Limits...
Computational analysis of an autophagy/translation switch based on mutual inhibition of MTORC1 and ULK1.

Szymańska P, Martin KR, MacKeigan JP, Hlavacek WS, Lipniacki T - PLoS ONE (2015)

Bottom Line: The model incorporates reciprocal regulation of mTORC1 and ULK1 by AMPK, mutual inhibition of MTORC1 and ULK1, and ULK1-mediated negative feedback regulation of AMPK.A sensitivity analysis indicates that the prediction of oscillatory behavior is robust to changes of the parameter values of the model.The model provides testable predictions about the behavior of the AMPK-MTORC1-ULK1 network, which plays a central role in maintaining cellular energy and nutrient homeostasis.

View Article: PubMed Central - PubMed

Affiliation: College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, Warsaw, Poland.

ABSTRACT
We constructed a mechanistic, computational model for regulation of (macro)autophagy and protein synthesis (at the level of translation). The model was formulated to study the system-level consequences of interactions among the following proteins: two key components of MTOR complex 1 (MTORC1), namely the protein kinase MTOR (mechanistic target of rapamycin) and the scaffold protein RPTOR; the autophagy-initiating protein kinase ULK1; and the multimeric energy-sensing AMP-activated protein kinase (AMPK). Inputs of the model include intrinsic AMPK kinase activity, which is taken as an adjustable surrogate parameter for cellular energy level or AMP:ATP ratio, and rapamycin dose, which controls MTORC1 activity. Outputs of the model include the phosphorylation level of the translational repressor EIF4EBP1, a substrate of MTORC1, and the phosphorylation level of AMBRA1 (activating molecule in BECN1-regulated autophagy), a substrate of ULK1 critical for autophagosome formation. The model incorporates reciprocal regulation of mTORC1 and ULK1 by AMPK, mutual inhibition of MTORC1 and ULK1, and ULK1-mediated negative feedback regulation of AMPK. Through analysis of the model, we find that these processes may be responsible, depending on conditions, for graded responses to stress inputs, for bistable switching between autophagy and protein synthesis, or relaxation oscillations, comprising alternating periods of autophagy and protein synthesis. A sensitivity analysis indicates that the prediction of oscillatory behavior is robust to changes of the parameter values of the model. The model provides testable predictions about the behavior of the AMPK-MTORC1-ULK1 network, which plays a central role in maintaining cellular energy and nutrient homeostasis.

Show MeSH
Parameter sensitivity analysis.Each bar corresponds to a rate constant in the model and indicates a range of values for that rate constant over which the following pattern of qualitative behavior is obtained as a stress input (AMPK* or rapamycin* level) is varied: operation in a translation state at low stresses, oscillations between translation and autophagy states at intermediate stresses, and operation in an autophagy state at high stresses. For red bars, the stress input is AMPK* level; we considered levels of AMPK* from 0 to 106 copies per cell. For blue bars, the stress input is rapamycin* level; we considered levels of rapamycin* from 0 to 105 copies per cell. To find the upper and lower bounds of a bar, we varied (in discrete steps) the value of its corresponding parameter individually100-fold above and 100-fold below the parameter’s nominal value, which corresponds to 1 on the vertical axis. For each parameter value tested, scans of AMPK* and rapamycin* levels were performed to determine whether responses to varying levels of stress follow the same pattern as the system with nominal parameter values. The height of a bar serves as a measure of robustness. We considered all rate constants of the model with the exception of p9. (Recall that the influence of p9 on system behavior has already been considered, in Fig. 7.)
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4356596&req=5

