Cellcycle control Chapter 7 of Aguda Friedman Amanda

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Cell-cycle control Chapter 7 of Aguda & Friedman Amanda Galante Cancer Dynamics RIT September

Cell-cycle control Chapter 7 of Aguda & Friedman Amanda Galante Cancer Dynamics RIT September 25, 2009

Cell-cycle checkpoints • Restriction point – Regulate initiation of DNA replication • G 2

Cell-cycle checkpoints • Restriction point – Regulate initiation of DNA replication • G 2 -M checkpoint – Checks DNA damage • Spindle checkpoint – Checks chromosome alignment

Restriction Point • ‘Commitment point’ for DNA replication • R point – time after

Restriction Point • ‘Commitment point’ for DNA replication • R point – time after which cell will enter S phase, even in absence of growth factors • Many cancers involve malfunctions of this checkpoint

G 2 DNA Damage Checkpoint (G 2 DDC) • Need to understand how coupled

G 2 DNA Damage Checkpoint (G 2 DDC) • Need to understand how coupled PD (phosphorylationdephosphorylation) cycles work • Need to establish bistability

PD cycle simple example

PD cycle simple example

Transcritical Bifurcation Point

Transcritical Bifurcation Point

Two PD cycles Note that the eigenvalues of the Jacobian are both negative, implying

Two PD cycles Note that the eigenvalues of the Jacobian are both negative, implying a stable s. s. Could be unstable if That is, we need a destabilizing feedback loop.

Coupled PD cycles Transcritical bistability condition:

Coupled PD cycles Transcritical bistability condition:

Applied to G 2 DDC

Applied to G 2 DDC

Results of G 2 DDC model • Made up rate parameters (not experimentally available)

Results of G 2 DDC model • Made up rate parameters (not experimentally available) • Was able to show transcritical bistability as • Note that MPF and Cdc 25 become active at same time – ‘hallmark of transcritical bifurcation in positively coupled cyclic reactions’

PD cycle conclusions • Established existence of transcritical bifurcation point for two coupled PD

PD cycle conclusions • Established existence of transcritical bifurcation point for two coupled PD cycles – Allows system to ‘check whether all components are ready for the next cell cycle event’ • MPF, Cdc 25, Wee 1 coupled PD cycles can be shown to generate bistability when including other reactions • Also applicable to R point for cyclin E/CDK 2 and Cdc 25 a

Mitotic spindle checkpoint Wikipedia - Kinetochore

Mitotic spindle checkpoint Wikipedia - Kinetochore

Model Assumptions • • • Final kinetochore attachment Cell-cycle progression triggered by a protein

Model Assumptions • • • Final kinetochore attachment Cell-cycle progression triggered by a protein c* c diffuses throughout nucleus ρ = kinetochore radius (0. 01 µm) R = nucleus radius (1 µm) D = diffusivity of c (1 µm 2/s)

Model Objectives 1. After final kinetochore attachment, a protein c which was previously in

Model Objectives 1. After final kinetochore attachment, a protein c which was previously in an inhibited state c* , becomes sufficiently activated at time Tb < 3 minutes 2. At steady state, c is predominantly in an inhibited state (want at least 90% inhibited, or Ac<0. 1). In this way, the system resets itself.

Model framework Doncic 2005

Model framework Doncic 2005

Direct Inhibition Model Summary: Tb = 1. 5 min – good! A = 0.

Direct Inhibition Model Summary: Tb = 1. 5 min – good! A = 0. 4 (i. e. 40% of c molecules are inhibited) -- too high

“Self-Propagating Inhibition” Model Summary: Tb = not happening… A < 0. 1

“Self-Propagating Inhibition” Model Summary: Tb = not happening… A < 0. 1

“Emitted Inhibition” Model Summary: Tb = 2. 5 min A = 0. 05 (i.

“Emitted Inhibition” Model Summary: Tb = 2. 5 min A = 0. 05 (i. e. the system resets itself)

Varying parameters

Varying parameters

Conclusions of Mitotic Spindle Checkpoint Model • Single unattached kinetochore activating protein is a

Conclusions of Mitotic Spindle Checkpoint Model • Single unattached kinetochore activating protein is a matter of speculation • Illustrates the impact of temporal & spatial constraints • Were able to develop a model which met the objectives – ‘Emitted Inhibition Model’

References Aguda, BD & A Friedman. Models of Cellular Regulation. Oxford University Press, 2008.

References Aguda, BD & A Friedman. Models of Cellular Regulation. Oxford University Press, 2008. Aguda, BD. (1999) ‘Instabilities in phosphorylation-dephosphorylation cascades and cell cycle checkpoints, ’ Oncogene 18, 2846 -2851. Aguda, BD. (1999) ‘A quantitative analysis of the kinetics of the G 2 DNA damage checkpoint system, ’ PNAS 96, 11352 -11357. Doncic, A, Ben-Jacob, E and N Barkai. (2006) ‘Evaluating putative mechanisms of the mitotic spindle checkpoint, ’ PNAS 102, 63326337. Other picture references • Wikipedia • http: //www. mun. ca/biology/desmid/brian/BIOL 206019/CB 19. html