Abstract : The focus of this thesis is modelling and analyzing systems biology using process algebra. We apply three process calculi into systems biology: the π -calculus and a variant, the Iπ-calculus; the κ-calculus and its finer-grained language, the mκ-calculus; and bigraphical reactive systems.
There are three parts of my thesis. First, we introduce the signal transduction with aberrance. A new extension of the Iπ-calculus, the Iπ-calculus, is introduced to model signal transduction with aberrance. The calculus is obtained by adding two aberrant actions into the Iπ-calculus. It is well-defined and biologically visible. The Iπ-calculus shows its expressive capability. However, it needs more information about its terms in the process of simulation, especially in the simulation of aberrant biochemical processes. Therefore, two auxiliary systems, a tag system and a typing system, are introduced to help understanding the Iπ-calculus model. The tag system is more intuitive. But it may be redundant in the recordings of information of terms. The simple typing system, however, is enough to deal with it. We show that the tag system is equal to the typing system in terms of expressive power.
Second, we propose the rigorous question of self-assembly in the protein-protein language, κ-calculus introduced by Vincent Danos and Cosimo Laneve. We use of reversible rules to embed the coarse one (the κ-calculus) into the finer one (the mκ-calculus). We prove that this simulation is correct mathematically.
Finally, we use bigraphs to model and analyze systems biology. First we give an example to show how to model biochemical processes using bigraphical reactive systems (BRSs for short). We take the normal ras activation as our instance. Then the expressive power of the bigraphical models is discussed. We indicate how theκ-calculus, the protein-protein language, can be translated into BRSs by one example, which shows that BRSs is a suitable model in biological studying as well.