Stochastic chemical kinetics and the quasi-steady-state assumption : application to the stochastic simulation algorithm and chemical master equation

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

From words to integers and beyond in corporate life

Poets have a licence to couch great truths in succinct, emotionally powerful, and perhaps slightly mysterious and ambiguous ways. On the other hand, it is the task of academics to explore such truths intellectually, in depth and detail, identifying the key constructs and their underlying relations and structures, hopefully without impairing the essential truth. So it could be said that in January 2013, around 60 academics gathered at the University of Texas, Austin under the benign and encouraging eye of their own muse, Professor Rod Hart, to play their role in exploring and explaining the underlying truth of Yan Zhen’s words. The goals of this chapter are quite broad. Rod was explicit and yet also somewhat Delphic in his expectations and aspirations for the chapter. Even though DICTION was a key analytic tool in most chapters, this chapter was not to be about DICTION per se, or simply a critique of the individual chapters forming this section of the book. Rather DICTION and these studies, as well as some others that got our attention, were to be more a launching pad for observations on what they revealed about the current state of understanding and research into the language of institutions, as well as some ‘adventurous’, but not too outlandish reflections on future challenges and opportunities.