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Robustness of cell cycle control and flexible orders of signaling events.

Zhu H, Mao Y - Sci Rep (2015)

Bottom Line: To quantitatively address the two questions, we have developed a novel cell cycle model upon experimental observations.It contains positive and negative E2F proteins and two Cdk inhibitors, and is parameterized, for the first time, to generate not only oscillating protein concentrations but also periodic signaling events.Events and their orders reconstructed under varied conditions indicate that proteolysis of cyclins and Cdk complexes by APC and Skp2 occurs highly robustly in a strict order, but many other events are either dispensable or can occur in flexible orders.

View Article: PubMed Central - PubMed

Affiliation: Bioinformatics Section, School of Basic Medical Sciences, Southern Medical University, Shatai Road, Guangzhou, 510515, China.

ABSTRACT
The highly robust control of cell cycles in eukaryotes enables cells to undergo strictly ordered G1/S/G2/M phases and respond adaptively to regulatory signals; however the nature of the robustness remains obscure. Specifically, it is unclear whether events of signaling should be strictly ordered and whether some events are more robust than others. To quantitatively address the two questions, we have developed a novel cell cycle model upon experimental observations. It contains positive and negative E2F proteins and two Cdk inhibitors, and is parameterized, for the first time, to generate not only oscillating protein concentrations but also periodic signaling events. Events and their orders reconstructed under varied conditions indicate that proteolysis of cyclins and Cdk complexes by APC and Skp2 occurs highly robustly in a strict order, but many other events are either dispensable or can occur in flexible orders. These results suggest that strictly ordered proteolytic events are essential for irreversible cell cycle progression and the robustness of cell cycles copes with flexible orders of signaling events, and unveil a new and important dimension to the robustness of cell cycle control in particular and to biological signaling in general.

No MeSH data available.


