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Modeling heterogeneous responsiveness of intrinsic apoptosis pathway.

Ooi HK, Ma L - BMC Syst Biol (2013)

Bottom Line: Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level.The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments.In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Bioengineering, The University of Texas at Dallas, 800 W, Campbell Rd, Richardson, TX 75080, USA.

ABSTRACT

Background: Apoptosis is a cell suicide mechanism that enables multicellular organisms to maintain homeostasis and to eliminate individual cells that threaten the organism's survival. Dependent on the type of stimulus, apoptosis can be propagated by extrinsic pathway or intrinsic pathway. The comprehensive understanding of the molecular mechanism of apoptotic signaling allows for development of mathematical models, aiming to elucidate dynamical and systems properties of apoptotic signaling networks. There have been extensive efforts in modeling deterministic apoptosis network accounting for average behavior of a population of cells. Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level.

Results: To address the inevitable randomness in the intrinsic apoptosis mechanism, we develop a theoretical and computational modeling framework of intrinsic apoptosis pathway at single-cell level, accounting for both deterministic and stochastic behavior. Our deterministic model, adapted from the well-accepted Fussenegger model, shows that an additional positive feedback between the executioner caspase and the initiator caspase plays a fundamental role in yielding the desired property of bistability. We then examine the impact of intrinsic fluctuations of biochemical reactions, viewed as intrinsic noise, and natural variation of protein concentrations, viewed as extrinsic noise, on behavior of the intrinsic apoptosis network. Histograms of the steady-state output at varying input levels show that the intrinsic noise could elicit a wider region of bistability over that of the deterministic model. However, the system stochasticity due to intrinsic fluctuations, such as the noise of steady-state response and the randomness of response delay, shows that the intrinsic noise in general is insufficient to produce significant cell-to-cell variations at physiologically relevant level of molecular numbers. Furthermore, the extrinsic noise represented by random variations of two key apoptotic proteins, namely Cytochrome C and inhibitor of apoptosis proteins (IAP), is modeled separately or in combination with intrinsic noise. The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments. Finally, simulations illustrate that the mean abundance of fluctuating IAP protein is positively correlated with the degree of cellular stochasticity of the intrinsic apoptosis pathway.

Conclusions: Our theoretical and computational study shows that the pronounced non-genetic heterogeneity in intrinsic apoptosis responses among individual cells plausibly arises from extrinsic rather than intrinsic origin of fluctuations. In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness.

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Two-parameter bifurcation diagrams of the modified model of intrinsic apoptosis pathway. Bifurcation analysis of our deterministic model against pairs among four selected parameters, namely Hill Constant in the positive feedback loop (Kc), cooperativity in the activation of CEA (n), degradation rate of caspase 9 (μ5), and rate constant of the inhibition of CEA by IAP (ku). 2D bistability diagrams are plotted with respect to Kc and ku(A), Kc and μ5(B), Kc and n(C), n and ku(D), n and μ5(E), μ5 and ku(F). The gray area depicts the location of paired parameter values at which the CEA response is bistable.
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Figure 3: Two-parameter bifurcation diagrams of the modified model of intrinsic apoptosis pathway. Bifurcation analysis of our deterministic model against pairs among four selected parameters, namely Hill Constant in the positive feedback loop (Kc), cooperativity in the activation of CEA (n), degradation rate of caspase 9 (μ5), and rate constant of the inhibition of CEA by IAP (ku). 2D bistability diagrams are plotted with respect to Kc and ku(A), Kc and μ5(B), Kc and n(C), n and ku(D), n and μ5(E), μ5 and ku(F). The gray area depicts the location of paired parameter values at which the CEA response is bistable.

