Issues in Reasoning about Interaction Networks in Cells: Necessity of Event Ordering Knowledge

In this paper we discuss several representation issues that we came across while modelling molecular interactions in cells of living organisms. One of the issues was that the triggering of events inside cells, an important modelling component, are not necessarily immediate, leading to multiple evolution models in the absence of additional information. Second, often an action or a trigger at one level of granularity of representation can be elaborated and refined. We show the problem that existing representation and modelling formalisms have in dealing with the above issues. We then present an action language which builds up on a previous language, and has the ability to express event ordering knowledge. We show that our language is able to adequately address the above-mentioned issues. Motivation and Introduction In this paper our goal is to use the action language approach for reasoning about actions to specify knowledge about various interactions inside cells of living beings, and to reason about these interactions. Inside the cell various interactions take place between genes, proteins and other biochemical molecules. These interactions influence most visible properties of cells and tissues, such as cells dying, cells proliferating, and cells becoming cancerous. As done in (Tran & Baral 2004; Baral et al. 2004), the interactions can be modelled to some extent as triggered actions. A theory of the cell specifies effects of actions and how actions are triggered or inhibited. Such a specification dictates how the cell evolves (i.e. changes through time). An evolution of the cell starts from a state which triggers certain actions; these actions change the state, which may trigger further actions; and so on. In this paper we delve deeper into the interaction process. To start with, unlike controllers in artificial domains such as softbots, or robots, triggers inside the cell do not necessarily fire immediately. For example, if a cell specification has the trigger “ f triggers a ” and the trigger “ f triggers b ”, it is not always the case that in a state where f is true both a and b immediately occur. One does not have the luxury of specifying exactly how long it takes before a trigger fires, as Copyright c © 2005, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. that information is usually not available and it may not even be a deterministic duration. In some cases, there is insufficient knowledge for one to say with certainty which of a and b occurs before the other. This is an example of a common phenomenon in interaction networks called specificity: a network can respond in different ways to the same input (Tan & Kim 1999). In other cases, some form of ordering between triggered action occurrences is known. Thus a representation and reasoning mechanism should model specificity as well as model event ordering information when appropriate. A related issue in modelling cell behavior is that one can (and often needs to) model at different granularities. As more details are known, an action or trigger at one level of granularity can be shown to consist of triggers and actions at a lower level of granularity. In this case, it is important that the reasoning mechanism, which has been able to reason correctly by incorporating observations about the cell behavior, does not make mistakes when an action or a trigger is replaced by its finer decomposition. The following hypothetical example illustrates some of the above points and shows the problem that one has without using event ordering information, as done in (Tran & Baral 2004) and in almost all other approaches (Reddy, Liebman, & Mavrovouniotis 1996; Peleg, Yeh, & Altman 2002; Regev, Silverman, & Shapiro 2001; Giordano, Martelli, & Schwind 2001; Khan et al. 2003; Talcott et al. 2004; Chabrier et al. 2004; Giunchiglia et al. 2004; Calvanese, de Giacomo, & Vardi. 2002; Fukuda & Takagi 2001; Reiter 1996).