Spatio-temporal models of synthetic genetic oscillators

  • Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.

    Citation: Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 249-262. doi: 10.3934/mbe.2017016

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  • Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.


    The Solomon Islands experienced, between 2010, a meteoric fall in the level of malaria incidence and prevalence [1]. Thanks ostensibly to the efforts of bilateral and multilateral partners and donors, annual parasite incidence (API) fell from 70 to 40 per 1,000 population. With such dramatic progress, international efforts were hailed as dramatic successes [2] and showcased as progress towards the beau ideal: malaria elimination and eradication, within most of our lifetimes [3].

    Yet, in 2017, it appeared that disaster had struck: API caseloads rose, again dramatically, to above 80 per 1,000 population. Explanations as diverse as program failures, globalization, migration, and climate change were cited for this reversal of progress [4], and these were at least in part fair explanations. Ironically, however, the true cause lay in the advancement of the country's heath system: with greater surveillance, resources, skills, and monitoring and evaluation capacity the Solomon Islands was, for the first time, able to provide a true picture of actual malaria prevalence—something that, it transpired, previous estimates had only touched upon.

    Although pre-2017 surveillance systems were recognized as being based on incomplete information [5], no one could have been aware of the vast scale of undetected malaria in the county—of the shadow line of actual as opposed to perceived incidence and prevalence, particularly in remote and previously inaccessible areas such as the Malaita and Central provinces, which alone account for the vast majority of reported cases [6].

    The true levels of malaria did, however, cause problems for international program support dependent on the demonstration of tangible progress towards both meeting treatment targets and lowering disease levels. In a cruel twist, the country's health system progress had demonstrated that both eradication progress and grant performance was severely underperforming.

    This, of course, was not the case: although the relative or perceived success of the program had changed dramatically, the absolute number of those treated for malaria and accessing bed nets had increased dramatically [7]. It is, in retrospect, only through these figures that one can gain a true understanding of the efforts and successes of the National Vector Borne Disease Control Programme.

    Yet even with that recognition, the question remains as to whether, based on a limited understanding of the true malaria disease burden, that malaria elimination should have been considered possible [8]. No doubt, such enticing goals are attractive to funders, and excite and invigorate the global health community in to working towards and contributing to individual and collective historical milestones. Yet, too often, such ambitious goals are dispiritingly unmet, leading to the risk of prospective aid scepticism.

    More immediately, the Solomon Islands is now subject to a malaria elimination reporting system, requiring a level of effort and detail totally impractical for facility staff in high prevalence provinces. Similar questions might need be faced by donors: are they basing projections and targets, too often, on incomplete information sets?

    If so, should greater leniency be shown towards those countries, districts or regions for which health surveillance information is known to be incomplete or unreliable? In turn, do such knowledge limitations question the very assumptions of accurate knowledge on which productive global health programs are based? In a final paradox, the true caseload of malaria in the Solomon Islands has revealed a situation that calls for more, rather than less, support.

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