In part 1 of this pair of talks, I presented the basic ideas and some applications of stability analysis of (bio)chemical systems based on a bipartite graph representation. In this talk, I will briefly present two further developments, first on the stability analysis of models described by delayed mass-action kinetics, and second on dynamics-preserving model simplification using the bipartite graph.

 

It is often convenient to use delay-differential equations to describe gene expression systems due to the significant time required (on biochemical timescales) to transcribe and translate genes. The delayed mass-action formalism was developed as an extension of the classical law of mass-action to enable the formulation of chemically sensible models with delays. A simple modification of the method presented in part 1 allows us to determine whether a model might be capable of delay-induced oscillations.

 

Many biochemical models contain hypothetical biochemical species. It is often of interest to know whether hypothetical species are essential to a system's dynamics, and we would also like to minimize the profusion of unknown parameters present in most biochemical models. Both of these considerations suggest that model reduction methods would be useful. We have recently turned to the problem of using the bipartite graph and its relationship to dynamics in order to reduce the complexity of a biochemical model while preserving its potential for given dynamics. I will briefly review our work to date on this problem.

 

WebEx Link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m581b61891e8876ccae59b3d15d5e95ba

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