Publisher Correction: A cdk1 gradient guides surface contraction waves in oocytes.

A Supplementary Information file from a different paper was inadvertently published with the original version of this Article. This file was replaced with the correct Supplementary Information file on 24 October 2017.

A cdk1 gradient guides surface contraction waves in oocytes.

Surface contraction waves (SCWs) in oocytes and embryos lead to large-scale shape changes coupled to cell cycle transitions and are spatially coordinated with the cell axis. Here, we show that SCWs in the starfish oocyte are generated by a traveling band of myosin II-driven cortical contractility. At the front of the band, contractility is activated by removal of cdk1 inhibition of the RhoA/RhoA kinase/myosin II signaling module, while at the rear, contractility is switched off by negative feedback originating downstream of RhoA kinase. The SCW's directionality and speed are controlled by a spatiotemporal gradient of cdk1-cyclinB. This gradient is formed by the release of cdk1-cyclinB from the asymmetrically located nucleus, and progressive degradation of cyclinB. By combining quantitative imaging, biochemical and mechanical perturbations with mathematical modeling, we demonstrate that the SCWs result from the spatiotemporal integration of two conserved regulatory modules, cdk1-cyclinB for cell cycle regulation and RhoA/Rok/NMYII for actomyosin contractility.Surface contraction waves (SCWs) are prominent shape changes coupled to cell cycle transitions in oocytes. Here the authors show that SCWs are patterned by the spatiotemporal integration of two conserved modules, cdk1-cyclinB for cell cycle regulation and RhoA/Rok/NMYII for actomyosin contractility.

Identification of optimal parameter combinations for the emergence of bistability.

Bistability underlies cellular memory and maintains alternative differentiation states. Bistability can emerge only if its parameter range is either physically realizable or can be enlarged to become realizable. We derived a general rule and showed that the bistable range of a reaction parameter is maximized by a pair of other parameters in any gene regulatory network provided they satisfy a general condition. The resulting analytical expressions revealed whether or not such reaction pairs are present in prototypical positive feedback loops. They are absent from the feedback loop enclosed by protein dimers but present in both the toggle-switch and the feedback circuit inhibited by sequestration. Sequestration can generate bistability even at narrow feedback expression range at which cooperative binding fails to do so, provided inhibition is set to an optimal value. These results help to design bistable circuits and cellular reprogramming and reveal whether bistability is possible in gene networks in the range of realistic parameter values.