Steady-state probabilities for attractors in probabilistic Boolean networks
نویسندگان
چکیده
Boolean networks form a class of disordered dynamical systems that have been studied in physics owing to their relationships with disordered systems in statistical mechanics and in biology as models of genetic regulatory networks. Recently they have been generalized to probabilistic Boolean networks (PBNs) to facilitate the incorporation of uncertainty in the model and to represent cellular context changes in biological modeling. In essence, a PBN is composed of a family of Boolean networks between which the PBN switches in a stochastic fashion. In whatever framework Boolean networks are studied, their most important attribute is their attractors. Left to run, a Boolean network will settle into one of a collection of state cycles called attractors. The set of states from which the network will transition into a specific attractor forms the basin of the attractor. The attractors represent the essential long-run behavior of the network. In a classical Boolean network, the network remains in an attractor once there; in a Boolean network with perturbation, the states form an ergodic Markov chain and the network can escape an attractor, but it will return to it or a different attractor unless interrupted by another perturbation; in a probabilistic Boolean network, so long as the PBN remains in one of its constituent Boolean networks it will behave as a Boolean network with perturbation, but upon a switch it will move to an attractor of the new constituent Boolean network. Given the ergodic nature of the model, the steady-state probabilities of the attractors are critical to network understanding. Heretofore they have been found by simulation; in this paper we derive analytic expressions for these probabilities, first for Boolean networks with perturbation and then for PBNs. r 2005 Elsevier B.V. All rights reserved.
منابع مشابه
A Tutorial on Analysis and Simulation of Boolean Gene Regulatory Network Models
Driven by the desire to understand genomic functions through the interactions among genes and gene products, the research in gene regulatory networks has become a heated area in genomic signal processing. Among the most studied mathematical models are Boolean networks and probabilistic Boolean networks, which are rule-based dynamic systems. This tutorial provides an introduction to the essentia...
متن کاملASSA-PBN: An Approximate Steady-State Analyser of Probabilistic Boolean Networks
We present ASSA-PBN, a tool for approximate steady-state analysis of large probabilistic Boolean networks (PBNs). ASSA-PBN contains a constructor, a simulator, and an analyser which can approximately compute the steadystate probabilities of PBNs. For large PBNs, such approximate analysis is the only viable way to study their long-run behaviours. Experiments show that ASSAPBN can handle large PB...
متن کاملControl of Stationary Behavior in Probabilistic Boolean Networks by Means of Structural Intervention
Probabilistic Boolean Networks (PBNs) were recently introduced as models of gene regulatory networks. The dynamical behavior of PBNs, which are probabilistic generalizations of Boolean networks, can be studied using Markov chain theory. In particular, the steady-state or long-run behavior of PBNs may reflect the phenotype or functional state of the cell. Approaches to alter the steady-state beh...
متن کاملIntervention in a family of Boolean networks
MOTIVATION Intervention in a gene regulatory network is used to avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is a collection of Boolean networks in which the gene state vector transitions according to the rules of one of the constituent networks and where networ...
متن کاملAn approximation method for solving the steady-state probability distribution of probabilistic Boolean networks
MOTIVATION Probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution usually includes construction of the transition probability matrix and computation of the steady-state probabil...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Signal Processing
دوره 85 شماره
صفحات -
تاریخ انتشار 2005