Minimum observability of probabilistic Boolean networks

This paper studies the minimum observability of probabilistic Boolean networks (PBNs), the main objective of which is to add the fewest measurements to make an unobservable PBN become observable. First of all, the algebraic form of a PBN is established with the help of semi-tensor product (STP) of matrices. By combining the algebraic forms of two identical PBNs into a parallel system, a method to search the states that need to be H-distinguishable is proposed based on the robust set reachability technique. Secondly, a necessary and sufficient condition is given to find the minimum measurements such that a given set can be H-distinguishable. Moreover, by comparing the numbers of measurements for all the feasible H-distinguishable state sets, the least measurements that make the system observable are gained. Finally, an example is given to verify the validity of the obtained results

Inferring context-sensitive probablistic boolean networks from gene expression data under multi-biological conditions

In recent years biological microarrays have emerged as a high-throughput data acquisition technology in bioinformatics. In conjunction with this, there is an increasing need to develop frameworks for the formal analysis of biological pathways. A modeling approach defined as Probabilistic Boolean Networks (PBNs) was proposed for inferring genetic regulatory networks [1]. This technology, an extension of Boolean Networks [2], is able to capture the time-varying dependencies with deterministic probabilities for a series of sets of predictor functions

Deterministic and Probabilistic Boolean Control Networks and their application to Gene Regulatory Networks

This thesis focuses on Deterministic and Probabilistic Boolean Control Networks and their application to some specific Gene Regulatory Networks. At first, some introductory materials about Boolean Logic, Left Semi-tensor Product and Probability are presented in order to explain in detail the concepts of Boolean Networks, Boolean Control Networks, Probabilistic Boolean Networks and Probabilistic Boolean Control Networks. These networks can be modelled in state-space and their representation, obtained by means of the left semi-tensor product, is called algebraic form. Subsequently, the thesis concentrates on presenting the fundamental properties of these networks such as the classical Systems Theory properties of stability, reachability, controllability and stabilisation. Afterwards, the attention is drawn towards the comparison between deterministic and probabilistic boolean networks. Finally, two examples of Gene Regulatory Networks are modelled and analysed by means of a Boolean Network and a Probabilistic Boolean Network.This thesis focuses on Deterministic and Probabilistic Boolean Control Networks and their application to some specific Gene Regulatory Networks. At first, some introductory materials about Boolean Logic, Left Semi-tensor Product and Probability are presented in order to explain in detail the concepts of Boolean Networks, Boolean Control Networks, Probabilistic Boolean Networks and Probabilistic Boolean Control Networks. These networks can be modelled in state-space and their representation, obtained by means of the left semi-tensor product, is called algebraic form. Subsequently, the thesis concentrates on presenting the fundamental properties of these networks such as the classical Systems Theory properties of stability, reachability, controllability and stabilisation. Afterwards, the attention is drawn towards the comparison between deterministic and probabilistic boolean networks. Finally, two examples of Gene Regulatory Networks are modelled and analysed by means of a Boolean Network and a Probabilistic Boolean Network

Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited

An approximate representation for the state space of a context-sensitive probabilistic Boolean network has previously been proposed and utilized to devise therapeutic intervention strategies. Whereas the full state of a context-sensitive probabilistic Boolean network is specified by an ordered pair composed of a network context and a gene-activity profile, this approximate representation collapses the state space onto the gene-activity profiles alone. This reduction yields an approximate transition probability matrix, absent of context, for the Markov chain associated with the context-sensitive probabilistic Boolean network. As with many approximation methods, a price must be paid for using a reduced model representation, namely, some loss of optimality relative to using the full state space. This paper examines the effects on intervention performance caused by the reduction with respect to various values of the model parameters. This task is performed using a new derivation for the transition probability matrix of the context-sensitive probabilistic Boolean network. This expression of transition probability distributions is in concert with the original definition of context-sensitive probabilistic Boolean network. The performance of optimal and approximate therapeutic strategies is compared for both synthetic networks and a real case study. It is observed that the approximate representation describes the dynamics of the context-sensitive probabilistic Boolean network through the instantaneously random probabilistic Boolean network with similar parameters