UL bit rate is controled by allocated PRBs and MCS. However, per logical channel, eNodeB can control using PBR and BSD.
Please go through the 3GPP 36.321 and check BSR part, eNB can prioritize logical channel by put LCs in different LCG , and UE report BSR based on LCG. e.g if UE start a new app with dedicated bearer , let's say QCI4 with has LCG 2 , eNB will satisfy QCI4 bandwidth request first since the default bearer with QCI9 normally assign to LCG3.