What is the relationship between Springer Nature & Frontiers?

In preparation for a presentation at the Open Access Days in Dresden, I collect information on the shares of commercial publishers in the APC-based Open Access business.

When I deal with this topic, I always stumble upon the publisher Frontiers:

• Back in 2013 Nature reported „Nature Publishing Group buys into open-access publisher“ and noted: „the company [Nature Publishing Group] said it was taking a majority investment“.
• Wikipedia tells us: „The investment spurred collaboration with Nature Publishing Group, such as the integration of Loop profiles into Nature journals on nature.com, as well as collaboration with other Holtzbrinck companies such as the Frontiers for Young Minds blog on Scientific American. Though Holtzbrinck still has a minority share in Frontiers, the two companies operate independently, and in 2014, the two groups „made the decision … to make a clean separation and never to mention again that [Nature Publishing Group] has some kind of involvement in Frontiers.“ Nevertheless, Wikipedia identifies the Holtzbrinck Publishing Group as the Frontiers Group’s parent company. Springer Nature in turn is the product of the merger of Springer Science+Business Media and Holtzbrinck Publishing Group’s Nature Publishing Group, Palgrave Macmillan, and Macmillan Education.
• As Leonid Schneider points out in 2015: „The current administrative board of Frontiers lists as signatory Michael Brockhaus, Head of Group Strategy at the Holtzbrinck Publishing Group.“ Meanwhile Mister Brockhaus left the board.

To be honest, the relationship between Frontiers and Springer Nature is somewhat unclear to me: Is Springer Nature holding shares in Frontiers (if so, to what extent?), is it only a strategic alliance, does Springer Nature only use Frontier’s services for a fee?

I would be very grateful for information and feedback by the readers of my blog!

Update: Leonid Schneider drew my attention to Richard Poynder’s interview with Kamila Markram, CEO and Co-Founder of Frontiers, in 2016.