Modeling reveals bistability and low-pass filtering in the network module determining blood stem cell fate

Abstract

Combinatorial regulation of gene expression is ubiquitous in eukaryotes with multiple inputs converging on regulatory control elements. The dynamic properties of these elements determine the functionality of genetic networks regulating differentiation and development. Here we propose a method to quantitatively characterize the regulatory output of distant enhancers with a biophysical approach that recursively determines free energies of protein-protein and protein-DNA interactions from experimental analysis of transcriptional reporter libraries. We apply this method to model the Scl-Gata2-Fli1 triad-a network module important for cell fate specification of hematopoietic stem cells. We show that this triad module is inherently bistable with irreversible transitions in response to physiologically relevant signals such as Notch, Bmp4 and Gata1 and we use the model to predict the sensitivity of the network to mutations. We also show that the triad acts as a low-pass filter by switching between steady states only in response to signals that persist for longer than a minimum duration threshold. We have found that the auto-regulation loops connecting the slow-degrading Scl to Gata2 and Fli1 are crucial for this low-pass filtering property. Taken together our analysis not only reveals new insights into hematopoietic stem cell regulatory network functionality but also provides a novel and widely applicable strategy to incorporate experimental measurements into dynamical network models.

Figure 1. Regulation of gene expression in the Scl-Gata2-Fli1 triad.

A. Scl, Gata2 and Fli1 form a triad module of TRs in the GRN of hematopoietic stem cells. The triad architecture consists of multiple positive feedback loops. Signals activating or deactivating the network are shown in magenta. Notch activates the transcription of Gata2 and Bmp4 activates the transcription of Gata2 and Fli1 by acting at the promoters. Gata1 binds to the Gata2 enhancer and downregulates Gata2 expression. B. The triad proteins regulate each other's transcription by acting at the Scl+19, Gata2-3 and Fli1+12 enhancers. These enhancers contain multiple binding sites that allow combinatorial control of gene expression. Only sites significantly affecting expression are shown C. Enhancer libraries similar to the one shown for Scl were constructed for all three proteins and subcloned with a suitable reporter in and in triad expressing cells to characterize the combinatorial control of gene expression. Typical results show the enhancement of gene expression from TR binding sites individually and in combination relative to enhancerless expression of the reporter.

Figure 2. Steady state signal-response analysis of the triad module to Notch, Bmp4 and Gata1 signals demonstrates irreversible bistability.

A. The action of Notch and Bmp4 at the promoters of switches the triad module from a low expression (OFF) state to a high expression (ON) state. Only Gata2 concentrations are shown for brevity. Solid lines represent stable and dotted lines represent unstable steady states. (Notch and Bmp4 concentrations are normalized by their respective binding affinities). Once the triad is in the ON state, the positive feedback loops in the modules architecture ensure that it remains in that state without signals (inset: the same plot in the linear scale). The switchability of the triad steady state response is sensitive to the values of and . In B and C, we use different values for these chromatin equilibrium constants and recalculate all free energy values using the analytical equations derived with experimental results. For in B, only Bmp4 can switch the triad from OFF to ON. For (C) neither Notch nor Bmp4 can switch the triad to ON state. D. Bistable response of the triad module to Gata1 repressor signal. Gata1 competes with Gata2 for binding sites on the Gata2-3 enhancer and can switch the triad from ON state to OFF by decreasing the recruitment of RNA polymerase to the Gata2 promoter by a factor . As a result the system irreversibly switches from ON to OFF. (note that this figure is shown in linear scale, the inset shows the deactivation in log-log scale for comparison with A). To evaluate the steady state dose response of each signal individually the concentrations of other signals were kept fixed at zero during simulation.

Figure 3. Selective deletion of enhancer binding sites can change the steady state response characteristics.

A. Deletion of any of the enhancer binding sites from the Scl+19 or Gata2-3 enhancers eliminates the high expression state of Scl, Gata2 and Fli1 seen in the wildtype HSCs. Black crosses mark the deleted sites, red crosses mark the interactions that are no longer significant as a result of the deletion. B. Mutations in the Scl or Fli1 binding site in the Fli1+12 enhancer allow triad activation but lead to reversible bistability-the ON state switches back to OFF in the absence of Notch and Bmp4. C. Deletion of the primary Gata2 binding site from the Fli1+12 enhancer makes the Scl interaction with the enhancer insignificant. This effectively makes Fli1 independent of external regulators Scl and Gata2. Fli1 expression is low for these mutants and monostable. Notch has no effect on Fli1 concentration. Gata2 and Scl show reversible bistability in response to Notch and Bmp4 in these mutants.

Figure 4. Comparison of dynamical responses of the triad and the reduced module to Notch, Bmp4 and Gata1 signals.

A. A time course of the switching from low expression to high expression state in response to a pulse of Notch. The inset shows that there is an increase in Gata2 concentration immediately after the introduction of Notch. Scl starts accumulating slowly in response to this increase in Gata2 concentration but Fli1 concentration is stagnant because enough Scl is not present to appreciably increase Fli1 expression. Once Scl has reached the required concentration (t_acc after start of Notch pulse) Gata2 and Fli1 concentrations increase rapidly to the ON state level. Thus switching of the triad to the high expression ON state is rate-limited by the slow accumulation of Scl B. The minimum Notch pulse-duration required for OFF→ON switching as a function of pulse amplitude. Black line is the full triad the red curve is the reduced module with constitutive Scl (cf. text for details). C. Same as (B) but for Bmp signal. D. Steady-state response of the reduced module (red) with the Scl concentration fixed at the value that ensures that the switching threshold is identical to that of the wild-type triad (black). Note that the unsteady state (separatrix-dotted curves) for the reduced module is much closer to the ON state. E. Controlled comparison for deactivation by Gata1 steady-state response with Scl concentration fixed to ensure that the deactivation thresholds for both modules are identical. F. Transient filtering of Gata1 signals is very similar for the two designs since Scl does not limit the rate of response to Gata1.