Dynamic patterns of gene regulation I: Simple two-gene systems

Widder, Stefanie; Schicho, Josef; Schuster, Peter

doi:10.1016/j.jtbi.2007.01.004

Cited by 51 publications

(65 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Biologically, the Hill coefficient is related to the molecular binding mechanism. In simple cases n is the number of protein monomers required for saturation of binding to the DNA [48]. The Hill function for inhibition, (see Figure 1(b)).…”

Section: Ordinary Differential Equationsmentioning

confidence: 99%

“…In doing so, we will integrate and expand analysis presented in [48] for a class of two-gene networks.…”

Section: A Representative Examplementioning

confidence: 99%

“…It is worth mentioning here that different versions of the activator-inhibitor network have been often studied in previous work, e.g. in [48] where no self-regulation is considered, and also in [11,13,26] where self-regulation of one or both genes is considered. In our case we shall not consider any self-regulation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparing different ODE modelling approaches for gene regulatory networks

Polynikis

Hogan

Bernardo

2009

Journal of Theoretical Biology

148

102

View full text Add to dashboard Cite

A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical models for the purposes of analysis and design. For example, to synthesize a gene regulatory network, the derivation of a mathematical model is important in order to carry out in silico investigations of the network dynamics and to investigate parameter variations and robustness issues. Different mathematical frameworks have been proposed to derive such models. In particular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed to model the dynamics of the concentrations of mRNAs and proteins. These models are usually characterized by the presence of highly nonlinear Hill function terms. A typical simplification is to reduce the number of equations by means of a quasi-steady-state assumption on the mRNA concentrations. This yields a class of simplified ODE models. A radically different approach is to replace the Hill functions by piecewise-linear approximations [5]. A further modelling approach is the use of discretetime maps [7] where the evolution of the system is modelled in discrete, rather than continuous, time. The aim of this paper is to discuss and compare these different modelling approaches, using a representative gene regulatory network. We will show that different models often lead to conflicting conclusions concerning the existence and stability of equilibria and stable oscillatory behaviours. Moreover, we shall discuss, where possible, the viability of making certain modelling approximations (e.g. quasi-steady-state mRNA dynamics or piecewise-linear approximations of Hill functions) and their effects on the overall system dynamics.

show abstract

Section: Ordinary Differential Equationsmentioning

confidence: 99%

“…In doing so, we will integrate and expand analysis presented in [48] for a class of two-gene networks.…”

Section: A Representative Examplementioning

confidence: 99%

See 1 more Smart Citation

Comparing different ODE modelling approaches for gene regulatory networks

Polynikis

Hogan

Bernardo

2009

Journal of Theoretical Biology

148

102

View full text Add to dashboard Cite

show abstract

“…A study of two gene systems is given in a separate paper [13]. Here we present an analysis of repressilator systems with an arbitrary number of identical genes and with arbitrarily strong repressor binding.…”

Section: Introductionmentioning

confidence: 99%

A generalized model of the repressilator

et al. 2006

Self Cite

View full text Add to dashboard Cite

Abstract:The repressilator is a regulatory cycle of n genes where each gene represses its successor in the cycle: 1 ⊣ 2 ⊣ . . . ⊣ n ⊣ 1. The system is modelled by ODEs for an arbitrary number of identical genes and arbitrarily strong repressor binding. A detailed mathematical analysis of the dynamical behavior is provided for two model systems: (i) a repressilator with leaky transcription and single-step cooperative repressor binding, and (ii) a repressilator with auto-activation and cooperative regulator binding. Genes are assumed to be present in constant amounts, transcription and translation are modelled by single-step kinetics, and mRNAs as well as proteins are assumed to be degraded by first order reactions. Several dynamical patterns are observed: Multiple steady states, periodic and aperiodic oscillations corresponding to limit cycles and heteroclinic cycles, respectively. The results of computer simulations are complemented by a detailed and complete stability analysis of all equilibria and of the heteroclinic cycle.

show abstract

“…During the last decade numerous experimental and theoretical studies were devoted to analyze its formal properties and its natural occurrence (Hasty et al (2001); Cherry and Adler (2000); Laurent and Kellershohn (1999); Novak and Tyson (2003); Widder et al (2007)). Although it pervades many different biological processes, it is reasonable to assume that cellular decision-making is not only based on binary solutions.…”

Section: Introductionmentioning

confidence: 99%

Why are cellular switches Boolean? General conditions for multistable genetic circuits

Macía

Widder

Solé

2009

Journal of Theoretical Biology

Self Cite

View full text Add to dashboard Cite

The logic of cellular decision making is largely controlled by regulatory circuits defining molecular switches. Such switching elements allow to turn a graded input signal into an all-or-nothing output. Traditional studies have focused on this bistable picture of regulation, but higher-order scenarios involving tristable and tetrastable states are possible too. Are these multiswitches allowed in simple gene regulatory networks? Are they likely to be observed? If not, why not? In this paper we present the examination of this question by means of a simple but powerful geometric approach. We examine the relation between multistability, the degree of multimerization of the regulators and the role of autoloops within a deterministic setting, finding that N-stable circuits are possible, although their likelihood to occur rapidly decays with the order of the switch. Our work indicates that, despite twocomponent circuits are able to implement multistability, they are optimal for Boolean switches. The evolutionary implications are outlined.

show abstract

Dynamic patterns of gene regulation I: Simple two-gene systems

Cited by 51 publications

References 29 publications

Comparing different ODE modelling approaches for gene regulatory networks

Comparing different ODE modelling approaches for gene regulatory networks

A generalized model of the repressilator

Why are cellular switches Boolean? General conditions for multistable genetic circuits

Contact Info

Product

Resources

About