Related in: MedlinePlus

The cell cycle model and definition of events.(A) Molecular interactions. The left panel shows protein interactions indicated by numbered links. Specifically, E2F1 in mammals is phosphorylated by CDKE and CDKB20 and CDKA6061 for degradation, but in Drosophila is specifically destructed by CRL4Cdt2 periodically6247. How CRL4Cdt2 is down-regulated after S phase is unclear63. Recent studies reveal that Cdt2 in CRL4Cdt2 is degraded by SCFFbxo11 and this degradation is prevented by phosphorylation of Cdt2 by CDKs64. Thus CDKs’ roles in preventing Cdt2 degradation may promote E2F1 destruction by CRL4Cdt2, agreeing with the initial observation that CDKs mediate E2F1 destruction. Directly or indirectly, we let CDKs mediate E2F1 degradation. Proteins with the symbol ^ indicate that they have a constant synthesis rate. Solid red and brown links ending with an arrow or a dot indicate activation or repression. Dashed brown links ending with bi- or uni-directional arrow(s) indicate binding and unbinding between proteins or protein transformation. Solid and dashed green links ending with a dot indicate degradation via ubiquitination by Skp2/APCFzy/APCFzr. ‘&’ means combined condition. The right panel shows abbreviations, full names, and initial values (Supplementary Table 4) of 25 proteins and complexes described by 25 ordinary differential equations. (B) Signaling events are defined upon nonlinear molecular interactions. Shown is expression of gene g repressed by two inhibitors I1 and I2 and activated by two activators A1 and A2 independently at two enhancers. Repressive and activating Hill functions (Hr and Ha in the equation of dg/dt), with half-maximal activating/inhibiting coefficients, describe how I1, I2, A1, and A2 nonlinearly regulate g (functional concentration ranges of these regulators are indicated by shadowed areas). When I1, I2, A1, or A2 exceeds their half-maximal activating/inhibiting coefficients, event I1_Rep_g, I2_Rep_g, A1_Act_g, or A2_Act_g occurs. When I1_Rep_g and I2_Rep_g are absent and A1_Act_g is present at an enhancer, or A2_Act_g is present at the other enhancer, g_Exp_G occurs.
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f1: The cell cycle model and definition of events.(A) Molecular interactions. The left panel shows protein interactions indicated by numbered links. Specifically, E2F1 in mammals is phosphorylated by CDKE and CDKB20 and CDKA6061 for degradation, but in Drosophila is specifically destructed by CRL4Cdt2 periodically6247. How CRL4Cdt2 is down-regulated after S phase is unclear63. Recent studies reveal that Cdt2 in CRL4Cdt2 is degraded by SCFFbxo11 and this degradation is prevented by phosphorylation of Cdt2 by CDKs64. Thus CDKs’ roles in preventing Cdt2 degradation may promote E2F1 destruction by CRL4Cdt2, agreeing with the initial observation that CDKs mediate E2F1 destruction. Directly or indirectly, we let CDKs mediate E2F1 degradation. Proteins with the symbol ^ indicate that they have a constant synthesis rate. Solid red and brown links ending with an arrow or a dot indicate activation or repression. Dashed brown links ending with bi- or uni-directional arrow(s) indicate binding and unbinding between proteins or protein transformation. Solid and dashed green links ending with a dot indicate degradation via ubiquitination by Skp2/APCFzy/APCFzr. ‘&’ means combined condition. The right panel shows abbreviations, full names, and initial values (Supplementary Table 4) of 25 proteins and complexes described by 25 ordinary differential equations. (B) Signaling events are defined upon nonlinear molecular interactions. Shown is expression of gene g repressed by two inhibitors I1 and I2 and activated by two activators A1 and A2 independently at two enhancers. Repressive and activating Hill functions (Hr and Ha in the equation of dg/dt), with half-maximal activating/inhibiting coefficients, describe how I1, I2, A1, and A2 nonlinearly regulate g (functional concentration ranges of these regulators are indicated by shadowed areas). When I1, I2, A1, or A2 exceeds their half-maximal activating/inhibiting coefficients, event I1_Rep_g, I2_Rep_g, A1_Act_g, or A2_Act_g occurs. When I1_Rep_g and I2_Rep_g are absent and A1_Act_g is present at an enhancer, or A2_Act_g is present at the other enhancer, g_Exp_G occurs.

Mentions: In the past decades experimental and computational biologists have tried to unveil the properties and control mechanisms of robust molecular signaling that are believed to be functionally important. The robustness of cell cycle control system in eukaryotic cells, due to its periodic activity and biological importance, has been intensively investigated. Most eukaryotic cells undergo four phases to finish a round of division. When growth factors drive a cell to enter into the G1 phase and pass through the restriction point (a point beyond which mitosis completion is ensured independently of the presence of growth factors), progression of the following S, G2, and M phases is controlled by the sequential activation of a family of cyclin/Cdk complexes (abbreviations shown in Fig. 1B are used hereafter, and italics beginning with a normal letter designate genes). In 1989, Hartwell and Weinert expressed that “The events of the cell cycle of most organisms are ordered into dependent pathways in which the initiation of late events is dependent on the completion of early events”1. This viewpoint stresses the importance of the order of signaling events for the robust control of cell cycles. However, so far in all experimental and computational investigations robustness is evaluated by examining if concentrations of targeted molecules in a cell or a mathematical model are sensitive to perturbations or parameters. This method bears two drawbacks. First, signaling happens in diverse contexts, and molecular responses to perturbations and parameters may reveal more about adaptiveness than robustness of the control mechanisms. Second, both protein concentrations and model parameters (such as binding affinity) are difficult to be accurately measured in experiments, leaving the order of, and dependency between, events still unclear. While Hartwell and Weinert defined that “control mechanisms enforcing dependency in the cell cycle are here called checkpoints”, it remains unknown whether the dependency is enforced by merely checkpoints or also by other events. In brief, the nature of the robustness of cell cycle control is still inadequately understood.


