Modeling Reveals Bistability and Low-Pass Filtering in the Network Module Determining Blood Stem Cell Fate

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

Role of Autoregulation and Relative Synthesis of Operon Partners in Alternative Sigma Factor Networks

<div><p>Despite the central role of alternative sigma factors in bacterial stress response and virulence their regulation remains incompletely understood. Here we investigate one of the best-studied examples of alternative sigma factors: the σ^B network that controls the general stress response of <i>Bacillus subtilis</i> to uncover widely relevant general design principles that describe the structure-function relationship of alternative sigma factor regulatory networks. We show that the relative stoichiometry of the synthesis rates of σ^B, its anti-sigma factor RsbW and the anti-anti-sigma factor RsbV plays a critical role in shaping the network behavior by forcing the σ^B network to function as an ultrasensitive negative feedback loop. We further demonstrate how this negative feedback regulation insulates alternative sigma factor activity from competition with the housekeeping sigma factor for RNA polymerase and allows multiple stress sigma factors to function simultaneously with little competitive interference.</p></div

Negative feedback minimizes competition between stress σ factors for RNA polymerase.

<p><b>A,B.</b> Simplified network diagrams of stress σ-factors σ^B and σ^W and housekeeping σ-factor σ^A competing with each other for RNA polymerase. σ^B and σ^W activities are regulated by negative and positive feedbacks in (A) and (B) respectively. In both cases, signaling proteins P_B and P_W control the stress-signal driven activation of σ^B and σ^W respectively. <b>C, D.</b> Dependence of free σ^B and σ^W levels on P_B at fixed P_W (= 2μM). In the wildtype negative feedback system (C), increase in σ^B phosphatase leads to an increase in both free σ^B (green curve) and free σ^W (red curve). In the positive feedback system (D), increase in σ^B phosphatase leads to an increase in free σ^B (green curve) and a decrease in free σ^W (red curve). <b>E, F.</b> σ^B and σ^W target promoter activities as a function of P_B at fixed P_W in the wildtype negative feedback system (E), and the positive feedback system (F). <b>G, H.</b> RNA polymerase bound σ^B (Rpol-σ^B) as a function of P_B at fixed P_W in the wildtype negative feedback system (G) and the positive feedback system (H). Increase in σ^B phosphatase (P_B) leads to an increase in Rpol-σ^B (green curve) and corresponding decreases ΔRpol-σ^W (core complex with σ^W, red area) and ΔRpol-σ^A (complex with σ^A, blue area).</p

σ^B general stress response network.

<p><b>A.</b> Network diagram of the σ^B general stress response. The network has two modules: a transcriptional module that inputs the free σ^B level and outputs the total concentrations of operon proteins RsbV (RsbV_T), RsbW (RsbW_T) and σ^B (B_T); and a post-translational module that uses RsbV_T, RsbW_T and B_T and the stress phosphatase levels as inputs to output the level of free σ^B. In the post-translational module, energy and environmental stresses activate the stress-sensing phosphatases RsbQP (QP) and RsbTU (TU) which dephosphorylate RsbV which in turn activates σ^B by releasing it from the σ^B-RsbW₂ complex. Note only the monomeric forms of RsbW and RsbV have been shown for simplicity. <b>B.</b> Simplified view of the σ^B network. The σ^B network works as a feedback loop wherein free level controls RsbV_T, RsbW_T and B_T levels via operon transcription and the three operon components together with the stress level determine the free σ^B level. The feedback loop sign is can be either positive or negative depending on whether increase in operon component levels impacts free σ^B level either positively or negatively. <b>C-E.</b> Dynamics of free σ^B in response to a step-increase in phosphatase concentration for different combinations of the relative synthesis rates of σ^B operon partners (λ_W = RsbW_T/B_T, λ_V = RsbV_T/B_T).</p

Pulsatile response of the σ^B network to stochastic phosphatase bursts during energy stress.

<p>Model simulations for σ^B network response where energy stress leads to an increase in stress-sensing phosphatase RsbQP burst size (A-D) or RsbQP burst frequency (E-H). <b>A,E.</b> Simulations show stochastic bursts in levels of RsbQP lead to pulses of σ^B target promoter activity. Light and dark green curves are sample trajectory from stochastic simulation at high and low stress respectively. Note that σ^B target promoter activity pulse amplitude increases significantly with increasing stress for burst size modulation (A) but not for burst frequency modulation (E). <b>B,F.</b> Mean σ^B pulse amplitude increases linearly as a function of mean phosphatase level for burst size modulation (B) but is insensitive to mean phosphatase level for burst frequency modulation (F). Green circles and errorbars show means and standard deviations calculated from stochastic simulations. Black line is a linear fit. <b>C,G.</b> With increasing mean phosphatase level, mean σ^B pulse frequency increases ultrasensitively for burst size modulation (C) and linearly for burst frequency modulation (G). Green circles and errorbars show means and standard deviations calculated from stochastic simulations. Black curves are a Hill-equation fit with <i>n</i>_<i>Hill</i> = 5.6 in (C) and a linear fit in (G) respectively. <b>D,H.</b> Mean σ^B target expression increases ultrasensitively as a function of mean phosphatase level for both burst size (D) and burst frequency (H) modulation. Green circles are the mean σ^B target expression calculated from stochastic simulations. Black curve is a Hill-equation fit with <i>n</i>_<i>Hill</i> = 2 in (D) and in <i>n</i>_<i>Hill</i> = 1.2 (H).</p

Negative feedback drives the pulsatile response of the σ^B network.

