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

Narula J, Smith AM, Gottgens B, Igoshin OA - PLoS Comput. Biol. (2010)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, Rice University, Houston, Texas, USA.

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.

Show MeSH
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.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2865510&req=5

pcbi-1000771-g002: 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.

Mentions: We use the model developed in the preceding sections to analyze the steady state response of the triad to Notch and Bmp4. By varying and and calculating free energies that conform to the experimental predictions of mutant enhancer expression rates we can explore all regions of the relevant parameter space. Bifurcation analysis of the steady state response shows that the triad module has two stable steady states (see Figure 2). For certain values of the chromatin equilibrium constants Notch and Bmp4 can switch the triad between a low expression OFF state and a high expression ON state (Figure 2A). This switch in expression levels is irreversible and sustained even without Notch and Bmp4 signals. Therefore transient Notch/Bmp4 signals may lock the triad into the ON state. This irreversible progression switch behavior is expected from the triad module which has been reported to play a significant role in the specification of HSCs in the hemogenic endothelium. We use the above-described approaches to estimate the parameters for our model. Equations (25)–(27) relate the gene expression results from the Scl+19 enhancer to the chromatin equilibrium constant . When we use these equations to estimate the free energies and the model results match the experimental results exactly. The matching is only possible for the values of equilibrium constant above a threshold: . This lower bound is simple a consequence of the fact that in the proposed thermodynamic framework the maximal possible enhancement is given by and the experimentally measurable enhancement is 820.51. Similarly the free energies for the Gata2-3 and Fli1+12 enhancers are estimated based on the experimental results and and respectively (cf. Methods section and Text S3 for details). The values of these constants are also limited from below by the respective maximal measured enhancer factors.


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

Narula J, Smith AM, Gottgens B, Igoshin OA - PLoS Comput. Biol. (2010)

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.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2865510&req=5

pcbi-1000771-g002: 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.
Mentions: We use the model developed in the preceding sections to analyze the steady state response of the triad to Notch and Bmp4. By varying and and calculating free energies that conform to the experimental predictions of mutant enhancer expression rates we can explore all regions of the relevant parameter space. Bifurcation analysis of the steady state response shows that the triad module has two stable steady states (see Figure 2). For certain values of the chromatin equilibrium constants Notch and Bmp4 can switch the triad between a low expression OFF state and a high expression ON state (Figure 2A). This switch in expression levels is irreversible and sustained even without Notch and Bmp4 signals. Therefore transient Notch/Bmp4 signals may lock the triad into the ON state. This irreversible progression switch behavior is expected from the triad module which has been reported to play a significant role in the specification of HSCs in the hemogenic endothelium. We use the above-described approaches to estimate the parameters for our model. Equations (25)–(27) relate the gene expression results from the Scl+19 enhancer to the chromatin equilibrium constant . When we use these equations to estimate the free energies and the model results match the experimental results exactly. The matching is only possible for the values of equilibrium constant above a threshold: . This lower bound is simple a consequence of the fact that in the proposed thermodynamic framework the maximal possible enhancement is given by and the experimentally measurable enhancement is 820.51. Similarly the free energies for the Gata2-3 and Fli1+12 enhancers are estimated based on the experimental results and and respectively (cf. Methods section and Text S3 for details). The values of these constants are also limited from below by the respective maximal measured enhancer factors.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, Rice University, Houston, Texas, USA.

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.

Show MeSH