Robustness of cell cycle control and flexible orders of signaling events.

Zhu H, Mao Y - Sci Rep (2015)

The cell cycle model and definition of events.(A) Molecular interactions. The left panel shows protein interactions indicated by numbered links. Specifically, E2F1 in mammals is phosphorylated by CDKE and CDKB20 and CDKA6061 for degradation, but in Drosophila is specifically destructed by CRL4Cdt2 periodically6247. How CRL4Cdt2 is down-regulated after S phase is unclear63. Recent studies reveal that Cdt2 in CRL4Cdt2 is degraded by SCFFbxo11 and this degradation is prevented by phosphorylation of Cdt2 by CDKs64. Thus CDKs’ roles in preventing Cdt2 degradation may promote E2F1 destruction by CRL4Cdt2, agreeing with the initial observation that CDKs mediate E2F1 destruction. Directly or indirectly, we let CDKs mediate E2F1 degradation. Proteins with the symbol ^ indicate that they have a constant synthesis rate. Solid red and brown links ending with an arrow or a dot indicate activation or repression. Dashed brown links ending with bi- or uni-directional arrow(s) indicate binding and unbinding between proteins or protein transformation. Solid and dashed green links ending with a dot indicate degradation via ubiquitination by Skp2/APCFzy/APCFzr. ‘&’ means combined condition. The right panel shows abbreviations, full names, and initial values (Supplementary Table 4) of 25 proteins and complexes described by 25 ordinary differential equations. (B) Signaling events are defined upon nonlinear molecular interactions. Shown is expression of gene g repressed by two inhibitors I1 and I2 and activated by two activators A1 and A2 independently at two enhancers. Repressive and activating Hill functions (Hr and Ha in the equation of dg/dt), with half-maximal activating/inhibiting coefficients, describe how I1, I2, A1, and A2 nonlinearly regulate g (functional concentration ranges of these regulators are indicated by shadowed areas). When I1, I2, A1, or A2 exceeds their half-maximal activating/inhibiting coefficients, event I1_Rep_g, I2_Rep_g, A1_Act_g, or A2_Act_g occurs. When I1_Rep_g and I2_Rep_g are absent and A1_Act_g is present at an enhancer, or A2_Act_g is present at the other enhancer, g_Exp_G occurs.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4588580&req=5

