows the level of CB as the bipotent cell transitions to the committed A state. In the phase plots, the arrows indicate the direction of commitment (averaged over 200 stochastic runs each): from the uncommitted state, the three possible commitment trajectories lead to pure lineage A, pure lineage B, and the bipotent state. In separate simulations starting with the bipotent state and with initial ligand concentrations sufficient to destabilize this state, the two possible commitment trajectories lead to pure lineage A and pure lineage B. Each trajectory has several nodes and the number at each node denotes the average time (in hours) it takes to reach the node from the initial state. Each black dot in A, B, D and E represents the endpoint (100,000 min) of an individual stochastic trajectory. The initial conditions for the trajectories are provided in the Supplementary Text S1.
Figure 6.
Comparison of multilineage commitment model to experimental data.
A. The classical model of hematopoiesis is given here as a branching diagram showing the differentiation paths from the common myeloid progenitor (CMP) to four distinct myeloid lineages (megakaryocyte, erythrocyte, neutrophil, and macrophage) via bipotent progenitors (GMP – granulocyte/macrophage progenitor and MEP – megakaryocyte/erythrocyte progenitor). Potential non-canonical routes of commitment, bypassing the bipotent state, are shown as gray arrows. B. Stochastic simulations of total receptor levels under strong competitive inhibition. Light green and red lines indicate the individual trajectories from the uncommitted cell to lineages A and B, respectively. The dark red and green lines denote the averaged trajectories of all stochastic runs. C. Stochastic simulation for total receptor levels under moderate competitive inhibition condition. Light blue, light red, and gray lines indicate the individual trajectories from the uncommitted cell to A, B, and the bipotent state, respectively. The dark blue line denotes the average value of all stochastic runs that commit to either lineage A or the bipotent state; the dark red line denotes the average value of all stochastic runs that commit to either lineage B or the bipotent state. D. Trajectories from microarray data showing upregulation of EPOR and GCSFR during erythrocyte (red) and neutrophil (green) commitment from the CMP, respectively. E. Trajectories from microarray data showing upregulation of TPOR and GCSFR during megakaryocyte (blue) and neutrophil (green) commitment from the CMP, respectively. F. Trajectories from microarray data showing upregulation of EPOR and TPOR during erythrocyte (red) and megakaryocyte (blue) commitment from the CMP. The trajectories in D–F represent the average of the multipotent, bipotent, and mature cells for a single lineage (see Supplementary Table S4), thus enabling a direct comparison to the model simulations. The error bars in D–F show the standard error of the mean. The symbols in F denote the 3-day (†, *) and 7-day (‡, #) time points during erythrocyte and megakaryocyte differentiation from the CMP, respectively. Statistical analysis was performed to deduce positive correlation in receptor pair upregulation by comparing the overall slope of each trajectory (inverted to lie along the x-axis, if appropriate) at both the 3-day and 7-day time points to a value of zero (no correlation) by a one-sample, one-tailed t-test (p-values: † (0.027), * (0.009), ‡ (0.060), # (0.008)).
Figure 7.
Proposed paradigm for hematopoiesis.
Extrinsic (instructive) and intrinsic (stochastic) cues can both play roles in commitment of progenitor cells. In addition to classical pathways of commitment (solid arrows), bypass mechanisms have been reported for HSCs [4] (dashed green arrow) and our model suggests that this may be possible for multipotent progenitors as well (dashed purple arrow).