Hiroyuki Kuwahara

In order to efficiently analyze the complicated regulatory systems often encountered in biological settings, abstraction is essential. This paper presents an automated abstraction methodology that systematically reduces the small-scale complexity found in genetic regulatory network models, while broadly preserving the large-scale system behavior. Our method first reduces the number of reactions by using rapid equilibrium and quasi-steady-state approximations as well as a number of other stoichiometry-simplifying techniques, which together result in substantially shortened simulation time. To further reduce analysis time, our method can represent the molecular state of the system by a set of scaled Boolean (or n-ary) discrete levels. This results in a chemical master equation that is approximated by a Markov chain with a much smaller state space providing significant analysis time acceleration and computability gains. The genetic regulatory network for the phage λ lysis/lysogeny decision switch is used as an example throughout the paper to help illustrate the practical applications of our methodology.

With the aid of model abstractions, biochemical networks can be analyzed at different levels of resolution: from low-level quantitative models to high-level qualitative ones. Furthermore, an ability to change the level of abstraction can be very useful when dealing with many biological systems, including gene regulatory networks. These systems typically have too many components and states to be practically studied using all-inclusive low-level models, yet they often manifest enough dynamical and functional complexity, making an entirely high-level qualitative representation similarly inadequate - thus necessitating a search for some intermediate level of abstraction. Finally, while most abstractions used in modeling of biochemical networks have traditionally been performed manually, doing so accurately in a large system is a tedious and time-consuming process that is highly susceptible to errors during model transformation. To address these issues, we have developed a methodology and implemented an automated modeling and analysis tool with variable abstraction level capabilities. In this paper, we use it for the analysis of switching in Type 1 pili expression dynamics and, in particular, for the problem of estimating the effect of H-NS and Lrp regulatory protein levels on phase variation rates in E. coli. Such behavior is notoriously difficult to study due to the size of the associated gene regulatory network and the characteristically stochastic dynamics involved, which result in very high analytical and computational demands. Here, we show how, by using our system, we are able to automatically abstract the switch network and accurately predict E. coli afimbriation rates, while, at the same time, accelerating the required computations by up to two orders of magnitude.

In order to efficiently analyze a large scale system in an automated and objective manner, abstraction is essential. This paper presents an automated abstraction methodology that systematically reduces the small scale complexity found in genetic regulatory network models, while broadly preserving the large scale system behavior. Our approach is to first reduce the number of reactions through a quasi-steady-state approximation-based algorithm. Second, it represents the exact molecular state of the system by a set of reduced Boolean (or n-ary) discrete levels. This results in a chemical master equation that is approximated by a Markov chain with a much smaller state space providing significant simulation time acceleration and computability gains.