Dynamical Properties of a Boolean Model of Gene Regulatory Network with Memory

Abstract

Classical random Boolean networks (RBN) are not well suited to describe experimental data from time-course microarray, mainly because of the strict assumptions about the synchronicity of the regulatory mechanisms. In order to overcome this setback, a generalization of the RBN model is described and analyzed. Gene products (e.g., regulatory proteins) are introduced, with each one characterized by a specific decay time, thereby introducing a form of memory in the system. The dynamics of these networks is analyzed, and it is shown that the distribution of the decay times has a strong effect that can be adequately described and understood. The implications for the dynamical criticality of the networks are also discussed.

New delay-dependent stability criteria of genetic regulatory networks subject to time-varying delays

“…Theorem 1: For given positive scalars τ 2 > τ 1 , σ 2 > σ 1 , μ and d, the GRNs (6) subject to (3) and (7) are globally asymptotically stable, if there exist positive-definite matrices P = [P ij ] 6×6 , Q i (i = 1, 2, · · · , 5), 3,4) such that the following matrix inequalities hold…”

In Silico Cell: Challenges and Perspectives

“…В настоящее время, арсенал методов, используемых для моделирования молекулярно-генетических систем, достаточно широк и включает дискретные, непрерывные, стохастические и комбинированные подходы. Среди них можно выделить Булевы сети [69,70], обобщенные логические сети [71,72], Байесовские сети [73], динамические Байесовские сети [74,75]; сети Петри [76,77], методы моделирования с использованием линейных (потоковых) [38] и кусочно-линейных [42,45] дифференциальных уравнений; методы моделирования с использованием дифференциальных уравнений, подходы, основанные на применении обыкновенных нелинейных дифференциальных уравнений, в том числе и с запаздывающими аргументами [47,[78][79][80][81], стохастическое моделирование [82][83][84].…”

Using Additive Expression Programming for Gene Regulatory Network Inference

“…In the past several years, many models have been proposed to tackle time series expression data and infer gene regulatory network, such as Boolean network [6][7], dynamic Bayesian network [8], neural network [9], Petri net [10][11], information theoretic approaches [12], the system of differential equation. The system of differential equations is powerful and flexible model to describe complex relations among components.…”