Oscillatory behavior in enzymatic control processes

Goodwin, Brian C.

doi:10.1016/0065-2571(65)90067-1

Cited by 883 publications

(700 citation statements)

References 7 publications

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“…Mathematical modelling of intracellular regulatory systems began with the work of Goodwin (Goodwin 1965). Mahaffy and co-workers developed this work introducing spatial structure (although only in 1-dimension) and also delays accounting for transcription and translation (Mahaffy and Pao 1984;Busenberg and Mahaffy 1985;Mahaffy 1988).…”

Section: Hes1 Mathematical Modelmentioning

confidence: 99%

Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways

Sturrock

Terry

Xirodimas

et al. 2011

Journal of Theoretical Biology

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The correct localisation of transcription factors is vitally important for the proper functioning of many intracellular signalling pathways. Experimental data has shown that many pathways exhibit oscillations in concentrations of the substances involved, both temporally and spatially. Negative feedback loops are important components of these oscillations, providing fine regulation for the factors involved. In this paper we consider mathematical models of two such pathways -Hes1 and p53-Mdm2.Building on previous mathematical modelling approaches, we derive systems of partial differential equations to capture the evolution in space and time of the variables in the Hes1 and p53-Mdm2 systems. Through computational simulations we show that our reaction-diffusion models are able to produce sustained oscillations both spatially and temporally, accurately reflecting experimental evidence and advancing previous models. The simulations of our models also allow us to calculate a diffusion coefficient range for the variables in each mRNA and protein system, as well as ranges for other key parameters of the models, where sustained oscillations are observed. Finally, by exploiting the explicitly spatial nature of the partial differential equations, we are also able to manipulate mathematically the spatial location of the ribosomes, thus controlling where the proteins are synthesized within the cytoplasm. The results of these simulations predict an optimal distance outside the nucleus where protein synthesis should take place in order to generate sustained oscillations. Preprint submitted to Journal of Theoretical BiologyDecember 8, 2010 Using partial differential equation models, new information can be gained about the precise spatio-temporal dynamics of mRNA and proteins. The ability to determine spatial localisation of proteins within the cell is likely to yield fresh insight into a range of cellular diseases such as diabetes and cancer.

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Section: Hes1 Mathematical Modelmentioning

confidence: 99%

Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways

Sturrock

Terry

Xirodimas

et al. 2011

Journal of Theoretical Biology

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“…The seminal work of Jacob, Monod, and Changeaux [1,2] on the regulation of gene expression in the lac operon initiated early studies on gene regulation through repression by specific proteins which demonstrated the possibility of oscillations in some special systems with few genes [3]. Numerical integration of differential equations with delay were used to model cyclic repression systems of the type 1 ⊣ 2 ⊣ .…”

Section: Introductionmentioning

confidence: 99%

A generalized model of the repressilator

et al. 2006

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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.

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“…These equations are often termed the 'Goodwin' model (Goodwin, 1965). The properties of equations (1) have been extensively studied, e.g., by Griffith (1968a,b) and Tyson and Othmer (1978).…”

mentioning

confidence: 99%

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

Smolen

Baxter

Byrne

2000

Bulletin of Mathematical Biology

280

161

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Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we compare current methods for modeling genetic networks. A common modeling technique, based on simply modeling genes as ON-OFF switches, is readily implemented and allows rapid numerical simulations. However, this method may predict dynamic solutions that do not correspond to those seen when systems are modeled with a more detailed method using ordinary differential equations. Until now, the majority of gene network modeling studies have focused on determining the types of dynamics that can be generated by common biochemical motifs such as feedback loops or protein oligomerization. For example, these elements can generate multiple stable states for gene product concentrations, state-dependent responses to stimuli, circadian rhythms and other oscillations, and optimal stimulus frequencies for maximal transcription. In the future, as new experimental techniques increase the ease of characterization of genetic networks, qualitative modeling will need to be supplanted by quantitative models for specific systems.

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Oscillatory behavior in enzymatic control processes

Cited by 883 publications

References 7 publications

Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways

Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways

A generalized model of the repressilator

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

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