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Bravo ensured that the home side made a strong start to the afternoon, finding the boundary rope just a couple of deliveries into James Anderson's first over of the session.
The play was briefly halted as Stuart Broad complained about footmarks on his run up to the crease, resulting in the groundstaff having to nail a patch of artificial grass over the area of concern.
Ben Stokes came into the attack for England, but Brathwaite seized the opportunity, picking up eight runs off the Durham man's first over.
The opening batsman kept the runs coming, and passed the 50 mark shortly before the end of the session, while completing his 100 partnership with Bravo a few overs later.
Brathwaite will resume on an unbeaten 62 in the evening session, while Bravo is just three short of his half-century.