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microRNA input into a neural ultradian oscillator controls emergence and timing of alternative cell states.

Goodfellow M, Phillips NE, Manning C, Galla T, Papalopulu N - Nat Commun (2014)

Bottom Line: Here we use experimental data to develop a mathematical model of the double-negative interaction between Hes1 and a microRNA, miR-9, with the aim of understanding how cells transition from one state to another.We show that the input of miR-9 into the Hes1 oscillator tunes its oscillatory dynamics, and endows the system with bistability and the ability to measure time to differentiation.Our results suggest that a relatively simple and widespread network of cross-repressive interactions provides a unifying framework for progenitor maintenance, the timing of differentiation and the emergence of alternative cell states.

View Article: PubMed Central - PubMed

Affiliation: 1] Faculty of Life Sciences, Michael Smith Building, The University of Manchester, Oxford Road, Manchester M13 9PT, UK [2] Present address: College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon EX4 4QF, UK.

ABSTRACT
Progenitor maintenance, timed differentiation and the potential to enter quiescence are three fundamental processes that underlie the development of any organ system. In the nervous system, progenitor cells show short-period oscillations in the expression of the transcriptional repressor Hes1, while neurons and quiescent progenitors show stable low and high levels of Hes1, respectively. Here we use experimental data to develop a mathematical model of the double-negative interaction between Hes1 and a microRNA, miR-9, with the aim of understanding how cells transition from one state to another. We show that the input of miR-9 into the Hes1 oscillator tunes its oscillatory dynamics, and endows the system with bistability and the ability to measure time to differentiation. Our results suggest that a relatively simple and widespread network of cross-repressive interactions provides a unifying framework for progenitor maintenance, the timing of differentiation and the emergence of alternative cell states.

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Presence of oscillations in the model when miR-9 acts only to affect the stability of Hes1 mRNA.(a) Different combinations of τ, p0 and S(r) are used to test for the presence of oscillations. The different coloured lines denote Hopf bifurcations for different values of τ as indicated. A Hopf bifurcation denotes the transition of a system from a stable to an unstable, oscillatory state or vice versa, as a parameter of the system is varied. Fixed points exist to the right of the curves whereas oscillations are present to the left. The inset shows the curve for τ=29. The dashed red line indicates the value of p0 for which two Hopf bifurcations exist for mRNA half-lives of ~35 and 20 min. (b) A window of oscillations emerges for changes in r, with p0 fixed at 390 and τ=29 min. (c) Example time series when r is fixed to the values given by crosses in (b). These r values give rise to the half-lives (ln(2)/S(r)) as indicated. n0=5, μp=22 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, r0=100, m0=5.
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f2: Presence of oscillations in the model when miR-9 acts only to affect the stability of Hes1 mRNA.(a) Different combinations of τ, p0 and S(r) are used to test for the presence of oscillations. The different coloured lines denote Hopf bifurcations for different values of τ as indicated. A Hopf bifurcation denotes the transition of a system from a stable to an unstable, oscillatory state or vice versa, as a parameter of the system is varied. Fixed points exist to the right of the curves whereas oscillations are present to the left. The inset shows the curve for τ=29. The dashed red line indicates the value of p0 for which two Hopf bifurcations exist for mRNA half-lives of ~35 and 20 min. (b) A window of oscillations emerges for changes in r, with p0 fixed at 390 and τ=29 min. (c) Example time series when r is fixed to the values given by crosses in (b). These r values give rise to the half-lives (ln(2)/S(r)) as indicated. n0=5, μp=22 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, r0=100, m0=5.

Mentions: The parameter that defines the steepness of Hes1 transcriptional autorepression, n0, was fixed to a value that has been shown to generate oscillations (that is, n0=5 (ref. 12), but the relative strength of transcriptional autorepression by Hes1 protein, p0, and the time delay in protein production, τ, were varied as shown in Fig. 2. The delay, τ, was allowed to take values in the physiologically plausible range of 20–30 min21. Figure 2 shows that, for each value of p0, oscillations exist as the half-life of Hes1 mRNA (ln(2)/S(r)) is decreased. Furthermore, when τ=29 min, a window of oscillations arises that lies within the experimentally determined values of mRNA stability when p0 is around 390 (arbitrary units) (inset of Fig. 2a,b). Example time series are shown in Fig. 2c. In contrast to the sustained oscillations when Hes1 mRNA half-life is around wild-type levels (ln(2)/S(r)=27 min (ref. 9)), oscillations dampen for parameters chosen outside the half-life boundaries reported in ref. 9.


microRNA input into a neural ultradian oscillator controls emergence and timing of alternative cell states.

