A dynamical model of oocyte maturation unveils precisely orchestrated meiotic decisions

Abstract

Maturation of vertebrate oocytes into haploid gametes relies on two consecutive meioses without intervening DNA replication. The temporal sequence of cellular transitions driving eggs from G2 arrest to meiosis I (MI) and then to meiosis II (MII) is controlled by the interplay between cyclin-dependent and mitogen-activated protein kinases. In this paper, we propose a dynamical model of the molecular network that orchestrates maturation of Xenopus laevis oocytes. Our model reproduces the core features of maturation progression, including the characteristic non-monotonous time course of cyclin-Cdks, and unveils the network design principles underlying a precise sequence of meiotic decisions, as captured by bifurcation and sensitivity analyses. Firstly, a coherent and sharp meiotic resumption is triggered by the concerted action of positive feedback loops post-translationally activating cyclin-Cdks. Secondly, meiotic transition is driven by the dynamic antagonism between positive and negative feedback loops controlling cyclin turnover. Our findings reveal a highly modular network in which the coordination of distinct regulatory schemes ensures both reliable and flexible cell-cycle decisions.

Figure 1. Temporal and structural organization of oocyte meiotic maturation.

(A) State transitions during mitotic cycles (mi) and meiotic maturation (me). Haploid and diploid states are indicated by one or two asterisks, respectively. The four main stages of meiosis are (a) meiotic resumption following the progesterone pulse, (b) metaphase of the first meiosis, (c) meiotic transition and (d) metaphase arrest during the second meiosis. (B) The typical time course of MPF kinase activity during the maturation process of Xenopus oocytes where the four main stages (a–d) are indicated. Experimental data are from (black circles), (orange diamonds), (blue triangles), (magenta plus), (green asterisks) and (red squares). The zeroes of the time axis have been calibrated and the MPF axis have been normalized to have the first peak of MPF activy occur at the same time and with the same amplitude for each time course. (C) Detailed representation of the network of translational and post-translational interactions regulating metazoan oocyte maturation. This network involves a tight and precise coupling between the MPF and MAPK pathways at multiple levels. See text for details.

Figure 2. Complex bistable dynamics during meiotic maturation.

(A) Time courses of various protein concentrations in response to a lasting progesterone pulse. We use the parameter set given by Table 2. In the top panel, time profiles are represented using a grayscale code which is normalized so that the maximal concentration of each protein corresponds to black. In the bottom panel, activities of MPF (red), ERK (brown), APC (blue) and Emi2 (green) are shown as functions of time, together with the constant progesterone signal (dashed line). (B) Bifurcation diagram showing the steady state of MPF activity as a function of progesterone level. Black solid and dotted lines are associated with stable and unstable equilibria, respectively. Circles indicates the occurence of a saddle-node bifurcation. The red dashed line shows the dynamic trajectory of MPF during progesterone-induced maturation.

Figure 3. Robustness of meiotic dynamics to signal and kinetic parameter variability.

Dynamical trajectories of [MPF] followed in time (top panels), and in state space ([MPF],[APC]) (bottom panels) during maturation in presence of two types of random variability. (A) Variations of progesterone input profile (green lines: pulse-like; red lines: step-like) and amplitude. (B) Variations of all kinetic parameter values with a (orange lines). Thick black lines correspond to the control case depicted in Fig. 2. In bottom panel of (A) is indicated the maturation stage (MetI: metaphase of meiosis I, AnaI: anaphase of meiosis I; MI-MII: transition from meiosis I to meiosis II; MetII: metaphase of meisosis II) associated with distinct portion of the state-space trajectory.

Figure 4. Identification of two network modules using parameter sensitivity analysis.

(A) Schematic representation of the first sensitivity measure, where , and correspond to variations in timing of first MPF peak and in MPF levels at the MI/MII transition and at the metaphase II arrest, respectively, in response to parameter variations. Right-side panels show two examples where only or indicators is sensitive to the parameter changed. (B) Schematic representation of the second sensitivity measure, where and correspond to displacements of saddle points I and IV in the bifurcation diagram of Fig. 2B, in response to parameter variations. Right-side panels show two examples in which only one saddle-node bifurcation point is sensitive to the parameter changed. (C) Systematic calculation of normalized sensitivities for all interaction parameters of the model (see Eqs.1 and 2 with , , , and ). The top panel shows the total sensitivities and . The bottom panel shows the normalized sensitivities (left bar) and (right bar). Asterisks (resp., circles) indicate when (resp., ). (D,E) The initial network can be redrawn as two networks that control different stages of maturation process, namely the G2/MI and MI/MII transitions. The and signs indicate the presence of positive and negative feedback loops, respectively.

Figure 5. Simulated MPF time courses associated with meiotic maturation defects.

Time course of MPF activity in normal condition (dashed line) and various altered conditions (full line). (A) Ablation of cyclin synthesis (). (B) Ablation of Mos synthesis (). (C) Ablation of Plx1 activity . (D) Ablation of MEK activity (). (E) Overexpression of Emi2 (). (F) Ablation of Emi2 synthesis ().

Figure 6. Feedback design principles of oocyte meiotic maturation.

(A)The auto-amplification positive-feedback loop switches on MPF activity (Red). (B) Coupled positive-feedback loops ensure a coherent switch of the MPF and MAPK activities (black). (C) The negative-feedback loop linking MPF and APC (blue) triggers a transient decrease of MPF activity that does not impact the high MAPK activities maintained by independent positive-feedback loops. (D) Delayed activation of a positive-feedback loop mediated by Emi2 (green) antagonizes the negative-feedback loop, so as to fully reactivate MPF.

Figure 7. Strategy for the adjustment of model parameters.

(A) The constraint that the MAPK module (upper panel) must behave as a bistable switch (example of a bifurcation diagram in middle panel) allows one to determine a parameter domain in a 7-dimensional parameter space (bottom panel). An arbitrary parameter set is chosen within this domain. (B) The constraint that the MPF-APC module (upper panel) must behave as an oscillator under constant stimulation or be excitable upon a transient stimulation, which is associated with a saddle-node bifurcation on an invariant circle (example of a bifurcation diagram in middle panel), allows one to determine a parameter domain in a 15-dimensional parameter space (bottom panel). An arbitrary parameter set is chosen within this domain. (C) The constraint that the whole network (upper panel) must display a maturation behavior associated with a specific time course of its components (MPF time course as an example in middle panel) allows one to determine a parameter domain in the remaining 32-dimensional parameter space (bottom panel). An arbitrary parameter set is chosen within this domain.