Goodfellow M et al. (2014), microRNA input into a neural ultradian oscillat...

XB-ART-52784

Nat Commun 2014 Jan 01;5:3399. doi: 10.1038/ncomms4399.

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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 .

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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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Species referenced: Xenopus
Genes referenced: hes1

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	Figure 1. Experimentally determined network interactions between Hes1 and miR-9.(a) Detailed visualization of the Hes1/miR-9 network. Solid arrows indicate production, whereas flat line ends represent repressive interactions. (b) Simplified network motif.
	Figure 2. 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.
	Figure 3. Presence of oscillations in the two-variable model when r acts via both mRNA degradation and translational repression.(a) Shows the location of Hopf bifurcations as r1 and r are varied. Here, oscillations exist to the right of the curve. The horizontal line indicates the value of r for which ln(2)/S(r)=25. The vertical dashed line indicates a value of r1=300. (b) as (a) but with y axis plotted in terms of mRNA half-life (ln(2)/S(r)). (c) A window of oscillations emerges for changes in r. The addition of translational repression allows a lower steady state for high r. Other parameters are p0=390, τ=29 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, n0=m0=m1=5, r0=100, μp=22 min.
	Figure 4. Oscillations and different steady-state levels of Hes1 in the full system for changes in the strength of repression of miR-9 by Hes1 (p1).(a) Shows a bifurcation diagram for changes in p1, with protein levels (p) given as output on the y axis. The circled area shows a magnified region of parameter space that contains oscillations (limit cycle maxima and minima given by red lines). (b,c) Show example of time series for a case of bistability (p1=272). The initial conditions (giving a constant history vector) are (b) m(0)=0, p(0)=0, r(0)=240 and (c) m(0)=0, p(0)=0, r(0)=100. Other parameters are p0=390, τ=29 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, n0=n1=m0=m1=5, r0=100, r1=300, μp=22 min, μr=1,000 min.
	Figure 5. The high Hes1 steady state can be readily excited into transient oscillations.(a) The model is initiated in the high Hes1 state in a bistable regime (parameters as default and p1=220, initial conditions m=14.6766, p=465.8128, r=33.1285). At 5,000 min, the Hes1 mRNA levels are instantaneously set to a value 10% higher than at this steady state (that is, m=16.1433). The system is excited into transient oscillations. (b) The model is initiated in the low Hes1 steady state (initial conditions m=28.9, p=0.4, r=1442.6). To excite the system, at t=5,000 min, a perturbation of 15 units of protein (an initial 30-fold increase) is added every minute for 4,000 min. Other parameters are p0=390, τ=29 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, n0=n1=m0=m1=5, r0=100, r1=300, μp=22 min, μr=1,000 min.
	Figure 6. Different durations of oscillations can be found for changing p1 or the initial levels of r.(a) Shows simulations with fixed r(0)=0 but changing p1. (b) Shows simulations with fixed p1=290 but changing r(0). Here, m(0)=0 and p(0)=0. Other parameters are p0=390, τ=29 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, n0=n1=m0=m1=5, r0=100, r1=300, μp=22 min, μr=1,000 min.
	Figure 7. The model can display bistability, sustained oscillations, stable high or low levels of Hes1 depending upon its parameterization.Local bifurcations are shown for changes in the miR-9 degradation rate, μr, the strength of repression of miR-9 production by Hes1, p1 and the shape of repression of miR-9 production by Hes1, n1. The presence of Hopf and fold bifurcations are indicated by blue and red solid lines, respectively. Fold bifurcations lead to the creation or elimination of a pair of fixed points. Blue regions, therefore, indicate the presence of oscillations, while red regions indicate bistability. White regions represent the case of a single steady state with either high or low Hes1 levels (as indicated by the annotation). (a) n1=1. (b) n1=5. Other parameters are p0=390, τ=29 min, bl=ln(2)/20 min−1, bu=ln(2)/35 min−1, n0=m0=m1=5, r0=100, r1=300, μp=22 min.

References [+] :

Baek, Persistent and high levels of Hes1 expression regulate boundary formation in the developing central nervous system. 2006, Pubmed