The process in which the lateral borders of the neural plate begin to migrate upwards to form the neural folds, caused by the proliferation of the underlying mesoderm. [ GOC:dgh GOC:cls http://www.ncbi.nlm.nih.gov/pubmed/15806586 GOC:jid http://purl.obolibrary.org/obo/go/references/0000021 GOC:dph ]