VOLUME 6 NUMBER 2 (July to December 2013)

Phil. Sci. Lett. 2013 6 (2) 138-146
available online: July 26, 2013

*Corresponding author
Email Address: delrosariorc@gis.a-star.edu.sg
Submitted: March 31, 2013
Revised: June 5, 2013
Accepted: June 15, 2013

ARTICLE

Mathematical analysis of bistabilityin reduced models of apoptosis

by Joseph Ray Clarence G. Damasco1, Marian P. Roque1, Ricardo C. H.del Rosario1,2*

1Institute of Mathematics, College of Science, University of the Philippines Diliman
2Current Address: Genome Institute of Singapore, 60 Biopolis St., 138672 Singapore
Apoptosis or programmed cell death is animportant process in multicellular organismssince it is involved in the decision to continueliving or to commit suicide. It is an intrinsic partof cellular development and homeostasis, andfailure in this mechanism can lead to serious disorders such ascancers, autoimmune diseases, and neurodegenerative disorders.The apoptotic pathway exhibits bistability, which is the capacityof a system to operate in two qualitatively distinct states. Weanalyze four basic mathematical models of apoptosis to study theprocesses that enable the system to perform the switch fromsurvival to death. Specifically, we study how cooperativity andinhibition, which are key features of the apoptotic signaltransduction network, enable the system to achieve bistability.Our contribution is the use of a purely analytical method tocompute the steady states and eigenvalues of the Jacobian matrixat steady state, and thus we are able to completely determineregions in the parameter space where each of the consideredmodels could exhibit bistability. We also discuss how changes insystem parameters such as production and degradation ratesaffect the capacity of the system to exhibit bistability.

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