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In-silico modeling of the mitotic spindle assembly checkpoint.

Ibrahim B, Diekmann S, Schmitt E, Dittrich P - PLoS ONE (2008)

Bottom Line: Our model is validated by simulation of ten perturbation experiments.Only in the controlled case, our models show (M)SAC behaviour at meta- to anaphase transition in agreement with experimental observations.Our simulations revealed that for (M)SAC activation, Cdc20 is not fully sequestered; instead APC is inhibited by MCC binding.

View Article: PubMed Central - PubMed

Affiliation: Bio System Analysis Group, Institute of Computer Science, Friedrich-Schiller-University Jena, Jena, Germany.

ABSTRACT

Background: The Mitotic Spindle Assembly Checkpoint ((M)SAC) is an evolutionary conserved mechanism that ensures the correct segregation of chromosomes by restraining cell cycle progression from entering anaphase until all chromosomes have made proper bipolar attachments to the mitotic spindle. Its malfunction can lead to cancer.

Principle findings: We have constructed and validated for the human (M)SAC mechanism an in silico dynamical model, integrating 11 proteins and complexes. The model incorporates the perspectives of three central control pathways, namely Mad1/Mad2 induced Cdc20 sequestering based on the Template Model, MCC formation, and APC inhibition. Originating from the biochemical reactions for the underlying molecular processes, non-linear ordinary differential equations for the concentrations of 11 proteins and complexes of the (M)SAC are derived. Most of the kinetic constants are taken from literature, the remaining four unknown parameters are derived by an evolutionary optimization procedure for an objective function describing the dynamics of the APC:Cdc20 complex. MCC:APC dissociation is described by two alternatives, namely the "Dissociation" and the "Convey" model variants. The attachment of the kinetochore to microtubuli is simulated by a switching parameter silencing those reactions which are stopped by the attachment. For both, the Dissociation and the Convey variants, we compare two different scenarios concerning the microtubule attachment dependent control of the dissociation reaction. Our model is validated by simulation of ten perturbation experiments.

Conclusion: Only in the controlled case, our models show (M)SAC behaviour at meta- to anaphase transition in agreement with experimental observations. Our simulations revealed that for (M)SAC activation, Cdc20 is not fully sequestered; instead APC is inhibited by MCC binding.

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Dynamical behavior of APC:Cdc20 concentration versus time for the Dissociation variant (A, C) and the Convey variant (B, D) each in the uncontrolled (A, B) and the controlled (C, D) case.Calculation results are presented for different values of the rate k−7 in [s−1 >(dissociation of MCC:APC) between 0.0008 and 0.08, because k−7 is unknown and crucial for model behavior, as indicated. The APC:Cdc20 concentration should be close to zero before attachment and should rise quickly after attachment. Spindle attachment occurs at t = 2000s (switching parameter u from 1 to 0). For the uncontrolled case (A, B), both variants cannot explain the checkpoint behavior; and the Convey variant is even less satisfying compared to the Dissociation variant. In the controlled case (C, D), both variants fully inhibit APC:Cdc20 before attachment and both show fast switching recovery for high k−7 values. The controlled Convey variant (D) is slightly faster (by about 5 mins) in switching compared to the controlled Dissociation (C) variant. Parameters setting according to Table 1 and Table 2.
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pone-0001555-g002: Dynamical behavior of APC:Cdc20 concentration versus time for the Dissociation variant (A, C) and the Convey variant (B, D) each in the uncontrolled (A, B) and the controlled (C, D) case.Calculation results are presented for different values of the rate k−7 in [s−1 >(dissociation of MCC:APC) between 0.0008 and 0.08, because k−7 is unknown and crucial for model behavior, as indicated. The APC:Cdc20 concentration should be close to zero before attachment and should rise quickly after attachment. Spindle attachment occurs at t = 2000s (switching parameter u from 1 to 0). For the uncontrolled case (A, B), both variants cannot explain the checkpoint behavior; and the Convey variant is even less satisfying compared to the Dissociation variant. In the controlled case (C, D), both variants fully inhibit APC:Cdc20 before attachment and both show fast switching recovery for high k−7 values. The controlled Convey variant (D) is slightly faster (by about 5 mins) in switching compared to the controlled Dissociation (C) variant. Parameters setting according to Table 1 and Table 2.

Mentions: Figure 2 displays the APC:Cdc20 concentrations over time. For both, Dissociation and Convey variant, we have selected the time range such that each concentration can reach steady state. For all calculations, the concentrations and rates of Table 2 were chosen including those for k7, k8, and k−8. We varied the rate of k−7 (dissociation of MCC:APC) between 0.0008 and 0.08, because k−7 is unknown and crucial for model behavior. For both model variants, we distinguished 2 scenarios: in one scenario reaction Eq. (7a) (or Eq. (7b)) of the checkpoint is valid all the time (“uncontrolled”), while in the other case this reaction is silenced until it is activated by microtubule attachment to the kinetochore (“controlled”). This property of the controlled case is realized by introducing the factor u′ for reaction Eq. (7a) and Eq. (7b).


In-silico modeling of the mitotic spindle assembly checkpoint.

