Our ongoing investigations into biologically plausible syntactic and semantic parsing have identified a novel methodology for processing complex structured information. This approach combines Vector Symbolic Architectures (a method for representing sentence structures as distributed vectors), the Neural Engineering Framework (a method for organizing biologically realistic neurons to approximate algorithms), and constraint-based parsing (a method for creating dynamic systems that converge to correct parsings). Here, we present some of our initial findings that show the promise of this approach for explaining the complex, flexible, and scalable parsing abilities found in humans.