<p><b>A.</b> Decoupled post-translational (blue curve) and transcriptional (black curve) responses of the σ^B network for λ_W = RsbW_T/B_T = 4, λ_V = RsbV_T/B_T = 4.5. σ^B and B_T represent the concentrations of free and total σ^B. Red circle marks the steady states of the full system. Note that RsbW_T and RsbV_T are assumed to always increase in proportion to the B_T for both post-translational and transcriptional responses. <b>B.</b> Sensitivity of the post-translational response (<i>LG</i>_<i>P</i>) to changes in total σ^B concentration (operon production). <b>C.</b> Representation of the σ^B pulsatile trajectory in the σ^B-B_T phase plane (green curve). Blue and cyan curves are the decoupled post-translational responses at high and low phosphatase concentrations. Black curve is the transcriptional response. <b>D.</b> (<i>λ</i>_<i>W</i>, <i>λ</i>_<i>V</i>) relative synthesis parameter space is divided into regions with positive (Region I), negative (Region II) and zero (Region III) post-translational sensitivity that respectively correspond to an effective positive, negative and no feedback in the σ^B network. Red and black lines represent the analytically calculated region boundaries <i>λ</i>_<i>W</i> = 2 + <i>λ</i>_<i>V</i> and <i>λ</i>_<i>W</i> = 2(1 + <i>λ</i>_<i>V</i><i>k</i>_<i>deg</i> / <i>k</i>_<i>k</i>).</p

Rate sensitivity of the σ^B pulsatile response to environmental stress.

<p><b>A.</b> Ramped increases in RsbTU complex concentration were used as model inputs to simulate different rates of stress increase in σ^B network. <b>B.</b> σ^B pulse amplitudes in the wildtype model (k_deg = 0.72 hr^-1 is the degradation rate of σ^B operon proteins) resulting from the ramped increases in phosphatase concentration shown in (A). <b>C,D.</b> σ^B pulse amplitudes resulting from the ramped increase in phosphatase concentration shown in (C) for various degradation/dilution rates (D). <b>E.</b> Non-linear dependence σ^B pulse amplitude on phosphatase ramp duration for various degradation/dilution rates. Circles and solid curves represent simulation results and Hill-equation fits respectively. Colors represent different k_deg values as in (D). <b>F.</b> K_ramp, the half-maximal constant of the non-linear dependence of amplitude on ramp duration, as a function of k_deg.</p

Negative feedback insulates the σ^B response from competition with houskeeping σ-factor σ^A.

<p><b>A.</b> Simplified network diagrams of stress σ-factor σ^B competing with housekeeping σ-factor σ^A for RNA polymerase. In all cases, a σ^B phosphatase controls the stress-signal driven activation of σ^B. (<b>B,C).</b> Trajectories of free σ^B (B) and σ^B target promoter activity (C) in response to stochastic phosphatase input for both networks at two different levels of σ^A (σ^A = 9μM—low competition-regime and σ^A = 12μM—high-competition regime for RNA polymerase). <b>D-E.</b> Mean free σ^B concentration (D) and mean σ^B target promoter activity (E) as a function of total σ^A concentration (A_T) for both networks in (A) at fixed mean phosphatase (mean P_T = 0.5 μM). Gray vertical line shows the total RNA polymerase level which was fixed at 10 μM.</p

List of parameters values used in the model for σ^B network.

<p>List of parameters values used in the model for σ^B network.</p

Slowdown of growth controls cellular differentiation

Abstract How can changes in growth rate affect the regulatory networks behavior and the outcomes of cellular differentiation? We address this question by focusing on starvation response in sporulating Bacillus subtilis. We show that the activity of sporulation master regulator Spo0A increases with decreasing cellular growth rate. Using a mathematical model of the phosphorelay—the network controlling Spo0A—we predict that this increase in Spo0A activity can be explained by the phosphorelay protein accumulation and lengthening of the period between chromosomal replication events caused by growth slowdown. As a result, only cells growing slower than a certain rate reach threshold Spo0A activity necessary for sporulation. This growth threshold model accurately predicts cell fates and explains the distribution of sporulation deferral times. We confirm our predictions experimentally and show that the concentration rather than activity of phosphorelay proteins is affected by the growth slowdown. We conclude that sensing the growth rates enables cells to indirectly detect starvation without the need for evaluating specific stress signals