Related papers: Boolean Network Approach to Negative Feedback Loop…
Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer…
We present the mechanism of interaction of Wnt network module, which is responsible for periodic sometogenesis, with p53 regulatory network, which is one of the main regulators of various cellular functions, and switching of various…
Recent studies suggest that PML (Promyelocytic Leukemia) suppresses p53 protein degradation by inhibiting MDM2 protein in the nucleus [1], and regulates a number of biological functions [2]. We modeled a PML-MDM2-p53 regulatory network by…
Network remodeling, or adaptation, in the presence of periodically driven forcings has hereto remained largely unexplored, despite the fact that a broad class of biological transport networks, e.g. animal vasculature, depends on periodic…
This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex…
Functional connectivity is a fundamental property of neural networks that quantifies the segregation and integration of information between cortical areas. Due to mathematical complexity, a theory that could explain how the parameters of…
A new formulation of Stochastic Model Predictive Output Feedback Control is presented and analyzed as a translation of Stochastic Optimal Output Feedback Control into a receding horizon setting. This requires lifting the design into a…
We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of ``stochastic feedback''. We illustrate this approach by considering the neuroautonomic regulation of the heart…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…
Dynamical properties of the transcriptional regulatory network of {\it Escherichia coli} and {\it Saccharomyces cerevisiae} are studied within the framework of random Boolean functions. The dynamical response of these networks to a single…
This paper presents a unified framework for analyzing the input-output behavior of discrete time complex networks viewed as open systems. Importantly, we focus on systems that are inherently modeled in discrete time-such as opinion…
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical…
Understanding the relationship between spontaneous stochastic fluctuations and the topology of the underlying gene regulatory network is of fundamental importance for the study of single-cell stochastic gene expression. Here by solving the…
We propose a novel theoretical biomolecular design to implement any Boolean circuit using the mechanism of DNA strand displacement. The design is scalable: all species of DNA strands can in principle be mixed and prepared in a single test…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This…
We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
Mixed feedback loops combining transcriptional and post-transcriptional regulations are common in cellular regulatory networks. They consist of two genes, encoding a transcription factor and a small non-coding RNA (sRNA), which mutually…