Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors

Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E. S.

doi:10.1063/1.4807733

Cited by 17 publications

(14 citation statements)

References 17 publications

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“…The detailed relation between ABN and a similar approach developed by Thomas and coworkers (Thomas and Richard, 1990) is discussed in a previous publication . Previous work has also shown that the ABN framework employed here can faithfully represent the behavior of differential equation models with sufficiently sharp sigmoidal response functions associated with the links Sun et al, 2013).…”

Section: Introductionmentioning

confidence: 89%

“…We reproduce here, with minor adjustments in notation, the description of the ABN modeling framework presented by Sun et al (2013). ABN models, in general, are designed to implement directly the three core features of a regulatory system: (1) the architecture of causal links between regulatory elements; (2) the logic of the response of each element to its regulators; and (3) the times required for targets to respond to changes in the states of their regulators.…”

Section: Appendix a Abn Model Frameworkmentioning

confidence: 99%

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Regulatory logic and pattern formation in the early sea urchin embryo

Sun

Cheng

Socolar

2014

Journal of Theoretical Biology

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We model the endomesoderm tissue specification process in the vegetal half of the early sea urchin embryo using Boolean models with continuous-time updating to represent the regulatory network that controls gene expression. Our models assume that the network interaction rules remain constant over time and the dynamics plays out on a predetermined program of cell divisions. An exhaustive search of two-node models, in which each node may represent a module of several genes in the real regulatory network, yields a unique network architecture that can accomplish the pattern formation task at hand--the formation of three latitudinal tissue bands from an initial state with only two distinct cell types. Analysis of an eight-gene model constructed from available experimental data reveals that it has a modular structure equivalent to the successful two-node case. Our results support the hypothesis that the gene regulatory network provides sufficient instructions for producing the correct pattern of tissue specification at this stage of development (between the fourth and tenth cleavages in the urchin embryo).

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Section: Introductionmentioning

confidence: 89%

Section: Appendix a Abn Model Frameworkmentioning

confidence: 99%

Regulatory logic and pattern formation in the early sea urchin embryo

Sun

Cheng

Socolar

2014

Journal of Theoretical Biology

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“…In certain limits, interactions between network elements become switch–like [Kauffman (1969); Glass (1975,b); Snoussi (1989); Mochizuki (2005); Alon (2006); Mendoza and Xenarios (2006); Davidich and Bornholdt (2008); Wittmann et al (2009); Franke (2010); Veliz-Cuba et al (2012); Casey et al (2006); Sun et al (2013)]. For example, the Hill function, f ( x ) = x n /( x n + J n ), approaches the Heaviside function, H ( x – J ), in the limit of large n , and the domain on which the network is modeled is naturally split into subdomains.…”

Section: Introductionmentioning

confidence: 99%

Piecewise Linear and Boolean Models of Chemical Reaction Networks

2014

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Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator.

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“…Boolean networks are seen as a way towards understanding large coupled systems that are too complex to be modeled in every detail, especially including amplitude-specific interactions [Ghi08,Nor07,Rib08,Soc03,Sun13]. For example, simple models such as Boolean networks are helpful in the fields of life sciences and geosciences.…”

Section: Boolean Networkmentioning

confidence: 99%

Dynamics of Complex Autonomous Boolean Networks

Rosin

2015

Springer Theses

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Network science provides a powerful framework for analyzing complex systems found in physics, biology, and social sciences. One way of studying the dynamics of networks is to engineer and measure them in the laboratory, which is particularly difficult with established approaches. In this thesis, I approach this problem using a hardware device with time-delay elements executing Boolean functions that can be connected to autonomous Boolean networks with chaotic, periodic, or excitable dynamics. I am able to make scientific discoveries for networks with each of these three different node dynamics, driven by the large flexibility and the non-ideal effects of the experiment complemented by analytical and numerical investigations.Using network realizations with periodic Boolean oscillators, I study socalled chimera states and find that they can disappear and reappear-the resurgence of chimera states. I measure the transient times of chimera states and find a power-law relationship between the average transient time and the phase space volume with an exponent of κ = −0.28 ± 0.10.I also study cluster synchronization in networks of coupled excitable systems. In these artificial neural networks, I find a breakdown of an established theoretical tool when the heterogeneity of the link time delays is greater than the neural refractory period. This phenomenon is used to derive a control scheme for spiking patterns generated by neural networks.Experimental implementations of these systems take advantage of the fast timescale of electronic logic gates, large scalability, and low price. These properties make the system attractive for technological applications, as I demonstrate by realizing a physical random number generator that has an ultra-high bitrate of 12.8 Gbit/s and a silicon neuron that is a thousand times faster than the fastest preceding silicon neuron. For the study of coupled oscillator networks, I develop a phase-locked loop allowing for multiple drivers that may be advantageous for clock synchronization. Instead of the common topologies with one driver per oscillator, it allows for heavily connected clock networks to increase robustness against failure.iii Z U S A M M E N FA S S U N G • D. P. Rosin, D. Rontani, and D. J. Gauthier. Ultrafast physical generation of random numbers using hybrid Boolean networks. Phys. Rev. E 87, 040902(R) (2013).• D. P. Rosin, D. Rontani, D. J. Gauthier, and E. Schöll. Excitability in autonomous Boolean networks. Europhys. Lett. 100, 30003 (2012).• D. P. Rosin, D. Rontani, D. J. Gauthier, and E. Schöll. Experiments on autonomous Boolean networks. Chaos 23, 025102 (2013).• D. P. Rosin, D. Rontani, and D. J. Gauthier. Synchronization of coupled Boolean phase oscillators. Phys. Rev. E 89, 042907 (2014).• D. P. Rosin, D. Rontani, E. Schöll, and D. J. Gauthier. Transient scaling and resurgence of chimera states in coupled Boolean phase oscillators.

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Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors

Cited by 17 publications

References 17 publications

Regulatory logic and pattern formation in the early sea urchin embryo

Regulatory logic and pattern formation in the early sea urchin embryo

Piecewise Linear and Boolean Models of Chemical Reaction Networks

Dynamics of Complex Autonomous Boolean Networks

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