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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

Representation of the domain Ω (red). A: The probability for no activation at time τ = 10min as a function of parameters λ and k-1. Other parameters are those of table I B : The mean time to threshold as a as a function of parameters λ and k-1. Other parameters are those of table I. C : The curve 1 is given as the level line associated τ = 10 min in figure B. The curve 2 is the level line associated with the probability P given by P(τ) = 0.95 in figure A. These two curves determine the domain Ω satisfying conditions C1 and C2.
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Figure 6: Representation of the domain Ω (red). A: The probability for no activation at time τ = 10min as a function of parameters λ and k-1. Other parameters are those of table I B : The mean time to threshold as a as a function of parameters λ and k-1. Other parameters are those of table I. C : The curve 1 is given as the level line associated τ = 10 min in figure B. The curve 2 is the level line associated with the probability P given by P(τ) = 0.95 in figure A. These two curves determine the domain Ω satisfying conditions C1 and C2.

Mentions: Using formula (23) for the probability P(τ1) and integrating numerically the time 〈τS〉 from the matrix equation (31), we determine a range of validity for these parameters by a geometrical domain Ω represented in figure 6, as the intersection Ω = Ω1 ∩ Ω2, where


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

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

Representation of the domain Ω (red). A: The probability for no activation at time τ = 10min as a function of parameters λ and k-1. Other parameters are those of table I B : The mean time to threshold as a as a function of parameters λ and k-1. Other parameters are those of table I. C : The curve 1 is given as the level line associated τ = 10 min in figure B. The curve 2 is the level line associated with the probability P given by P(τ) = 0.95 in figure A. These two curves determine the domain Ω satisfying conditions C1 and C2.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Representation of the domain Ω (red). A: The probability for no activation at time τ = 10min as a function of parameters λ and k-1. Other parameters are those of table I B : The mean time to threshold as a as a function of parameters λ and k-1. Other parameters are those of table I. C : The curve 1 is given as the level line associated τ = 10 min in figure B. The curve 2 is the level line associated with the probability P given by P(τ) = 0.95 in figure A. These two curves determine the domain Ω satisfying conditions C1 and C2.
Mentions: Using formula (23) for the probability P(τ1) and integrating numerically the time 〈τS〉 from the matrix equation (31), we determine a range of validity for these parameters by a geometrical domain Ω represented in figure 6, as the intersection Ω = Ω1 ∩ Ω2, where

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