f1: The cell cycle model and definition of events.(A) Molecular interactions. The left panel shows protein interactions indicated by numbered links. Specifically, E2F1 in mammals is phosphorylated by CDKE and CDKB20 and CDKA6061 for degradation, but in Drosophila is specifically destructed by CRL4Cdt2 periodically6247. How CRL4Cdt2 is down-regulated after S phase is unclear63. Recent studies reveal that Cdt2 in CRL4Cdt2 is degraded by SCFFbxo11 and this degradation is prevented by phosphorylation of Cdt2 by CDKs64. Thus CDKs’ roles in preventing Cdt2 degradation may promote E2F1 destruction by CRL4Cdt2, agreeing with the initial observation that CDKs mediate E2F1 destruction. Directly or indirectly, we let CDKs mediate E2F1 degradation. Proteins with the symbol ^ indicate that they have a constant synthesis rate. Solid red and brown links ending with an arrow or a dot indicate activation or repression. Dashed brown links ending with bi- or uni-directional arrow(s) indicate binding and unbinding between proteins or protein transformation. Solid and dashed green links ending with a dot indicate degradation via ubiquitination by Skp2/APCFzy/APCFzr. ‘&’ means combined condition. The right panel shows abbreviations, full names, and initial values (Supplementary Table 4) of 25 proteins and complexes described by 25 ordinary differential equations. (B) Signaling events are defined upon nonlinear molecular interactions. Shown is expression of gene g repressed by two inhibitors I1 and I2 and activated by two activators A1 and A2 independently at two enhancers. Repressive and activating Hill functions (Hr and Ha in the equation of dg/dt), with half-maximal activating/inhibiting coefficients, describe how I1, I2, A1, and A2 nonlinearly regulate g (functional concentration ranges of these regulators are indicated by shadowed areas). When I1, I2, A1, or A2 exceeds their half-maximal activating/inhibiting coefficients, event I1_Rep_g, I2_Rep_g, A1_Act_g, or A2_Act_g occurs. When I1_Rep_g and I2_Rep_g are absent and A1_Act_g is present at an enhancer, or A2_Act_g is present at the other enhancer, g_Exp_G occurs.
Mentions: In the past decades experimental and computational biologists have tried to unveil the properties and control mechanisms of robust molecular signaling that are believed to be functionally important. The robustness of cell cycle control system in eukaryotic cells, due to its periodic activity and biological importance, has been intensively investigated. Most eukaryotic cells undergo four phases to finish a round of division. When growth factors drive a cell to enter into the G1 phase and pass through the restriction point (a point beyond which mitosis completion is ensured independently of the presence of growth factors), progression of the following S, G2, and M phases is controlled by the sequential activation of a family of cyclin/Cdk complexes (abbreviations shown in Fig. 1B are used hereafter, and italics beginning with a normal letter designate genes). In 1989, Hartwell and Weinert expressed that “The events of the cell cycle of most organisms are ordered into dependent pathways in which the initiation of late events is dependent on the completion of early events”1. This viewpoint stresses the importance of the order of signaling events for the robust control of cell cycles. However, so far in all experimental and computational investigations robustness is evaluated by examining if concentrations of targeted molecules in a cell or a mathematical model are sensitive to perturbations or parameters. This method bears two drawbacks. First, signaling happens in diverse contexts, and molecular responses to perturbations and parameters may reveal more about adaptiveness than robustness of the control mechanisms. Second, both protein concentrations and model parameters (such as binding affinity) are difficult to be accurately measured in experiments, leaving the order of, and dependency between, events still unclear. While Hartwell and Weinert defined that “control mechanisms enforcing dependency in the cell cycle are here called checkpoints”, it remains unknown whether the dependency is enforced by merely checkpoints or also by other events. In brief, the nature of the robustness of cell cycle control is still inadequately understood.

Bottom Line: To quantitatively address the two questions, we have developed a novel cell cycle model upon experimental observations.It contains positive and negative E2F proteins and two Cdk inhibitors, and is parameterized, for the first time, to generate not only oscillating protein concentrations but also periodic signaling events.Events and their orders reconstructed under varied conditions indicate that proteolysis of cyclins and Cdk complexes by APC and Skp2 occurs highly robustly in a strict order, but many other events are either dispensable or can occur in flexible orders.

View Article: PubMed Central - PubMed

Affiliation: Bioinformatics Section, School of Basic Medical Sciences, Southern Medical University, Shatai Road, Guangzhou, 510515, China.

ABSTRACT
The highly robust control of cell cycles in eukaryotes enables cells to undergo strictly ordered G1/S/G2/M phases and respond adaptively to regulatory signals; however the nature of the robustness remains obscure. Specifically, it is unclear whether events of signaling should be strictly ordered and whether some events are more robust than others. To quantitatively address the two questions, we have developed a novel cell cycle model upon experimental observations. It contains positive and negative E2F proteins and two Cdk inhibitors, and is parameterized, for the first time, to generate not only oscillating protein concentrations but also periodic signaling events. Events and their orders reconstructed under varied conditions indicate that proteolysis of cyclins and Cdk complexes by APC and Skp2 occurs highly robustly in a strict order, but many other events are either dispensable or can occur in flexible orders. These results suggest that strictly ordered proteolytic events are essential for irreversible cell cycle progression and the robustness of cell cycles copes with flexible orders of signaling events, and unveil a new and important dimension to the robustness of cell cycle control in particular and to biological signaling in general.

No MeSH data available.


Related in: MedlinePlus