Ibrahim B, Diekmann S, Schmitt E, Dittrich P - PLoS ONE (2008)

Dynamical behavior of APC:Cdc20 concentration versus time for the Dissociation variant (A, C) and the Convey variant (B, D) each in the uncontrolled (A, B) and the controlled (C, D) case.Calculation results are presented for different values of the rate k−7 in [s−1 >(dissociation of MCC:APC) between 0.0008 and 0.08, because k−7 is unknown and crucial for model behavior, as indicated. The APC:Cdc20 concentration should be close to zero before attachment and should rise quickly after attachment. Spindle attachment occurs at t = 2000s (switching parameter u from 1 to 0). For the uncontrolled case (A, B), both variants cannot explain the checkpoint behavior; and the Convey variant is even less satisfying compared to the Dissociation variant. In the controlled case (C, D), both variants fully inhibit APC:Cdc20 before attachment and both show fast switching recovery for high k−7 values. The controlled Convey variant (D) is slightly faster (by about 5 mins) in switching compared to the controlled Dissociation (C) variant. Parameters setting according to Table 1 and Table 2.
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Related In: Results  -  Collection

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pone-0001555-g002: Dynamical behavior of APC:Cdc20 concentration versus time for the Dissociation variant (A, C) and the Convey variant (B, D) each in the uncontrolled (A, B) and the controlled (C, D) case.Calculation results are presented for different values of the rate k−7 in [s−1 >(dissociation of MCC:APC) between 0.0008 and 0.08, because k−7 is unknown and crucial for model behavior, as indicated. The APC:Cdc20 concentration should be close to zero before attachment and should rise quickly after attachment. Spindle attachment occurs at t = 2000s (switching parameter u from 1 to 0). For the uncontrolled case (A, B), both variants cannot explain the checkpoint behavior; and the Convey variant is even less satisfying compared to the Dissociation variant. In the controlled case (C, D), both variants fully inhibit APC:Cdc20 before attachment and both show fast switching recovery for high k−7 values. The controlled Convey variant (D) is slightly faster (by about 5 mins) in switching compared to the controlled Dissociation (C) variant. Parameters setting according to Table 1 and Table 2.
Mentions: Figure 2 displays the APC:Cdc20 concentrations over time. For both, Dissociation and Convey variant, we have selected the time range such that each concentration can reach steady state. For all calculations, the concentrations and rates of Table 2 were chosen including those for k7, k8, and k−8. We varied the rate of k−7 (dissociation of MCC:APC) between 0.0008 and 0.08, because k−7 is unknown and crucial for model behavior. For both model variants, we distinguished 2 scenarios: in one scenario reaction Eq. (7a) (or Eq. (7b)) of the checkpoint is valid all the time (“uncontrolled”), while in the other case this reaction is silenced until it is activated by microtubule attachment to the kinetochore (“controlled”). This property of the controlled case is realized by introducing the factor u′ for reaction Eq. (7a) and Eq. (7b).

Bottom Line: Our model is validated by simulation of ten perturbation experiments.Only in the controlled case, our models show (M)SAC behaviour at meta- to anaphase transition in agreement with experimental observations.Our simulations revealed that for (M)SAC activation, Cdc20 is not fully sequestered; instead APC is inhibited by MCC binding.

View Article: PubMed Central - PubMed

Affiliation: Bio System Analysis Group, Institute of Computer Science, Friedrich-Schiller-University Jena, Jena, Germany.

ABSTRACT

Background: The Mitotic Spindle Assembly Checkpoint ((M)SAC) is an evolutionary conserved mechanism that ensures the correct segregation of chromosomes by restraining cell cycle progression from entering anaphase until all chromosomes have made proper bipolar attachments to the mitotic spindle. Its malfunction can lead to cancer.

Principle findings: We have constructed and validated for the human (M)SAC mechanism an in silico dynamical model, integrating 11 proteins and complexes. The model incorporates the perspectives of three central control pathways, namely Mad1/Mad2 induced Cdc20 sequestering based on the Template Model, MCC formation, and APC inhibition. Originating from the biochemical reactions for the underlying molecular processes, non-linear ordinary differential equations for the concentrations of 11 proteins and complexes of the (M)SAC are derived. Most of the kinetic constants are taken from literature, the remaining four unknown parameters are derived by an evolutionary optimization procedure for an objective function describing the dynamics of the APC:Cdc20 complex. MCC:APC dissociation is described by two alternatives, namely the "Dissociation" and the "Convey" model variants. The attachment of the kinetochore to microtubuli is simulated by a switching parameter silencing those reactions which are stopped by the attachment. For both, the Dissociation and the Convey variants, we compare two different scenarios concerning the microtubule attachment dependent control of the dissociation reaction. Our model is validated by simulation of ten perturbation experiments.

Conclusion: Only in the controlled case, our models show (M)SAC behaviour at meta- to anaphase transition in agreement with experimental observations. Our simulations revealed that for (M)SAC activation, Cdc20 is not fully sequestered; instead APC is inhibited by MCC binding.

Show MeSH
Related in: MedlinePlus