Catalyzes the interconversion of methylthioribose-1-phosphate (MTR-1-P) into methylthioribulose-1-phosphate (MTRu-1-P). Independently from catalytic activity, promotes cell invasion in response to constitutive RhoA activation by promoting FAK tyrosine phosphorylation and stress fiber turnover. {ECO:0000255|HAMAP-Rule:MF_03119, ECO:0000269|PubMed:19620624}. This is the function of MRI1 (methylthioribose-1-phosphate isomerase 1, ENSG00000037757).