Mentions: The governing ODEs of the modified model of intrinsic apoptosis pathway are listed in the Methods section. Simulations of the modified ODE model show that when given a step input of low concentration of CC, the time courses of CEA gradually settle at a near-zero steady state starting from different initial CEA concentrations, while given a relatively high concentration of CC, CEA eventually settles at a high steady state (Figure 2C). Such behavior with two stable output steady states indicates that bistability is achieved by the modified ODE model. In addition, the time trajectories agree with experimental results in that the CEA response is not elicited until after a few hours of delay time (>2hrs).The switching-on kinetic of CEA activation is sigmoidal shape and completed within ∼1hr, presenting all-or-none switch-like behavior [13,63]. Indeed, one-parameter bifurcation analysis of the modified ODE model confirms that the steady-state response of CEA is bistable with respect to the input signal of CC, where two stable steady states coexist between the input concentrations of 0.08 μM and 0.83 μM (Figure 2D). The bifurcation curve has two saddle-node bifurcation points SN1 and SN2, giving rise to a middle unstable branch and two stable branches, where the upper and lower branches correspond to the apoptosis and survival fates, respectively. When the concentration of CC approaches SN1 and SN2, hysteretic behavior occurs: the system remains at near-zero CEA activity at low amount of CC, until an ON threshold (0.83 μM) is reached, whereby CEA activity switches to the apoptosis state abruptly; inversely, the CEA activity switches from the apoptosis state to the survival state only if the CC concentration falls below the OFF threshold (0.08 μM). The system properties of bistability and hysteresis could confer robustness to the apoptotic responsiveness by allowing cells that are not committed to apoptosis to remain at survival state, even in the event of mildly noisy input. In addition, two-dimensional bifurcation analysis with respect to four selected parameters, namely the Hill constant that regulates the CEA-mediated positive feedback loop (Kc), the cooperativity of activation of CEA (n), the degradation rate of c9a(μ5) and the inhibition rate of CEA by IAP (ku), show that the bistability property of the modified model exists in extended parameter space around the nominal parameter set (Figure 3) and is hence a robust behavior.


Modeling heterogeneous responsiveness of intrinsic apoptosis pathway.

Ooi HK, Ma L - BMC Syst Biol (2013)

Two-parameter bifurcation diagrams of the modified model of intrinsic apoptosis pathway. Bifurcation analysis of our deterministic model against pairs among four selected parameters, namely Hill Constant in the positive feedback loop (Kc), cooperativity in the activation of CEA (n), degradation rate of caspase 9 (μ5), and rate constant of the inhibition of CEA by IAP (ku). 2D bistability diagrams are plotted with respect to Kc and ku(A), Kc and μ5(B), Kc and n(C), n and ku(D), n and μ5(E), μ5 and ku(F). The gray area depicts the location of paired parameter values at which the CEA response is bistable.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
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Figure 3: Two-parameter bifurcation diagrams of the modified model of intrinsic apoptosis pathway. Bifurcation analysis of our deterministic model against pairs among four selected parameters, namely Hill Constant in the positive feedback loop (Kc), cooperativity in the activation of CEA (n), degradation rate of caspase 9 (μ5), and rate constant of the inhibition of CEA by IAP (ku). 2D bistability diagrams are plotted with respect to Kc and ku(A), Kc and μ5(B), Kc and n(C), n and ku(D), n and μ5(E), μ5 and ku(F). The gray area depicts the location of paired parameter values at which the CEA response is bistable.
Mentions: The governing ODEs of the modified model of intrinsic apoptosis pathway are listed in the Methods section. Simulations of the modified ODE model show that when given a step input of low concentration of CC, the time courses of CEA gradually settle at a near-zero steady state starting from different initial CEA concentrations, while given a relatively high concentration of CC, CEA eventually settles at a high steady state (Figure 2C). Such behavior with two stable output steady states indicates that bistability is achieved by the modified ODE model. In addition, the time trajectories agree with experimental results in that the CEA response is not elicited until after a few hours of delay time (>2hrs).The switching-on kinetic of CEA activation is sigmoidal shape and completed within ∼1hr, presenting all-or-none switch-like behavior [13,63]. Indeed, one-parameter bifurcation analysis of the modified ODE model confirms that the steady-state response of CEA is bistable with respect to the input signal of CC, where two stable steady states coexist between the input concentrations of 0.08 μM and 0.83 μM (Figure 2D). The bifurcation curve has two saddle-node bifurcation points SN1 and SN2, giving rise to a middle unstable branch and two stable branches, where the upper and lower branches correspond to the apoptosis and survival fates, respectively. When the concentration of CC approaches SN1 and SN2, hysteretic behavior occurs: the system remains at near-zero CEA activity at low amount of CC, until an ON threshold (0.83 μM) is reached, whereby CEA activity switches to the apoptosis state abruptly; inversely, the CEA activity switches from the apoptosis state to the survival state only if the CC concentration falls below the OFF threshold (0.08 μM). The system properties of bistability and hysteresis could confer robustness to the apoptotic responsiveness by allowing cells that are not committed to apoptosis to remain at survival state, even in the event of mildly noisy input. In addition, two-dimensional bifurcation analysis with respect to four selected parameters, namely the Hill constant that regulates the CEA-mediated positive feedback loop (Kc), the cooperativity of activation of CEA (n), the degradation rate of c9a(μ5) and the inhibition rate of CEA by IAP (ku), show that the bistability property of the modified model exists in extended parameter space around the nominal parameter set (Figure 3) and is hence a robust behavior.

