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Using default constraints of the spindle assembly checkpoint to estimate the associated chemical rates.

Dao Duc K, Holcman D - BMC Biophys (2012)

Bottom Line: Our purpose is to use these opposed constraints to estimate the associated chemical rates.We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached.By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute for Biology (IBENS), Group of Computational Biology and Applied Mathematics, Ecole Normale Supérieure, 46 rue d'Ulm 75005 Paris, France. holcman@ens.fr.

ABSTRACT

Unlabelled: :

Background: Default activation of the spindle assembly checkpoint provides severe constraints on the underlying biochemical activation rates: on one hand, the cell cannot divide before all chromosomes are aligned, but on the other hand, when they are ready, the separation is quite fast, lasting a few minutes. Our purpose is to use these opposed constraints to estimate the associated chemical rates.

Results: To analyze the above constraints, we develop a markovian model to describe the dynamics of Cdc20 molecules. We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached.

Conclusions: By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.

No MeSH data available.


Related in: MedlinePlus

Markov diagram for the probability of number of Cdc20 molecules. Cdc20 at state k is generated and destroyed at rate λ(S -- k) and k-1k respectively. Diffusing Cdc20 molecules bind to the APC/C complex to trigger the separation of sister chromatids.
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Figure 2: Markov diagram for the probability of number of Cdc20 molecules. Cdc20 at state k is generated and destroyed at rate λ(S -- k) and k-1k respectively. Diffusing Cdc20 molecules bind to the APC/C complex to trigger the separation of sister chromatids.

Mentions: which accounts for all the activations which have happened before time t from all the states k. Starting with k active Cdc20 molecules and no activation, there are three possible transitions (figure 2): 1) one Cdc20 molecule is inhibited, so that k-1 active molecules are left 2) one Cdc20 molecule activates the APC/C 3) one Cdc20 molecule is generated, leading to the transition from k to k+1 active molecules. Thus, the probabilities pk satisfy the chemical master equations [18,20]


Using default constraints of the spindle assembly checkpoint to estimate the associated chemical rates.

Dao Duc K, Holcman D - BMC Biophys (2012)

Markov diagram for the probability of number of Cdc20 molecules. Cdc20 at state k is generated and destroyed at rate λ(S -- k) and k-1k respectively. Diffusing Cdc20 molecules bind to the APC/C complex to trigger the separation of sister chromatids.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3368725&req=5

Figure 2: Markov diagram for the probability of number of Cdc20 molecules. Cdc20 at state k is generated and destroyed at rate λ(S -- k) and k-1k respectively. Diffusing Cdc20 molecules bind to the APC/C complex to trigger the separation of sister chromatids.
Mentions: which accounts for all the activations which have happened before time t from all the states k. Starting with k active Cdc20 molecules and no activation, there are three possible transitions (figure 2): 1) one Cdc20 molecule is inhibited, so that k-1 active molecules are left 2) one Cdc20 molecule activates the APC/C 3) one Cdc20 molecule is generated, leading to the transition from k to k+1 active molecules. Thus, the probabilities pk satisfy the chemical master equations [18,20]

Bottom Line: Our purpose is to use these opposed constraints to estimate the associated chemical rates.We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached.By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute for Biology (IBENS), Group of Computational Biology and Applied Mathematics, Ecole Normale Supérieure, 46 rue d'Ulm 75005 Paris, France. holcman@ens.fr.

ABSTRACT

Unlabelled: :

Background: Default activation of the spindle assembly checkpoint provides severe constraints on the underlying biochemical activation rates: on one hand, the cell cannot divide before all chromosomes are aligned, but on the other hand, when they are ready, the separation is quite fast, lasting a few minutes. Our purpose is to use these opposed constraints to estimate the associated chemical rates.

Results: To analyze the above constraints, we develop a markovian model to describe the dynamics of Cdc20 molecules. We compute the probability for no APC/C activation before time t, the distribution of Cdc20 at equilibrium and the mean time to complete APC/C activation after all chromosomes are attached.

Conclusions: By studying Cdc20 inhibition and the activation time, we obtain a range for the main chemical reaction rates regulating the spindle assembly checkpoint and transition to anaphase.

No MeSH data available.


Related in: MedlinePlus