pone.0116550.g008: Parameter sensitivity analysis.Each bar corresponds to a rate constant in the model and indicates a range of values for that rate constant over which the following pattern of qualitative behavior is obtained as a stress input (AMPK* or rapamycin* level) is varied: operation in a translation state at low stresses, oscillations between translation and autophagy states at intermediate stresses, and operation in an autophagy state at high stresses. For red bars, the stress input is AMPK* level; we considered levels of AMPK* from 0 to 106 copies per cell. For blue bars, the stress input is rapamycin* level; we considered levels of rapamycin* from 0 to 105 copies per cell. To find the upper and lower bounds of a bar, we varied (in discrete steps) the value of its corresponding parameter individually100-fold above and 100-fold below the parameter’s nominal value, which corresponds to 1 on the vertical axis. For each parameter value tested, scans of AMPK* and rapamycin* levels were performed to determine whether responses to varying levels of stress follow the same pattern as the system with nominal parameter values. The height of a bar serves as a measure of robustness. We considered all rate constants of the model with the exception of p9. (Recall that the influence of p9 on system behavior has already been considered, in Fig. 7.)

Mentions: To further characterize how system behavior depends on parameter values, we systematically varied single parameter values with the goal of delimiting the region of parameter space where patterns of responses to inputs match those of the model with nominal parameter values (i.e., the parameter values of Table 1). We also sought to identify the most sensitive parameters. The results are summarized in Fig. 8. The sensitivity analysis of Fig. 8 was performed by varying each of 22 parameters (all rate constants) alone, with other parameters set at their nominal values. The range of variation for each parameter was 100-fold below and 100-fold above the nominal parameter value. The behavior of the system over the range of variation was determined through simulations (see Fig. C in S2 File and Materials and Methods). We checked the simulation results for a characteristic pattern of responses to increasing levels of the two system inputs, AMPK* and rapamycin*. We considered levels of AMPK* from 0 to 106 copies per cell (under the condition where rapamycin is absent) and levels of rapamycin* from 0 to 105 copies per cell (under the condition where the level of AMPK* is 3×104 copies per cell). The bars in Fig. 8 indicate parameter values where the following pattern of responses was observed: a predominant translation state at low input levels, oscillation between a translation state and an autophagy state at intermediate input levels, and a predominant autophagy state at high input levels (Panel A of Fig. C in S2 File).


Computational analysis of an autophagy/translation switch based on mutual inhibition of MTORC1 and ULK1.

Szymańska P, Martin KR, MacKeigan JP, Hlavacek WS, Lipniacki T - PLoS ONE (2015)

Parameter sensitivity analysis.Each bar corresponds to a rate constant in the model and indicates a range of values for that rate constant over which the following pattern of qualitative behavior is obtained as a stress input (AMPK* or rapamycin* level) is varied: operation in a translation state at low stresses, oscillations between translation and autophagy states at intermediate stresses, and operation in an autophagy state at high stresses. For red bars, the stress input is AMPK* level; we considered levels of AMPK* from 0 to 106 copies per cell. For blue bars, the stress input is rapamycin* level; we considered levels of rapamycin* from 0 to 105 copies per cell. To find the upper and lower bounds of a bar, we varied (in discrete steps) the value of its corresponding parameter individually100-fold above and 100-fold below the parameter’s nominal value, which corresponds to 1 on the vertical axis. For each parameter value tested, scans of AMPK* and rapamycin* levels were performed to determine whether responses to varying levels of stress follow the same pattern as the system with nominal parameter values. The height of a bar serves as a measure of robustness. We considered all rate constants of the model with the exception of p9. (Recall that the influence of p9 on system behavior has already been considered, in Fig. 7.)
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4356596&req=5