Bottom Line: Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level.The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments.In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Bioengineering, The University of Texas at Dallas, 800 W, Campbell Rd, Richardson, TX 75080, USA.

ABSTRACT

Background: Apoptosis is a cell suicide mechanism that enables multicellular organisms to maintain homeostasis and to eliminate individual cells that threaten the organism's survival. Dependent on the type of stimulus, apoptosis can be propagated by extrinsic pathway or intrinsic pathway. The comprehensive understanding of the molecular mechanism of apoptotic signaling allows for development of mathematical models, aiming to elucidate dynamical and systems properties of apoptotic signaling networks. There have been extensive efforts in modeling deterministic apoptosis network accounting for average behavior of a population of cells. Cellular networks, however, are inherently stochastic and significant cell-to-cell variability in apoptosis response has been observed at single cell level.

Results: To address the inevitable randomness in the intrinsic apoptosis mechanism, we develop a theoretical and computational modeling framework of intrinsic apoptosis pathway at single-cell level, accounting for both deterministic and stochastic behavior. Our deterministic model, adapted from the well-accepted Fussenegger model, shows that an additional positive feedback between the executioner caspase and the initiator caspase plays a fundamental role in yielding the desired property of bistability. We then examine the impact of intrinsic fluctuations of biochemical reactions, viewed as intrinsic noise, and natural variation of protein concentrations, viewed as extrinsic noise, on behavior of the intrinsic apoptosis network. Histograms of the steady-state output at varying input levels show that the intrinsic noise could elicit a wider region of bistability over that of the deterministic model. However, the system stochasticity due to intrinsic fluctuations, such as the noise of steady-state response and the randomness of response delay, shows that the intrinsic noise in general is insufficient to produce significant cell-to-cell variations at physiologically relevant level of molecular numbers. Furthermore, the extrinsic noise represented by random variations of two key apoptotic proteins, namely Cytochrome C and inhibitor of apoptosis proteins (IAP), is modeled separately or in combination with intrinsic noise. The resultant stochasticity in the timing of intrinsic apoptosis response shows that the fluctuating protein variations can induce cell-to-cell stochastic variability at a quantitative level agreeing with experiments. Finally, simulations illustrate that the mean abundance of fluctuating IAP protein is positively correlated with the degree of cellular stochasticity of the intrinsic apoptosis pathway.

Conclusions: Our theoretical and computational study shows that the pronounced non-genetic heterogeneity in intrinsic apoptosis responses among individual cells plausibly arises from extrinsic rather than intrinsic origin of fluctuations. In addition, it predicts that the IAP protein could serve as a potential therapeutic target for suppression of the cell-to-cell variation in the intrinsic apoptosis responsiveness.

Show MeSH
Related in: MedlinePlus