ID: 1708.07882

The Role of Criticality of Gene Regulatory Networks in Morphogenesis

August 12, 2017

View on ArXiv

Similar papers 3

The Structure and Dynamics of Gene Regulation Networks

February 14, 2008

83% Match
Murat Tuğrul
Molecular Networks

The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations for their dynamics, is not always suitable. The graph theoretical models may serve as a rough but powerful tool in such cases. In this thesis, I first consider the network modeling for the representation of the biological systems. Both the...

Find SimilarView on arXiv

Influence of a Structure on System's Dynamics on Example of Boolean Networks

September 6, 1999

83% Match
O. SPbSU Kirillova
Disordered Systems and Neura...

In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation. The regular structures do not give a critical regime in the investigated cases. Hierarchy together with the irregular structure reveals characteristic features of criticality.

Find SimilarView on arXiv

Kauffman Boolean model in undirected scale free networks

July 13, 2007

83% Match
Piotr Fronczak, Agata Fronczak, Janusz A. Holyst
Disordered Systems and Neura...
Statistical Mechanics

We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including scale-free topology of connections $P(k)\sim k^{-\gamma}$. We show that in infinite scale-free networks the transition between frozen and chaotic phase occurs for $3<\gamma < 3.5$. The observation is interesting for two reasons. First, since most of critical phenomena in scale-free networks reveal their non-trivial character for $\...

Find SimilarView on arXiv

Temporal, structural, and functional heterogeneities extend criticality and antifragility in random Boolean networks

September 15, 2022

83% Match
Amahury Jafet López-Díaz, Fernanda Sánchez-Puig, Carlos Gershenson
nlin.AO
cs.DM
cs.IT
math.DS
math.IT
q-bio.QM

Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger, stronger, or faster than others. In homogeneous systems, criticality -- a balance between change and stability, order and chaos -- is usually found for a very narrow region in the parameter space, close to a phase transition. Using random Boolean n...

Find SimilarView on arXiv

Symmetry in Critical Random Boolean Network Dynamics

March 14, 2014

83% Match
Shabnam Hossein, Matthew D. Reichl, Kevin E. Bassler
Statistical Mechanics
Adaptation and Self-Organizi...
Biological Physics

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions th...

Find SimilarView on arXiv

Critical Points for Random Boolean Networks

October 19, 2001

83% Match
James F. Lynch
Adaptation and Self-Organizi...

A model of cellular metabolism due to S. Kauffman is analyzed. It consists of a network of Boolean gates randomly assembled according to a probability distribution. It is shown that the behavior of the network depends very critically on certain simple algebraic parameters of the distribution. In some cases, the analytic results support conclusions based on simulations of random Boolean networks, but in other cases, they do not.

Find SimilarView on arXiv

Boolean Dynamics with Random Couplings

April 26, 2002

83% Match
Leo Kadanoff, Susan Coppersmith, Maximino Aldana
Adaptation and Self-Organizi...
Cellular Automata and Lattic...

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 Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the...

Find SimilarView on arXiv

Relevant components in critical random Boolean networks

June 20, 2006

83% Match
V. Kaufman, B. Drossel
Disordered Systems and Neura...

Random Boolean networks were introduced in 1969 by Kauffman as a model for gene regulation. By combining analytical arguments and efficient numerical simulations, we evaluate the properties of relevant components of critical random Boolean networks independently of update scheme. As known from previous work, the number of relevant components grows logarithmically with network size. We find that in most networks all relevant nodes with more than one relevant input sit in the s...

Find SimilarView on arXiv

Morphological complex networks: Can individual morphology determine the general connectivity and dynamics of networks?

March 31, 2005

83% Match
Luciano da Fontoura Costa
Molecular Networks
Disordered Systems and Neura...

This article discusses how the individual morphological properties of basic objects (e.g. neurons, molecules and aggregates), jointly with their particular spatial distribution, can determine the connectivity and dynamics of systems composed by those objects. This problem is characterized as a particular case of the more general shape and function paradigm, which emphasizes the interplay between shape and function in nature and evolution. Five key issues are addressed: (a) ho...

Find SimilarView on arXiv

Evolution of Activity-Dependent Adaptive Boolean Networks towards Criticality: An Analytic Approach

April 27, 2017

83% Match
Taichi Haruna
Adaptation and Self-Organizi...
Molecular Networks

We propose new activity-dependent adaptive Boolean networks inspired by the cis-regulatory mechanism in gene regulatory networks. We analytically show that our model can be solved for stationary in-degree distribution for a wide class of update rules by employing the annealed approximation of Boolean network dynamics and that evolved Boolean networks have a preassigned average sensitivity that can be set independently of update rules if certain conditions are satisfied. In pa...

Find SimilarView on arXiv