We study the problem of integrating syntactic information from constituency trees into a neural model in Frame-semantic parsing sub-tasks, namely Target Identification (TI), FrameIdentification (FI), and Semantic Role Labeling (SRL). We use a Graph Convolutional Network to learn specific representations of constituents, such that each constituent is profiled as the production grammar rule it corresponds to. We leverage these representations to build syntactic features for each word in a sentence, computed as the sum of all the constituents on the path between a word and a task-specific node in the tree, e.g. the target predicate for SRL. Our approach improves state-of-the-art results on the TI and SRL of ~1%and~3.5% points, respectively (+2.5% additional points are gained with BERT as input), when tested on FrameNet 1.5, while yielding comparable results on the CoNLL05 dataset to other syntax-aware systems.