The interaction between the eukaryotic translation initiation factor 4E (eIF4E) and eIF4E binding proteins (4E-BP) is a promising template for the inhibition of eIF4E and the treatment of diseases such as cancer and a spectrum of autism disorders, including the Fragile X syndrome (FXS). Here, we report an atomically detailed model of the complex between eIF4E and a peptide fragment of a 4E-BP, the cytoplasmic Fragile X interacting protein (CYFIP1). This model was generated using computer simulations with enhanced sampling from an alchemical replica exchange approach and validated using long molecular dynamics simulations. 4E-BP proteins act as post-transcriptional regulators by binding to eIF4E and preventing mRNA translation. Dysregulation of eIF4E activity has been linked to cancer, FXS, and autism spectrum disorders. Therefore, the study of the mechanism of inhibition of eIF4E by 4E-BPs is key to the development of drug therapies targeting this regulatory pathways. The results obtained in this work indicate that CYFIP1 interacts with eIF4E by an unique mode not shared by other 4E-BP proteins and elucidate the mechanism by which CYFIP1 interacts with eIF4E despite having a sequence binding motif significantly different from most 4E-BPs. Our study suggests an alternative strategy for the design of eIF4E inhibitor peptides with superior potency and specificity than currently available.