pone.0116550.g008: Parameter sensitivity analysis.Each bar corresponds to a rate constant in the model and indicates a range of values for that rate constant over which the following pattern of qualitative behavior is obtained as a stress input (AMPK* or rapamycin* level) is varied: operation in a translation state at low stresses, oscillations between translation and autophagy states at intermediate stresses, and operation in an autophagy state at high stresses. For red bars, the stress input is AMPK* level; we considered levels of AMPK* from 0 to 106 copies per cell. For blue bars, the stress input is rapamycin* level; we considered levels of rapamycin* from 0 to 105 copies per cell. To find the upper and lower bounds of a bar, we varied (in discrete steps) the value of its corresponding parameter individually100-fold above and 100-fold below the parameter’s nominal value, which corresponds to 1 on the vertical axis. For each parameter value tested, scans of AMPK* and rapamycin* levels were performed to determine whether responses to varying levels of stress follow the same pattern as the system with nominal parameter values. The height of a bar serves as a measure of robustness. We considered all rate constants of the model with the exception of p9. (Recall that the influence of p9 on system behavior has already been considered, in Fig. 7.)
Mentions: To further characterize how system behavior depends on parameter values, we systematically varied single parameter values with the goal of delimiting the region of parameter space where patterns of responses to inputs match those of the model with nominal parameter values (i.e., the parameter values of Table 1). We also sought to identify the most sensitive parameters. The results are summarized in Fig. 8. The sensitivity analysis of Fig. 8 was performed by varying each of 22 parameters (all rate constants) alone, with other parameters set at their nominal values. The range of variation for each parameter was 100-fold below and 100-fold above the nominal parameter value. The behavior of the system over the range of variation was determined through simulations (see Fig. C in S2 File and Materials and Methods). We checked the simulation results for a characteristic pattern of responses to increasing levels of the two system inputs, AMPK* and rapamycin*. We considered levels of AMPK* from 0 to 106 copies per cell (under the condition where rapamycin is absent) and levels of rapamycin* from 0 to 105 copies per cell (under the condition where the level of AMPK* is 3×104 copies per cell). The bars in Fig. 8 indicate parameter values where the following pattern of responses was observed: a predominant translation state at low input levels, oscillation between a translation state and an autophagy state at intermediate input levels, and a predominant autophagy state at high input levels (Panel A of Fig. C in S2 File).

Bottom Line: The model incorporates reciprocal regulation of mTORC1 and ULK1 by AMPK, mutual inhibition of MTORC1 and ULK1, and ULK1-mediated negative feedback regulation of AMPK.A sensitivity analysis indicates that the prediction of oscillatory behavior is robust to changes of the parameter values of the model.The model provides testable predictions about the behavior of the AMPK-MTORC1-ULK1 network, which plays a central role in maintaining cellular energy and nutrient homeostasis.

View Article: PubMed Central - PubMed

Affiliation: College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, Warsaw, Poland.

ABSTRACT
We constructed a mechanistic, computational model for regulation of (macro)autophagy and protein synthesis (at the level of translation). The model was formulated to study the system-level consequences of interactions among the following proteins: two key components of MTOR complex 1 (MTORC1), namely the protein kinase MTOR (mechanistic target of rapamycin) and the scaffold protein RPTOR; the autophagy-initiating protein kinase ULK1; and the multimeric energy-sensing AMP-activated protein kinase (AMPK). Inputs of the model include intrinsic AMPK kinase activity, which is taken as an adjustable surrogate parameter for cellular energy level or AMP:ATP ratio, and rapamycin dose, which controls MTORC1 activity. Outputs of the model include the phosphorylation level of the translational repressor EIF4EBP1, a substrate of MTORC1, and the phosphorylation level of AMBRA1 (activating molecule in BECN1-regulated autophagy), a substrate of ULK1 critical for autophagosome formation. The model incorporates reciprocal regulation of mTORC1 and ULK1 by AMPK, mutual inhibition of MTORC1 and ULK1, and ULK1-mediated negative feedback regulation of AMPK. Through analysis of the model, we find that these processes may be responsible, depending on conditions, for graded responses to stress inputs, for bistable switching between autophagy and protein synthesis, or relaxation oscillations, comprising alternating periods of autophagy and protein synthesis. A sensitivity analysis indicates that the prediction of oscillatory behavior is robust to changes of the parameter values of the model. The model provides testable predictions about the behavior of the AMPK-MTORC1-ULK1 network, which plays a central role in maintaining cellular energy and nutrient homeostasis.

Show MeSH