Boolean versus continuous dynamics on simple two-gene modules

Gehrmann, Eva; Drossel, Barbara

doi:10.1103/physreve.82.046120

Cited by 19 publications

(27 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast to Theorem 6, very large separation of time scales destroys the consistency for the first system studied in [4], despite the fact that its Boolean approximation is one-stepping. Thus the mechanism for consistency at other time scales that is reported in [4] must be different.…”

Section: Related Resultsmentioning

confidence: 72%

See 1 more Smart Citation

Two classes of ODE models with switch-like behavior

Just¹,

Korb²,

Elbert³

et al. 2013

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

In cases where the same real-world system can be modeled both by an ODE system ⅅ and a Boolean system 𝔹, it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively equivalent predictions. In this note we introduce two broad classes of relatively simple models that provide a convenient framework for studying such questions. In contrast to the widely known class of Glass networks, the right-hand sides of our ODEs are Lipschitz-continuous. We prove that if 𝔹 has certain structures, consistency between ⅅ and 𝔹 is implied by sufficient separation of time scales in one class of our models. Namely, if the trajectories of 𝔹 are “one-stepping” then we prove a strong form of consistency and if 𝔹 has a certain monotonicity property then there is a weaker consistency between ⅅ and 𝔹. These results appear to point to more general structure properties that favor consistency between ODE and Boolean models.

show abstract

Section: Related Resultsmentioning

confidence: 72%

“…Gehrmann and Drossel [4] obtained results about consistency between ODE models for two small gene regulatory networks and their Boolean approximations. In contrast to Glass networks and [17], in these models the right-hand sides of the ODEs are Lipschitz-continuous, as they are in the models studied here.…”

Section: Related Resultsmentioning

confidence: 99%

Two classes of ODE models with switch-like behavior

Just¹,

Korb²,

Elbert³

et al. 2013

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…The mathematical validity of generalized modelling was recently confirmed by rigorous proofs [34], whereas applicability to actual problems from different fields was demonstrated in several recent publications [32,[38][39][40][41][42][43][44].…”

Section: Dynamical Equivalence Of Food Websmentioning

confidence: 88%

Mesoscale symmetries explain dynamical equivalence of food webs

2012

View full text Add to dashboard Cite

Abstract. A goal of complex system research is to identify the dynamical implications of network structure. While early results focused mainly on local or global structural properties, there is now growing interest in mesoscale structures that comprise more than one node but not the whole network. A central challenge is to discover under what conditions the occurrence of a specific mesoscale motif already allows conclusions on the dynamics of a network as a whole. In this paper, we investigate the dynamics of ecological food webs, complex heterogeneous networks of interacting populations. Generalizing the results of MacArthur and Sánchez-García (2009 Phys. Rev. E 80 26117), we show that certain mesoscale symmetries imply the existence of localized dynamical modes. If these modes are unstable the occurrence of the corresponding mesoscale motif implies dynamical instability regardless of the structure of the embedding network. In contrast, if the mode is stable it means that the symmetry can be exploited to reduce the number of nodes in the model, without changing the dynamics of the system. This result explains a previously observed dynamical equivalence between food webs containing a different number of species.

show abstract

“…When studying the dynamical patterns or attractors of model GRNs [20][21][22], predictions depend on the choice of models, e.g., the scaling of the number of attractors with respect to system size in random Boolean networks [23]. While a Boolean approximation to sigmoidal switching interactions seems robust in many cases [24][25][26], several oversimplifications of established models, such as synchronous update of node states, negligence of transmission delays, and homogeneous network elements, can restrict the dynamics or yield artifacts.…”

Section: Introductionmentioning

confidence: 99%

Transient dynamics and their control in time-delay autonomous Boolean ring networks

et al. 2017

View full text Add to dashboard Cite

Biochemical systems with switch-like interactions, such as gene regulatory networks, are well modeled by autonomous Boolean networks. Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, most models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation. To address this issue, we we have developed an experimental testbed to realize a time-delay autonomous Boolean network with three inhibitory nodes, known as a repressilator, and use it to study the dynamics that arise as time delays along the links vary. We observe various nearly-periodic oscillatory transient patterns with extremely long lifetime, which emerge in small network motifs due to the delay, and which are distinct from the eventual asymptotically stable periodic attractors. For repeated experiments with a given network, we find that stochastic processes give rise to a broad distribution of transient times with an exponential tail. In some cases, the transients are so long that it is doubtful the attractors will ever be approached in a biological system that has a finite lifetime. To counteract the long transients, we show experimentally that small, occasional perturbations applied to the time delays can force the trajectories to rapidly approach the attractors.

show abstract

Boolean versus continuous dynamics on simple two-gene modules

Cited by 19 publications

References 32 publications

Two classes of ODE models with switch-like behavior

Two classes of ODE models with switch-like behavior

Mesoscale symmetries explain dynamical equivalence of food webs

Transient dynamics and their control in time-delay autonomous Boolean ring networks

Contact Info

Product

Resources

About