Goodfellow M, Phillips NE, Manning C, Galla T, Papalopulu N - Nat Commun (2014)

Presence of oscillations in the model when miR-9 acts only to affect the stability of Hes1 mRNA.(a) Different combinations of τ, p0 and S(r) are used to test for the presence of oscillations. The different coloured lines denote Hopf bifurcations for different values of τ as indicated. A Hopf bifurcation denotes the transition of a system from a stable to an unstable, oscillatory state or vice versa, as a parameter of the system is varied. Fixed points exist to the right of the curves whereas oscillations are present to the left. The inset shows the curve for τ=29. The dashed red line indicates the value of p0 for which two Hopf bifurcations exist for mRNA half-lives of ~35 and 20 min. (b) A window of oscillations emerges for changes in r, with p0 fixed at 390 and τ=29 min. (c) Example time series when r is fixed to the values given by crosses in (b). These r values give rise to the half-lives (ln(2)/S(r)) as indicated. n0=5, μp=22 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, r0=100, m0=5.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3959193&req=5

f2: Presence of oscillations in the model when miR-9 acts only to affect the stability of Hes1 mRNA.(a) Different combinations of τ, p0 and S(r) are used to test for the presence of oscillations. The different coloured lines denote Hopf bifurcations for different values of τ as indicated. A Hopf bifurcation denotes the transition of a system from a stable to an unstable, oscillatory state or vice versa, as a parameter of the system is varied. Fixed points exist to the right of the curves whereas oscillations are present to the left. The inset shows the curve for τ=29. The dashed red line indicates the value of p0 for which two Hopf bifurcations exist for mRNA half-lives of ~35 and 20 min. (b) A window of oscillations emerges for changes in r, with p0 fixed at 390 and τ=29 min. (c) Example time series when r is fixed to the values given by crosses in (b). These r values give rise to the half-lives (ln(2)/S(r)) as indicated. n0=5, μp=22 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, r0=100, m0=5.
Mentions: The parameter that defines the steepness of Hes1 transcriptional autorepression, n0, was fixed to a value that has been shown to generate oscillations (that is, n0=5 (ref. 12), but the relative strength of transcriptional autorepression by Hes1 protein, p0, and the time delay in protein production, τ, were varied as shown in Fig. 2. The delay, τ, was allowed to take values in the physiologically plausible range of 20–30 min21. Figure 2 shows that, for each value of p0, oscillations exist as the half-life of Hes1 mRNA (ln(2)/S(r)) is decreased. Furthermore, when τ=29 min, a window of oscillations arises that lies within the experimentally determined values of mRNA stability when p0 is around 390 (arbitrary units) (inset of Fig. 2a,b). Example time series are shown in Fig. 2c. In contrast to the sustained oscillations when Hes1 mRNA half-life is around wild-type levels (ln(2)/S(r)=27 min (ref. 9)), oscillations dampen for parameters chosen outside the half-life boundaries reported in ref. 9.

Bottom Line: Here we use experimental data to develop a mathematical model of the double-negative interaction between Hes1 and a microRNA, miR-9, with the aim of understanding how cells transition from one state to another.We show that the input of miR-9 into the Hes1 oscillator tunes its oscillatory dynamics, and endows the system with bistability and the ability to measure time to differentiation.Our results suggest that a relatively simple and widespread network of cross-repressive interactions provides a unifying framework for progenitor maintenance, the timing of differentiation and the emergence of alternative cell states.

View Article: PubMed Central - PubMed

Affiliation: 1] Faculty of Life Sciences, Michael Smith Building, The University of Manchester, Oxford Road, Manchester M13 9PT, UK [2] Present address: College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, Devon EX4 4QF, UK.

ABSTRACT
Progenitor maintenance, timed differentiation and the potential to enter quiescence are three fundamental processes that underlie the development of any organ system. In the nervous system, progenitor cells show short-period oscillations in the expression of the transcriptional repressor Hes1, while neurons and quiescent progenitors show stable low and high levels of Hes1, respectively. Here we use experimental data to develop a mathematical model of the double-negative interaction between Hes1 and a microRNA, miR-9, with the aim of understanding how cells transition from one state to another. We show that the input of miR-9 into the Hes1 oscillator tunes its oscillatory dynamics, and endows the system with bistability and the ability to measure time to differentiation. Our results suggest that a relatively simple and widespread network of cross-repressive interactions provides a unifying framework for progenitor maintenance, the timing of differentiation and the emergence of alternative cell states.

Show MeSH