A Linear Approach to Fault Analysis and Intervention in Boolean Systems

Abstract

The mutations of a complex systemic disease like cancer can be modeled as stuck-at faults in the Boolean system paradigm. For a class of multiple faults, the fault identification is exceptionally significant under the incomplete access of all the underlying proteins of the system. A comprehensive linear framework has been developed in this manuscript to identify the class of faults under a set of homeostatic input conditions. An algorithm is developed to design new reporters to improve the observability. The other aspect of this manuscript lies in controlling the manifestation of the mutations, which is the essential objective of systems medicine research. The primary goal is to synthesize a cocktail of drug molecules (combination therapy) from a set of existing targeted drugs. The controllability results are included in this paper to understand the problem formally. An improvement of controllability algorithm is discussed to design new target drugs if the available drugs fail to accommodate the underlying fault set. The results are presented for Boolean maps and Boolean control networks. Biological examples are given to highlight the relevant results.